A form a basis for R3.
To show that the columns of A form a basis for R3 , we need to show that they are linearly independent and span R3.
To show linear independence, we need to find constants c1 , c2 and c3 , not all zero , such that c1(4,1,0) + c2 (1,0,-2) + c3(0,1,-5) = (0,0,0).
This gives us a system of linear equations , which we can write in augumented matrix form as :
[4 1 0 | 0]
[1 0 1 | 0]
[0 -2 -5 | 0]
we can use row operations to reduce this matrix to row echelon form:
[4 1 0 | 0]
[0 -2 -5 | 0]
[0 0 1 | 0]
From this we can see that the only solution is c1 = c2 = c3 = 0, which means that columns of A are linearly independent.
To show that the columns of A span R3 , we can take any vector
(x, y, z) in R3 and write it as a linear combination of the columns of A :
(x, y, z) = a(4,1,0) + b(1,0,-2) + c(0,1,-5)
Solving for a , b and c, we get
a = (4x - y)/ 14
b = (2y + 5z - 2x)/ 14
c = -z/ 14
Since we can express any vector in R3 as a linear combination of the columns of A, they span R3 .
Therefore , the columns of A form a basis for R3.
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Michael wants to know if support for a local referendum on gay rights is related to political party affiliation. He conducts a survey of 200 local residents and asks them their political party affiliation and whether they intend to vote for or against the referendum. He learns that 16 people who say they are republican are for the referendum and 54 are against. Of those who say they are democrat, 72 people are for the referendum and 28 are against it. Some people identified as "other" and among that group, 3 were against the referendum and 27 were in favor of it. How would you represent the data in a table? Identify the null and alternative hypothesis. Conduct the appropriate analysis with a=.05. What should Michael conclude?
The answer is the test statistic (13.765) is greater than the critical value (5.991), we reject the null hypothesis. Therefore, we can conclude that there is a significant relationship between political party affiliation and support for the referendum on gay rights.
To represent the data in a table, we can create a contingency table:
For Against
Republican 16 54
Democrat 72 28
Other 27 3
Null hypothesis (H₀): There is no relationship between political party affiliation and support for the referendum on gay rights.
Alternative hypothesis (H₁): There is a relationship between political party affiliation and support for the referendum on gay rights.
To analyze the data, we can perform a chi-square test of independence. This test will determine if there is a significant association between political party affiliation and support for the referendum.
Applying the chi-square test at a significance level (α) of 0.05, we can calculate the test statistic and compare it to the critical value from the chi-square distribution with (rows - 1) × (columns - 1) degrees of freedom.
Let's calculate the expected frequencies for each cell assuming the null hypothesis is true:
For Against Total
Republican 27 43 70
Democrat 48 52 100
Other 12 18 30
Total 87 113 200
Now, we can calculate the chi-square statistic:
χ² = Σ[(O - E)² / E]
where O is the observed frequency and E is the expected frequency.
Performing the calculations, we find:
χ² ≈ 13.765
To determine the critical value, we need to find the degrees of freedom, which is equal to (rows - 1) × (columns - 1) = (3 - 1) × (2 - 1) = 2.
Using a chi-square distribution table or a statistical software, we find that the critical value for a significance level of 0.05 and 2 degrees of freedom is approximately 5.991.
Since the test statistic (13.765) is greater than the critical value (5.991), we reject the null hypothesis. Therefore, we can conclude that there is a significant relationship between political party affiliation and support for the referendum on gay rights.
In Michael's survey data, political party affiliation is related to the support for the referendum. Further analysis and interpretation of the results are needed to understand the nature and strength of this relationship.
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approximate the sum of the series correct to four decimal places. [infinity] (−1)n − 1n2 8n n = 1
To approximate the sum of the series [infinity] (−1)n−1n^2/(8n), we can use a numerical method such as the partial sum method.
Let's calculate the partial sums of the series and add up terms until the sum converges to a desired level of accuracy. We will stop adding terms once the absolute difference between two consecutive partial sums is less than the desired accuracy.
Let's start by calculating the partial sums:
S_1 = (-1)^1-1(1^2)/(81) = 1/8
S_2 = (-1)^2-1(1^2)/(82) + (-1)^1-1(2^2)/(82) = 1/8 - 1/16 = 1/16
S_3 = (-1)^3-1(1^2)/(83) + (-1)^2-1(2^2)/(83) + (-1)^1-1(3^2)/(83) = 1/8 - 1/16 - 1/24 = -1/24
We can observe that the partial sums alternate between positive and negative values. This indicates that the series does not converge to a specific value but oscillates between two values.
