AABC is dilated by a factor of 2 to produce AA'B'C!
What is A'B, the length of AB after the dilation? What is the measure of A'?

The proportion of students with a z-score between -1.20 and -0.30 is about 0.304. So for every 100 students.

What is the z-score?

Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below the mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.

Assuming that the grading follows a standard normal distribution (i.e., with a mean of 0 and a standard deviation of 1), we can use the z-score formula to find the proportions of students that fall within each grade range:

For an A grade: z-score > 1.65

For a B grade: 0.67 < z-score ≤ 1.65

For a C grade: -0.40 < z-score ≤ 0.67

For a D grade: -1.60 < z-score ≤ -0.40

To convert from the standard normal distribution to the distribution with the course mean and standard deviation, we can use the formula:

z-score = (x - mean) / standard deviation

We don't know the actual mean and standard deviation for the course, so we'll use the given range for the D grade (-1.60 < x < -0.4σ) to estimate the standard deviation. Since the D grade range is 1.2 standard deviations wide (from -1.60 to -0.4σ), we can solve for the standard deviation:

1.2σ = -1.60

σ = -1.60 / 1.2

σ = 1.33

(Note that we have a negative value for σ, which is not possible for a standard deviation. This is because we are using the estimated value of σ to convert from the standard normal distribution to the course distribution, which may not perfectly match the actual distribution of grades.)

Now we can use the z-score formula with the estimated mean and standard deviation to find the proportions of students in each grade range:

For an A grade: z-score > 1.65

z-score = (x - mean) / standard deviation

z-score = (1.65 - 0) / 1.33

z-score = 1.24

From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score greater than 1.24 is about 0.107. So for every 100 students, we can expect about:

A grades: 100 * 0.107 = 10.7 or approximately 11

For a B grade: 0.67 < z-score ≤ 1.65

z-score = (0.67 - 0) / 1.33

z-score = 0.50

From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score between 0.50 and 1.24 is about 0.205. So for every 100 students, we can expect about:

B grades: 100 * 0.205 = 20.5 or approximately 21

For a C grade: -0.40 < z-score ≤ 0.67

z-score = (-0.40 - 0) / 1.33

z-score = -0.30

From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score between -0.30 and 0.50 is about 0.307. So for every 100 students, we can expect about:

C grades: 100 * 0.307 = 30.7 or approximately 31

For a D grade: -1.60 < z-score ≤ -0.40

z-score = (-1.60 - 0) / 1.33

z-score = -1.20

Hence, From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score between -1.20 and -0.30 is about 0.304. So for every 100 students,

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(a). At α = .05, we reject the null hypothesis and conclude that people who fly frequently are more likely to be able to sleep during flights.

(b). At α = .01, we fail to reject the null hypothesis and do not have sufficient evidence to conclude that people who fly frequently are more likely to be able to sleep during flights.

a. Hypothesis test at α = .05:

Null hypothesis (H0): The proportion of people who can sleep during flights is the same for those who fly frequently and the general population.

Alternative hypothesis (Ha): The proportion of people who can sleep during flights is higher for those who fly frequently.

To conduct the hypothesis test, we can use the z-test for comparing proportions.

Sample proportion of frequent flyers who can sleep: p1 = 285/510

= 0.5588

Proportion of Americans who can sleep during flights (from Expedia): p2 = 0.52

The formula for the test statistic (z) is:

z = (p1 - p2) / \(\sqrt{}\)((p1 × (1 - p1) / n1) + (p2 × (1 - p2) / n2))

Where n1 = sample size of frequent flyers = 510

n2 = sample size from Expedia = unknown (since we only have the proportion)

Since the null hypothesis states that the proportions are the same, we can assume n1 = n2.

Calculating the test statistic:

z = (0.5588 - 0.52) / \(\sqrt{}\)((0.5588 × (1 - 0.5588) / 510) + (0.52 × (1 - 0.52) / 510))

z ≈ 1.775

Using a standard normal distribution table or a calculator, we find that the critical z-value at α = .05 (one-tailed test) is approximately 1.645.

