The final image points are: L'(-2,-1), K'(0,-2), J'(2,-3)
How to explain the transformationIt should be noted that to innitiate the first transformation, we must translate three units in a positive y-direction and two units to the left along the x-axis. This is accomplished via adding three to the respective points' measurements on the y-axis and immediately subtracting two from the x-coordinates. Consequently, the consecutive coordinates of J, K, and L become:
J(3,3), K(5,2), L(3,1)
Subsequently, the second alteration requires that we reflect across the x-axis; this can simply be achieved by inverting the y-values of each given point. In conclusion, the modified coordinates of J', K', and L' are now:
J'(3,-3), K'(5,-2), L'(3,-1)
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a school needed a total of $3,546 in Supplies for grade 3,4 and 5 if they spilt the supplies evenly how much did they spend on each grade?
Answer: $1.182
Step-by-step explanation: 3.546 divided by 3
Answer:
$1,182
Step-by-step explanation:
I just took the total of $3546 and divided the total by the three grade levels so 3 and I got the answer 3,546. But honestly i'm not sure if it's right lol, so if it's incorrect let me know and I'll work into it more.
How does this work lol?
Answer:
this is the Pythagorean theorem this is the formula a^2 + b^2 = c^2
Step-by-step explanation:
please mark as brainliest have a great day :D
For a certain company, the cost function for producing x items is C(x)=50x+250
and the revenue function for selling x items is R(x)=−0.5(x−120)2+7,200
. The maximum capacity of the company is 170
items.
Profit when producing 70
items=?
Profit when producing 80
items=?
Can you explain, from our model, why the company makes less profit when producing 10 more units?
Answer:
Profit when producing 70 items = $3,050
Profit when producing 80 items = $1,350
Step-by-step explanation:
To find the profit when producing a certain number of items, we need to subtract the cost from the revenue:
Profit = Revenue - Cost
Let's calculate the profit for producing 70 items:
Revenue when producing 70 items:
R(70) = -0.5(70-120)^2 + 7,200 = $6,800
Cost of producing 70 items:
C(70) = 50(70) + 250 = $3,750
Profit when producing 70 items:
Profit = Revenue - Cost = $6,800 - $3,750 = $3,050
Similarly, let's calculate the profit for producing 80 items:
Revenue when producing 80 items:
R(80) = -0.5(80-120)^2 + 7,200 = $5,600
Cost of producing 80 items:
C(80) = 50(80) + 250 = $4,250
Profit when producing 80 items:
Profit = Revenue - Cost = $5,600 - $4,250 = $1,350
We can see that the profit is less when producing 10 more units because the cost of producing those additional units exceeds the revenue generated from selling them. In other words, the marginal cost (the cost of producing one additional unit) is greater than the marginal revenue (the revenue generated from selling one additional unit) beyond a certain point.
This is an example of the law of diminishing returns, which states that as we increase the quantity of inputs while keeping other inputs constant, the marginal product (output per unit of input) eventually decreases.
Hope this helps!
Verify the following Pythagorean identity for all values of x and y:
(x² + y²)² = (x² - y²)² + (2xy)²
The identity (x² + y²)² = (x² - y²)² + (2xy)²
What is an identity?An identity is a mathematical equation which shows that one side of the equation is equivalent and equal to the other side of the equation.
To verify the following Pythagorean identity for all values of x and y:
(x² + y²)² = (x² - y²)² + (2xy)², we need to shows that
left-hand side L.H.S = right hand side
So, we proceed as follows
L.H.S = (x² + y²)²
Expanding the brackets, we have that
(x² + y²)² = (x² + y²)(x² + y²)
= (x²)² + 2x²y² + (y²)²
= (x²)² + (y²)² + 2x²y²
Now, we know that (a - b)² = a² + b² - 2ab. So,
a² + b² = (a - b)² + 2ab
Let a = x² and b = y²
So, we have that
(x²)² + (y²)² = (x² - y²)² + 2x²y²
So, substituting this into the equation, we have that
(x²)² + (y²)² + 2x²y² = (x² - y²)² + 2x²y² + 2x²y²
= (x² - y²)² + 4x²y²
= (x² - y²)² + 2²x²y²
= (x² - y²)² + (2xy)²
So, Since L.H.S = R.H.S
(x² + y²)² = (x² - y²)² + (2xy)²
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1.- If f(x)= x^8, then f'(x) =
2.- If g(x)= -4x^4 then g'(x) =
3.- If h(x)= 1/x^5 then h'(x) =
1.