To approximate the sum, we will calculate partial sums until the difference between two consecutive partial sums is less than the desired accuracy. Let's say we want the accuracy to be 0.0001.
Let's continue calculating partial sums:
S_4 = (-1)^4-1(1^2)/(84) + (-1)^3-1(2^2)/(84) + (-1)^2-1(3^2)/(84) + (-1)^1-1(4^2)/(84) = 1/8 - 1/16 - 1/24 + 1/32 = -1/48
S_5 = (-1)^5-1(1^2)/(85) + (-1)^4-1(2^2)/(85) + (-1)^3-1(3^2)/(85) + (-1)^2-1(4^2)/(85) + (-1)^1-1(5^2)/(8*5) = 1/8 - 1/16 - 1/24 + 1/32 + 1/40 = 1/120
The difference between S_4 and S_5 is 1/120 - (-1/48) = 1/120 + 1/48 = 1/80, which is greater than 0.0001.
Therefore, we can approximate the sum of the series as -1/48, correct to four decimal places.
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corine in making potato salad for each bowl of potato salad she needs 1/4 cup of potatoes how many cups of potatoes will she use if she makes 32 bowls of potato salad ?
Answer:
8 cups of potatoes are needed
Step-by-step explanation:
One way of doing this work is to write out
1/4 cup 1 cup
------------- , which is equivalent to ------------ (a unit rate)
1 bowl 4 bowl
and then multiply this unit rate by 32 bowls:
(1/4)(32 bowls) = 8 cups of potatoes are needed
The product of 3 consecutive even integers is equal to the cube of the first plus the square of the second plus twice the square of the third. Find the integers. Please show work.
Answer:
6, 8 and 10 and -2, 0, 2
There are two roots x = -2 and 6,
but the since I don't believe 0 is an even number the answer is 6, 8 and 10
I was incorrect according to G0ggle zero is an even number so another answer is -2, 0, 2
Step-by-step explanation:
read the question and convert the English to mathematics
x, y and z even consecutive number
y = x+2
z = y+2 = x+4
and
xyz = x³ + y² + 2z² substitiute x terms in for y and z
x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solve for x by graphing on DEMOS
x = -2, 6 solved algebraically below
x = -2 y=0 z=2
x = 6 y=8 z=10
Checked both answers
xyz = x³ + y² + 2z²
-2(0)2 = -8 + 0 + 8 when x = -2
0 = 0
and
6(8)(10) = 6³ + 8² +2(10)² when x = 6
480 = 216+64+200
= 480
x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solved algebraically
(x²+2x)(x+4) = x³ + x² +4x +4 + 2x² + 16x + 32
x³ + 6x² + 8x = x³ + x² +4x +4 + 2x² + 16x + 32
x³ + 6x² + 8x = x³ + 3x² + 20x + 36
3x² - 12x - 36 = 0 factor out the 3
3[x² - 4x - 12] = 0
3(x+2)(x-6) = 0 x = -2 and -12
The students in Mr. Andersen's science class counted the number of leaves on each of 11 different rose bushes. The data they collected is:
26, 54, 38, 65, 58, 35, 52, 43, 55, 41, 61
What is the range of the set of data?
Answer:
35
Step-by-step explanation:
subtract highest and lowest numbers
Emmy is tossing bean bags at a target. She hit the target on 9 out of her last 18 tries. Considering this data, how many hits would you expect Emmy to get during her next 16 tosses?
Answer:
I would expect Emmy to get 8 hits in her next 16 tosses.
Emmy is to get 8 hits in her next 16 tosses.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of samples
Given that Emmy is tossing bean bags at a target. She hit the target on 9 out of her last 18 tries. Considering this data.
The probability is,
P = 9 / 18
P = 0.5
The expected number of the hits on the target in 16 tosses will be;-
Number = 16 x 0.5
Number = 8
Therefore, Emmy is to get 8 hits in her next 16 tosses.
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give the slope of the line with equation 17x = -34; then graph the line
Answer:
Slope: Undefined
Step-by-step explanation:
Can someone help me with this. Will Mark brainliest.
Answer:
(1.5, -4)
Step-by-step explanation:
( -1, -5) and (4, -3)
[tex](\frac{-1+4}{2} ,\frac{-5-3}{2} )\\\\(\frac{3}{2} ,\frac{-8}{2} )\\\\(1.5,-4)[/tex]
Find a Mobius transformation f such that f(0) = 0, f(1) = 1, f([infinity]) = 2, or explain why such a transformation does not exist.
A Möbius transformation is a transformation of the form f(z) = (az+b)/(cz+d), where a, b, c, and d are complex numbers and ad-bc ≠ 0. The complex number z maps to f(z).