Since the test statistic (1.775) is greater than the critical value (1.645), we reject the null hypothesis.

B) Hypothesis test at α = .01:

Using the same setup as in part (a), we can calculate the test statistic:

z ≈ 1.775

The critical z-value at α = .01 (one-tailed test) is approximately 2.326.

Since the test statistic (1.775) is less than the critical value (2.326), we fail to reject the null hypothesis.

Conclusion: A). At α = .05, we reject the null hypothesis and conclude that people who fly frequently are more likely to be able to sleep during flights.

B). At α = .01, we fail to reject the null hypothesis and do not have sufficient evidence to conclude that people who fly frequently are more likely to be able to sleep during flights.

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The complete question is-

Sleeping on Flights. According to Expedia, 52% of Americans report that they generally can sleep during flights. Are people who fly frequently more likely to be able to sleep during flights? Suppose we have a random sample of 510 individuals who flew at least 25,000 miles last year and 285 indicated that they were able to sleep during flights.

a. Conduct a hypothesis test to determine if the results justify concluding that people who fly frequently are more likely to be able to sleep during flights. Use α = .05.

b. Conduct the same hypothesis test you performed in (a) at α = .01. What is your conclusion?

Answer:

r = 7

Step-by-step explanation:

Step 1: Write out equation

4r + 7 = 35

Step 2: Subtract 7 on both sides

4r + 7 - 7 = 35 - 7

4r = 28

Step 3: Divide both sides by 4

4r/4 = 28/4

r = 7

Solve 4r+7=35

4r=35-7

4r=28

r=7

:)

Answer: (y − 0) = -(1/6)(x − 6)  or y=-(1/6)(x-6)

Step-by-step explanation:

An equation in Point Slope form:  y − y1 = m(x − x1), where m is the slope and x1 and y1 are provided as a single point, (x1,y1).  We have slope(m) = -(1/6) and are given (6,0).  Therefore:

 (y − 0) = -(1/6)(x − 6)  (Point slope form)

y = -(1/6)(x-6)

Rewriting this into standard form, y = mx + b

y = -(1/6)x + 1

The value of x in the heptagon shown in the diagram is: 110°.

A heptagon can be described as a polygon that has 7 sides and 7 interior angles. Where n is the number of sides of an n-sided polygon, the formula for finding the total sum of the polygon is:

(n - 2)180.

Therefore, the sum of the interior angles of the heptagon = (5 - 2)180 = 900°.

This means that all the angles in the heptagon shown in the diagram would be equal to 900°. Therefore:

135 + 125 + 105 + 140 + 135 + 150 + x = 900

790 + x = 900

x = 900 - 790

x = 110°.

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Answer:

5y - 2

Step-by-step explanation:

1/3 ( 15y - 6 ) = (15y - 6) / 3 = 5y - 2

Done! Hope you learned how to do this/understood this and have a great day! Please mark me as brainliest, vote 5.0 on my answer and thank me to show some support! Bye!

Answer:

[B] 16 dollars and 16 cents

Step-by-step explanation:

Given:

Darrell’s restaurant bill is $89.75. If Darrell leaves an 18% tip, how much tip does the server receive?

A:1.62 cents

B:16 dollars and 16 cents

C:73.59 dollars

D:109.51 dollars

Solve:

$89.75 × 18% = 16.155 ≈ 16.16

Kavinsky

Answer: B. 16 dollars and 16 cents

Step-by-step explanation:

89.75 * .18 = $16.155

If x i , i = 1, 2, 3, are independent exponential random variables with rates λi , i = 1, 2, 3, then

(a) P{x1 < x2 < x3} = P{x2 > x1} * P{x3 > x2} = (λ1 / (λ1 + λ2)) * (λ2 / (λ2 + λ3)) = λ1 / (λ1 + λ2) * λ2 / (λ2 + λ3)

