The vertices of a triangle are listed below.
What is the area of the triangle?
A. 16 square units
B. 32 square units
OC. 19.3 square units
OD. 8 square units
L(2, 2), M(6, -2), N(2, -6)

Answers

Answer 1

The area of the triangle from the vertices of the triangle is B. 32 square units

What is the area of the triangle from the vertices of a triangle

From the question, we have the following parameters that can be used in our computation:

The vertices of a triangle are

L(2, 2), M(6, -2), N(2, -6)

The area of the triangle is calculated using

Area = 1/2 * |Lx * (My - Ny) + Mx * (Lx - Ny) + Nx * (Lx - My)|

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * |2 * (-2 + 6) + 6 * (2 + 6) + 2 * (2 + 2)|

Evaluate

Area = 32

Hence, the area is B. 32 square units

Read more about area at

https://brainly.com/question/24487155

#SPJ1


Related Questions

Find the missing angles for angle 1 and angle 2 measurements round to the nearest 10th of a degree 

Answers

The missing angles in the right angle triangle are as follows:

∠1 = 53.1°

∠2 = 36.9°

How to find the angle of a right triangle?

A right angle triangle is a triangle that has one of its angles as 90 degrees. The angles of the right angle triangle can be found using trigonometric ratios.

The sum of angles in a triangle is 180 degrees.

Therefore,

cos ∠1 = adjacent / hypotenuse

Hence,

cos ∠1 = 18 / 30

∠1 = cos⁻¹ 0.6

∠1 = 53.1301023542

∠1 = 53.1 degrees

Therefore,

∠2 = 180 - 90 - 53.1

∠2 = 36.9 degrees

learn more on right triangle here: https://brainly.com/question/29051936

#SPJ1

What is an equation of the line that passes through the points (-4, 8) and (6,3)?

Answers

Answer:-42

Step-by-step explanation:

I’m the figure the equation of the line is given if you want the y=mx+b
Let us use (-4,8)
8=1/2*-4+b
8=-2+b
b=8+2
b=10

for a nonsingular matrix a and nonzero scalar β, show that (βa)^(-1) = 1/β A^(-1)

Answers

To show that (βa)^(-1) = 1/β A^(-1), we can use the definition of the inverse of a matrix.

To show that (βA)^(-1) = 1/β A^(-1) for a nonsingular matrix A and a nonzero scalar β, follow these steps:

1. Let's consider a nonsingular matrix A and a nonzero scalar β.
2. Multiply both sides of the equation by (βA).

On the left side, we have:
(βA)(βA)^(-1)

On the right side, we have:
(βA)(1/β A^(-1))

3. Apply the property of inverse matrices:

(βA)(βA)^(-1) = I, where I is the identity matrix.

4. On the right side, distribute the (βA) to both terms in the parentheses:
(βA)(1/β A^(-1)) = β(1/β) A(A^(-1))

5. β(1/β) simplifies to 1, and applying the property of inverse matrices again, A(A^(-1)) = I, so:
1 * I = I

Thus, we have shown that (βA)^(-1) = 1/β A^(-1) for a nonsingular matrix A and a nonzero scalar β.

To learn more about inverse of a matrix visit : https://brainly.com/question/27924478

#SPJ11

The median is ...
A) the middle number in a numerical data set when the values have been arranged in
numerical order.
B) the number or numbers occurring most frequently in a data set.
C) a measure of dispersion.
D) The difference of the highest value and lowest value in the data set.

Answers

Answer:

A) the middle number in a numerical data set when the values have been arranged in numerical order.

Under what condition on bı, b2, b3 is this system solvable? Include b as a fourth column in elimination. Find all solutions when that condition holds: x + 2y – 2z = bi 2x + 5y - 4z = 62 4x + 9y - 8z = 63. 6 whnt on

Answers

The system is solvable only if [tex]$-b_1 + 2b_2 - b_3 = 0$[/tex]. All solutions for the given condition are [tex]${(x, y, z) \mid x = \frac{1}{2}(2t - b_1 - b_2), y = \frac{1}{5}(4t + 2b_1 - 5b_2), z = t}$[/tex].

We can set up the augmented matrix as follows:

[tex]\begin{bmatrix}1 & 2 & -2 & b_1 \ 2 & 5 & -4 & b_2 \ 4 & 9 & -8 & b_3\end{bmatrix}[/tex]

We can row reduce this matrix to determine when the system is solvable and to find any solutions. Performing row operations, we get:

[tex]\begin{bmatrix}1 & 2 & -2 & b_1 \ 0 & 1 & 0 & 2b_1 - 5b_2 \ 0 & 0 & 0 & -b_1 + 2b_2 - b_3\end{bmatrix}[/tex]

So the system is solvable if and only if [tex]$-b_1 + 2b_2 - b_3 = 0$[/tex]. In this case, we can solve for z in terms of y and x by expressing z as a free variable and solving for x and y in terms of z. We get:

[tex]\begin{align*}z &= t \y &= \frac{1}{5}(4t + 2b_1 - 5b_2) \x &= \frac{1}{2}(2t - b_1 - b_2) \\end{align*}[/tex]\begin{align*}

z &= t \

y &= \frac{1}{5}(4t + 2b_1 - 5b_2) \

x &= \frac{1}{2}(2t - b_1 - b_2) \

\end{align*}

where t is any real number. So the solutions are given by the set:

[tex]${(x, y, z) \mid x = \frac{1}{2}(2t - b_1 - b_2), y = \frac{1}{5}(4t + 2b_1 - 5b_2), z = t}$[/tex]

where t is any real number, and [tex]$-b_1 + 2b_2 - b_3 = 0$[/tex].

Know more about system here:

https://brainly.com/question/30054947

#SPJ11

if g(x)=t(x)/e^3x, find and simplify g′(x)

Answers

If g(x)=t(x)/e^3x, then the simplified form of g'(x) = (t'(x) - 3t(x)) / e^3x

The quotient rule is a formula used to find the derivative of a function that is expressed as a quotient of two functions. The quotient rule is a useful tool in calculus for finding the derivative of a wide range of functions.

To find the derivative of g(x), we can use the quotient rule

g'(x) = [(e^3x)(t'(x)) - (t(x))(3e^3x)] / (e^3x)^2

where t'(x) represents the derivative of t(x) with respect to x.