f'(x) = 8 · x^(8-1) = 8·x^7
2.
g'(x) = -4· 4·x^(4-1) = -16·x^3
3.
h(x) = 1/x^5 = x^(-5), so
h'(x) = -5·x^(-5-1) = -5·x^(-6) or -5 / x^6
based on the value of r^2, which modeling equation is best fit for the data set? a. y=16.5839•1.0185^x
b. y=0.985515x-2.81333
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
d. y=0.00182197x^2+0.785098x+1.195
Okay, let's analyze the r^2 values for the 4 options:
a. y=16.5839•1.0185^x
r^2 is undefined, as this is an exponential model. We cannot determine how well it fits the data based only on r^2.
b. y=0.985515x-2.81333
This is a linear model, so r^2 would be between 0 and 1. Without knowing the actual r^2 value, we cannot determine how good the fit is.
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
This is a 3rd order polynomial model. Again, without the r^2 value, we cannot determine the quality of fit. It could be a good or poor fit.
d. y=0.00182197x^2+0.785098x+1.195
If this model has the highest r^2 value (closest to 1), it would indicate the best fit to the data of the options.
In summary, without seeing the actual r^2 values calculated from the data for each model, we cannot definitively say which option is the "best fit". The model with the r^2 closest to 1 would likely be the best, but r^2 only tells part of the story. Other factors like complexity, interpretability, and residual analysis also matter. But based solely on r^2, the quadratic model d seems the most likely to be the best fit, as long as its r^2 value is high.
Does this help explain the approach? Let me know if you have any other questions!
Please help me with these 6th grade math questions. Thank you so much!
The number line is shown below:
How to solveThe given inequality:
x -5 < 11
Add 5 on both sides
x -5 + 5 < 11 + 5
Add x < 16
Thus, this is represented in the number line below:
A graphical illustration of numbers in a line is known as a number line. It is utilized for indicating the relation between values, and also to do calculations such as subtraction, multiplication, division, etc. The figures get bigger from left to right and diminishes from right to left.
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Convert the rectangular coordinates to polar coordinates with
r > 0 and 0 ≤ < 2.
(1, −2)
Help I'm stuck with this one :(
If you want to transform rectangular coordinates (x, y) into its polar counterpart (r, θ), do the following:
The StepsFirstly, obtain r by computing the distance from the origin to point (x,y), making use of the Pythagorean theorem or simply put, by evaluating r = sqrt(x^2 + y^2).
Secondly, acquire θ which denotes the angle formed between the positive x-axis and a line correlating the origin and the coordinate (x,y). Calculate this via inverse tangent function: θ = atan2(y, x).
Thirdly, in case the measurement for θ is indicated in radians while you require degrees instead, multiply by 180/π to convert it.
Usually expressed as (r, θ), where r indicates proximity disentangled between the origin and the point (x,y), whilst θ identifies the aforementioned angle.
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Experiment 4: You have a bag of 15 scrabble tiles. 3 of the
tiles are the letter O. And the other 2 tiles are the letter U.
a. What is the probability of getting an O on the first draw?
b. What is the probability of getting a U if you didn't replace the O?
What is the probability of getting O and then U if you don't
replace the O?
c.
Answer:
a. The probability of getting an O on the first draw can be calculated by dividing the number of O tiles by the total number of tiles in the bag:
```
P(O on first draw) = 3/15 = 0.2
```
Therefore, the probability of getting an O on the first draw is 0.2 or 20%.
b. After removing one O tile, there are 14 tiles left in the bag, of which 2 are U tiles. Therefore, the probability of getting a U if you didn't replace the O is:
```
P(U without replacing O) = 2/14 = 1/7 ≈ 0.143
```
Therefore, the probability of getting a U if you didn't replace the O is approximately 0.143 or 14.3%.
c. The probability of getting O and then U if you don't replace the O can be calculated as follows:
```
P(O and then U) = P(O on first draw) * P(U without replacing O)
= 3/15 * 2/14
= 1/35
≈ 0.029
```
Therefore, the probability of getting O and then U if you don't replace the O is approximately 0.029 or 2.9%.