(b) P{x1 < x2 | max(x1, x2, x3) = x3} = P{x1 < x2} / e^(-(λ1+λ2)x3)

(c) E[max(xi) | x1 = a] = a + 1 / (λ1 + λ2 + λ3)

(a) To find the probability that x1 < x2 < x3, we can use the fact that the minimum of the three exponential random variables follows an exponential distribution with rate λ1 + λ2 + λ3. Therefore, we have:

P{x1 < x2 < x3} = P{x2 > x1} * P{x3 > x2} = (λ1 / (λ1 + λ2)) * (λ2 / (λ2 + λ3)) = λ1 / (λ1 + λ2) * λ2 / (λ2 + λ3)

(b) To find the probability that x1 < x2 given that max(x1, x2, x3) = x3, we can use Bayes' rule. We have:

P{x1 < x2 | max(x1, x2, x3) = x3} = P{x1 < x2, x3 = max(x1, x2, x3)} / P{max(x1, x2, x3) = x3}

Since x3 is the maximum of the three variables, we have:

P{max(x1, x2, x3) = x3} = P{x1 ≤ x3} * P{x2 ≤ x3} = e^(-λ1x3) * e^(-λ2x3) = e^(-(λ1+λ2)x3)

Then, we can write:

P{x1 < x2, x3 = max(x1, x2, x3)} = P{x1 < x2, x3 = x3} = P{x1 < x2}

Therefore,

P{x1 < x2 | max(x1, x2, x3) = x3} = P{x1 < x2} / e^(-(λ1+λ2)x3)

(c) To find the expected value of the maximum xi, given that x1 = a, we can use the fact that the maximum of the exponential random variables follows an Erlang distribution with shape parameter k=3 and rate parameter λ1 + λ2 + λ3. Therefore, we have:

E[max(xi) | x1 = a] = a + 1 / (λ1 + λ2 + λ3)

This is because the Erlang distribution has a mean of k/λ, and in this case k=3 and λ=λ1+λ2+λ3. So, the expected value of the maximum is a plus one over the sum of the rates.

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Answer:3

Step-by-step explanation:

Ok listen I don't know if this is right and if it is not I am sorry so if it is let me know please. And if it's wrong let me know. Thank you.

Answer:

The financial incentive had a significant effect on the proportion of individuals who quit smoking

Step-by-step explanation:

To determine if the financial incentive had a significant effect on the proportion of individuals who quit smoking, we can conduct a hypothesis test.

Null hypothesis: The proportion of individuals who quit smoking in the financial rewards group is the same as the proportion who quit smoking in the traditional group.

Alternative hypothesis: The proportion of individuals who quit smoking in the financial rewards group is greater than the proportion who quit smoking in the traditional group.

We can use a one-tailed z-test for proportions to test this hypothesis, with a significance level of 0.05.

First, we calculate the pooled proportion of individuals who quit smoking:

p = (number of individuals who quit smoking in financial rewards group + number of individuals who quit smoking in traditional group) / (total number of individuals in both groups)

p = \(\frac{(0.15 * 439 + 0.05 * 439)}{878}\)

p = 0.1

Next, we calculate the standard error of the difference between the two proportions:

SE = \(\sqrt{(p(1-p) * ((1/n1) + (1/n2)))}\)

where n1 is the sample size of the financial rewards group (439) and n2 is the sample size of the traditional group (439).

SE = \(\sqrt{(0.1 * 0.9 * ((1/439) + (1/439)))\)

SE = 0.022

Finally, we calculate the test statistic:

z = (p1 - p2) / SE

where p1 is the proportion of individuals who quit smoking in the financial rewards group (0.15) and p2 is the proportion of individuals who quit smoking in the traditional group (0.05).

z = (0.15 - 0.05) / 0.022

z = 4.55

The critical z-value for a one-tailed test with a significance level of 0.05 is 1.645.

