Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups, and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Draw a conclusion and interpret the decision.
A. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.10 level of significance to support Fran's claim that there is a significant difference between the mean number of miles run each week by group runners and individual runners.
B. We reject the null hypothesis and conclude that there is insufficient evidence at a 0.10 level of significance to support Fran's claim that there is a significant difference between the mean number of miles run each week by group runners and individual runners.
C.We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.10 level of significance to support fran's claim that there is a significant difference between the mean number of miles run each week by group runners and individual runners.
D. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.10 level of significance to support Fran's claim that there is a significant difference between the mean number of miles run each week by group runners and individual runners.

Answer: b

Step-by-step explanation: on edge

Answer: C. 30 StartRoot 3 EndRoot

Step-by-step explanation:

Took the test/exam

Answer:

a*n = -8 + (n - 1)6

Step-by-step explanation:

Explicit formula:

a*n = a*1 + (n - 1)d

a*1 = first term

n = nth term or the place

d = difference

Set: -8, -2, 4, 10

-8 ---> -2 = 6 added

Fill it in.

a*1 = -8

n = n

d = 6

Solution:

a^n = -8 + (n -1)6

Answer: She needs to get 99 on her next test.

Step-by-step explanation:

Answer:

the answer is x = 0

Step-by-step explanation:

Cancel equal terms on both sides of the equation:

[tex]5x = 0[/tex]

Divide both side of the equation by 5.

[tex]x = 0[/tex]

Therefore, the answer is x = 0

Answer:

5x - 10 = -10

+10 +10

5x = 0

divide by 5 on both sides:

x = 0

Answer:

8

Step-by-step explanation:

You only have 8 socks and its a combination of both socks and t-shirts.  Hope this helps!

Answer:

80

Step-by-step explanation:

10*8=80

Answer:

y=1

Step-by-step explanation:

x is 0 so there is no point putting that in in the equation y=mx+b you do have the b which is 1 so that is your equation

Answer:

4.20

Step-by-step explanation:

First find the total cost of the nametags

105 * .12

12.60

Then divide by the 3 teachers

12.60/3 =4.20

Each teacher will pay 4.20

Answer:

700 words

Step-by-step explanation:

280: 4

x:10

280/4 = x/10

4times x is equal to 4x and 280 times 10 is equal to 2800

4x=2800

2800 divided by x is 700.

The answer is 700 words per 10 minutes.

Answer:

10.35

Step-by-step explanation:

He has $300 (15x$20). He spends 144.75. He has 155.25 in total. That leaves 10.35 (155.25/15) to spend on each student.

Answer:

B

Step-by-step explanation:

Answer:

[tex]f^{-1} = \frac{ 7(x-4)}{2}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{2x}{7} + 4[/tex]

Required

The inverse function

[tex]f(x) = \frac{2x}{7} + 4[/tex]

Replace f(x) with y

[tex]y = \frac{2x}{7} + 4[/tex]

Swap x and y

[tex]x = \frac{2y}{7} + 4[/tex]

Multiply through by 7

[tex]7x = 2y + 28[/tex]

Solve for 2y

[tex]2y = 7x - 28[/tex]

Solve for y

[tex]y = \frac{ 7x-28}{2}[/tex]

Factorize

[tex]y = \frac{ 7(x-4)}{2}[/tex]

Write as:

[tex]f^{-1} = \frac{ 7(x-4)}{2}[/tex]

Answer:

147 degrees

Step-by-step explanation:

all the angles of a triangle add up to 180 degrees. so, you must perform the operation 180-(83+64) which equals 33. this is the angle supplementary to angle 1. to find angle 1, you must subtract 180 and 33 since supplementary angles add up to 180 degrees. this is equal to 147 degrees.

Answer:

55

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

9514 1404 393

Answer:

  x = 1/2

Step-by-step explanation:

There are some different ways to find the area of a donut shape. One is to multiply its centerline length by its width. We'll use that here to find the shaded area of the sector.

The centerline radius of shaded area A is ...

  (6x -2) cm + (1/2)(4x cm) = 8x -2 cm

The length of the centerline is ...

  s = rθ = (8x -2)(π/4) . . . . . . for a central angle of 45° = π/4 radians

Then the area A is ...

  area A = (π/4)(8x -2)(4x) = 2πx(4x -1) . . . cm^2

__

The radius of circle B is ((4 -4x) cm)/2 = (2 -2x) cm. The area of circle B is ...

  A = πr^2 = π(2 -2x)^2 cm^2

We're told the two areas are equal, so we have ...

  2πx(4x -1) = π(2 -2x)^2 . . . . . . . expressions for the areas are equal

  8x^2 -2x = 4x^2 -8x +4 . . . . . . divide by π, eliminate parentheses

  4x^2 +6x -4 = 0 . . . . . . . . . . . . subtract the right-side expression

  2(2x -1)(x +2) = 0 . . . . . . . . . . . factor

  x = 1/2 or -2 . . . . . . . only the positive solution is useful here

The value of x is 1/2.

Answer:

x - 89.95 ≤ 30.05= x ≤ 120

add 89.95 to both sides of the equation. Since on the right side 89.95 is already there it cancells eachother out leaving x. After adding 89.95 to 30.05 you should get an answer of 120.

The money Sarah's dad wants to spend in all if Sarah's dad bought her a scooter that costs $89.95, He can spend up to $30.05 on a helmet, which is less than or equal to $120, x ≤ 120.

Inequality is a relationship that compares two numbers or other mathematical expressions in an unequal way. Inequalities are the name given to certain algebraic mathematical expressions.

