Use the diagram below to find the distance between points (-6, 5) and (-1, -7).

Find the least squares regression equation using the school year (in number of years after 2000) for the input variable and the

Ad libitum [116K]

Answer-

The least squares regression equation using the school year (in number of years after 2000) for the input variable and the average cost (in thousands of dollars) for the output variable is "y=0.937x+12.765" .

Solution-

The independent variable / input variable= x = Number of years after 2000 ( = year-2000)

The dependent variable / output variable = y = Average cost in thousands of dollars

(The table has been attached herewith.)

To find the regression equation for a group of (x,y) points,

We have to calculate the slope and y-intercept, then we can put those values in the equation y = mx + c ( Slope - Intercept formula)

We know that,

$Slope=m=\frac{N\sum xy -\sum x\sum y}{N\sum x^{2}- (\sum x)^{2}}$

Putting the values from the table,

$m=\frac{(8 \times 1020.206)-(52 \times 150.894)}{(8 \times 3810)-(52^2)}$

( ∵ Instead of 150,894 we have to put 150.894 as we have find the line for year and thousands of dollars )

$\Rightarrow m =\frac{8161.648-7846.488}{3040-2704} =\frac{315.16}{336}=0.937$

Now, for the y-intercept,

$c =\frac{\sum y -m(\sum x)}{N}$

Putting the values,

$c=\frac{150.894-(52 \times 0.937)}{8}=\frac{102.125}{8}=12.765$

Now, putting the values of c and m, in the Slope-Intercept formula,

$y=0.937x+12.765$

3 0

4 years ago

Jennifer is ordering cake for her wedding reception. If one cake feed 18 people, how many cakes does she need to order for 150 p

ehidna [41]

Answer:

8 1/3 cakes

Step-by-step explanation:

Step 1:

1 : 18 Ratio

Step 2:

1 : 18 = x : 150 Proportion

Step 3:

150 = 18x Multiply

Step 4:

150 ÷ 18 = x Divide

Answer:

x = 8 1/3

Hope This Helps :)

8 0

3 years ago

In a group of 25 students, 6 study both Art and Biology. 10 study Biology but not Art. 3 study neither subject. Given that a ran

olga2289 [7]

Answer:

1/2

Step-by-step explanation:

There are a total of 25 students. 3 don't study art or biology. 10 study only biology. 6 study both art and biology. This means the remaining students only study art.

1. Calculate the number of students taking art

only art: 25 - 3 - 6 - 10 = 6

number of students taking art and biology: 6

total number of students taking art: 12

2. Calculate the probability

Out of the 12 total students taking art, 6 are in art and biology.

6/12 = 1/2

6 0

3 years ago

Franco read 3/8 of a chapter of his history book in 1/5 of an hour. At this rate, how many chapters of his history book can he r

Irina18 [472]

He can read $1\frac{7}{8}$ chapters of his history book in 1 hour.

Explanation

Franco read 3/8 of a chapter of his history book in 1/5 of an hour.

Suppose, he can read $x$ chapters of his book in 1 hour at this rate.

So, the equation according to the ratio of 'the chapter to the time' will be....

$\frac{x}{1}= \frac{\frac{3}{8}}{\frac{1}{5}}\\ \\ \frac{x}{1}=\frac{3}{8}*\frac{5}{1}\\ \\ \frac{x}{1}=\frac{15}{8} \\ \\ x= \frac{15}{8}= 1\frac{7}{8}$

So, he can read $1\frac{7}{8}$ chapters of his history book in 1 hour.

6 0

4 years ago

19. Amanda bought a 6-cup bag of shredded cheese for $6.89. She used 2.25 cups to make lasagna and 1.25 cups to make pizza. How

SVETLANKA909090 [29]

Answer:

2.50

Step-by-step explanation:

ok, so we start out with a 6 cup bag of cheese. But then she uses 2.25 cups to make lasgna, and 1.25 cups to make pizza. we need to see how much cheese is left after she used the cups. First lets add the 2 cups: 1.25 + 2.25. Lets first add 1 + 2 = 3, then .25 + .25 = .50. Lets now add 3, and .50, and that gives us 3.50. Now to see how much cheese is left, we must subtract 6 minus 3.50, which gives us a total of 2.50. I hope that helped!

5 0

3 years ago