2.46 strong association but no correlation. here is a data set that illustrates an important point about correlation: corr x 25 35 45 55 65 y 10 30 50 30 10 (a) make a scatterplot of y versus x. (b) describe the relationship between y and x. is it weak or strong? is it linear? (c) find the correlation between y and x. (d) what important point about correlation does this exercise illustrate?

The solution of the quadratic equation is x = 2. Therefore, \(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)  or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

The quadratic formula can be use to solve the quadratic equation as follows:

x² - 4x + 4 = 0

Modelling it to quadratic equation, ax² + bx + c

Hence,

using quadratic formula,

\(\frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(\frac{-b-\sqrt{b^{2}-4ac } }{2a}\)

where

Hence,

a = 1

b = -4

c = 4

Therefore,

\(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\) or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

Finally

x = 2

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Answer:

-12

Step-by-step explanation:

x+61+61+70=180

x+122+70=180

x+192=180

x=-12

The length of the curve is l = ∫80(1+3(y-9)/(32y))^(1/2) dy

To find the length of the curve, we use the formula:

l = ∫a^b [(1 + [f'(x)]^2)^(1/2)] dx

In this case, we are given the equation for y in terms of x, so we need to find y' to use in the formula.

Starting with x = y√3(y-9)/(32y1/2), we can rearrange to solve for y in terms of x:

y = x^2 / [3(x^2/9 + 1)]

Next, we find the derivative of y with respect to x:

y' = [6x / (9x^2 + 27)] - [2x^3 / (9x^2 + 27)^(3/2)]

Simplifying:

y' = 6x / [9(x^2 + 3)] - 2x^3 / [9(x^2 + 3)^(3/2)]

Now we can substitute y' into the formula for l:

l = ∫0^8 [(1 + [6x / (9(x^2 + 3)) - 2x^3 / (9(x^2 + 3)^(3/2))]^2)^(1/2)] dx

Simplifying:

l = ∫0^8 [(1 + 9(x-9)^2 / (32x^2))^(1/2)] dx

To make the integral easier to solve, we can substitute u = 1 + 9(x-9)^2 / (32x^2), which gives:

l = ∫1.5^5.5 [2/3 * u^(1/2) * (u - 1)^(1/2) / (9(u-1) + 8(u-1)^(3/2))] du

Using integration by substitution and partial fractions, we can solve for l:

l = 16/27 [ (13/16)^{3/2} - (5/16)^{3/2} + 2(13/16)^{1/2} - 2(5/16)^{1/2} ]

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Answer:

-14 -8

Step-by-step explanation:

Answer

-14,-8

i did this on ttm and got it correct

Required value of x, m∠A, m∠B, m∠D, m∠E, m∠G, m∠H, m∠K are 30.1°, 164.2°, 120.4°, 4.4°, 137°, 114.3°, 231.5°,210.7° respectively.

What is the sum of all interior angles of a nonagon?

The sum of the interior angles of a nonagon is 1260 degrees, we can use this information to set up an equation,

m∠A + m∠B + m∠C + m∠D + m∠E + m∠F + m∠G + m∠H + m∠K = 1260°

Substituting the given angle measures,

\((2x+104) + 4x + 118 + (136-4x) + 137 + 69 + (3x+24) + (76+5x) + 7x = 1260\)

Simplifying and solving for x,

20x + 658 = 1260

20x = 602

x = 30.1

Using this value of x, we can find the angle measures as follows:

m∠A = 2x+104 = 2(30.1)+104 = 164.2°

m∠B = 4x = 4(30.1) = 120.4°

m∠D = 136-4x = 136-4(30.1) = 4.4°

m∠E = 180°-43° = 137°

m∠G = 3x+24 = 3(30.1)+24 = 114.3°

m∠H = 76+5x = 76+5(30.1) = 231.5°

m∠K = 7x = 7(30.1) = 210.7°

Therefore, the value of x is 30.1 degrees, and the angle measures are:

m∠A = 164.2°

m∠B = 120.4°

m∠D = 4.4°

m∠E = 137°

m∠G = 114.3°

m∠H = 231.5°

m∠K = 210.7°

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The vector field F(x, y) = (2x - 4y) i + (-4x + 10y - 5) j is a conservative vector field. The function f(x, y) that satisfies ∇f = F is f(x, y) = \(x^{2}\) - 4xy + 5y + C, where C is a constant.

To determine whether a vector field is conservative, we check if its curl is zero. If the curl is zero, then the vector field is conservative and can be expressed as the gradient of a scalar function.

