# Twenty-four males aged 25 to 29 were selected from the Framingham Heart Study. Twelve were smokers and 12 were non-smokers. The subjects were paired with one being a smoker and the other a non-smoker. Otherwise, each pair was similar with regard to age and physical characteristics. One piece of data that was collected on each of the pairs of subjects was systolic blood pressure readings. The data is shown here. You are asked to determine whether the data indicate that the mean systolic blood pressure for smokers is higher than the mean systolic blood pressure for non-smokers. Conduct the appropriate test using a significance level of 0.025.

1 + 0.25y; $3.25

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

"The cost for children under twelve at a certain buffet restaurant is a base charge of a dollar (1) plus twenty-five cents for each year of the child's age.(0.25 y) "

So, to obtain the cost we have to multiply 0.25 by the child's age (y) and add 1 dollar.

Mathematically speaking:

Cost(y) = 1 + 0.25y

If the child is nine years old, we simply have to replace the variable y for the number 9.

C = 1+0.25(9)=1+2.25=3.25

Feel free to ask for more if needed or if you did not understand something.

Yes, Sara can conclude the difference is significant because a 2-minute difference is not likely to happen by chance.

15 miles

Step-by-step explanation:

.25 = 1/4

one forth of twelve (12/4) is 3

add 3 onto 12 and you get 15

Answer is Yes, Sara can conclude the difference is significant because a 2-minute difference is not likely to happen by chance.

Step-by-step explanation:

C

Step-by-step explanation:

The equation of a line is given by

and

slope (m) is given by:

Where (x_1,y_1) are the first set of point in the line and (x_2,y_2) is the second set of point

Let's take 2 points arbitrarily. (0,0) & (25,20)

Let's plug it and find the equation:

Now

C is the correct answer.

Part 1) Option C) y = negative one divided by thirty six x²

Part 2) Option A) y = one divided by thirty six x²

Part 3) Vertex: (0, 0); Focus: one divided by sixteen comma zero; Directrix: x = negative one divided by sixteen; Focal width: 0.25

Part 4) Option C) x = one divided by twelve y²

Step-by-step explanation:

Part 1) Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.

we know that

The vertex form of the equation of the vertical parabola is equal to

where

Vertex ----> (h,k)

Focus ----> F(h,k+p)

directrix -----> y=k-p

we have

F(0,-9)

so

h=0

k+p=-9 -----> equation A

y=9

so

k-p=9 ----> equation B

Adds equation A and equation B

k+p=-9

k-p=9

-----------

2k=0

k=0

so

Find the value of p

0+p=-9

p=-9

substitute in the equation

Convert to standard form

isolate the variable y

Part 2) Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 9)

we know that

The vertex form of the equation of the vertical parabola is equal to

where

Vertex ----> (h,k)

Focus ----> F(h,k+p)

directrix -----> y=k-p

we have

Vertex (0,0) -----> h=0,k=0

F(0,9)

so

k+p=9------> 0+p=9 -----> p=9

substitute in the equation

Convert to standard form

isolate the variable y

Part 3) Find the vertex, focus, directrix, and focal width of the parabola.

x = 4y²

we know that

The vertex form of the equation of the horizontal parabola is equal to

where

Vertex ----> (h,k)

Focus ----> F(h+p,k)

directrix -----> x=h-p

we have

----->

so

Vertex (0,0) ------> h=0,k=0

4p=1/4 ------> Focal width

p=1/16

Focus F(0+1/16,0) ----> F(1/16,0)

directrix -----> x=0-1/16 -----> x=-1/16

therefore

Vertex: (0, 0); Focus: one divided by sixteen comma zero; Directrix: x = negative one divided by sixteen; Focal width: 0.25

Part 4) Find the standard form of the equation of the parabola with a focus at (3, 0) and a directrix at x = -3.

we know that

The vertex form of the equation of the horizontal parabola is equal to

where

Vertex ----> (h,k)

Focus ----> F(h+p,k)

directrix -----> x=h-p

we have

Focus F(3,0)

so

h+p=3 ------> equation A

k=0

directrix x=-3

so

h-p=-3 ------> equation B

Adds equation A and equation B and solve for h

h+p=3

h-p=-3

------------

2h=0 -----> h=0

Find the value of p

h+p=3 ------> 0+p=3 ------> p=3

substitute in the equation

Convert to standard form

isolate the variable x

Part A: Scatter plot with best-fit line attached. You'll find the line to have equation (approximately)

The positive slope suggests that test scores and study time are directly are proportional.

Part B: Same as in a previous question you had posted. Pick two points on the provided line and compute the slope as best you can. For example, I might pick (2, 30) and (4, 40), which gives a slope of

and assuming the line passes through (2, 30) exactly, it would have equation