To find the Möbius transformation f such that f(0) = 0, f(1) = 1, f([infinity]) = 2, we follow these steps:
Step 1: Map 0 to 0 We need to map 0 to 0, so we set f(0) = 0. So, we get 0 = (a(0) + b) / (c(0) + d). This gives us b = 0. Step 2: Map infinity to 2We need to map [infinity] to 2, so we set f([infinity]) = 2. So, we get 2 = (a[infinity] + b) / (c[infinity] + d). This gives us a/c = 2/d. Cross-multiplying the terms, we get ad = 2c.
Let us assume that d = 1, then we have a = 2c.
We can substitute this value of a in the Möbius transformation, and we get f(z) = (2cz) / (cz + 1).Step 3: Map 1 to 1To map 1 to 1, we evaluate the Möbius transformation at z = 1. We get f(1) = (2c) / (c + 1) = 1.
Solving this, we get c = -1/2. Therefore, the Möbius transformation is f(z) = (2z) / (z - 2).
Hence, we have found the required Möbius transformation f(z) = (2z) / (z - 2) such that f(0) = 0, f(1) = 1, and f([infinity]) = 2.
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Answer this question
y is less than or equal to three more than the product of x and negative two thirds put it on standard form
What is the area of the triangle?
5
4
3
units2
Answer:
area of triangle =1/2 p×b=1/2×4×3=6unit²
A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores were recorded before and after the training. The results means of two populations are shown below. Assume that two dependent samples have been randomly selected from normally distributed populations. Using a 0.01 level of significance, test the claim that the training technique is effective in raising the gymnast scores?
before 9.5, 9.4, 9.6, 9.5, 9.5, 9.6, 9.7
after 9.6, 9.6, 9.6, 9.4, 9.6, 9.9, 9.5
There is insufficient evidence to support the claim that the training technique is effective in raising the gymnasts scores.
In hypothesis testing, we often use significance levels such as 0.01 to determine whether or not there is enough evidence to support the hypothesis.
Here is the solution to the given problem.
The null hypothesis is that the training technique is not effective in raising the gymnasts' scores.
It is expressed as
H0: µd = 0.
The alternative hypothesis is that the technique is effective in raising the gymnasts' scores.
It is expressed as
Ha: µd > 0.
The significance level α = 0.01 is given.
Therefore, the given problem can be tested using a one-tailed t-test.
This is because the alternative hypothesis states that the mean difference between the two populations is greater than zero.
A t-test is appropriate because the sample sizes are less than 30.
The difference between the before and after competition scores of each gymnast should be calculated.
This gives us the difference scores, which are as follows:
0.1, 0.2, -0.02, -0.1, 0.1, 0.3, -0.2.
Next, we compute the mean and standard deviation of the differences. We have:
n = 7d
= 0.0714Sd
= 0.1466
Then we compute the t-statistic:
t = (d - µd) / (Sd / √n)
t = (0.0714 - 0) / (0.1466 / √7)
t = 1.5184
The degrees of freedom for this test are (n - 1) = 6.
Using a t-distribution table with 6 degrees of freedom and a significance level of 0.01 for a one-tailed test, we find that the critical t-value is 2.998.
For the given problem, the test statistic t = 1.5184 is less than the critical value of 2.998.
Therefore, we do not reject the null hypothesis.
There is insufficient evidence to support the claim that the training technique is effective in raising the gymnast scores.
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HELP
I WILL GIVE YOU BRAINLIEST
Give the solution to this quadratic.
y = 3(x-1)^2
Answer:
y=3x^2-6x+3
Step-by-step explanation:
6th grade math plz help
Answer:
The question needs more information but you can see that all the numbers in the 1st column are multiplied by 6 to equal the number in column 2
Step-by-step explanation:
3 x6 =18
6 x 6= 36
9 x6= 54
12 x6 =72
Can anyone solve these please, cos I'm nucklehead and my brain won't work
×-10=13
t+20=44
y
_ =7
5
Answer:
Hello There!!