Step-by-step explanation:
Plot - 1 1/4 and 5/2 on the number line below.
The number line where we plotted 1 1/4 and 5/2 is added as an attachment
Plotting -1 1/4 and 5/2 on a number lineFrom the question, we have the following parameters that can be used in our computation:
-1 1/4 and 5/2
To start with, we convert both numbers to the same form
i.e. decimal or fraction
When converted to fractions, we have
-5/4 and 5/2
Rewrite the denominators of the fractions
So, we have
-5/4 and 10/4
This means that we can plot -5/4 at -5 and 10/4 at point 10 where the difference in each interval is 1/4
Using the above as a guide, we have the following:
The number line is attached
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Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range.
y = negative 0.5 x squared + 0.7 x minus 5.1
a.
D: all real numbers
R: (y less-than-or-equal-to negative 5.1)
c.
D: all real numbers
R: (y less-than-or-equal-to negative 4.855)
b.
D: all real numbers
R: (y greater-than-or-equal-to 4.855)
d.
D: all real numbers
R: (y less-than-or-equal-to negative 5.345)
Please select the best answer from the choices provided
A
B
C
D
The domain is all real numbers, and the range is (y ≤ -4.855). (option b)
To sketch the graph of a quadratic equation, you can use a graphing calculator, which is a handy tool that can produce a visual representation of the equation. For instance, let's take the quadratic equation y = -0.5x² + 0.7x - 5.1 and sketch its graph using a graphing calculator.
When we enter this equation into the graphing calculator, we can see a U-shaped curve that is symmetric about the vertical line passing through the vertex. The vertex is the point where the parabola changes direction and is given by the formula x = -b/2a, y = f(x), where f(x) is the value of y at the vertex.
Now let's examine the given options and determine their domain and range based on the graph of the quadratic equation.
all real numbers, R: (y ≤ -4.855)
For this option, we can observe that the parabola opens upward, and the vertex is at (0.7, -5.35).
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Why do polling companies often survey 1060 individuals when they wish to estimate a population proportion with a margin of error 3% with 95% confidence?
Polling companies survey 1060 individuals to estimate a population proportion with a margin of error of 3% with 95% confidence because it strikes a balance between cost and accuracy, and it is based on statistical calculations that aim to achieve a reasonable level of precision while minimizing the margin of error.
When a polling company selects a sample size of 1060 individuals, it is based on statistical calculations that aim to achieve a 3% margin of error with 95% confidence. The sample size needs to be large enough to reduce the margin of error and increase the level of confidence in the results.
The margin of error decreases as the sample size increases, and it is inversely proportional to the square root of the sample size. Therefore, a larger sample size leads to a smaller margin of error. However, increasing the sample size also increases the cost and time required to conduct the survey.
Polling companies aim to strike a balance between the cost and the desired level of accuracy, which is typically a margin of error of 3-5% with 95% confidence. A sample size of 1060 individuals is often considered a reasonable compromise between cost and accuracy, as it provides a small enough margin of error to be useful while being feasible to conduct within a reasonable time and budget.
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Based on the graph below, what will be the coordinates of the point that represents the number of snowballs needed to make 2 snowmen?
the coordinates of the point that represents the number of snowballs needed to make 2 snowmen should be option C. which is (2,6)
Find the equation of the plane passing through the lines of intersection of the planes :
2x - 7y + 4z = 3 , 3x - 5y + 4z + 11 = 0 and the point ( -2 , 1 , 3 ).
The equation of the plane passing through the lines of intersection of the planes 2x - 7y + 4z = 3 and 3x - 5y + 4z + 11 = 0 and the point (-2, 1, 3) is
-13x - 8y + z + 90 = 0
We have,
To find the equation of the plane passing through the intersection of two planes, we need to first find the direction vector of the line of intersection of the two planes.
