Drawn from a standard deck of cards what’s the probability that you randomly choose a jack knowing that a face card was drawn

The following table shows the percent increase of donations made on behalf of a non-profit organization for the period of 1984 t

pashok25 [27]

Giving the table below which shows <span>the percent increase of donations made on behalf of a non-profit organization for the period of 1984 to 2003.
</span>
Year: 1984 1989 1993 1997 2001 2003

Percent: 7.8 16.3 26.2 38.9 49.2 62.1

The scatter plot of the data is attached with the x-axis representing the number of years after 1980 and the y-axis representing the percent increase <span>of donations made on behalf of a non-profit organization.

To find the equation for the line of regression where </span><span>the x-axis representing the number of years after 1980 and the y-axis representing the percent increase of donations made on behalf of a non-profit organization.
$\begin{center}
\begin{tabular}{ c| c| c| c| }
 x & y & x^2 & xy \\ [1ex] 
 4 & 7.8 & 16 & 31.2 \\ 
 9 & 16.3 & 81 & 146.7 \\ 
13 & 26.2 & 169 & 340.6 \\ 
17 & 38.9 & 289 & 661.3 \\ 
21 & 49.2 & 441 & 1,033.2 \\ 
23 & 62.1 & 529 & 1,428.3 \\ [1ex]
\Sigma x=87 & \Sigma y=200.5 & \Sigma x^2=1,525 & \Sigma xy=3,641.3 
\end{tabular}
\end{center}$
</span>
Recall that the equation of the regression line is given by
$y=a+bx$
where
$a= \frac{(\Sigma y)(\Sigma x^2)-(\Sigma x)(\Sigma xy)}{n(\Sigma x^2)-(\Sigma x)^2} = \frac{200.5(1,525)-87(3,641.3)}{6(1,525)-(87)^2} \\ \\ = \frac{305,762.5-316793.1}{9,150-7,569} = \frac{-11,030.6}{1,581} =-6.977$
and
$b= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{n(\Sigma x^2)-(\Sigma x)^2} = \frac{6(3,641.3)-(87)(200.5)}{6(1,525)-(87)^2} \\ \\ = \frac{21,847.8-17,443.5}{9,150-7,569} = \frac{4,404.3}{1,581} =2.7858$

Thus, the equation of the regresson line is given by
$y=-6.977+2.7858x$

The graph of the regression line is attached.

Using the equation, we can predict the percent donated in the year 2015. Recall that 2015 is 35 years after 1980. Thus x = 35.

The percent donated in the year 2015 is given by
$-6.977+2.7858(35)=-6.977+97.503=90.526$

Therefore, the percent donated in the year 2015 is predicted to be 90.5

7 0

3 years ago

Find the value of y so that WX is perpendicular to YZ

Alexxandr [17]

step 1

Find out the slope WX

W(2,-3) and X(-4,9)

m=(9+3)/(-4-2)

m=12/-6

m=-2

step 2

Find out the slope YZ

Y(5,y) and Z(-1,1)

m=(1-y)/(-1-5)

m=(1-y)/-6

m=(y-1)/6

step 3

Remember that

If two lines are perpendicular

then

their slopes are negative reciprocal

that means

(y-1)/6=1/2 -----> because the negative reciprocal of -2 is 1/2

solve for y

2y-2=6

2y=6+2

2y=8

8 0

9 months ago

Find the value of the expression 2x3 + 3y2 − 17 when x = 3 and y = 4. 26 85 943 1,927

Jet001 [13]

Answer:

85

Step-by-step explanation:

2x^3 + 3y^2 − 17

2(3)^3 + 3(4)^2 − 17

2*27 + 3*16 -17

54 + 48 -17 = 85

4 0

2 years ago

Read 2 more answers

infra made a chicken dish for dinner she at an 18 Oz package of vegetables in a 14 oz package of rice to 14 oz of chicken what w

JulsSmile [24]

18 + 14 + 14 = 46 oz

Then there are 16 oz in a pound so we take 46 oz ÷ 16 oz and we get 46/16 in fraction form. Then we simplify this out and get 2 7/8 pounds.

6 0

3 years ago

A zucchini plant in Darnell’s garden was 10 centimeters tall when it was first planted. Since then, it has grown approximately 0

Mariulka [41]

Answer:

Let's start with part B. if it was originally 10 cm tall and it goes up 0.5 cm. each day, then we know that to go up one cm it needs two days. With that information we can say that 8*2 = 16. So it needs 17 days to go up 8.5 cm which would make it 18.5 cm tall.

Step-by-step explanation:

f(x) = 0.5x + 10

0.5x + 10 = 18.5

0.5x = 18.5 - 10

0.5x = 8.5

x = 8.5/0.5

x = 17 days

6 0

2 years ago