Step-by-step explanation:
1.×-10=13. 13+10=23
2.t+20=44. 44-20=24
3.y/5=7. 5×7=35
You do the inverse operations to find the unknown number.For example if it is minus you do plus. e.g x-7=19 . 19+7=26
hope this helps,have a great
Jimrgrant or Someone Answer this PLZ
Answer:
C and A
Step-by-step explanation:
For the triangle to be isosceles then the legs are congruent, that is
XZ = XY , substitute values
5x - 1 = 3x + 5 ( subtract 3x from both sides )
2x - 1 = 5 ( add 1 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3 → C
(10)
The diagonals of a square bisect each other
Calculate PR using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2-y_{1})^2 }[/tex]
with (x₁, y₁ ) = P(0, 0) and (x₂, y₂ ) = R(6, - 8)
PR = [tex]\sqrt{(6-0)^2}+(-8-0)^2[/tex]
= [tex]\sqrt{6^2+(-8)^2}[/tex]
= [tex]\sqrt{36+64}[/tex]
= [tex]\sqrt{100}[/tex]
= 10
Then
PT = 0.5 × 10 = 5 → A
Factor the expression: 2x^2 +21x+49
Answer:
(2x+7)(x+7)
Step-by-step explanation:
Berverly has 2 pens she buys 1 more pen enter the numerical expressions in the box that models this situation
Answer:
2 + 1 = 3
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Berverly already has = 2 pens
Berverly bought = 1 pen
Then to show this situation in numerical expression, we have to add both values, then
= 2 + 1 = 3
Hence, this shows that the total number of pens Berverly has after buying is 3.
a cylinder with the radius of 12 feet and height of 1.2 feet. What is the total surface area of the cylinder in square feet?
Answer:
995.26
Step-by-step explanation:
I'm not sure but this is what I got
WILL GIVE BRAINLIEST what is
453252 x 213414
Answer:
96730322328
Step-by-step explanation:
I hope this helps
CAN SOMEONE PLEASE HELP!!! I DONT UNDERSTAND. I WILL GIVE BRAINLIEST!!!
Answer:
586.76
Step-by-step explanation:
Take the area of the rectangular prism = 348
Find the area of the cylinder = 477.52
Divide the cylinder by 2 = 238.76
Add both together = 586.76
In a particular region, 6% of the population is thought to have a certain disease. A standard diagnostic test has been found to correctly identify 91% of the people who have the disease. However, the test also incorrectly diagnoses 8% of those who do not have the disease as having the disease (in other words, the person does not have the disease but the test tells them that they do). A randomly selected person in the region is tested for the disease. (a) What is the probability the test comes back positive
Answer:
The positive predictive value ≈ 30.012%
Step-by-step explanation:
(a) The given percentage of the people in the region that have the disease, P(D) = 6% = 0.06
The percentage people correctly identified as having the disease by the standard diagnostic test = 91%
The percentage of people incorrectly identified as having the disease by the standard diagnostic test, P(T + |H) = 8%
Therefore, the sensitivity of the test, P(T + |D) = 0.91
The specificity of the test, P(T - |H) = 1 - 0.08 = 0.92
Therefore, the probability that a person is healthy, P(H) = 1 - 0.06 = 0.94
Therefore, in a population of 1,000 people, 60 people have the disease, with a sensitivity of 91%, the test will correctly pic 0.91×66 = 60.06 people correctly with the disease and 0.91 × 940 = 855.4 people without the disease
The number of non-diseased that test positive by the test is 0.08 × 1000 = 80 people which are false positives
Therefore, the number of diseased diagnosed as negative is 0.08 × 60 = 4.8
Therefore, we have;
[tex]\begin{array}{cccc}&Deseased&Non-diseased& Diseased + Non-diseased\\Test \ +ve&60.06&80& 140.06\\Test \ -ve&4.8&855.4&\end{array}[/tex]
The positive predictive value = Diseased +ve/(Diseased +ve + Non-diseased +ve)
[tex]The \ positive \ predictive \ value = \dfrac{Diseased +ve}{Diseased +ve + Non-diseased +ve} \times 100[/tex]
Therefore;
The positive predictive value = 60.06/(60.06 + 140.06) × 100 ≈ 30.012%
Help please the question is in the photo
A cylinder has been cut out of a solid. Find the volume of the remaining solid. Round answer to the nearest tenth.
Answer:
98.19
Step-by-step explanation:
Volume of whole cube minus volume of cylinder. volume of cylinder is pi x r^2 x h
The volume of remaining solid is 46.44 in³
What is Volume?Volume is the measure of the capacity that an object holds.
For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml. Volume can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains. The best way to visualize volume is to think of it in terms of the space.
How To Calculate the Volume?Here are the steps to calculate volume of any solid shape:
Identify all the given parameters that are useful and are required to substitute in the respective volume formula. Such as the radius to be 'r' and height to be 'h', the slant height, diameter, etc.Make sure all the parameters are of the same units.Substitute the values in the volume formula of the respective shapes.Write the units as cubic units.edge= 6
Volume of cube= l³
= 6*6*6
=216 in³
Now, Volume of cylinder
=πr²h
= 3.14 * 3 * 3 * 6
=169.56 in³
Volume of remaining solid= 216- 169.56
=46.44 in³
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Glenn needs to cut pieces of ribbon that are each 1 meter long to make ribbon key chains. If he has 6 pieces of ribbon that are each 1 dekameter long, how many 1−meter pieces of ribbon can he cut?