We can simplify this expression by factoring out e^3x from the numerator

g'(x) = [e^3x(t'(x) - 3t(x))] / e^6x

Now we can cancel out the e^3x terms

g'(x) = (t'(x) - 3t(x)) / e^3x

Learn more about quotient rule here

brainly.com/question/29255160

#SPJ4

if two cards are drawn one at at time from a standard deck of cards. what is the probability of drawing a 4 and then a non face card without replacement

Answers

Answer: 10/663 or 1.51% chance

Step-by-step explanation: drawing a 4 is a 1/52 chance, and then drawing a non face card is 40/51 chance. you have to multiply those together to get 40/2652 or 10/663 chance. 10/663 is a 1.51% chance

Below is the graph of equation y= |x−2|-1. Use this graph to find all values of x for the given values of y.

y>0

Answers

Step-by-step explanation:

if x=4. then it be |4-2|-1= 1

x=5 5-2-1 so 2

and so on

For positive acute angles A and B, it is known that tan ⁡A = 11/60 ​and sin ⁡B = 3/5. Find the value of cos ⁡ ( A + B ) in simplest form.

Answers

Answer:

  cos(A+B) = 207/305

Step-by-step explanation:

You want the simplest form of cos(A+B), where tan(A) = 11/60 and sin(B) = 3/5.

Cosine of sum

The identity for the cosine of the sum of angles is ...

  cos(A+B) = cos(A)cos(B) -sin(A)sin(B)

In order to use this formula, we would need to find the sine and cosine of A, and the cosine of B.

Angle A

The two numbers in the ratio for tan(A) represent legs of a right triangle. The hypotenuse of that triangle is ...

  c² = a² +b²

  c² = 11² +60² = 121 +3600 = 3721

  c = √3721 = 61

Then the trig values of interest are ...

sin(A) = 11/61cos(A) = 60/61

Angle B

The cosine of angle B is ...

  cos(B) = √(1 -sin²(B)) = √(1 -(3/5)²) = √(16/25) = 4/5

Sum

Then our cosine is ...

  cos(A+B) = (60/61)(4/5) -(11/61)(3/5) = (60·4 -11·3)/(61·5)

  cos(A+B) = 207/305

nollostidu2 bed enbelwand ris obsMA
7. A physician assistant applies gloves prior to examining each patient. She sees an
с и
3. smith
average of 37 patients each day. How many boxes of gloves will she need over the
span of 3 days if there are 100 gloves in each box?
sibain dossi
tawans
8. A medical sales rep had the goal of selling 500 devices in the month of November.
He sold 17 devices on average each day to various medical offices and clinics. By
how many devices did this medical sales rep exceed to fall short of his November
goal?
9. There are 56 phalange bones in the body. 14 phalange bones are in each hand. How
many phalange bones are in each foot?
10. Frank needs to consume no more than 56 grams of fat each day to maintain his
current weight. Frank consumed 1 KFC chicken pot pie for lunch that contained 41
grams of fat. How many fat grams are left to consume this day?
LAO
11. The rec center purchases premade smoothies in cases of 50. If the rec center sells
an average of 12 smoothies per day, how many smoothies will be left in stock after
4 days from one case?
12. Ashton drank a 24 oz bottle of water throughout the day at school. How many
ounces should he consume the rest of the day if the goal is to drink the
recommended 64 ounces of water per day?
13. Kathy set a goal to walk at least 10 miles per week. She walks with a friend 3
times each week and averages 2.5 miles per walk. How many more miles will she
need to walk to meet her goal for the week?

Answers

She will need to purchase 3 boxes of gloves.

He exceeded his goal by 10 devices.

There are 28 phalange bones in each foot.

There will be 2 smoothies left in stock after 4 days from one case.

Frank needs to consume no more than 15 grams of fat for the rest of the day.

How to calculate the word problem

Since there are 100 gloves in each box, she will need 222/100 = 2.22 boxes of gloves. Since she cannot purchase a partial box, she will need to purchase 3 boxes of gloves.

The medical sales rep sold devices for a total of 17 x 30 = 510 devices in November. Since his goal was to sell 500 devices, he exceeded his goal by 510 - 500 = 10 devices.

Since there are 56 phalange bones in the body and 14 phalange bones in each hand, there are 56 - (14 x 2) = <<56-(14*2)= 28 phalange bones in each foot.

Frank needs to consume no more than 56 - 41 = 15 grams of fat for the rest of the day.

The rec center sells 12 smoothies per day for 4 days, for a total of 12 x 4 = 48 smoothies. Therefore, there will be 50 - 48 = 2 smoothies left in stock after 4 days from one case.

Since Ashton drank a 24 oz bottle of water, he still needs to drink 64 - 24 = 40 ounces of water for the rest of the day.

Kathy walks a total of 3 x 2.5 =7.5 miles with her friend each week. Therefore, she still needs to walk 10 - 7.5 = 2.5 more miles to meet her goal for the week.

Learn more about word problem on

https://brainly.com/question/21405634

#SPJ1

Sketch the region enclosed by the given curves. Y = 2/x, y = 8x, y = > 0







Find its area. _________​

Answers

8ln(4) is the area encompassed by the curves y = 2/x, y = 8x, and the x-axis.

To determine the area bounded by the given curves, we must first determine the points of intersection. Because y > 0, we only consider the section of the curve between these two points when we solve y = 2/x and y = 8x.

On integrating y = 2/x with respect to x, we will get the area under the curve. We will use limit x = 1/4 to x = 2. For the area above the x axis, the limits will be x = 1/4 to x = 2 for integration of y = 8x with respect to x.

As a result, the area contained by the curves is equal to the difference between these two areas, which is 8ln(4).

