Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.





What does a rate of change of zero mean in this situation?
a.
The median age of a man at the time of his first marriage is, on the average, constant.
b.
The median age of a man at the time of his first marriage is, on the average, decreasing.
c.
The median age of a man at the time of his first marriage is, on the average, increasing.
d.
The rate of change cannot be zero in this situation.


ITs not D so dont say it if you dont know the answer dont reply i put up this post for those who need to get the answer because all other post are wrong.

Answer: 34

Step-by-step explanation:

To find 8% of 425 coins, multiply 425 by 0.08 (which is the decimal equivalent of 8%).

425 * 0.08 = 34

So, 8% of 425 coins is 34 coins.

An image of polygon VWYZ has a line of reflection across the x-axis. So option A is correct.

In geometry, the line of reflection is the line over which a figure is reflected. When a point is reflected over a line, it moves the same distance on the opposite side of the line. The line of reflection is perpendicular to the figure at the point of reflection and is equidistant from the figure and its reflection.

A polygon is a closed two-dimensional shape with straight sides. The sides are line segments that intersect only at their endpoints, called vertices. Polygons can have any number of sides, but they must have at least three. Common examples of polygons include triangles, squares, rectangles, pentagons, hexagons, and octagons.

The formula for the line of reflection in a Cartesian coordinate system is:

x = a

where a is the equation of the line of reflection.

This formula represents a vertical line that passes through the point (a, 0) and reflects points across the line of reflection to their corresponding images on the other side.

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Answer:

reflection across x=2

Step-by-step explanation:

the picture should be able to explain itself! :)))

One expression that has a value between -4 and -3 is (-7/2) - 3.

Expression in math is a combination of numbers, symbols, and operations that represent a value, quantity, or an idea. Expressions can be used to represent equations, relationships between quantities, solutions to problems, and more. They can also be used to represent functions, which are a special type of expression that assign a unique output to a given input.

This expression can be simplified to (-1/2) - 3, which evaluates to -3.5. This value is between -4 and -3, as desired.

To confirm this, we can plug -3.5 into the original expression and see that it evaluates to -3.5: (-7/2) - 3 = -7/2 - 3 = -7/2 + (-3) = -7/2 - 3(-1/2) = -7/2 - (-3/2) = -7/2 + 3/2 = -7 + 3/2 = -7/2 + 3 = -4 + 3 = -1/2 = -3.5.

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After calculation, we can conclude that the required angle x is 56° respectively.

A pair of rays (half-lines) with a shared terminal are combined to form an angle.

The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

Angles created by two rays are in the plane where the rays are located.

So, we can calculate inner angle A because it will result in a 180o angle.

180º - 116º = 64º = Angle A

Now multiply angle A by angle C.

64º + 60º = 124º

Take it away from 180°.

180º - 124º = 56º

Consequently, angle X is measured at 56°.

Therefore, after calculation, we can conclude that the required angle x is 56° respectively.

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Answer: $18.6

Step-by-step explanation: If we take a look at the sale off the shoes cost which is $43.4 and look at the sale amount (30%) which is 18 dollars and 60 cents the answer is: 18.6 or $18.6 off

We can classify the polynomial as a "trinomial" with a degree of 3.

The given polynomial is:

9x^3 + 4x^2 - 7

The degree of a polynomial is the highest power of the variable present in the polynomial. In this case, the degree of the polynomial is 3, because the highest power of x in the polynomial is 3.

The number of terms in a polynomial is the number of individual expressions added or subtracted together. In this case, the polynomial has three terms: 9x^3, 4x^2, and -7.

Therefore, we can classify the polynomial as a "trinomial" with a degree of 3.

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Answer:

To differentiate the given expression, we will need to use both the product rule and the quotient rule.

Let's first rewrite the expression using the reciprocal identity for cosine:

sin y/cos x = sin y * (cos x)^(-1)

Now we can use the product rule and the quotient rule to find the derivative with respect to m:

d/dm [sin y * (cos x)^(-1)] = sin y * d/dm[(cos x)^(-1)] + (cos x)^(-1) * d/dm[sin y]

Using the chain rule, we can find the derivative of (cos x)^(-1) with respect to m:

d/dm[(cos x)^(-1)] = -1/(cos^2 x) * (-sin x) * (dx/dm)

d/dm[(cos x)^(-1)] = sin x/cos^2 x * (dx/dm)

Using the chain rule again, we can find the derivative of sin y with respect to m:

d/dm[sin y] = cos y * (dy/dm)

Substituting these expressions back into the original equation, we get:

d/dm [sin y/cos x] = sin y * [sin x/cos^2 x * (dx/dm)] + cos y * (dy/dm) * (cos x)^(-1)

Simplifying this expression, we get:

d/dm [sin y/cos x] = (sin y * sin x/cos^2 x) * (dx/dm) + (cos y/cos x) * (dy/dm)

Therefore, the derivative of sin y/cos x with respect to m is (sin y * sin x/cos^2 x) * (dx/dm) + (cos y/cos x) * (dy/dm).

The weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.

The nth term of an arithmetic sequence can be found using the formula:

an = a1 + (n-1)d.

The merchant received 7/10 of a pound of diamonds and divided them into 7 equal lots. To find the weight of each lot, we need to divide 7/10 by 7:

(7/10) ÷ 7 = (7/10) × (1/7) = 1/10

Therefore, the weight of the diamonds in each lot was 1/10 of a pound, or 0.1 pound.

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According to the question the volume of soil in Pedro's planter box is 56 cubic feet (ft³).

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is measured in units of cubic centimeters (cm3), cubic meters (m3) or liters. Volume is an important concept in many areas of mathematics, including geometry, calculus and physics. It is also a key concept in many other disciplines, including engineering, architecture and the sciences. Volume is an important property of a solid object, and it is often used to quantify the size or capacity of an object. Volume can be calculated by multiplying the length, width and height of an object. It can also be calculated using the formula for the volume of a cylinder, cone, sphere or other shapes.

To calculate this, we need to multiply the length of the planter box (7 ft) by the width (4 ft) by the height of the soil (2 ft). This gives us the following equation: 7 ft x 4 ft x 2 ft
= 56 ft³.

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Answer:

hope this helps

Step-by-step explanation:

The total closing costs for this mortgage can be calculated as follows:

Loan origination fee: 1% of $85,000 = $850

Broker loan fee: $1,640

Lender document and underwriting fees: $350

Lender tax and wire fees: $210

Fee to title company: $225

Title insurance fee: $320

Title reconveyance fee: $70

Document recording fee: $40Total closing costs = $850 + $1,640 + $350 + $210 + $225 + $320 + $70 + $40

Total closing costs = $3,705

Therefore, the total closing costs for this mortgage are $3,705.

Therefore, Fatima's monthly payment would be $460.23.

Interest is the amount of money that is charged by a lender to a borrower for the use of money or a loan. It is usually calculated as a percentage of the principal amount (the amount of money borrowed) and can be either simple or compound, depending on the type of loan. Interest is typically paid by the borrower to the lender over a set period of time, such as monthly, quarterly, or annually. The interest rate can be fixed or variable, and is determined by a variety of factors including the borrower's creditworthiness, the amount of the loan, and the length of the repayment period.

Here,

To calculate the monthly payment for a car loan, we need to use the formula:

M = P [ i(1 + i)ⁿ] / [ (1 + i)ⁿ – 1]

Where:

M = monthly payment

P = principal (the amount of the loan)

i = monthly interest rate (annual interest rate divided by 12)

n = number of months

First, we need to calculate the monthly interest rate:

i = 4.7% / 12

= 0.003917

Next, we need to calculate the number of months:

n = 5 years x 12 months/year

= 60 months

Now, we can plug in the values and solve for M:

M = 25,000 [ 0.003917(1 + 0.003917)⁶⁰ ] / [ (1 + 0.003917)⁶⁰ – 1]

M = $460.23 (rounded to the nearest cent)

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Answer:

7 and 31 it asks

the 3rd and 6th is

The 1st and 2nd terms of this Fibonacci sequence, given the 3rd and 6th terms would be 2 and 5.

Let's denote the first and second terms of the Fibonacci sequence as F1 and F2. The Fibonacci sequence is defined by the recurrence relation:

F(n) = F(n-1) + F(n-2)

We are given that the 3rd term (F3) is 7 and the 6th term (F6) is 31. We can use this information to set up the following equations:

F3 = F2 + F1 = 7

F6 = F5 + F4 = 31

We can also express F4 and F5 in terms of F1 and F2:

F4 = F3 + F2 = (F2 + F1) + F2 = F1 + 2F2

F5 = F4 + F3 = (F1 + 2F2) + (F2 + F1) = 2F1 + 3F2

Now, let's substitute equation (4) into equation (2):

F6 = 2F1 + 3F2 + F1 + 2F2 = 31

3F1 + 5F2 = 31

By trial and error, we can find the possible values for F1 and F2 that satisfy this equation:

F1 = 1, F2 = 6: 3(1) + 5(6) = 3 + 30 = 33 (not a solution)

F1 = 2, F2 = 5: 3(2) + 5(5) = 6 + 25 = 31 (solution)

The solution is F1 = 2 and F2 = 5, so the first two terms of the Fibonacci sequence are 2 and 5.

