- 7th Grade Work -

Aiden's class voted on whether or not to do science fair projects in groups. Out of 40 votes, 24 were in favor of working in groups. What percentage of the votes were in favor of working in groups

The Probability density Function of Z is given by:
\(f_Z(z)\) = { 2z, 0 ≤ z ≤ 1   , 0  otherwise. }

To find the CDF of Z = |X - Y|, we need to consider two cases:
Case 1: z < 0

If z < 0, then P(Z < z) = 0 since Z is always non-negative.

Case 2: z ≥ 0
If z ≥ 0, then we can express the event {Z < z} in terms of X and Y as follows:
{Z < z} = {(X,Y) : |X - Y| < z}
This event corresponds to a square region in the unit square with vertices at (0,0), (1-z, z), (z,1-z), and (1,1).
The area of this square is \(1 - (1-z)^2 = 2z - z^2.\)
Since X and Y are independent and uniformly distributed in [0,1], the joint PDF of (X,Y) is fXY(x,y) = 1 for 0 ≤ x,y ≤ 1, and zero elsewhere.

Therefore, the probability of the event {Z < z} is given by the double integral:

P(Z < z) = ∫\(\int {Z < z} f_{XY}(x,y) dxdy\)

= ∫∫|x-y| < z 1 dxdy

\(= 2 \int z^0 y^z 1 dxdy\)

= 2∫\(z^0\)(z-y) dy

= z^2.

Thus, the CDF of Z is given by:

FZ(z) = P(Z ≤ z)

= 0, if z < 0

= z², if 0 ≤ z ≤ 1

= 1, if z > 1.

To find the PDF of Z, we can differentiate the CDF:

fZ(z) = d/dz FZ(z)

= 2z, if 0 ≤ z ≤ 1

= 0, otherwise.

Therefore, the PDF of Z is given by:

\(f_Z(z)\) = { 2z, 0 ≤ z ≤ 1

0, otherwise. }

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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The height of the trapezoid needs to be 30/11 units in order for the trapezoid to have area 30.

To find the height of the trapezoid, we can use the formula for the area of a trapezoid, which is:

A = (1/2)h(b1 + b2)

where A is the area of the trapezoid, h is the height, b1 and b2 are the lengths of the parallel bases.

We know that the lengths of the parallel bases are 8 and 14, and we want the area to be 30. Substituting these values into the formula, we get:

30 = (1/2)h(8 + 14)

Simplifying the right-hand side, we get:

30 = 11h

Dividing both sides by 11, we get:

h = 30/11

Therefore, the height of the trapezoid needs to be 30/11 units in order for the trapezoid to have area 30.

To see why this works, we can visualize the trapezoid as a rectangle with a smaller right triangle on top. The height of the rectangle is equal to the height of the trapezoid, and the width is equal to the average of the lengths of the bases, which is (8+14)/2 = 11. The area of the rectangle is therefore 11h, and the area of the triangle on top is (1/2)bh, where b is the difference between the lengths of the bases, which is 14-8 = 6. The total area of the trapezoid is the sum of the area of the rectangle and the area of the triangle, which is:

A = 11h + (1/2)(6)(h) = 11.5h

Setting this equal to 30 and solving for h, we get the same result as before:

11.5h = 30

h = 30/11

Therefore, the height of the trapezoid needs to be 30/11 units in order for the trapezoid to have area 30.

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Answer:

x = 25

y = 6

Step-by-step explanation:

< B = < M

2x - 20 = 30

2x = 50

x = 25

AB = LM

7y - 8 = 2y + 22

5y = 30

y = 6

Answer:

i answered this question so the other guy can get brainliest he deserves it

Step-by-step explanation:

B. 20; 3,460

smiley face

Answer:

y  = 0.70x-  10.00

Step-by-step explanation:

--  Since one friend gave you 10.00 ,subtractthis from the 13.50 to give you the amount earned by walking the 5 miles

--  13.5-10.00  =  $3.50  

--  Since you walked 5 miles, divide by 5 to give you 0.70 per mile earned.

So, an equation that represents the amount of money earned is:  

y  = 0.70x-  10.00  . This is in slope-intercept form; the slope is $0.70 and represents the amount of money earned per mile  and the intercept is $10.00 and represents the initial amount of money that you were given.