Since our calculated z-value is greater than the critical z-value, we reject the null hypothesis and conclude that the proportion of individuals who quit smoking in the financial rewards group is significantly greater than the proportion who quit smoking in the traditional group.

Therefore, we can say that the financial incentive had a significant effect on the proportion of individuals who quit smoking.

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The pH values can be used to calculate the concentration of hydrogen ions in a solution. The hydrogen ion concentration is represented by [H+].

When pH = 3.80, the [H+] can be calculated using the formula:

[H+] = 10^(-pH)

= 10^(-3.80)

= 1.585 x 10^(-4)

M, the [H+] is 1.585 x 10^(-4) M.

When pH = 12.15, the [H3O+] can be calculated using the formula:

pH + pOH

= 14pOH

= 14 - pH

= 14 - 12.15

= 1.85[H3O+]

= 10^(-pH)

= 10^(-1.85)

= 1.39 x 10^(-2)

M, the [H3O+] is 1.39 x 10^(-2) M.

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The point at which the NPV profile intersects the horizontal axis represents the breakeven point, where the net present value of a project is zero. It indicates the level of cash flows or discount rate at which the present value of cash inflows equals the present value of cash outflows.

The Net Present Value (NPV) is a financial metric used to assess the profitability of an investment. The NPV profile plots the NPV values at different discount rates or cash flow levels. When the NPV profile intersects the horizontal axis, it signifies that the NPV is zero, indicating that the project's cash inflows equal its cash outflows in present value terms.

This breakeven point is an important reference point as it helps determine the minimum required cash flows or discount rate for the project to be financially viable. Below the breakeven point, the project generates a negative NPV, indicating a loss, while above the breakeven point, it generates a positive NPV, indicating a profit.

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Answer:

9,450ft in 3.5 minutes

Step-by-step explanation:

2700*3=8100

2700/2=1350

8100+3150=9450

The angle for the given line is -180 degree.

In the given graph,

A straight line is showing,

We know that,

A line is a one-dimensional figure with no breadth and just length. A line is made up of a series of points that stretch in opposite directions indefinitely. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

Lines in geometry are classified into horizontal and vertical lines, parallel and perpendicular lines. These lines are crucial in the building of many sorts of polygons. A square, for example, is formed by four lines of equal lengths, but a triangle is formed by linking three lines end to end.

The given line is horizontal line,

And each point of it is one dimensional

therefore,

The given angles 140 degree and -120 is never possible

Hence the angle of line be -180 degree.

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Belle bought 24 apples, and Amy bought 34 apples and Amy paid approximately $2.35 per apple.

Let x be the number of apples Belle bought.

Then, Amy bought 10 more apples than Belle, so Amy bought x + 10 apples.

Since each of them spent $40, we can write:

40 = cost of x apples for Belle

40 = cost of (x + 10) apples for Amy

We know that Amy used a coupon that gave her a 20% discount. This means that she paid 80% of the original price for her apples. We can write:

0.8 * (cost of (x + 10) apples for Amy) = cost of x apples for Belle

Now we can solve for x:

0.8 * (40 + 40) = 32 + 0.8 * 10 + 32

0.8 * 80 = 8 + 32 + x

64 = x + 40

x = 24

So Belle bought 24 apples, and Amy bought 34 apples (10 more than Belle)

To find the cost per apple for Amy, we can divide her total cost by the number of apples:

cost per apple for Amy = (40 + 40) / (x + 10) = 80/34

Therefore, Amy paid approximately $2.35 per apple.

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Answer:

the correct answer is

.........it's 42°......

Step-by-step explanation:

45 + 77 =122

180 - 122=58

58 +80 = 138

180 - 138 = 42

In the given equation, as the value of y increase, the value of x also

increases.