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We have to find the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$.

The Taylor Polynomial is given by:

(x)=∑

k=0

n

​k!

f

(k)

(a)

​(x−a)

k

where $f^{(k)}(a)$ is the $k$th derivative of $f(x)$ evaluated at $a$.

Using this formula, we can find the Taylor Polynomial as follows:

\begin{align*}

f(x) &= e^x \

f'(x) &= e^x \

f''(x) &= e^x \

f'''(x) &= e^x \

\end{align*}

Evaluating each derivative at $x=0$, we get:

\begin{align*}

f(0) &= e^0 = 1 \

f'(0) &= e^0 = 1 \

f''(0) &= e^0 = 1 \

f'''(0) &= e^0 = 1 \

\end{align*}

Substituting these values into the formula for the Taylor Polynomial, we get:

\begin{align*}

P_3(x) &= \frac{f(0)}{0!}(x-0)^0 + \frac{f'(0)}{1!}(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{3!}(x-0)^3 \

&= 1 + x + \frac{x^2}{2} + \frac{x^3}{6}

\end{align*}

Therefore, the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$, is $P_3(x) = 1 + x + \frac{x^2}{2} + \frac{x^3}{6}$.

Jackson's total cost after the discount and before tax would be $24.67.

When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.

To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).

Here we have

Jackson has a 10% discount at his local hardware store.

Let 'x' be the cost before tax

After a 10% discount,

The amount that Jackson could pay 90% of the cost

Given that he wants to buy $ 27.40  

The cost of items after discount = 90% of 27.40

= [ 90/100 ] × 27.40

= [ 0.9 ] × 27.40

= 24.66

Therefore,

Jackson's total cost after the discount and before tax would be $24.67.

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Answer:

the value of $s$ is 13.

Step-by-step explanation:

We are given that $r=9$ and $4r+3s=75$. We can use the value of $r$ to find $s$.

Substituting $r=9$ into the second equation, we get:

$4(9) + 3s = 75$

Simplifying the left-hand side, we get:

$36 + 3s = 75$

Subtracting 36 from both sides, we get:

$3s = 39$

Dividing both sides by 3, we get:

$s = 13$

Therefore, the value of $s$ is 13.

Answer:

6 years = $22,536.50

12 years = $25,394.69

18 years = $28,615.38

Step-by-step explanation:

The find the value of the investment after the given number of years, first create an equation for A in terms of t using the compound interest formula.

[tex]\boxed{\sf A=P\left(1+\frac{r}{n}\right)^{nt}}[/tex]

where:

Given values:

Substitute the given values into the formula to create an equation for the value of the investment, A, in terms of time in years, t:

[tex]\implies \sf A=20000\left(1+\dfrac{0.02}{2}\right)^{2t}[/tex]

[tex]\implies \sf A=20000\left(1+0.01\right)^{2t}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{2t}[/tex]

[tex]\hrulefill[/tex]

To find the value of the investment after 6 years, substitute t = 6 into the equation:

[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 6}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{12}[/tex]

[tex]\implies \sf A=20000(1.12682503...)[/tex]

[tex]\implies \sf A=22536.5006026...[/tex]

Therefore, the value of the investment after 6 years is $22,536.50 rounded to the nearest cent.

[tex]\hrulefill[/tex]

To find the value of the investment after 12 years, substitute t = 12 into the equation:

[tex]\implies \sf A=20000\left(1.01\right)^{2 \cdot 12}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{24}[/tex]

[tex]\implies \sf A=20000\left(1.2697346...\right)[/tex]

[tex]\implies \sf A=25394.69297...[/tex]

Therefore, the value of the investment after 12 years is $25,394.69 rounded to the nearest cent.

[tex]\hrulefill[/tex]

To find the value of the investment after 18 years, substitute t = 18 into the equation:

[tex]\implies \sf A=20000\left(1.01\right)^{2\cdot 18}[/tex]

[tex]\implies \sf A=20000\left(1.01\right)^{36}[/tex]

[tex]\implies \sf A=20000\left(1.43076878...\right)[/tex]

[tex]\implies \sf A=28615.37567...[/tex]

Therefore, the value of the investment after 18 years is $28,615.38 rounded to the nearest cent.

g(x) is decreasing function on the interval (-4/5, 0).

Calculus is a branch of mathematics that deals with the study of rates of change and the accumulation of small changes to find the overall effect. It provides a framework for modeling and analyzing a wide range of phenomena, from the motion of objects to the behavior of complex systems.