To know more about Area under curve, visit,

https://brainly.com/question/30452445

#SPJ4

Please provide Guidance ASAP on how to calculate the last question and answer this question.
How many years will it take to reach 50,000 pairs and what unrealistic assumptions were made in prediting the time it would take to reach 50,000 pairs?
Table 7. Analysis of Bald Eagle Recovery
What is the shape of the curve? J-shaped exponential curve
Doubling time from 1,000 to 2,000 4.73 years
Doubling time from 2,000 to 4,000 9.47 years
Doubling time from 4,000 to 8,000 18.94 years
Average doubling time 11.05 years
Doubling time increasing or decreasing? increasing
Starting number of breeding pairs 791 Year 1974
Theoretical prediction to reach 1,582 pairs Year 1979
Theoretical prediction to reach 3,164 pairs Year 1987
Theoretical prediction to reach 6,328 pairs Year 2002
Theoretical prediction to reach 12,636 pairs Year 2030
How many years to reach 50,000 pairs? 235 years

Answers

To calculate the time it would take to reach 50,000 pairs, we can use the average doubling time provided in the table. The shape of the curve is a J-shaped exponential curve.

which means that the number of pairs increases at an accelerating rate over time. Since the average doubling time is 11.05 years, we can determine the number of times we need to double the initial number of breeding pairs (791) to reach 50,000 pairs. By successively doubling the number of pairs and keeping track of the years passed, we reach 50,000 pairs in 235 years (as given in the table).

However, there are unrealistic assumptions made in predicting the time to reach 50,000 pairs. The main assumption is that the doubling time remains constant, while in reality, factors such as environmental limitations, availability of resources, and human intervention could cause the rate of growth to change over time.

Additionally, the model assumes that there are no significant negative events (such as disease outbreaks or natural disasters) that could negatively impact the bald eagle population during this period.

To know more factors click here

brainly.com/question/29128446

#SPJ11

SPSS is an analytics software. Its manual sales (# sold) per quarter for seven years are provided in a spreadsheet, along with a growth variable "time trend". Your task is to advice management on when it would be best for SPSS to invest money in online advertising in order to increase sales.Construct an appropriate regression model after first examining a scatter plot of the sales data. State your final estimated equation along with p-values.Interpret the slope coefficients from the model.Finally, state in one sentence your advice to management regarding online advertising, making sure to explicitly use the analytics in justifying your recommendation.

Answers

To help management decide when to invest in online advertising for increasing SPSS manual sales, you should follow these steps:

1. Open the spreadsheet containing the sales data and the time trend variable.

2. Examine a scatter plot of the sales data to identify any trends or patterns.

3. Using SPSS or another statistical software, construct a linear regression model with manual sales as the dependent variable and the time trend as the independent variable.

4. Analyze the output, focusing on the estimated equation, slope coefficients, and p-values.

Assuming you've completed the analysis and obtained the following example results: - Estimated equation: Sales = a + b(Time Trend) - Slope coefficient (b): 1.2 - P-value: 0.01 Interpretation: The slope coefficient of 1.2 indicates that for every unit increase in the time trend variable, manual sales are expected to increase by 1.2 units.

The p-value of 0.01, which is less than the typical significance level of 0.05, suggests that the relationship between the time trend and sales is statistically significant.

Advice to management: Based on the analytics, investing in online advertising when the time trend is increasing will likely result in higher manual sales, as the significant positive relationship between time trend and sales suggests a strong connection between the two variables.

Learn more about SPSS software,

https://brainly.com/question/15571603

#SPJ11

To help management decide when to invest in online advertising for increasing SPSS manual sales, you should follow these steps:

1. Open the spreadsheet containing the sales data and the time trend variable.

2. Examine a scatter plot of the sales data to identify any trends or patterns.

3. Using SPSS or another statistical software, construct a linear regression model with manual sales as the dependent variable and the time trend as the independent variable.

4. Analyze the output, focusing on the estimated equation, slope coefficients, and p-values.

Assuming you've completed the analysis and obtained the following example results: - Estimated equation: Sales = a + b(Time Trend) - Slope coefficient (b): 1.2 - P-value: 0.01 Interpretation: The slope coefficient of 1.2 indicates that for every unit increase in the time trend variable, manual sales are expected to increase by 1.2 units.

The p-value of 0.01, which is less than the typical significance level of 0.05, suggests that the relationship between the time trend and sales is statistically significant.

Advice to management: Based on the analytics, investing in online advertising when the time trend is increasing will likely result in higher manual sales, as the significant positive relationship between time trend and sales suggests a strong connection between the two variables.

Learn more about SPSS software,

https://brainly.com/question/15571603

#SPJ11

Complete the square to re-write the quadratic function in vertex form

Answers

Answer:

[tex]y= (x+\frac{1}{2})^2-8.25[/tex]

Step-by-step explanation:

First, we move the c in [tex]ax^2+bx+c[/tex] to the other side of the equation by adding 8 onto both sides:

[tex]x^2+x=8[/tex].

Then, since [tex]x^2\\[/tex] has no coefficient, we make the left side a perfect square trinomial by adding [tex](\frac{b}{2})^2[/tex] on both sides of the equation. We do this because adding this to the equation will make the left side equal to [tex](x\pm\frac{b}{2})^2[/tex] (plus-minus because the sign depends on if b is negative or positive):

[tex]x^2+x+\frac{1}{4}=8+\frac{1}{4}[/tex].

Then, simplify the left side:

[tex](x+\frac{1}{2})^2=8.25[/tex]

Finally, subtract 8.25 on both sides to make it vertex form:

[tex]y= (x+\frac{1}{2})^2-8.25[/tex]

Nicole writes the expression (2.5x -7)( 3). She rewrites the expression using the distributive property. Which expression could Nicole have written using the distributive property? A. 7.5x - 4 C. 7.5x - 21 B. 5.5x - 4 D. 5.5x + 10

Answers

Answer:

C. 7.5x - 21

Step-by-step explanation:

We can distribute the 3 to both the 2.5x and the -7

(3 * 2.5x) + (3 * -7)

7.5x - 21

suppose a is 3x3 and det(a) = 1. what is det(2a)?

Answers

The value of det(2A) = 8 from the given data, and value of det(A).

Suppose a is a 3x3 matrix and det(a) = 1. To find det(2a), we can use the property that det(kA) = k^n * det(A), where k is a constant and A is an n x n matrix. In this case, k = 2 and n = 3. Therefore, det(2a) = 2^3 * det(a) = 8 * 1 = 8. So, det(2a) is equal to 8.


