CNNBC recently reported that the mean annual cost of auto insurance is 1022 dollars. Assume the standard deviation is 272 dollars, and the cost is normally distributed. You take a simple random sample of 39 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X bar? X bar - N(
b. What is the distribution of x bar? x bar - N(
c. What is the probability that one randomly selected auto insurance is more than $990?
d. a simple random sample of 39 auto insurance policies, find the probability that the average cost is more than $990. ​

The correct option is A which is federal tax.

The type of tax that funds military defence in the United States is the federal income tax. This is a tax levied by the federal government on individuals, businesses, and other entities based on their income. A portion of this tax revenue is allocated towards funding the military, including salaries for personnel, equipment, and operations.

It's important to note that not all of the federal income tax revenue is earmarked for military defence. The federal government uses this revenue to fund a variety of programs and services, including healthcare, education, infrastructure, and more. The allocation of funds towards military defence is determined by Congress and can vary from year to year based on national security needs.

Other taxes, such as state income tax, local income tax, and FICA tax (which funds Social Security and Medicare), do not directly fund military defence. However, all taxpayers contribute to the national defence in some way, as the federal government relies on a variety of revenue sources to fund its operations and programs, including military defence.

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The image of the given point P = (-4, 6) as required to be determined in the task content is; (-6, -4).

It follows from the task content that the image point of P = (-4, 6) after a 90° counterclockwise rotation is to be determined.

Recall, for a point (x, y) , the image point after a 90° counterclockwise rotation is; (-y, x).

Ultimately, since the point P is; P = (-4, 6).

The image point is; (-6, -4).

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The trigonometric ratios for angle a are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For this problem, the hypotenuse is of [tex]3\sqrt{13}[/tex], while the side lengths relative to angle A are given as follows:

Hence the trigonometric ratios are given as follows:

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The distance from the floor when t = 6.5 seconds is about 13.7 cm.

We are given that;

H(t)=A cos (Bt) +D

Now,

b. To write an equation of the form H(t) = A cos (Bt) + D for the graph, we need to find the values of A, B, and D.

A is the amplitude of the cosine function, which is half the difference between the maximum and minimum values of H(t). In this case, the maximum value is 36 and the minimum value is 12, so:

A = (36 - 12) / 2 A = 12

D is the vertical shift of the cosine function, which is the average of the maximum and minimum values of H(t). In this case:

D = (36 + 12) / 2 D = 24

B is related to the period of the cosine function, which is the time it takes for one complete cycle. In this case, the period is 8 seconds, because H(t) repeats its values every 8 seconds. The formula for B is:

B = 2π / period

So:

B = 2π / 8 B = π / 4

Therefore, the equation is:

H(t) = 12 cos (π/4 t) + 24

c. To find the distance from the floor when t = 6.5 seconds, we need to plug in t = 6.5 into the equation and evaluate H(t). Using a calculator, we get:

H(6.5) = 12 cos (π/4 × 6.5) + 24 H(6.5) ≈ 13.7

Therefore, by the equation answer will be 13.7 cm.

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The probability of events A or B occurring is 0.80 or 80%.

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

Probability can be calculated by dividing the number of favourable outcomes by the total number of possible outcomes.

To find P(A or B), we need to use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Substituting the given values, we get:

P(A or B) = 0.60 + 0.30 - 0.10

= 0.80

Therefore, the probability of events A or B occurring is 0.80 or 80%.

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Answer:

π(5^2 - 2^2) = 21π square inches, or about 65.97 square inches

The inequality is solved and the number is x ≥ 12

Given data ,

Let the number be represented as x

Now , sum of three times a number and -4 is at least twice the number plus 8

And , 3x - 4 ≥ 2x + 8

To solve for "x", we can start by isolating the "x" term on one side of the inequality

3x - 4 ≥ 2x + 8

Subtract 2x from both sides , we get

3x - 2x - 4 ≥ 2x - 2x + 8

x - 4 ≥ 8

Add 4 to both sides , we get

x - 4 + 4 ≥ 8 + 4

x ≥ 12

Hence , the inequality is x ≥ 12

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An equation of the line in slope-intercept form include the following: y = 4x + 3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (0, 3) and a slope of 4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 4(x - 0)  

y - 3 = 4x

y = 4x + 3

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Answer:

completed I/8 of a panting in a week

Step-by-step explanation:

The equation represents circle A is (x + 1)² + (y + 1)² = 25. (option d)

To represent a circle on a coordinate plane, we use an equation called the equation of the circle. This equation is derived from the distance formula, which you might have learned in your geometry class. The equation of a circle with center (a, b) and radius r is given by:

(x - a)² + (y - b)² = r²

In this question, the center of the circle is given as A (1, 1). So, the equation of the circle will be of the form:

(x - 1)² + (y - 1)² = r²

To find the value of r, we can use the fact that point B (5, 4) lies on the edge of the circle. The distance between the center of the circle (1, 1) and point B (5, 4) is equal to the radius of the circle. Using the distance formula, we can find the distance between these two points:

r = √((5 - 1)² + (4 - 1)²) = √(16 + 9) = √(25) = 5

So, the equation of the circle can be written as:

(x - 1)² + (y - 1)² = 5²

Simplifying this equation, we get:

(x - 1)² + (y - 1)² = 25

Therefore, the correct answer is option d) (x + 1)² + (y + 1)² = 25.