Calculus is divided into two main branches: differential calculus and integral calculus. Differential calculus deals with the study of rates of change, slopes of curves, and the computation of derivatives. Integral calculus deals with the study of accumulation of small changes, computation of areas, and the computation of integrals.

To determine where g(x) is decreasing, we need to find where its derivative is negative.

The derivative of g(x) is:

g'(x) = 5x⁴ + 4x³

To find where g'(x) < 0, we can factor out a common term of x³ to get:

g'(x) = x³(5x + 4)

So, g'(x) < 0 when:

x³ < 0 and 5x + 4 < 0

This condition is not possible, as x³ is never negative.

x³ > 0 and 5x + 4 < 0

This condition is satisfied when -4/5 < x < 0.

Therefore, g(x) is decreasing function on the interval (-4/5, 0).

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Answer:

5.  x = 60

6.  F' (1, 4)

Step-by-step explanation:

5.  The angles shown are same side exterior angles, so they are supplementary (add to 180)

(x + 85) + 35 = 180

x + 120 = 180

x = 180 - 120 = 60

x = 60

6.  The line x = 1 is a vertical line, passing through the x=axis at (1, 0).  All x coordinates on this line equal 1.

The point F (3,4) is reflected in the line x = 1 at the point F' (1, 4)

Answer:

[tex]5x^4(2x+1)^4(4x+1)[/tex]

Step-by-step explanation:

Okay so we have to use the product rule for this i.e.

d/dx[uv] = u'v + uv'

d/dx[x^5(2x+1)^5] =

[tex]5x^4(2x+1)^5 + x^5 * 2 * 5(2x+1)^4\\\\= 5x^4(2x+1)^5 + 10x^5(2x+1)^4\\\\= (2x+1)^4[5x^4(2x+1) + 10x^5]\\\\= (2x+1)^4[10x^5 + 5x^4 + 10x^5]\\\\= (2x+1)^4(20x^5+5x^4)\\\\=5x^4(2x+1)^4(4x+1)[/tex]

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The exact acreage of wheat expansion during the first 5 years of the 1940s would require access to historical data .Land prices increased significantly due to the high demand for wheat and the increased production.

The Great Plains region includes parts of the United States and Canada, specifically the central and western portions of North America. In the United States, it includes parts of Montana, North Dakota, South Dakota, Nebraska, Kansas, Oklahoma, Texas, Colorado, Wyoming, and New Mexico. In Canada, it includes parts of Alberta, Saskatchewan, and Manitoba.

During the 1940s, the Great Plains region of the United States, which includes states such as Kansas, Nebraska, Oklahoma, and parts of other surrounding states, experienced a significant expansion in wheat production. This period is often referred to as the "wheat boom" era.

During the early 1940s, there was a high demand for wheat due to World War II, as wheat was a staple crop used to feed soldiers and provide food aid to war-torn regions. This resulted in increased wheat production in the Great Plains region. However, the exact acreage of wheat expansion during the first 5 years of the 1940s would require access to historical data .

As for the prices of land being sold during that time, it is also difficult to provide precise information without specific data. Land prices can vary depending on various factors such as location, quality of land, demand, and economic conditions. However, it is generally known that during the wheat boom era of the 1940s, land prices in the Great Plains region increased significantly due to the high demand for wheat and the increased production. The exact percentage of increase would require access to historical data and research.

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Answer:

In order to determine whether 387 is a term of a sequence, we need to know the rule or formula for generating the sequence. Without this information, it is not possible to determine whether 387 is a term of the sequence or not.

If we assume that the sequence is an arithmetic sequence, where each term is obtained by adding a fixed constant to the previous term, we can use the following formula to determine whether 387 is a term of the sequence:

an = a1 + (n-1)d

where a1 is the first term of the sequence, d is the common difference between consecutive terms, and n is the term we are trying to find.

If we substitute the values for the first few terms of the sequence, we can check whether 387 is a term or not. For example, if the first few terms of the sequence are:

a1 = 3

a2 = 8

a3 = 13

a4 = 18

and so on, with a common difference of 5 between consecutive terms, we can use the formula to find the value of the 129th term of the sequence:

a129 = a1 + (129-1)d

a129 = 3 + 128(5)

a129 = 643

Since 387 is not equal to 643, it is not a term of this sequence. However, without knowing the rule or formula for generating the sequence, it is impossible to say for certain whether 387 is a term or not.

Answer: $9.66

Step-by-step explanation: perimeter = 345mm + 345mm + 345mm + 345mm = 1380

We need 1380 millimeters which is equivalent to 1.38 meters.