Let's calculate the curl of F = (2x - 4y) i + (-4x + 10y - 5) j:

∇ x F = (∂F₂/∂x - ∂F₁/∂y) i + (∂F₁/∂x - ∂F₂/∂y) j

= (-4 - (-4)) i + (2 - (-4)) j

= 0 i + 6 j

Since the curl is zero, F is a conservative vector field. Therefore, there exists a function f such that ∇f = F.

To find f, we integrate each component of F with respect to the corresponding variable:

∫(2x - 4y) dx = \(x^{2}\) - 4xy + g(y)

∫(-4x + 10y - 5) dy = -4xy + 5y + h(x)

Here, g(y) and h(x) are arbitrary functions of y and x, respectively.

Comparing the expressions with f(x, y), we see that f(x, y) = \(x^{2}\) - 4xy + 5y + C, where C is a constant, satisfies ∇f = F.

Therefore, the function f(x, y) = \(x^{2}\) - 4xy + 5y + C is such that F = ∇f, confirming that F is a conservative vector field.

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a. mean = 27, standard deviation 1.673

b. The calculated t-statistic (1.21) is not greater than the critical value (2.571), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

c. The p-value (0.274) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

a. To determine the mean and standard deviation of the given data, calculate the following:

Mean:

(28 + 27 + 25 + 28 + 29 + 25) / 6

= 162 / 6 = 27 miles (mean)

Standard Deviation:

First, calculate the deviation from the mean for each data point:

(28 - 27) = 1

(27 - 27) = 0

(25 - 27) = -2

(28 - 27) = 1

(29 - 27) = 2

(25 - 27) = -2

Then, square each deviation:

1² = 1

0² = 0

(-2)² = 4

1² = 1

2² = 4

(-2)² = 4

Calculate the variance by summing the squared deviations and dividing by (n-1):

(1 + 0 + 4 + 1 + 4 + 4) / (6-1)

= 14 / 5 = 2.8

Finally, take the square root of the variance to get the standard deviation:

√2.8 ≈ 1.673 (standard deviation)

b. To test whether the tire company's claim of increased life expectancy is legitimate, we can perform a one-sample t-test using the critical value approach.

Given that the sample size is small (n = 6) and the population standard deviation is unknown, we will use a t-distribution. The null and alternative hypotheses are as follows:

Null Hypothesis (H0): The average life expectancy of the new tires is equal to the previous average of 26,000 miles.

Alternative Hypothesis (Ha): The average life expectancy of the new tires is greater than 26,000 miles.

Using the critical value approach at the 0.01 level of significance, we will calculate the t-statistic and compare it to the critical value.

Degrees of freedom (df) = n - 1 = 6 - 1 = 5

Calculate the t-statistic:

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

t = (27 - 26) / (1.673 / √(6))

t ≈ 1.21

Using a t-table, find the critical value for a one-tailed test with 5 degrees of freedom at the 0.01 level of significance. For this example, let's assume the critical value is 2.571.

Since the calculated t-statistic (1.21) is not greater than the critical value (2.571), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

c. To repeat the test using the p-value approach, we compare the p-value to the significance level (α = 0.01).

Using a t-distribution table, we find the p-value associated with the calculated t-statistic of 1.21. For this example, let's assume the p-value is 0.274.

Since the p-value (0.274) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.

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Given question is incomplete, the complete question is below

A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires life expectancy has increased. In order to test the legitimacy of its advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data.

Life expectancy (In thousands of miles)

28

27

25

28

29

25

a. Determine the mean and the standard deviation

b. at the .01 level of significance using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed.

c. Repeat the test using the p-value approach.

Answer:

125 km per hour

Step-by-step explanation:

divide 500 by 4 to find the averge

Answer:

\( \sf \: 125km/hr\)

Step-by-step explanation:

Average speed = \( \sf \: \frac{distance \: travelled}{time \: taken} \)

Ave. speed = \( \sf \frac{500km}{4hr} = 125kmhr {}^{ - 1} \)

Hence, the average spred is 125km/h respectively.

The solutions are:

1. If MY || LE, then MY || IK

2. MY = 52 cm.

3. MY = 109 cm.

4. IK = 6.4 cm.

5. LE = 45 cm.

LIKE is a trapezoid with median MY.

The formula is described as,

m = 1/2(b1 + b2)

2. If IK = 56 cm and LE = 48 cm, to find MY:

For that as per the formula for the median,

MY = 1/2(56 + 48)

MY = 52

3. If IK = 142 cm and LE = 76 cm, to find MY:

For that as per the formula for the median,

MY = 1/2(142 + 76)

MY = 109 cm.

4. If MY 45.7 cm and LE = 85 cm, to find IK:

For that as per the formula for the median,

45.7 = 1/2(85 + IK)

2(45.7 - 85/2) = IK

IK = 6.4 cm.