Answer:

16 Days

Step-by-step explanation:

$8 x 1 = 8

$8 x 16 =  128

16 Days!!!!

If Alicyn makes $8 everyday for babysitting her little sister, It'll take her 16 days to make $128.

Answer:

16 days

Step-by-step explanation:

8x _ = 128

8x 16= 128

Rewriting in standard form puts the x variable before the y variable:

-2x + 6y = 5

A is the value with x, B is the value with y and c is after the equal sign.

A = -2, B =6, C= 5

The standard form of the equation of f(x) is option a -x² - 6x + 7

Given,

The graph shows a downward open parabola.

The vertex points are:

(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)

Now,

We have to find the standard form of the function f(x):

As from the graph:

Parabola opens downward, so the function will be negative.

We have the options with:

a = -1, b = -6 and c = 7

Now,

Use x = -b/2a

x = 6/2 × -1 = 6/-2 = -3

Now,

f(x) = -x² - 6x + 7

f(-3) = -(-3)² - 6(-3) + 7

f(-3) = -9 + 18 + 7

f(-3) = 9 + 7

f(-3) = 16

That is, the points for the vertex in this equation is (-3, 16)

Then, the standard form of the equation of f(x) is option a -x² - 6x + 7

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The interpretation of R-square in this simple regression model is that 87% of the variation in the dollar price of unleaded gas can be explained by the variation in the dollar price of crude oil, which is option A.

R-square is a measure of how much of the variability in the dependent variable (dollar price of unleaded gas) is explained by the independent variable (dollar price of crude oil).

An R-square of 0.87 means that 87% of the variation in the dependent variable can be explained by the independent variable. Therefore, option A correctly interprets the meaning of R-square in this regression model.

Option B is incorrect as it suggests the opposite relationship, and option C is incorrect as it refers to the sum of squared errors, not the R-square. Option D is also incorrect as R-square does not measure the accuracy of the forecasting model.

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--The given question is incomplete, the complete question is given

" Consider the following results of a simple regression model of dollar price of unleaded gas (dependent variable) and dollar price of crude oil independent variable): If the Table Does not display, this is the data: Coefficient T Stats Intercept Crude Oil 0.56 0.0457 28.27 73.34 Icoefficient Ilt-statistics Intercept 10.56 28.27 Crude Oil 0.0457 73.34 R-square - 0.87 What is the interpretation of R-square? O a. 87% of the movement in crude oil price can be explained by the changes in unleaded gas price. 6.87% of the movement in unleaded gas price can be explained by the changes in crude oil price O c. the sum of squared errors is close to 8796. O d.87% of the time this forecasting model will correctly predict the price of unleaded gas."--

Answer:

so 109 people likes skateboard and 80 people like skateboard and 11 people dont

Step-by-step explanation:

80+11=122        122-13=109 so its 109

Answer:

y = -4x + 2

Step-by-step explanation:

Given the following data;

Points (x1, y1) = (0, 2)

Perpendicular line = y = ¼x + 5

To find the equation of the straight line passing;

Mathematically, the equation of a straight line is given by the formula: y = mx + c

Where;

From the question, we can deduce that the slope (m) of the perpendicular line is ¼.

y = ¼x + 5 = mx + c

Since the points are perpendicular to the equation of line, it must have a slope that is its negative reciprocal because the slopes of perpendicular lines are negative reciprocals of each other.

Therefore, ¼ = -4

Next, we would write the equation of the straight line using the following formula;

y - y1 = m(x - x1)

Substituting into the formula, we have;

y - 2 = -4(x - 0)

y - 2 = -4x - 0

y - 2 = -4x

y = -4x + 2

Answer:

See Explanation

Step-by-step explanation:

\( \because \angle 1 \) and \( \angle 2 \) are complementary.

\( \therefore m\angle 1+m\angle 2=90\degree... (1)\)

\( \because \angle 2 \) and \( \angle 3 \) are complementary.

\( \therefore m\angle 2+m\angle 3=90\degree... (2)\)

From equations (1) & (2), we find:

\( m\angle 1+m\angle 2=m\angle 2+m\angle 3

\)

\( m\angle 1+m\angle 2-m\angle 2=m\angle 3

\)

\( m\angle 1=m\angle 3\)

Thus proved.