We can multiply the number of meters by the cost of meters to find the total

Answer:

Estimated difference: 88 - 6 = 82

Actual difference: 87.71 - 5.8 = 81.91

By using synthetic substitution on f(x)=x²-9x+5, f(x) = -13. Hence option C is the correct answer.

Synthetic substitution is a method used to evaluate a polynomial function for a specific value of the independent variable. This method involves setting up a table with the coefficients of the polynomial and the value we are substituting. Then, we use synthetic division to perform the substitution and find the corresponding value of the function.

1) To use synthetic substitution, we first write the coefficients of the polynomial in descending order of their powers.

2) Next, we set up a table with the coefficients and the value we are substituting, which is typically denoted by a vertical line.

3) Then, we use synthetic division to perform the substitution. To do this, we bring down the first coefficient, multiply it by the substitution value, and write the result underneath the next coefficient. We then add this result to the next coefficient, and repeat the process until we reach the last coefficient. The final value is the result of the substitution, which is the value of the function for the given argument.

To use synthetic substitution, we first set up a table with the coefficients of the polynomial f(x) and the value we are substituting, which is 3 in this case:

x \ f(x)        1         -9        5

3  

Then, we bring down the first coefficient, which is 1, and multiply it by the substitution value, 3, to get 3. We write this value underneath the second coefficient:

x \ f(x)        1         -9        5

3           3

Next, we add the 3 and the -9 to get -6, and multiply this value by the substitution value, 3, to get -18. We write this value underneath the third coefficient:

x \ f(x)        1         -9        5

3           3            -6

Finally, we add the -18 and the 5 to get -13, which is the value of f(3):

x \ f(x)        1         -9        5

3           3            -6          -13

Therefore, f(3) = -13.

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The median of the data set is: 95.5

What is median?

median is the number at the middle of the given data.

To find the median of the data set {102, 74, 86, 74, 96, 95, 103, 102}, we first need to arrange the values in order from lowest to highest:

74, 74, 86, 95, 96, 102, 102, 103

Since the data set has an even number of values, the median is the mean of the two middle values. In this case, the two middle values are 95 and 96.

Therefore, the median of the data set is: (95 + 96) / 2 = 95.5

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The answer of the given question based on the fraction is ,  a value that is greater than 1/2.

A fraction is mathematical expression that represents part of  whole or ratio between the two numbers. It is expressed in the form of a ratio of two integers, with a numerator and a denominator separated by a horizontal or slanted line called a fraction bar.

Fractions that are closer to 1 than to 0 have a value that is greater than 1/2. This is because 1/2 is exactly halfway between 0 and 1 on the number line.

So, any fraction that has a numerator greater than its denominator is closer to 1 than to 0. For example:

2/3 is closer to 1 than to 0 because it is greater than 1/2

7/8 is closer to 1 than to 0 because it is greater than 1/2

3/4 is closer to 1 than to 0 because it is greater than 1/2

On the other hand, fractions that have a value less than 1/2 are closer to 0 than to 1. For example:

1/4 is closer to 0 than to 1 because it is less than 1/2

3/10 is closer to 0 than to 1 because it is less than 1/2

2/5 is closer to 0 than to 1 because it is less than 1/2

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The answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).

(B) The right choice is Option B, which is Option II which is narrower.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.

Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

So, let X represent the amount of time (in seconds) needed to complete a 100-meter race with Tom.

His population's mean 100-meter race finishing time falls within a 99% confidence interval of 12.8081 and 15.5919.

x = 14.2

s²= 0.9867

s= 0.9933

t α2, n-1 = 3.7074

The margin of error= 1.3919

lower bound= 12.8081

upper bound= 15.5919

Therefore, the answers to both the subparts using the confidence interval are shown:
(A) His population's mean finishing time for the 100-meter event has a 99% confidence interval of (12.8081,15.5919).

(B) The right choice is Option B, which is Option II which is narrower.

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Correct question:

Tom is preparing for a 100 meters race competition. During his practice last week, a sample of seven 100

meters races is reviewed, and the finishing times (in seconds) were as below:

13.4

15.6

13.1

14.5

14.2

13.3

15.3

It is reasonable to assume his finishing times are normally distributed.

(a) Construct a 99% confidence interval estimate of his population mean finishing time of 100 meters race.

(b) If the confidence interval estimate of his population mean finishing time of 100 meters is constructed at 95% instead of 99%, would the new confidence interval be (I) wider, (II) narrower, or (III) the same as the interval constructed at part (a)? (Just state your answer, no calculation is needed in part (b))