5. If MY 37.5 cm and IK = 120 cm, to find LE.

For that as per the formula for the median,

2(120/2- 37.5) = LE

LE = 45 cm.

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Answer:

8 inches

Step-by-step explanation:

Given:

t = 2 ( 2h/32 ) ^1/2 ( or: t = 2 * sqrt ( 2h/32) ).

Step 1: First Player

0.9 = 2 * sqrt( 2h/32 )   / ^2 ( we will square both sides of equation )

0.81 = 4* 2h/32

0.81 = h/4

h 1 = 0.81 * 4 = 3.24 ft

Step 2: Second Player

0.8 = 2 * sqrt( 2h/32 ) /^2

0.64 = 4 * 2 h/32

h 2 = 0.64 * 4 = 2.56 ft

Step 3: Simplify

h 2 - h 1 = 3.24 - 2.56 = 0.68 ft

and since 12 in = 1 ft:

0.68 * 12 = 8.16 in ≈ 8 in.

(i) To find the solution for yt in the given equation yt = yt−1 + εt + 0.3εt−1, we can rewrite it as yt - yt−1 = εt + 0.3εt−1. By applying the lag operator L, we have (1 - L)yt = εt + 0.3εt−1.

Solving for yt, we get yt = (1/L)(εt + 0.3εt−1). The solution for yt involves lag operators and depends on the values of εt and εt−1.  (ii) For the equation yt = 1.2yt−1 + εt, to find the s-step-ahead forecast Et[yt+s], we can recursively substitute the lagged values. Starting with yt = 1.2yt−1 + εt, we have yt+1 = 1.2(1.2yt−1 + εt) + εt+1, yt+2 = 1.2(1.2(1.2yt−1 + εt) + εt+1) + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to ensure that the coefficient on yt−1, which is 1.2 in this case, is less than 1 in absolute value. If it is greater than 1, the process will be explosive and not stationary. To achieve stationarity, we can either decrease the value of 1.2 or introduce appropriate differencing operators.

(iii) For the equation yt = yt−1 + t + εt, finding the solution for yt and the s-step-ahead forecast Et[yt+s] involves incorporating the time trend t. By recursively substituting the lagged values, we have yt = yt−1 + t + εt, yt+1 = yt + t + εt+1, yt+2 = yt+1 + t + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to remove the time trend component. We can achieve this by differencing the series. Taking first differences of yt, we obtain Δyt = yt - yt-1 = t + εt. The differenced series Δyt eliminates the time trend, making the model stationary. We can then apply forecasting techniques to predict Et[Δyt+s], which would correspond to the s-step-ahead forecast Et[yt+s] for the original series yt.

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The number of late insurance claim payouts per 100 should be measured with a p-chart. Therefore, the correct option is (e) p-chart.

A p-chart is a type of control chart used to monitor the proportion of nonconforming items in a sample, where nonconforming items are those that do not meet a certain quality standard or specification. In this case, the proportion of late insurance claim payouts would be the proportion of nonconforming items.

A p-chart is appropriate when the sample size is constant and the number of nonconforming items per sample can be either small or large. It is used to monitor the stability of a process and to detect any changes or shifts in the proportion of nonconforming items over time.

An X-bar chart and R-chart are used to monitor the mean and variability of a continuous variable, respectively, and would not be appropriate for measuring the number of nonconforming items.

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The difference between the two approximations is approximately 26.80 so option D is the correct answer.

We have,

To approximate the definite integral  \(e^{x^2}\) from 0 to 2 using two inscribed rectangles of equal width, divide the interval [0, 2] into two subintervals of equal width (h = 2/2 = 1).

Then calculate the area of each rectangle by evaluating the function at the left endpoints of the subintervals.

Now,

Approximation using inscribed rectangles:

Approximation 1

= f(0) * h + f(1) * h

\(= e^{0^2} * 1 + e^{1^2} * 1\)

= 1 + e

Next, use the trapezoidal rule with n = 2 to approximate the definite integral.

Approximation using the trapezoidal rule with n = 2:

Approximation 2 = (h/2) * [f(0) + 2f(1) + f(2)]

= (1/2) * [f(0) + 2f(1) + f(2)]

\(= (1/2) [e^{0^2} + 2e^{1^2} + e^{2^2}] \\ = (1/2) [1 + 2e + e^4]\)

Difference = Approximation 2 - Approximation 1

\(= (1/2) [1 + 2e + e^4] - (1 + e)\\= (1/2) [1 + 2e + e^4 - 2 - 2e - e)\\= (1/2) (e^4 - e - 1)\)

Difference ≈ 26.80

Therefore,

The difference between the two approximations is approximately 26.80.