Let's call the two planes P1 and P2, which are given by the equations:
P1: 2x - 7y + 4z = 3
P2: 3x - 5y + 4z + 11 = 0
To find the direction vector of the line of intersection of P1 and P2, we can take the cross product of the normal vectors of P1 and P2. The normal vectors are:
n1 = <2, -7, 4>
n2 = <3, -5, 4>
Taking the cross-product of n1 and n2.
n1 x n2 = <-13, -8, 1>
This vector is parallel to the line of intersection of P1 and P2. We can use this vector as the direction vector for the line.
Now, we need to find a point on the line.
We can use the point of intersection of P1 and P2 as a point on the line.
To find this point, we can solve the system of equations:
2x - 7y + 4z = 3
3x - 5y + 4z + 11 = 0
Subtracting the first equation from the second, we get:
x + 2y + 7 = 0
Solving for x in terms of y,.
x = -2y - 7
Substituting this expression for x into the first equation, we get:
-4y - 14 - 7y + 4z = 3
Simplifying.
-11y + 4z = 17
Choosing y = 1.
-11 + 4z = 17
Solving for z.
z = 7
Substituting y = 1 and z = 7 into the equation for x.
x = -2(1) - 7 = -9
So a point on the line is (-9, 1, 7).
Now, we can use the point (-9, 1, 7) and the direction vector <-13, -8, 1> to write the equation of the plane passing through the line of intersection of P1 and P2.
Let's call this plane P3.
Using the point-normal form of the equation of a plane.
-13(x + 9) - 8(y - 1) + (z - 7) = 0
Expanding and simplifying, we get:
-13x - 8y + z + 90 = 0
Thus,
The equation of the plane passing through the lines of intersection of the planes 2x - 7y + 4z = 3 and 3x - 5y + 4z + 11 = 0 and the point (-2, 1, 3) is:
-13x - 8y + z + 90 = 0
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2(x-1)+3(x+1)=4(x+4)
1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.
That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.
1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.
That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.
Answer:
x = 15
Step-by-step explanation:
Simplifying the expression:
2(x - 1) + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4x + 16Add the numbers:
2x - 2 + 3x + 3 = 4x + 162x + 3x - 2 + 3 = 4x + 162x + 3x + 1 = 4x + 16Combine like terms:
2x + 3x + 1 = 4x + 165x + 1 = 4x + 16Subtract 1 from both sides:
5x + 1 - 1 = 4x + 16 - 15x = 4x + 15Subtract 4x from both sides:
5x - 4x = 4x - 4x + 15x = 15Answer:
x = 15
Step-by-step explanation:
Simplifying the expression:
2(x - 1) + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4x + 16Add the numbers:
2x - 2 + 3x + 3 = 4x + 162x + 3x - 2 + 3 = 4x + 162x + 3x + 1 = 4x + 16Combine like terms:
2x + 3x + 1 = 4x + 165x + 1 = 4x + 16Subtract 1 from both sides:
5x + 1 - 1 = 4x + 16 - 15x = 4x + 15Subtract 4x from both sides:
5x - 4x = 4x - 4x + 15x = 15Decimal word problem
pls help
Can someone give me a decimal word problem that involves subtraction and division plssss with the answer step by stepp plsss help i begg u guys lovee uuu guyss
Thus, decimal word problem that involves subtraction and division-
The two empty water container weighs 0.64 kg and 1.728 kg when filled with water. Find the water weigh?
Explain about the decimal word problem:The decimal point, which distinguishes between a decimal number's whole number and fractional component, is a little dot. Decimal numbers include 4.14, 3.786, 5.453, and 123.5687 as examples.
Any number of digits can be used to represent the decimal places in a decimal number.The decimal places are the digits that come after the decimal point and are arranged in the following order: tenths, hundredths, thousandths, ten-thousandths, and so forth.decimal word problem : (subtraction and division)
The two empty water container weighs 0.64 kg and 1.728 kg when filled with water. Find the water weigh?