Hi! I'm happy to help you with your question. Suppose matrix A is a 3x3 matrix and det(A) = 1. We want to find the determinant of matrix 2A.

Step 1: Multiply the matrix A by 2. This means that each element of matrix A is multiplied by 2, resulting in the matrix 2A.

Step 2: Compute the determinant of the new matrix, det(2A). Since A is a 3x3 matrix, when you multiply it by a scalar (in this case, 2), the determinant will be affected by the scalar raised to the power of the matrix size (3). So, det(2A) = 2^3 * det(A).

Step 3: Substitute the given value of det(A) = 1 into the equation. So, det(2A) = 2^3 * 1.

Step 4: Calculate the result: det(2A) = 8 * 1 = 8.

Therefore, det(2A) = 8.

Learn more about det(A) here:

https://brainly.com/question/13638265

#SPJ11

Use the following scenario in your answering of questions 9 and 10. (Use the same answer choices for each question.) From a sampling frame of 1000 individuals (500 men and 500 women), a sample of 100 is to be selected, with the desired sample consisting of 40 men and 60 women. 9. Which of the following methods describes probability sampling? 10. Which of the following methods describes stratified sampling? A. Each person is assigned a three digit number (from 000 to 999). On a Random Digit Table, numbers are read, three at a time. The first hundred three-digit numbers read will represent the people in the sample. B. To make the sampling frame a more manageable size, only people with birthdays from June 1 to December 31 will be considered. From that reduced sampling frame, the method described in Answer Choice A will be used. C. Every man in the sampling frame will be assigned 8 sequential 4-digit numbers (from 0000 to 3999; example: 0000, 0001, 0002, 0003, 0004, 0005, 0006, 0007), and every woman in the sampling frame will be assigned 12 sequential 4-digit numbers (from 4000 to 9999; example: 4000, 4001, 4002, 4003, 4004, 4005, 4006, 4007, 4008, 4009, 4010, 4011). From a Random Digit Table, groupings of 4 numbers will be read and the first 100 subjects with their number read will be in the sample (duplicate selections will be ignored). D. From an alphabetized list of people in the sampling frame, the first hundred are selected. E. Each man in the sampling frame is assigned two sequential three-digit numbers (from 000 to 999; example: 000, 001). From a Random Digit Table, groupings of three numbers at a time are read. The first 40 three-digit numbers will represent the men selected (duplicate selections will be ignored). Then, each woman in the sampling frame will be assigned two sequential three-digit numbers (from 000 to 999; example: 000, 001). From a Random Digit Table, groupings of three numbers at a time are read. The first 60 three-digit numbers will represent the women selected (duplicate selections are ignored). These 40 men and 60 women will together form the sample of 100 people.

Answers

9. A - Each person is assigned a three-digit number (from 000 to 999). On a Random Digit Table, numbers are read, three at a time. The first hundred three-digit numbers read will represent the people in the sample.

10. C - Every man in the sampling frame will be assigned 8 sequential 4-digit numbers and every woman in the sampling frame will be assigned 12 sequential 4-digit numbers. From a Random Digit Table, groupings of 4 numbers will be read and the first 100 subjects with their number read will be in the sample (duplicate selections will be ignored).

9. Method A is probability sampling because each individual in the sampling frame has an equal chance of being selected, and the selection is based on random digits.

10. Method C is stratified sampling because the sampling frame is divided into two strata based on gender, and each stratum is sampled separately using a random selection method. This allows for a more representative sample by ensuring that both men and women are adequately represented in the sample.

To learn more about sampling frame, here

https://brainly.com/question/13208787

#SPJ4

9. A - Each person is assigned a three-digit number (from 000 to 999). On a Random Digit Table, numbers are read, three at a time. The first hundred three-digit numbers read will represent the people in the sample.

10. C - Every man in the sampling frame will be assigned 8 sequential 4-digit numbers and every woman in the sampling frame will be assigned 12 sequential 4-digit numbers. From a Random Digit Table, groupings of 4 numbers will be read and the first 100 subjects with their number read will be in the sample (duplicate selections will be ignored).

9. Method A is probability sampling because each individual in the sampling frame has an equal chance of being selected, and the selection is based on random digits.

10. Method C is stratified sampling because the sampling frame is divided into two strata based on gender, and each stratum is sampled separately using a random selection method. This allows for a more representative sample by ensuring that both men and women are adequately represented in the sample.

To learn more about sampling frame, here

https://brainly.com/question/13208787

#SPJ4

Each student in Mrs. Wimberly’s six science classes planted a bean in a Styrofoam cup. All beans came from the same source, were planted using the same bag of soil, and were watered the same amount. Mrs. Wimberly has 24 students in each of her six classes. In first period, 21 of the 24 bean seeds sprouted.





Which statement about the seeds in the remaining five classes is NOT supported by this information?
Responses
A 87.5% of the bean seeds should sprout.87.5% of the bean seeds should sprout.
B More than 100 bean seeds should sprout.More than 100 bean seeds should sprout.
C 1 out of 8 bean seeds will not sprout.1 out of 8 bean seeds will not sprout.
D At least 20 bean seeds will not sprout.At least 20 bean seeds will not sprout.

Answers

With the help of percentage, 87.5% of the bean seeds should sprout.87.5% of the bean seeds should sprout.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is often used to represent a portion or a rate of change.

According to given information:

The given information states that 21 out of 24 bean seeds sprouted in the first period. This means that 87.5% (or 21/24) of the seeds sprouted in that period. Therefore, statement A is supported by the information given.

Statement B suggests that more than 100 bean seeds should sprout, but this is not necessarily true based on the information provided. The total number of seeds planted is not given, so we cannot determine whether more than 100 seeds should sprout. Therefore, statement B is not supported by the information given.

Statement C suggests that 1 out of 8 bean seeds will not sprout. However, this statement is not necessarily true based on the information given. It is possible that more or fewer than 1 out of 8 bean seeds did not sprout. Therefore, statement C is not supported by the information given.

Statement D suggests that at least 20 bean seeds will not sprout. This statement is not necessarily true based on the information given. It is possible that fewer than 20 bean seeds did not sprout. Therefore, statement D is not supported by the information given.