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Answer:

C

Step-by-step explanation:

Look at the picture

Answer:

[tex]m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} [/tex]

[tex]7 = - \frac{8}{3} ( - 3) + b[/tex]

[tex]7 = 8 + b[/tex]

[tex]b = - 1[/tex]

[tex]y = - \frac{8}{3} x - 1[/tex]

The y-intercept is -1.

Answer:

D) 4

Step-by-step explanation:

Since g(x) is the inverse of f(x), g(f(x))=x. Therefore, we need to find the value of x such that f(x) = 1. Looking at the table, we can see that f(4) = 1, so g(1) = 4.

Therefore, the correct answer is (D) 4.

The blank spaces in the statements area. S, R, and Q  are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.

Points that lie on the same straight line are collinear points.

If two lines are lie on the same plane, they are referred to as coplanar lines.

(a.) S, R, and Q are on a straight line. Therefore S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are on the same plane. Therefore:

Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

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76 meters is the perimeter of the rectangle given.

The length of the rectangle is 3 meters and the width is 35 meters.

To find the perimeter, we can use the formula:

Perimeter = 2(Length + Width)

Substituting the values we obtained:

Perimeter = 2(3 + 35) = 2(38) = 76 meters

Therefore, the perimeter of the rectangle is 76 meters.

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Complete question:

The rectangle has an area of 35x3 square meters. Find its perimeter.

The inequality that represents p, the number of people the theater can seat is p ≤ 25

From the question, we have the following parameters that can be used in our computation:

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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Answer:

it is 3/3 3/6 I hope this helped

Answer:

average rate of change = (16 - 1)/(4 - 1)

= 15/3 = 5

The total number of students in Ms. Morales's class is either 20 or 30, depending on the value of x.

Let the ratio of boys to girls in Ms. Morales's class be 3x:7x, where 3x represents the number of boys and 7x represents the number of girls.

The total number of students in the class is equal to the sum of the number of boys and the number of girls, which is 3x + 7x = 10x.

We don't know the value of x, but we do know that the class size is between 22 and 34 students.

Therefore, we can set up an inequality based on the total number of students:

22 ≤ 10x ≤ 34

Dividing all parts of the inequality by 10, we get:

2.2 ≤ x ≤ 3.4

Since x represents a whole number of students, the possible values for x are 3 (if there are 30 students in the class) or 2 (if there are 20 students in the class).

If x = 3, then the total number of students is:

10x = 10(3) = 30

If x = 2, then the total number of students is:

10x = 10(2) = 20

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You would have an open circle. A way to remember it is that < and > is open and ≥ and ≤ mean closed circle. A way to also remember which way to go is remembering this cool strategy.

<ess than

>greater than

Less means left. Greater means right. So your graph would look like something along the lines of:

As the class sizes range from 22 to 34 students, the answer must be 30,

Let the number of girls in the class "3x" and the number of boys "7x".

Then the total number of students in the class is:

Total students = 3x + 7x = 10x

We don't know the value of "x" yet, but we do know that the total number of students is between 22 and 34.

So we can set up an inequality:

22 ≤ 10x ≤ 34

Divide both sides of the inequality by 10:

2.2 ≤ x ≤ 3.4

Therefore, x can be either 3 or 4.

If x = 3, then the total number of students is:

Total students = 3x + 7x = 30

If x = 4, then the total number of students is:

Total students = 3x + 7x = 40

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The graph of g(x) is on the image at the end, and the correct option for the transformation is B.

We define a horizontal dilation of scale factor k as:

g(x) = f(k*x)

if k > 1, we have a stretch.

if  0 < k < 1, we have a shink of scale factor 1/k

Here we have:

g(x) = f (5x) = 5x - 4

We can notice that k = 5, then we have a stretch, thus, the correct option is B.

The graph of function g(x) can be seen in the image at the end.,

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The test statistic is z₀ = 2.65 and the P-value is 0.004. The null hypothesis is rejected at the 5% level of significance, and we conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8.