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Step-by-step explanation:

here is ur answer pls check it

Answer: x = 10

Step-by-step explanation:ln20+ln5=2lnx

ln(20x5)=lnx^2

ln100=1nx^2

100=x^2

square root

x=10

The true solution is x = 10 of the expression ln 20 + ln 5 = 2 ln x which is correct answer would be option (B).

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

According to the problem, we will use some of the basic logarithmic properties,

Given expression,

⇒ ln 20 + ln 5 = 2 ln x

⇒ ln(20×5) = lnx²

⇒ ln100 = lnx²

Take anti logarithms on both sides,

⇒ 100 = x²

Taking the square root,

⇒ x = 10

Hence, the true solution is x = 10.

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line e is parallel to line m because angle 1 + angle 2 = 180°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Represent the adjascent angle to angle 2 by x and adjascent angle to angle 1 by y

therefore ;

2 = y ( corresponding angles are equal)

1 = x ( corresponding angles are equal)

angle 1+y = 180 ( angle on a straight line)

angle 2 + x = 180

<1= 180-y

<2 = 180 -x

and both equations

< 1 +<2 = 180

therefore since < 1 +<2 = 180, then line e is parallel to line m

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Answer:

B.) \(46.8m^{3}\)

Step-by-step explanation:

The area enclosed by the ellipse is π(a^2 + b^2).

To find the area enclosed by the ellipse defined by x = a cos(t) and y = b sin(t), where 0 ≤ t ≤ 2π, we can use the formula for the area of a polar curve.

The formula for the area A enclosed by a polar curve r = f(θ), where α ≤ θ ≤ β, is given by:

A = 0.5 ∫[α,β] f(θ)^2 dθ

In this case, the polar curve is defined by r = √(x^2 + y^2), so we need to find the square of the distance from the origin to a point on the ellipse.

Substituting the equations for x and y into the expression for r, we have:

r^2 = (a cos(t))^2 + (b sin(t))^2

= a^2 cos^2(t) + b^2 sin^2(t)

Now we can calculate the area using the given limits of t:

A = 0.5 ∫[0,2π] (a^2 cos^2(t) + b^2 sin^2(t)) dt

Since cos^2(t) + sin^2(t) = 1, the integral simplifies to:

A = 0.5 ∫[0,2π] (a^2 cos^2(t) + b^2 sin^2(t)) dt

= 0.5 ∫[0,2π] (a^2 cos^2(t)) dt + 0.5 ∫[0,2π] (b^2 sin^2(t)) dt

= 0.5a^2 ∫[0,2π] cos^2(t) dt + 0.5b^2 ∫[0,2π] sin^2(t) dt

Using the trigonometric identity cos^2(t) = (1 + cos(2t))/2 and sin^2(t) = (1 - cos(2t))/2, we can rewrite the integrals:

A = 0.5a^2 ∫[0,2π] (1 + cos(2t))/2 dt + 0.5b^2 ∫[0,2π] (1 - cos(2t))/2 dt

= 0.5a^2 [t/2 + sin(2t)/4]∣[0,2π] + 0.5b^2 [-t/2 + sin(2t)/4]∣[0,2π]

Evaluating the integrals at the limits of integration, we get:

A = 0.5a^2 [(2π)/2 + sin(4π)/4 - 0/2 - sin(0)/4] + 0.5b^2 [-(2π)/2 + sin(4π)/4 - 0/2 - sin(0)/4]

= 0.5a^2 π + 0.5b^2 π

= π(a^2 + b^2)

Therefore, the area enclosed by the ellipse x = a cos(t), y = b sin(t), 0 ≤ t ≤ 2π is π times the sum of the squares of the semi-major and semi-minor axes, which is π(a^2 + b^2).

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The equation 2/5x=7/20x+1/4 represents the possible ways to begin solving x.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question

-3/4+2/5x = 7/20x-1/2

If we add 3/4 to both sides of the equation, we get

2/5x = 7/20x + 1/4

If we subtract 2/5x from both sides of the equation, we get

-3/4 = -1/20x -1/2

If we subtract 7/20x from both sides of the equation, we get

-3/4 +1/20x = -1/2

Thus, the equation 2/5x=7/20x+1/4 represents the possible ways to begin solving x.

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The question seems to be incomplete the correct question would be

Horatio is solving the equation -3/4+2/5x=7/20x-1/2. Which equations represent possible ways to begin solving for x? Check all that apply.

2/5x=7/20x+1/4

2/5x=7/20x+5/4

-3/4=-1/20x-1/2

-3/4=3/4x-1/2

-3/4+1/20x=-1/2

As calculated from the given data Jane's calorie intake is 1200 per day.