Given:

Sarah's dad bought her a scooter that cost $89.95,

He can spend up to $30.05 on a helmet,

Assume the x is the money Sarah's dad wants to spend in all,

Write the inequality as shown below,

x - 89.95 ≤ 30.05

Solve the inequality by adding 89.95 on both sides,

x - 89.95  + 89.95   ≤ 30.05 + 89.95  

x ≤ 120

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Answer: 20 cm²

Step-by-step explanation:

To find the property tax, you would multiply the mill rate by 0.01

To find the property tax, you would multiply the assessed value of the property by the mill rate.

Given that the assessed value is $225,000 and the mill rate is 14.5, we need to multiply these two values to calculate the property tax.

Property Tax = Assessed Value × Mill Rate

Property Tax = $225,000 × 14.5

To simplify the calculation, we can convert the mill rate to a decimal by dividing it by 1,000.

Mill Rate = 14.5 ÷ 1000 = 0.0145

Property Tax = $225,000 × 0.0145

Property Tax = $3,262.50

Therefore, to find the property tax, you would multiply the mill rate by 0.01 (option c).

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Answer: The first, The second, and the number line one love!

Step-by-step explanation:

=======================================================

Work Shown:

We'll apply these log rules

[tex]\text{Log Rule 1: } \ \ \ \ln\left(\frac{x}{y}\right) = \ln(x) - \ln(y)\\\\[/tex]

[tex]\text{Log Rule 2: } \ \ \ \ln\left(x^y\right) = y\ln(x)\\\\[/tex]

These log rules can be used for logs of any base, and not just natural logs.

[tex]z = \ln\left(\frac{\sqrt{x}}{y}\right)\\\\z = \ln\left(\sqrt{x}\right)-\ln\left(y\right) \text{ ... Use log rule 1}\\\\z = \ln\left(x^{1/2}\right)-\ln\left(y\right)\\\\z = \frac{1}{2}\ln\left(x\right)-\ln\left(y\right) \text{ ... Use log rule 2}\\\\z = \frac{1}{2}u-v\\\\[/tex]

Therefore,

[tex]\ln\left(\frac{\sqrt{x}}{y}\right) = \frac{1}{2}u-v\\\\[/tex]

when [tex]u = \ln(x) \ \text{ and } \ v = \ln(y)\\\\[/tex]

Answer:

It will cost $532 to paint the barn

Step-by-step explanation:

First we need to find the area of the barn's walls.

2 (length x height) + 2 (width x height)

=2 (80x30) + 2 (50x30)

=2 (2400) + 2(1500)

=4800+3000

=7800 ft^2

Now we can find the amount of gallons needed, then the total cost.

7800 ft^2/420 ft^2  

=18.57 gallons

=19 gallons  

19 gallons x $28

=$532

Answer:

520

Step-by-step explanation:

Area:

[tex]2(80*30) + 2(50*30) = 7800[/tex]

Price

[tex]\frac{7800}{420}*28 = 520[/tex]

Answer:

Following are the responses to the given question:

Step-by-step explanation:

[tex]H_o : p =0.31\\\\H_a: p \neq 0.31\\\\n = 8606 \\\\ p^ = 0.32[/tex]

[tex]TS = \frac{(p^ - p)}{\sqrt{(\frac{pq}{n})}}[/tex]

      [tex]= \frac{(0.32-0.31)}{\sqrt{(\frac{0.31\times 0.69}{8368})}}\\\\=\frac{0.01}{5.4}\\\\=0.00185\\\\[/tex]

Answer:

I) coordinate of P is (11, 5.5)

II) Points are not collinear

Step-by-step explanation:

I) Let the coordinates of P be (a, b)

We are told that its x-coordinate is twice its y-coordinate. Thus, a = 2b

Now, P is equidistant from R(-2, 4) and S(6,-4). Thus;

PR = PS

Using the formula for distance between two coordinates, we have;

√((a - (-2))² + (b - 4)²) = √((a - 6)² + (b - (-4))²)

This gives;

(a + 2)² + (b - 4)² = (a - 6)² + (b + 4)²

Since a = 2b,then we have;

(2b + 2)² + (b - 4)² = (2b - 6)² + (b + 4)²

4b² + 8b + 4 + b² - 8b + 16 = 4b² - 12b + 36 + b² + 8b + 16

Simplifying this gives;

20 = 42 - 4b

42 - 20 = 4b

4b = 22

b = 22/4

b = 11/2

b = 5.5

Since a = 2b

Then a = 2 × 5.5

a = 11

Thus, coordinate of P is (11, 5.5)

II) Formula for area of triangle formed by three points is given as;

A = ½|(x1 - x2) (x2 - x3)|

|(y1 - y2) (y2 - y3)|

x1 - x2 = 11 - (-2) = 13

x2 - x3 = -2 - 6 = -8

y1 - y2 = 5.5 - 4 = 1.5

y2 - y3 = 4 - (-4) = 8

Thus;

A = ½|13 -8|

|1.5 8|

A = ½((13 × 8) - (1.5 × - 8))

A = ½(104 + 12)

A = 58

Since the area is not zero, then it means the points are not collinear.

Answer:

-64

Step-by-step explanation:

By looking at the numbers, we can identify that this is a geometric sequence and the ratio would be 2. The formula to find the nth term in a geometric series is:

[tex]t *r^{n-1}[/tex]

where t is the first term and r is the ratio. We can substitute in the information we know:

[tex]-\frac{1}{2} *2^{n-1}[/tex]

We are looking for the eighth term, so we substitute 8 where n is:

[tex]-\frac{1}{2}*2^{8-1}[/tex]

We can simplify:

[tex]-\frac{1}{2}*2^7[/tex]

[tex]-2^6[/tex]

[tex]-64[/tex]