Answer: 60
Step-by-step explanation:
1=10. x6=60
find the nth maclaurin polynomial for the function. f(x) = sin(x), n = 3
P3(x) = ___
The third-degree Maclaurin polynomial for f(x) = sin(x) is P3(x) = x - (x^3) / 6.
To find the nth Maclaurin polynomial for the function f(x) = sin(x) when n = 3, we need to compute the polynomial up to the third-degree term.
The Maclaurin polynomial for a function f(x) centered at x = 0 is given by the formula:
Pn(x) = f(0) + f'(0)x + (f''(0)x^2) / 2! + (f'''(0)x^3) / 3! + ...
Let's calculate the nth Maclaurin polynomial for f(x) = sin(x) when n = 3:
First, we find the values of the function and its derivatives at x = 0:
f(0) = sin(0) = 0
f'(x) = cos(x), so f'(0) = cos(0) = 1
f''(x) = -sin(x), so f''(0) = -sin(0) = 0
f'''(x) = -cos(x), so f'''(0) = -cos(0) = -1
Using these values, we can write the Maclaurin polynomial:
P3(x) = 0 + 1x + (0x^2) / 2! + (-1x^3) / 3!
Simplifying further, we have:
P3(x) = x - (x^3) / 6.
Therefore, the third-degree Maclaurin polynomial for f(x) = sin(x) is:
P3(x) = x - (x^3) / 6.
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Help ASAP 15 Points
The hot water heater in the Alvarez's home holds 70 gallons of water. Each shower taken uses 5.4 gallons
of water. How much water is left after 3 showers. (Hint: Write an equation relating the number of showers and
the number of gallons left in the tank)
Answer:
53.8 gallons
Step-by-step explanation:
5.4*3=16.2
5.4 (gallons used per shower) * 3 (number of showers) = 16.2 (gallons used in 3 showers)
70-16.2=53.8
70 (Water in tank) - 16.2 (gallons used in 3 showers) = 53.8 (gallons of water left)
Hope this helps! Please brainliest!!!
Answer:
A(3) = 53.8 gallons left after 3 showers
Step-by-step explanation:
A(x) = volume of water left in tank = 70 gallons - (5.4 gallons)x, where x is the number of showers already taken.
After 3 showers, the volume of water left is A(3) = 70 gal - (5.4 gallons)(3), or
A(3) = 53.8 gallons left after 3 showers
Draw a graph which has the following adjacency matrix: [2 1 1 0] 1 0 0 1 1 0 0 1 0 1 1 0 (b) Label the vertices of your graph A,B,C,D (in any order). (c) How many different paths of length 10 are there from the vertex you labelled A to the vertex you labeled D in the graph you draw in part (a)? Show your working.
In the drawing a graph is there with labeling of vertices A,B,C,D with matrix [tex]\begin{bmatrix}2 &1 & 1&0\\1 & 0 & 0&1\\1&0&0&1\\0&1&1&0\end{bmatrix}[/tex].
Given that,
a. We have to draw a graph which has the following adjacency matrix
[tex]\begin{bmatrix}2 &1 & 1&0\\1 & 0 & 0&1\\1&0&0&1\\0&1&1&0\end{bmatrix}[/tex]
Taking the matrix rows and column as A,B,C,D.
Therefore, In the drawing the graph is with matrix.
(b) We have to label the vertices of your graph A,B,C,D.
The drawing can be seen with the label of vertices A,B,C,D.
(c) We have to find how many different paths of length are there from the vertex you labelled A to D
A →A →B →A→A→B→A→C→D
A→A→A→A→A→C→D
A→A→A→A→A→B→D
Therefore, In the drawing a graph is there with labeling of vertices A,B,C,D with matrix [tex]\begin{bmatrix}2 &1 & 1&0\\1 & 0 & 0&1\\1&0&0&1\\0&1&1&0\end{bmatrix}[/tex].
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PLEASE HELP I WILL GIVE BRAINLIEST IF YOU DO BOTH
please give me a real answer
Answer:
Q2. angle 5 +angle 6=90°
angle 5+ 6°=90°
angle 5=90°-6°
angle 5=84°
Q.3 angle 8+angle 9=90°
angle 8 + 11°=90°
angle 8=90°-11°
angle 8=79°
Can we just get rid of math forever?
Answer:
I don't think so .... :(((