To test the hypothesis using the P-value approach, we can follow these

Check whether the sample size is large enough for the normal approximation to the binomial distribution. The requirements are satisfied if np₀ >= 10 and n(1-p₀) >= 10,

where p₀ is the hypothesized proportion under the null hypothesis. In this case, p₀ = 0.8, n = 125, so np₀ = 100 and n(1-p₀) = 25, both of which are greater than 10.

The null hypothesis is H₀: p = 0.8 (the true proportion is 0.8).

The alternative hypothesis is H₁: p > 0.8 (the true proportion is greater than 0.8).

Under the null hypothesis, the test statistic follows a standard normal distribution.

The test statistic is calculated as:

z₀ = (x - np₀) / sqrt(np₀(1-p₀))

where x is the number of successes in the sample.

Plugging in the values, we get:

z₀ = (105 - 1250.8) / √(1250.8 x 0.2)

z₀ = 2.65

Calculate the P-value.

The P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample, assuming the null hypothesis is true.

Since this is a right-tailed test (H₁: p > 0.8), we calculate the area to the right of the test statistic.

Using a standard normal table or calculator, we find that the area to the right of z₀= 2.65 is 0.004.

Therefore, the P-value is 0.004.

Make a decision and interpret the results.

Using a significance level of α = 0.05, we compare the P-value to α.

Since the P-value (0.004) is less than α (0.05), we reject the null hypothesis.

We conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8 at a 5% level of significance.

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A hypothesis is a put forth explanation of a phenomenon (plural: hypotheses). Therefore, p-value given is 0.0062.

A hypothesis is a put forth explanation of a phenomenon (plural: hypotheses). A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.

H:p<=0.8

Ha: p>0.8

alpha=0.01 P{reject H:H is true}

critical value z>2.326

z=(0.9-0.8)/sqrt (0.8*0.2/100); sqrt of 0.0016=.04

z=(0.1/.04)=2.5

probability z> 2.5 is 0.0062

check with one sample proportion test on calculator, z=2.5

Reject H

p-value given is 0.0062

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Answer:

To find out how much money per cheerleader still needs to be raised for the trip, we need to divide the remaining amount by the number of cheerleaders:

Total amount needed = $9,500

Amount raised so far = $8,340

Amount still needed = $9,500 - $8,340 = $1,160

Number of cheerleaders = 16

Amount per cheerleader still needed = $1,160 ÷ 16 = $72.50

Therefore, $72.50 per cheerleader still needs to be raised for the trip.

The proof that Daniel and Edward receive money in the ratio of their ages is shown below.

A ratio expresses the number of times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, while the orange-to-total fruit ratio is 8:14.

Given that Daniel and Edward receive money in the ratio of their ages. And the age of Daniel and Edward is 8 years and 12 years, respectively. Therefore, it can be written as,

Ratio of Ages

=Age of Daniel: Age of Edward

= 8 years : 12 years =

= 2 : 3

Ratio of the amount received by them

= Amount received by Daniel: Amount received by Edward

= $30 : $45

= 2 : 3

Since, Ratio of Ages = Ratio of the amount received by them.
Therefore, it can be concluded that Daniel and Edward receive money in the ratio of their ages.

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The complete question is:
Daniel is 8 years old and Edward is 12 years old. Their parents give them money in the ratio of their ages. If Daniella receives $30, then Show that Edward receives $45.

The outlier of the graph is

An outlier is an isolated data point that significantly differs from the entirety of the points within a dataset. It is an observation that resides an exceptional distance away compared to other values in a random sample from a population.

Outliers can be identified employing various statistical techniques, like graphical methods (for instance, box plots, scatterplots) and numerical procedures (e.g., Z-score, IQR method).

The problem used a scatter plot plot to show that the outlier is (5, 1)

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The expression that uses the commutative property to make it easier to evaluate is (-1/3)  × (-9) × 2/5.

The commutative property is derived from the word "commute" which implies moving around or swapping numbers. The commutative property involves moving the numbers around while the result still remains the same.

Mathematically, if switching the arrangement of the operands does not alter the result of the arithmetic operation then that certain arithmetic operation is commutative.

From the given information, the commutative property that can be used for (-1/3) × 2/5 × (-9) to make it easier to solve is (-1/3)  × (-9) × 2/5.

This is because the commutative property follows the analogy:

In addition, it will be easier to solve (-1/3) × (-9) first, then multiply it with 2/5.

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From the four options the positively skewed distribution is fourth one.

Hence the correct option is given by (D).

Positively skewed distribution is a distribution with its tail is more pronounced on the right side than it is on the left. Since the distribution is positively skewed, then the value is positive.

The median, mode and other statistical observation data are on left side of the arithmetic mean.

The graph for positively skewed distribution is given by,

Clearly from the given four graphs, fourth graph that is option (D) is looking like positively skewed distribution.

Hence the correct option will be (D).

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