To know more about percentage visit:

https://brainly.com/question/24877689

#SPJ1

If Ax = ax for nxn matrix A, nx1 matrix x, and a E R, determine a scalar ß with the property that A²x = Bx.

Answers

If Ax = ax for nxn matrix A, nx1 matrix x, and a E R, then the given initial value problem of the derivative is: y = (-4/3) sin(x) + (4√3/3) cos(x)

The given differential equation is:

d²y/dx² + y = 0

To solve this equation, we assume the solution to be of the form y = A sin(kx) + B cos(kx), where A and B are constants and k is a constant to be determined.

Taking the derivatives of y with respect to x, we get:

dy/dx = Ak cos(kx) - Bk sin(kx)

d²y/dx² = -Ak² sin(kx) - Bk² cos(kx)

Substituting the values in the differential equation, we get:

(-Ak² sin(kx) - Bk² cos(kx)) + (A sin(kx) + B cos(kx)) = 0

Simplifying, we get:

(Ak² + 1) sin(kx) + (Bk² + 1) cos(kx) = 0

Since sin(kx) and cos(kx) are linearly independent, the coefficients of each must be zero. Therefore, we have the following two equations:

Ak² + 1 = 0 ...(1)

Bk² + 1 = 0 ...(2)

Solving the equations for k, we get:

k = ±i

Thus, the general solution of the differential equation is:

y = A sin(x) + B cos(x)

To solve for the constants A and B, we use the given initial conditions:

y(π/3) = 0 and y'(π/3) = 2

Substituting the values in the above equation, we get:

A sin(π/3) + B cos(π/3) = 0

and

A cos(π/3) - B sin(π/3) = 2

Solving the equations for A and B, we get:

A = -4/3 and B = 4√3/3

Therefore, the solution of the given initial value problem is:

y = (-4/3) sin(x) + (4√3/3) cos(x)

To know more about derivatives refer here:

https://brainly.com/question/30365299

#SPJ11

find the median for -4, 5, 12, 11, -6, 7, 20, 4, 16, 10, 13

Answers

Answer:

10

Step-by-step explanation:

The median is the number in the middle when they are in order

-6, -4, 4, 5, 7, 10, 11, 12, 13, 16, 20

The median is 10
Cause the median is the number in the middle when they are all in order

Let f(x) = x3 + 3x2 -9x + 14
on what interval is f increasing (include the endpoints in the interval)?

Answers

From the test points, we find that f(x) is increasing on the interval (1, ∞), including the endpoint 1 for the function f(x) = x3+ 3x2 - 9x + 14.

To determine on what interval f(x) is increasing, we need to find the derivative of f(x) and solve for when it is greater than zero.
f'(x) = 3x^2 + 6x - 9

Setting f'(x) > 0, we can solve for x: 3x^2 + 6x - 9 > 0

Dividing by 3, we get: x^2 + 2x - 3 > 0

Factoring, we have: (x + 3)(x - 1) > 0

This expression is greater than zero when both factors are either both positive or both negative.

Thus, we have two intervals: x < -3 and x > 1

Testing values in each interval, we can see that f(x) is increasing on:
(-infinity, -3) and (1, infinity)

Therefore, the interval on which f(x) is increasing (including the endpoints) is: [-3, 1]

To determine the interval on which the function f(x) = x^3 + 3x^2 - 9x + 14 is increasing, we first need to find its critical points by taking the derivative and setting it equal to 0.

f'(x) = 3x^2 + 6x - 9

Now, set f'(x) to 0 and solve for x:

0 = 3x^2 + 6x - 9

We can factor out a 3:

0 = 3(x^2 + 2x - 3)

Now, factor the quadratic equation:

0 = 3(x - 1)(x + 3)

So, the critical points are x = 1 and x = -3.

To determine if f(x) is increasing or decreasing in each interval, we can use a number line with the critical points:

-∞ < x < -3,  -3 < x < 1,  1 < x < ∞

Choose a test point in each interval and evaluate f'(x):

For x = -4: f'(-4) = -16 (negative)
For x = 0: f'(0) = -9 (negative)
For x = 2: f'(2) = 15 (positive)

Visit here to learn more about Function:

brainly.com/question/1503051

#SPJ11

20. In a school of 300 students, only 225 cleared an exam. If a sample of 10 of these students is taken, then the standard deviation of the sample proportion will be A) 0.03 B) 0.08 C) 0.24 D) 0.14 E) 0.02

Answers

The standard deviation of the sample proportion will be 0.14. So, the correct option is option D) 0.14.

The formula for the standard deviation of a sample proportion is given by:
standard deviation = √[p(1-p)/n]
where p is the proportion of successes in the population (i.e. the proportion of students who cleared the exam), and n is the sample size.

In this case, p = 225/300 = 0.75, since in the school of 300 students 225 students cleared the exam. The sample size is n = 10, as sample of 10 of these students is taken.

Plugging these values into the formula, we get:

standard deviation = √[0.75(1-0.75)/10] = √[0.01875] = 0.1366

Rounding to two decimal places, the answer 0.14.

Know more about standard deviation here:

https://brainly.com/question/475676

#SPJ11

1. Tom is gathering data on the music preferences of his classmates. He randomly surveyed
a sample of the total student population. There are 1,200 total students on campus.
Type
Pop
Rock
R&B
Rap
Country
Electronica
Other
Total
Proportion:
Number of
Students
30
28
22
24
17
11
18
150
a. Write and solve a proportion to find the approximate number of students on campus
who prefer R&B music.
Proportion:
Solution:
b. Write and solve a proportion to find the approximate number of students on campus
who prefer Pop or Rock music.
Solution:
Apr 22
dmentum Permission granted to copy for classroom use
3:10

Answers

Using the concept of proportion, we have that:

1) Approximate number of students who prefer R & B is: 176 students

2) Approximate number of students who prefer R & B is:  464 students

How to find the proportion from the table of values?

Normally in table of values, we can easily tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are all the same, the table shows a proportional relationship.

We are told that there are a total of 1200 total students on the campus.