From the details given in the question we can say that Jane doesn't likes milk. Hence, she lacks dairy fat  in her food. As per the given case she likes vegetables and eats fruit a lot. Therefore, and the grams of total caloric intake for her should be 1200 calories per day.

She does, however, lack fats from dairy products like milk. A child of 8 years old is thought to need at least 2 cups of milk or its equivalent each day. Jane is getting enough carbohydrates because she consumes 225 gram per day as opposed to the recommended 130 gram.

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Answer:

2.5

Step-by-step explanation:

Area of A is 50 cm ^2

length of A is 10

Area of B is 50/2 cm^2 or 25cm^2

area for all rectangles is length * width

so area of B divided by length of b is width of b

25/10 = 2.5

width of b is 2.5

Answer:

238

Step-by-step explanation:

First, you must find the ratio between the one measurement of the larger octagon and the smaller octagon. Just divide 28 by 4 to get 7. This is what you have to multiply the perimeter by to get the larger octagon's perimeter.  34 times 7 equals 238. There are multiple ways to do this problem but this way is the simplest. If this helped you, please click the "Thanks" button!

The answer to the integral ∫sec²(3x-2) dx is (1/3)tan(3x-2) + C, where C is the constant of integration. To evaluate the integral ∫sec²(3x-2) dx, we can use the u-substitution method. This method involves selecting a suitable substitution that makes the integral easier to evaluate. In this case, the substitution u = 3x-2 would be useful.

To use u-substitution, we first need to find the derivative of u with respect to x, which is du/dx = 3. We can then solve for dx by dividing both sides by 3, giving us dx = du/3.

Substituting u and dx in terms of u into the integral, we get:

∫sec²(3x-2) dx = ∫sec²u (du/3)

Now we can evaluate the integral by using the formula for the integral of sec²x, which is tan x + C. Substituting back x in terms of u, we get:

∫sec²(3x-2) dx = (1/3)∫sec²u du = (1/3)tan(3x-2) + C

Therefore, the answer to the integral ∫sec²(3x-2) dx is (1/3)tan(3x-2) + C, where C is the constant of integration.

In conclusion, the u-substitution u = 3x-2 is useful in evaluating the given integral, and it allows us to simplify the integral using a well-known formula for the integral of sec²x.

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Descriptive statistical analysis can be conducted on the data collected for computer repair service calls, and the worksheet "comprep5" contains information on the time taken for 30 service calls.

Descriptive statistical analysis involves the use of numerical and graphical methods to summarize and describe the main features of a data set. In the case of the computer repair service calls, the data collected on the time taken for 30 service calls can be analyzed using descriptive statistics to provide information on measures of central tendency, such as mean and median, as well as measures of variability, such as range and standard deviation.

The worksheet "comprep5" likely contains the raw data for the 30 service calls, which can be used to conduct the descriptive analysis.

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--The complete question is, What type of analysis can be conducted on the data collected for computer repair service calls, and what information is available in the worksheet entitled "comprep5"?--

Answer:

y = mx + b

Step-by-step explanation:

so you first put the points on the graph and connect them with a slanted line.

Next, for your equation start of with y =

then, your going to find your slope, after you find it put it in front of x (slope x) (Ex; if the slope was 3 then it would look like this 3x)

finally you write + and the y intercept (at which point the line goes through the y axis)

the equation together should look like y = slope x + y intercept

Answer:

(-3, -5)

Step-by-step explanation:

When reflected over the x-axis, the x remains the same, and the y change to their opposite sign.

So, the answer is (-3, -5)

Replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

Based on the statistical analysis, replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections.

To test this hypothesis, we will use a paired t-test, which compares the means of two sets of paired data. The null hypothesis is that there is no significant difference between the mean accident rates before and after installing roundabouts, while the alternative hypothesis is that the mean accident rate after installing roundabouts is significantly lower than before.

Here are the steps to conduct the paired t-test:

Using the given data, the differences between the accident rates before and after installing roundabouts are:

-0.6, 0.2, 0.6, -0.1, 0

The mean of the differences is 0.02, and the standard deviation is 0.43. There are 5 paired observations, so the degrees of freedom are 4.

Using the formula, we get:

t = 0.02 / (0.43 / √(5)) = 0.14

The critical t-value at a 0.05 level of significance and 4 degrees of freedom is 2.776 from a t-distribution table.

Since the calculated t-value (0.14) is less than the critical t-value (2.776), we fail to reject the null hypothesis. Therefore, we can conclude that replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

Learn more about the null hypothesis

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