The number of sacks of trash that Jorge's brother picked up is given as follows:

3.75 sacks.

The number of sacks of trash that Jorge's brother picked up is obtained applying the proportions in the context of the problem.

Jorge picks up 2 1/2 sacks of trash, which is a mixed number, hence the decimal number that represents this amount is given as follows:

2 + 1/2 = 2 + 0.5 = 2.5 sacks.

His brother picks up 1 1/2 times as much as Jorge, which is 1 + 1/2 = 1.5 times the amount picked by Jorge, hence the number of sacks of trash that Jorge's brother picked up is obtained as follows:

2.5 x 1.5 = 3.75 sacks.

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Answer:  93.75%

Step-by-step explanation:  We can assume any price and find the percentage change.  I'll choose $100, since it is easy to work with.

The first 25% reduction means we subtract $25 from the $100, for a sales price of $75.  We then increase the sales price by 25%  (1.25*75) = $93.75.

$93.75/$100 = 93.75% of the original price

The value of p in the arithmetic sequence is -1.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The common difference (d) is:

d = (p + 5) - (2p + 5) and d = (2p + 7) - (p + 5)

(p + 5) - (2p + 5) = (2p + 7) - (p + 5)

-p = p + 2

p = -1

The value of p in the arithmetic sequence is -1.

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The value of p in the sequence is 3

Arithmetic sequence is a type of sequence which have a common difference between each term in the sequence.

•First term (T₁) = 2p – 3

•2nd term (T₂) = p + 5

•3rd term (T₃) = 2p + 7

•Value of p =?

Common difference = T₂ – T₁ = T₃ – T₂

Using the above, the value of p can be obtained as follow:

T₂ – T₁ = T₃ – T₂

(p + 5) – (2p – 3) = (2p + 7) – (p + 5)

Clear brackets

p + 5 – 2p + 3 = 2p + 7 – p – 5

Collect like terms

p – 2p – 2p + p = 7 – 5 – 5 – 3

–2p = –6

Divide both side by –2

p = –6 / –2

p = 3

Therefore, the value of p is 3

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Answer:

15% off means take $3.75 off the regular price

Step-by-step explanation:

$25(0.15) = $3.75

$25 - $3.75 = $21.75  sale price

The concept is the Vertical Lines. The Vertical Lines are a pair of opposing, congruent angles created by intersecting lines. It is option A.

An upward line is a line on the direction plane where every one of the focuses on the line have a similar x-coordinate. Because they are perpendicular to the ground and extend toward the sky, vertical lines frequently convey a sense of height.

At the point when two straight lines cross each other vertical points are shaped. Every vertical angle is equal and congruent.

By super-imposing the two pairs of non-adjacent angles created by intersecting two lines, vertical angles are congruent.

Every vertical angle has the same length. We call angles congruent when their measurements are the same.

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Question:

Which of coming up next is best depicted as a couple of inverse points shaped by crossing lines?

A. Vertical angles

B. Supplementary angles

C. Complementary angles

D. Linear pair

Answer:

The answer to this question is 54

Step-by-step explanation:

120 x .55 = 66

120 - 66 = 54

Answer:

54

Step-by-step explanation:

120 x 0.55 = 64

120-64 = 54

(a) The function for the model giving revenue in dollars is R(x) = 6250(0.927x).

(b) If each movie costs the store $10.00, the function for the model that gives profit in dollars is P(x) = R(x) - 10x.

(c) Without the table provided, it is not possible to complete the rates of change of revenue and profit.