2 water pitcher's weight when empty and full with water is 0.64 kg and 1.728 kg, respectively. We must determine the water's weight. We must deduct the weight of the container when it is empty from the weight of a container when it is full of water in order to determine the weight of the water.Division: Weight of one water container = 0.64 / 2 = 0.34 kg.
Subtraction: Weight of water : 0.728 - 0.34 = 0.385 kg.
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Find a polynomial with integer coefficients that satisfies the following conditions :
Degree of polynomial : 3
Zeros : 2, 4
-intercept : −96
Answer the question below
Answer:
B represents a function.
The stem-and-leaf plot displays the amount of time, in minutes, that 10 players spent practicing their serving skills for an upcoming tennis tournament.
1 2, 2, 9
2 0, 2, 6
3 1, 1
4 0
5
6 8
Key: 3|1
means 31
Part A: Calculate the mean, median, mode, and range for the data given. Show your work. (8 points)
Part B: Should the tennis players report the mean or median value to show they are less prepared for the tournament? Explain based on the scenario. (4 points)
Part A:
To calculate the mean, we add up all the values and divide by the total number of values:
12 + 12 + 19 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 281
Mean = 281 / 10 = 28.1
To find the median, we need to find the middle value. Since there is an even number of values, we take the average of the two middle values:
Median = (22 + 26) / 2 = 24
The mode is the value that appears most frequently. In this case, there is no mode as no value appears more than once.
The range is the difference between the highest and lowest values:
Range = 68 - 12 = 56
Part B:
The median may be a better measure of central tendency in this scenario as there is an outlier value of 68 that can skew the mean. Since outliers can have a significant impact on the mean, reporting the median may give a better representation of the typical amount of time spent practicing for the tournament. Therefore, the tennis players should report the median value.
Evaluate each expression (a) log7 1/7 =
(b) log 3 27 = 9
If you drive from Dublin to Galway at a constant speed of 70 miles per hour, but pause
for 30 minutes for lunch, how long is your trip in total? Round your final answer to the
nearest tenth of an hour
Solve the system of equations.
y = 2 - 6x
1/2y - x = 1
Question 4 options:
(0,-2)
(2,0)
(-2,0)
(0,0)
(1,-4)
Answer:
a
Step-by-step explanation:
Answer:
Step-by-step explanation:
y=2 and x=0 making it (0,2)
Triangle NMO has vertices at N(−5, 2), M(−2, 1), O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −2. N′(1, 2), M′(−2, 1), O′(−1, 3) N′(−5, −6), M′(−2, −5), O′(−3, −7) N′(−5, 0), M′(−2, −1), O′(−3, 1) N′(9, 2), M′(6, 1), O′(7, 3)
The vertices of image N′M′O′ if the preimage is reflected over x = −2 include the following: D. N′(9, 2), M′(6, 1), O′(7, 3)
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
Similarly, the reflection of a point (x, y) over the line x = a is modeled by this transformation rule:
(x, y) → (-2a - x, y)
(x, y) → (-2(-2) - x, y)
(x, y) → (4a - x, y)
By applying a reflection over x = -2 to the coordinate of the given triangle NMO, we have the following coordinates:
(x, y) → (4 - x, y).
N (−5, 2) → (9, 2)
M(−2, 1) → (6, 1)
O(−3 , 3) → (7, 3)
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Answer:
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Step-by-step explanation:
I am in the middle of taking the test and even made a graph to check my work! This should be the correct answer
Jan has set the sales target for 35,000 ice cream makers, which she thinks she can achieve by an additional fixed selling expense of $200,000 for advertising. All other costs remain as per the data in the above table. What will be the operating profit if the additional $200,000 is spent on advertising and sales rise to 35,000 units?
The company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.
What do sales mean?Sales generally refer to the total amount of goods or services that a business sells during a given period of time, typically measured in monetary terms. Sales can also refer to the process of selling products or services, including activities such as prospecting, lead generation, sales presentations, and closing deals.
According to the given informationTo calculate the operating profit with sales of 35,000 units and an additional selling expense of $200,000, we need to first calculate the total revenue and the total cost, and then subtract the total cost from the total revenue.