Reasons:

A direct variation is a relationship that exists between two variables. It is

also known as a direct proportion which can be expressed as; y = k·x

Where k is a number

The given equation is 4·y = 16·x

Dividing both sides by 4 gives;

\(\displaystyle \frac{4 \cdot y}{4} = \frac{16 \cdot x}{4} = \frac{4 \times 4 \cdot x}{4}\)

Which gives;

y = 4·x

Comparing the above equation with the equation for a direct variation gives;

y = 4·x

y = k·x

Therefore;

k = 4

The equation, y = 4·x, and therefore, the equation from which it is derived, 4·y = 16·x, is a direct variation.

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Option C is correct

The given logarithmic equation is:

f(x) = log(x + 1) - 4

For a logarithmic equation of the form:

f(x) = log(a + b) - c

the y-intercept = -c

Comparing the two equations above:

The y-intercept = -4

Taking note of the point above, the logarithmic function f(x) = log(x + 1) - 4 is plotted below

Answer:

C

Step-by-step explanation:

The whole numbers W = {0,1,2,3,...}

and the integer numbers I = { ...,-1,0,1,2,3,...}

Then

\(W\subset I\)

So, choose C.

The most appropriate choice for HCF will be given by-

Number of identical bouquets that can be made out of 21 white tulips and 91 red tulips if no flowers are left out = 7

What is HCF?

HCF means highest common factor. HCF of two number a and b is the highest number that divides both a and b.

Number of white tulips = 21

Number of red tulips = 91

Number of identical bouquets that can be made out of 21 white tulips and 91 red tulips if no flowers are left out = HCF (21, 91)

Now,

\(21 = 3\times 7\\91 = 7\times 13\\\)                

HCF (21, 91) = 7

Number of identical bouquets that can be made out of 21 white tulips and 91 red tulips if no flowers are left out = 7

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Answer:

The last angle is 100°. A triangle is 180° and the two given angles are both 40°, meaning that 80°of the triangle is already given so the angle that's left is 100°.

Answer: Juan

Step-by-step explanation: Because if you divide 27 by 30 that makes 0.9 which if you multiply by a hundred you have 90 which means that Kim scored 80% and Juan scored 90%.

To find f, we need to integrate the given second derivative of f twice. We start by integrating the second derivative with respect to x to obtain the first derivative:

f'(x) = ∫f ″(x) dx = 24x^(4)/4 - 18x^(3)/3 + 10x^2/2 + c_1

      = 6x^4 - 6x^3 + 5x^2 + c_1

where c_1 is a constant of integration.

Next, we integrate f'(x) with respect to x to obtain f(x):

f(x) = ∫f'(x) dx = ∫[6x^4 - 6x^3 + 5x^2 + c_1] dx

       = 6x^(5)/5 - 6x^(4)/4 + 5x^(3)/3 + c_1x + c_2

where c_2 is a constant of integration.

Therefore, the solution for f is:

f(x) = 6x^(5)/5 - 6x^(4)/4 + 5x^(3)/3 + c_1x + c_2

where c_1 and c_2 are constants of integration.

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Answer:

90

Step-by-step explanation:

A group of 10 people is choose a chairperson and vice-chairperson. They put all 10 peoples names into a bar. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and Vice-chair are there ?

This is calculated using the Permutation formula

nPr = n!/(n - r)!

Where:

n = 10 people

r = 2 = 2 positions to be filled , Chairman and Vice chairman

Hence:

10P2 = 10!/(10 - 2)!

= 90 ways

Answer:

3n/10

Step-by-step explanation:

Answer: x=1

Step-by-step explanation:

Assume that "log" is the base-10 logarithm

log (2x)+log (5)=1

log 10{10}(2x)+log (5)=1

Assume that "log" is the base-10 logarithm

\log 10{10}(2x)+\log (5)=1

\log 10{10}(2x)+\log10{10}(5)=1

Apply the logarithm product identity

\log 10{10}(2x)+\log 10{10}(5)=1

log 10{10}(2x x 5)}=1