(d) The table indicates that there is a range of prices beginning near $14 for which the rate of change of revenue is constant (revenue is increasing at a steady rate), while the rate of change of profit is positive (profit is increasing). The specific values for the rates of change would need to be obtained from the provided table.

a) The function for the model giving revenue in dollars can be found by multiplying the number of movies sold (n(x)) by the average price per movie (x). Therefore, the function is R(x) = 6250(0.927x).

b) The profit in dollars can be calculated by subtracting the cost per movie from the revenue. Since each movie costs $10.00, the function for the model giving profit is P(x) = R(x) - 10n(x), where R(x) is the revenue function and n(x) is the number of movies sold.

c) Without a specific table provided, it is not possible to complete the table of rates of change of revenue and profit.

d) Based on the information given, we can observe that there is a range of prices beginning near $14 where the rate of change of revenue is decreasing (revenue is decreasing) while the rate of change of profit is positive. This indicates that although the revenue is decreasing, the profit is still increasing due to the decrease in cost per movie. The exact values for the rates of change cannot be determined without additional information or specific calculations.

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Answer:

it is the $14 pack

Step-by-step explanation:

the reason it is the $14 pack is because you can buy 2 of them for $28 dollars and wont have o pay #135 or $260 for something like that.

Answer:

1/3

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

1 1/3 = 4/3        4 = 4/1

4/3  /  4/1     = 4/3  X 1/4  =  4/12 = 1/3

a) The null and alternative hypothesis for hypothesis testing are

H₀ : p = 0.5

Hₐ : p< 0.5

and test-static value is -0.73. The P-value for z < - 0.73 is 0.2327. Also, p-value> α

So, conclusion is that data is not provide strong evidence to support the claim.

b) The confidence interval is

We have a sample of american adults who do not have a four-year college degree and are not currently enrolled in school.

Random sample size = 331

The percentage of students who decided not to go to college because they could not afford school, p = 48% = 0.48.

a) Null and alternative hypothesis are defined as H₀ : p = 0.5

Hₐ : p< 0.5

So, correct choice is option (b).

Test- Statistic: Test statistic value is

z =( p-cap - p )/√p(1 - p)/n

where, p-cap --> sample proportion

So, z = (0.48 - 0.5)/√0.5(0.5)/331

= -0.73

Using the Z- distribution table, the p-value for z < -0.73 is equals to 0.2327.

Now, we see that 0.2327 > significance level, so there is no evidence to reject the null hypothesis. Therefore, newspaper articles claim is not true.

b)

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Complete question:

6.12 is college worth it? Part I: Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

(a) A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence.

i) Conduct a hypothesis test to determine if these data provide strong evidence supporting this statement. The hypotheses for this test are:

H₀: p= .5 Hₐ: P < .5

H₀: p= .5 Hₐ: p=5

H₀: p= .5 Hₐ:p-.5

The test statistic is: ___(please round to two decimal places)

The p-value associated with this hypothesis test is ___ (please round to four decimal places)

(b) Would you expect a confidence interval for the proportion of American adults who decide not to go to college because they cannot afford it to include 0.5?

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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Answer:

Answers

product, and assign a number to each person. ... 0.82. 12–13. 9. 0.18. 1.00. Total. 50. 1.00. F requency. 0. 1. 2. 3. 4. 5. 6. 7. 8 ... 3.12 (a) x = 25661.3333, ˜x = 25514.5 (b) Skewed ... N(8.25, 0.0002857).

Answer:

the answer is c

Step-by-step explanation:

i just took the test

To find the linear distance traveled by a wheel, you need to consider its circumference and the number of complete revolutions it has made. The linear distance traveled is equal to the product of the circumference of the wheel and the number of revolutions.

Here's how you can calculate it:

Determine the circumference of the wheel: Measure the distance around the outer edge of the wheel. This can be done by using a measuring tape or by multiplying the diameter of the wheel by π (pi).

Determine the number of complete revolutions: Count the number of times the wheel has made a full rotation. This can be done by observing a reference point on the wheel and counting the complete cycles it completes.

Calculate the linear distance: Multiply the circumference of the wheel by the number of complete revolutions. This will give you the total linear distance traveled by the wheel.

For example, if a wheel has a circumference of 2 meters and completes 5 revolutions, the linear distance traveled would be 2 meters (circumference) multiplied by 5 (revolutions), resulting in a total distance of 10 meters.

In summary, to find the linear distance traveled by a wheel, multiply the circumference of the wheel by the number of complete revolutions it has made. This calculation allows you to determine the total distance covered by the wheel.

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\(4\)\(x^{2}\)\(+8x-21\)

Step-by-step explanation:

y = kx

y = 6 (13)

y = 78