1) Total number of students = 1200

Total number surveyed = 150

Total who prefer R & B music = 22

Thus:

Approximate number of students who prefer R & B = (22/150) * 1200

= 176 students

2) Total number of students = 1200

Total number surveyed = 150

Total who prefer Pop or Rock music = 30 + 28 = 58

Thus:

Approximate number of students who prefer R & B = (58/150) * 1200

= 464 students

Read more about proportion at: https://brainly.com/question/1781657

#SPJ1

what is the purpose of truth tables? how do number systems (i.e., derived from binary) relate to truth tables? finally, how does set theory relate to truth tables.

Answers

The intersection of two sets can be represented using a truth table that shows the input values and the resulting output value that represents the intersection of the two sets.

The purpose of truth tables is to help analyze logical statements and determine their truth values based on the different combinations of inputs or variables. Truth tables display all possible outcomes of a logical operation and allow for a clear visualization of the relationship between inputs and outputs.

Number systems, particularly those derived from binary, are closely related to truth tables because they involve the use of binary digits or bits (0 and 1) to represent numbers and perform logical operations. Truth tables can be used to determine the output of binary logical operations, such as AND, OR, and NOT, based on the input values.

Set theory, on the other hand, is related to truth tables in the sense that it deals with the study of sets, which can be represented using truth tables. Truth tables can be used to determine the membership of elements in a set and to evaluate logical statements involving sets. For example, the intersection of two sets can be represented using a truth table that shows the input values and the resulting output value that represents the intersection of the two sets.

To learn more about intersection visit;

brainly.com/question/30792974

#SPJ11

find the value of the constant k such that the function is a probability density function on the indicated interval. f(x) = k √x [0, 1]k=

Answers

The value of the constant k such that the function f(x) = k √x [0, 1] is a probability density function is k = 3/2.

To find the value of the constant k such that the function f(x) = k √x [0, 1] is a probability density function, we need to ensure that the integral of f(x) over the interval [0,1] equals 1.

So, we need to find k such that ∫0^1 k √x dx = 1.

Integrating, we get:
∫0^1 k √x dx = k(2/3)x^(3/2)|0^1 = k(2/3)

Setting this equal to 1, we have:
k(2/3) = 1

Solving for k, we get:
k = 3/2√1

Therefore, the value of the constant k such that the function f(x) = k √x [0, 1] is a probability density function is k = 3/2.

Know more about Probability Density here:

https://brainly.com/question/29129585

#SPJ11

A researcher obtains a t =2.98 for a repeated-measures study using a sample of n = 8 participants. Based on this t value, what is the correct decision for a two-tailed test and an alpha of .05?
a. Return the null hypothesis.
b. Reject the null hypothesis.
c. Cannot answer the question with the information provided.
d. Fail to reject the null hypothesis.

Answers

Your answer: b. Reject the null hypothesis.

Explanation:

In a repeated-measures study using a sample of n = 8 participants, the researcher obtained a t-value of 2.98. For a two-tailed test with an alpha of .05.

To determine the correct decision for a two-tailed test with an alpha level of 0.05 based on a t-value of 2.98 for a repeated-measures study with a sample size of n = 8, we need to compare the t-value to the critical t-value for a two-tailed test at alpha level of 0.05 with 7 degrees of freedom, which is n - 1.

Using a t-table or a t-distribution calculator with 7 degrees of freedom and an alpha level of 0.05, we can find the critical t-value for this sample size is approximately 2.365(rounded to three decimal places).

Since the obtained t-value (2.98) is greater than the critical t-value (2.365), we would reject the null hypothesis.

Therefore, the correct decision for a two-tailed test with an alpha of 0.05 based on the given t-value of 2.98 is:

b. Reject the null hypothesis.

Know more about the alpha level click here:

https://brainly.com/question/13059612

#SPJ11

8.20. simplify (r∩s) ∩(s∩(r∩s)) as much as possible, using the set property theorems and exercise 8.16

Answers

The simplified expression is just the set s. First, we can use the associative property of intersection to rearrange the parentheses: (r∩s) ∩(s∩(r∩s)) = (r∩s) ∩((r∩s)∩s)


We can use the commutative property of intersection to switch the order of r and s in the first set:

(r∩s) ∩((r∩s)∩s) = (s∩r) ∩((r∩s)∩s)

Now, we can use the distributive property of intersection over intersection to expand (r∩s)∩s:

(s∩r) ∩((r∩s)∩s) = (s∩r) ∩r∩s

Finally, we can use the associative and commutative properties of intersection to rearrange the sets again and simplify:

(s∩r) ∩r∩s = s∩r∩r∩s = s∩(r∩r)∩s = s∩s = s

Therefore, the simplified expression is just the set s.

Learn more about parentheses here: brainly.com/question/28146414

#SPJ11

Please help! I'm stuck and have a test tomorrow.

Answers

The lengths of the given line segments using Pythagoras theorem are:

ON = 15.75

M O = 21.75

How to use Pythagoras theorem?

We know from circle geometry that the tangent to a circle is usually perpendicular to the radius of that circle at the point of tangency.

perpendicular to ON.

Now, we are given that:

MN = 15

MP = 6

We also see that ON = OP by radius definition. Thus:

Using Pythagoras theorem we have:

(6 + ON)² = 15² + ON²

36 + 12ON + ON² = 225 + ON²

36 + 12ON = 225

12ON =  225 - 36

ON = 189/12

ON = 15.75

Thus:

M O = 6 + 15.75

M O = 21.75

Read more about Pythagoras Theorem at: https://brainly.com/question/654982

#SPJ1

The random variable X takes values -1. 0. 1 with probabilities 1/8, 2/8. 5/8 respectively (a) Compute E(X) (b) Give the probability function of Y- X2 and use it to compute EY) (c) Compute Var(X): You may use shortcut formular.

Answers

a) The expected value of X is 5/8.

b) The expected value of Y-[tex]X^2[/tex] is 1/16.

c) The variance of X is 21/64.

(a) The expected value of a discrete random variable X with possible values x1, x2, ..., xn and corresponding probabilities p1, p2, ..., pn is given by:

E(X) = Σ(pi [tex]\times[/tex] xi) for i = 1 to n

Using this formula, we can calculate the expected value of X as follows:

E(X) = (1/8[tex]\times[/tex](-1)) + (2/8 [tex]\times[/tex]0) + (5/8 [tex]\times[/tex] 1) = 5/8

Therefore, the expected value of X is 5/8.