From the table provided, we can see that the selling price per unit is $900 and the variable cost per unit is $600. Therefore, the contribution margin per unit is:
Contribution margin per unit = Selling price per unit - Variable cost per unit
= $900 - $600
= $300
Since the sales target is 35,000 units, the total contribution margin is:
Total contribution margin = Contribution margin per unit x Number of units sold
= $300 x 35,000
= $10,500,000
The total cost can be calculated as follows:
Total cost = Fixed cost + Variable cost
= $3,500,000 + ($600 x 35,000)
= $25,100,000
Adding the additional selling expense of $200,000, the new total cost becomes:
New total cost = $25,100,000 + $200,000
= $25,300,000
Therefore, the operating profit with sales of 35,000 units and an additional selling expense of $200,000 is:
Operating profit = Total revenue - Total cost
= ($900 x 35,000) - $25,300,000
= $10,500,000 - $25,300,000
= -$14,800,000
This indicates that the company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.
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4. Gabriel wants to learn how to play darts, so
he researches the costs of different dartboards
at stores in his area. What would be the most
appropriate way for him to display his data?
Answer will be marked!!
Answer:
a line graph
Step-by-step explanation:
19 center: (8, 2), point on circle: (14, -1)
The radius of this circle with center (8, 2) is equal to 6.71 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given points into the distance formula, the radius of this circle can be calculated as follows;
Distance = √[(14 - 8)² + (-1 - 2)²]
Distance = √[(6)² + (-3)²]
Distance = √[36 + 9]
Distance = √45
Distance = 6.71 units.
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Complete Question:
What is the radius of the circle with Center: (8, 2), Point on Circle: (14,-1)? 2 decimal places
Five friends-Allison, Beth, Carol, Diane, and Evelyn- have identical calculators and are studying for a statistics exam. They set their calculators down in a pile before taking a study break and then pick them up in random order when they return from the break. What is the probability that at least one of the five gets her own calculator? [Hint: Let A be the event that Alice gets her own calculator, and define events B, C, D, and E analogously for the other four stu- dents.] How can the event (at least one gets her own calcu- lator} be expressed in terms of the five events A, B, C, D, and E? Now use a general law of probability. [Note: This is called the matching problem. Its solution is easily extended to individuals. Can you recognize the result when n is large (the approximation to the resulting series)?]
Draw fraction strips to show the following fractions: 4/6,1/6, and 5/6. Then write the three fractions in order from least to greatest.
Given this equation what is the value of y at the indicated point?
We are given the equation of a parabola, [tex]y=-x^2+2[/tex]. The question asks us to find both values of a point given the the x-coordinate which is -3. To find the y-coordinate, simply plug in -3 for x into the equation of the parabola.
[tex]y=-x^2+2 \Longrightarrow y=-(-3)^2+2 \Longrightarrow y=-(9)+2 \Longrightarrow y=-9+2[/tex]
[tex]\Longrightarrow y=-7[/tex]
Thus, the point is (-3,-7)
Lauren over-filled the homemade pecan pie that she was baking for Thanksgiving, so the pie needed additional cooking time. Lauren decided to place a strip of aluminum foil around the edge of the crust so that it would not burn. If Lauren used a pie pan with a 12-inch diameter, how long, to the nearest inch, should the strip of foil be?
A. 19 inches
B. 24 inchess
C. 113 inchess
D. 38 inchess
Hence the correct option is D. 38inches long, to the nearest inch, should the strip of foil be.
What is the circumference?The circumference of a circle in mathematics is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. In according to broader the perimeter is the length of any closed figure of curve.
What is diameter?A straight line and cuts through the middle of a body or figure. particularly the length of a diameter is a line segment passing through the center of a circle with its ends on the circumference.
We determine the circumference of the pie pan in order to determine the length of the aluminium foil strip required.
Circumference =2[tex]\pi[/tex]r.
where, r = circle of radius and [tex]\pi[/tex] = mathematical constant =3.14.
The pie pan of radius = half of its diameter=12 inches/2= 6 inches.
Now, the pie pan of circumference is:
Circumference: 2 [tex]\pi[/tex]r=2[tex]\pi[/tex] *6 inches= 37.7 inches
Therefore , the length of the aluminium foil strip = 38 inches,
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