(b) To find the probability function of Y-[tex]X^2[/tex], we need to find the possible values of Y-[tex]X^2[/tex] and their corresponding probabilities.

Y takes values -1, 0, 1 with probabilities 1/8, 2/8, 5/8 respectively. Therefore, Y-X^2 takes values (-1 - [tex](-1)^2[/tex]), (0 - [tex]0^2[/tex]), (1 - [tex]1^2[/tex]), which simplify to -2, 0, and 0, respectively.

The probabilities of Y-X^2 taking these values can be found by considering all possible combinations of the values of X and Y. For example, when X = -1 and Y = -1, we have Y-[tex]X^2[/tex] = -1 - [tex](-1)^2[/tex] = -2. The probability of this occurring is 1/8 [tex]\times[/tex]1/8 = 1/64. Continuing in this way, we can find the probabilities for all possible values of Y-[tex]X^2[/tex]:

Y-[tex]X^2[/tex] = -2 with probability 1/64

Y-[tex]X^2[/tex] = 0 with probability 3/8

Y-[tex]X^2[/tex] = 2 with probability 5/64

Now we can calculate the expected value of Y-[tex]X^2[/tex] as follows:

E(Y-[tex]X^2[/tex]) = (-2 [tex]\times[/tex] 1/64) + (0 [tex]\times[/tex] 3/8) + (2 [tex]\times[/tex] 5/64) = 1/16

Therefore, the expected value of Y-[tex]X^2[/tex] is 1/16.

(c) The variance of a discrete random variable X with possible values x1, x2, ..., xn and corresponding probabilities p1, p2, ..., pn is given by:

Var(X) = E(X^2) - [E(X)[tex]]^2[/tex]

To calculate Var(X), we need to first calculate E(X^2). Using the formula for expected value, we have:

E(X^2) = (1/8 [tex]\times[/tex][tex](-1)^2[/tex]) + (2/8 [tex]\times[/tex] [tex]0^2[/tex]) + (5/8 [tex]\times[/tex] [tex]1^2[/tex]) = 7/8

Now we can calculate Var(X) using the formula above:

Var(X) = E([tex]X^2[/tex]) - [E(X)[tex]]^2[/tex] = 7/8 - (5/8[tex])^2[/tex] = 21/64

Therefore, the variance of X is 21/64.

To learn more about probability visit: https://brainly.com/question/30034780

#SPJ11

1 point) find the general solution to y′′′ 8y′′ 20y′=0. in your answer, use c1,c2 and c3 to denote arbitrary constants and x the independent variable.

Answers

The general solution to y′′′ + 8y′′ + 20y′ = 0 is: y(x) = e^(-4x)(c1 cos(2x) + c2 sin(2x)) + c3

How to find the general solution?

The characteristic equation of the given third-order linear homogeneous differential equation is:

r^3 + 8r^2 + 20r = 0

Dividing both sides by r gives:

r^2 + 8r + 20 = 0

The roots of this quadratic equation can be found using the quadratic formula:

r = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 8, and c = 20. Plugging in these values, we get:

r = (-8 ± sqrt(8^2 - 4(1)(20))) / 2(1)

= -4 ± 2i

Since the roots are complex and come in a conjugate pair, the general solution to the differential equation is:

y(x) = e^(-4x)(c1 cos(2x) + c2 sin(2x)) + c3

where c1, c2, and c3 are arbitrary constants.

Therefore, the general solution to y′′′ + 8y′′ + 20y′ = 0 is:

y(x) = e^(-4x)(c1 cos(2x) + c2 sin(2x)) + c3

where c1, c2, and c3 are arbitrary constants.

Learn more about differential equations

brainly.com/question/14620493

#SPJ11

Other Questions
determine the ph of a 0,681 m solution of nan3 (ka for hn3 = 1.9 105). what quantity in moles of naoh need to be added to 200.0 ml of a 0.200 m solution of hf to make a buffer with a ph of 2.80? (ka for hf is 6.8 10) A supernova explosion of a 2.001031 kg star produces 1.001044 kg of energy. (a) How many kilograms of mass are converted to energy in the explosion? (b) What is the ratio m / m of mass destroyed to the original mass of the star? Time tickets should be approved byA.the audit committee.B.the payroll department.C.co-workers.D.the employee's supervisor. f(x)= x. What is g(x)?O A. g(x)=xOB. g(x) = (x)OC. g(x) = 3xOD. g(x) = (x)g(x)-5-5-yf(x) = x(3, 1)5 there is a specific term for the currents that are observed immediately after the potential is stepped down from a potential where there is a steady state conductance, to one where there is none. what is this term? Since the program is static, the code needs to be modifies and rebuilt if we want to change the commands to execute. In this part, we make our program dynamic instead of static.The following requirements should be implemented:1) Source file will be called DynPipe.cpp, executable called dynpipe.2) The piped commands to execute need to be passed as arguments to dynpipe, and not hardcoded.3) The MAX number of argument should not exceed 5 and not less than 2, otherwise print an error message.4) Each argument should be a UNIX/Linux command with its parameters. The first argument will be the first to execute, followed by the second one, etc. We will assume that only valid commands can be used, for simplicity.Example of possible command executions:Program ExecutionShell Equivalentdynpipe "ls -ltr" "grep 3376"ls -ltr | grep 3376dynpipe "ls -ltr" "grep 3376" "grep hi" "wc -l"ls -ltr | grep 3376 | grep hi | wc -ldynpipe "ls -ltr"errorWhat I've done so far is a TwoPipesThreeChildren execution of "ls -ltr | grep 3376 | wc -1" which is static. In the code below, 3 child processes execute the 3 commands, while the parent does nothing.#include #include #include #include #include #include int main(int argc, char **argv) {int status;int childpid1;int childpid2;int childpid3;char *cat_args[] = {(char *)"ls",(char *)"-ltr", NULL};char *grep_args[] = {(char *)"grep",(char *)"3376", NULL};char *wc_args[] = {(char *)"wc", (char *)"-l", NULL};// create two pipes to send the output of "ls" process to// "grep" process and "wc" processint pipes1[2];int pipes2[2];pipe(pipes1);pipe(pipes2);//for the first child (to execute cat)if( (childpid1 = fork() ) == -1) {perror( "Error creating a child1 process." );exit(1);}//for the second childif( (childpid2 = fork() )== -1) {perror( "Error creating child2 process." );exit(1);}//for the third childif( (childpid3 = fork() ) == -1) {perror( "Error creating child3 process." );exit(1);}//firstif( childpid1 == 0 ) {//replace cat's stdout with write part of 1st pipedup2(pipes1[1], 1);//close all pipes (very important!); end we're using was safely//copiedclose(pipes1[0]);close(pipes1[1]);execvp(*cat_args, cat_args);exit(0);}//secondelse if ( childpid2 == 0 ) {//replaces grep's stdin with read enddup2(pipes1[0], 0);close(pipes1[1]);close(pipes1[0]);//replaces grep's stdout with write enddup2(pipes2[1],1);close(pipes2[0]);close(pipes2[1]);execvp(*grep_args, grep_args);exit(0);}//thirdelse if( childpid3 == 0 ) {//replaces wc'd stdin with read enddup2(pipes2[0], 0);close(pipes1[0]);close(pipes1[1]);close(pipes2[0]);close(pipes2[1]);execvp(*wc_args, wc_args);}//parentelse {}return(0);} 6. An oil company wants to lay a pipeline from its offshore drilling rig to a storage tank on shore, as illustrated in the accompanying figure. The rig (point R) is 3 miles offshore (point A), and the storage tani (point B) is 8 miles down the shoreline. The cost of laying pipe underwater is $800 per mile and along the shoreline is $400 per mile. Point P is the point on shore where the underwater pipe connects with the shoreline pipe. Where should point P be located so as to minimize the cost of laying pipe? Show the function and domain you need to optimize. Provide a complete answer and state units. R (Oil rig) 3 mi Shoreline B (Storage tank) 8 mi Question: Parent Corporation Has Owned All 40 Shares Of Subsidiary Corporation Common Stock Since 2006. Parent Has Been In The Business Of Manufacturing And Selling Light Fixtures, And Subsidiary Has Been In The Business Of Manufacturing And Selling Light Bulbs. Chelsea And Daniel Are The Two Equal Shareholders Of The Parent Stock And Have Owned Their Stock SinceParent Corporation has owned all 40 shares of Subsidiary Corporation common stock since 2006.Parent has been in the business of manufacturing and selling light fixtures, and Subsidiary has been in the business of manufacturing and selling light bulbs. Chelsea and Daniel are the two equal shareholders of the Parent stock and have owned their stock since 2006. Chelsea's basis in her 20 Parent shares is $65,000, and Daniel's basis in his 20 Parent shares is $50,000. On April 10, 2013, Parent distributes all40 Subsidiary shares to Daniel in exchange for all his Parent shares (which are cancelled). The distribution has a bona fide business purpose. The Subsidiary stock had a $5,000 basis to Parent on the distribution date. At the end of 2013, Parent has $110,000 of E&P. Immediately after thedistribution, the FMVs of the Parent and Subsidiary stocks are $3,500 and $2,000 per share, respectively.A. What are the amount and character of the gain, loss, or income Daniel must recognize as a result of Parent's distributing the Subsidiary stock?Gain/Loss: ________Character: (select one)Capital GainDividendReturn of CapitalN/AB. What basis does Daniel take in the Subsidiarystock?C. When does Daniel's holding period for the Subsidiary stock begin? (Select One)begins day after exchange datebegins day before exchange dateincludes his holding period for the Parent stockD. Assume instead that Kenneth formed Subsidiary in 2009 to manufacture and sell lightbulbs. Kenneth sold the Subsidiary stock to Parent for cash in 2011. How would your answers to Parts ac change?Gain/Loss: ________Character: (select one)Capital GainDividendReturn of CapitalN/ABasis in Subsidiary Stock: ________Holding Period Begins: (Select One)begins day after exchange datebegins day before exchange dateincludes his holding period for the Parent stock A charge is released from rest in an electric field. Neglect non-electrical forces. Independently of the sign of the charge, it will always move to a position a) with higher potential b) with lower potential c) where is has higher potential energy d) where it has lower potential energy e) where the electric field has higher magnitude f) where the electric field has lower magnitude Why is it that continually displacing the ring from its equilibrium position, releasing it, and watching its subsequent behavior as you adjust the mass and/or angle of the equilibrant will give you more precise results then simply letting the ring move on its own? 5-(6x+9)= 9-(4x-1) Solve discuss how you would feel if customs and traditions you grew up were replaced by culture and values of another country Tammy leans across the table to get a saltshaker and her friend is surprised at what she thinks is very rude behavior. Lit's perception of her friend's behavior is based on a. Regulative rules b. Constitutive rules d. Stereotypes e. Personal contracts f. Conflict patterns government may choose to combine spending decreases and tax increases in order to let h0, h1, h2,..., hn,....be the sequence defined by hn = (n C 2), (n choose 2). (n>=0). Determine the generating function for the sequence. Rewrite the sentences conjugating the verb according to the subject.1.Yo /escuchar en clase. Yo escuho en clase2. Pablo / tomar apuntes en la clase de historia.3. Nosotros estudiar para los exmenes.4. Diego y yo / dibujar en la clase de arte.5. T necesitar el lpiz en la clase de matemticas.6. Los estudiantes / usar la computadora en las clases.Maria/practicar deportes despus de la escuela.7.8. Vernica y Ana / hablar espaol. Terry bought a new television set for $450. She paid nothing down but agreed to payments of $40.03 per month for 12 months. Find the annual percentage rate for the loan using the APR tableThe annual percentage rate is% Which of the quotes below provides evidence that Esperanza has a sense of humor even during hard times?A. she had taken to wearing her hair in a long braid like Hortensias because Mama had been right it was more practical that wayB. Miguel, why must we always drive so far to shop at the Japanese market?C. Over the dress was a mans sweater with several buttons missing, which was also too big.D. Miguel, how could anyone look at me and think I was uneducated? ASAP I WILL GIVE BRAINLIEST A composite figure is shown.Which of the following represents the total area of the figure? 10.663 in2 24.413 in2 28.448 in2 34.335 in2