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3 years ago

Problem:

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

4 0

Answer:

The answer is: <em><u>y = 9.25x </u></em>

Step-by-step explanation:

Let the equation for the proportionality relation is y = mx .......... (1), where y represents the money that Craig earns for a duty of x hours.

Here, m is the constant of proportionality and we have to find its value.

Given that Craig earns $37 for 4 hours duty.

So, from equation (1), we have 37 = 4m, ⇒ m = 9.25

Therefore, the equation becomes y = 9.25x. (Answer)

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A coach is assessing the correlation between the number of hours spent practicing and the average number of points scored in a g

cricket20 [7]

Answer:

a) $r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

b) $m=\frac{90}{15}=6$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

c) For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

Step-by-step explanation:

We have the following data:

Number of hours spent practicing (x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score in the game (y) 5 8 11 14 17 20 23 26 29

Part a

The correlation coefficient is given:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=9 $\sum x = 18, \sum y = 153, \sum xy = 396, \sum x^2 =51, \sum y^2 =3141$

$r=\frac{9(396)-(18)(153)}{\sqrt{[9(51) -(18)^2][9(3141) -(153)^2]}}=1$

We have a perfect linear relationship between the two variables

Part b

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=51-\frac{18^2}{9}=15$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=396-\frac{18*153}{9}=90$

And the slope would be:

$m=\frac{90}{15}=6$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{18}{9}=2$

$\bar y= \frac{\sum y_i}{n}=\frac{153}{9}=17$

And we can find the intercept using this:

$b=\bar y -m \bar x=17-(6*2)=5$

So the line would be given by:

$y=6 x +5$

Part c

For this case the slope indicates that for each increase of the number of hours in 1 unit we have an expected increase in the score about 6 units.

And the intercept 5 represent the minimum score expected for any game

5 0

3 years ago

Find the nth term for the sequence 8, 14, 20, 26

harina [27]

It adds six every time so the answer is 56

4 0

3 years ago

What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)?

irakobra [83]

1.5x+6-3=4.5(x-2)
1.5x+6-3=4.5x-9
1.5x+3=4.5x-9
1.5x-4.5x+3=-9
1.5x-4.5x=-9-3
-3x=-9-3
-3=-12

X=4

6 0

3 years ago

Read 2 more answers

If a space of 18 inches is allowed for each person, how many persons can be seated in a row of bleacher seats 90 feet long?

REY [17]

Answer:

31 people

Step-by-step explanation:

think of it like a line,

first person at zero then add 3 feet per person so...

1 + 90/3 = 31 people

kinda funny that the problem isnt accounting for the size of the people

6 0

4 years ago

Alycia created a personal budget for the upcoming month. She received a salary of $2,700 and had various fixed and variable expe

Luda [366]

Answer:

C. 32%

Step-by-step explanation:

First, you have to determine the amount they spent on entertainment and food:

Salary $2,700

Taxes: 10%: $270

Fixed expenses: $1,161

Savings: $405

$2,700-$270-$1,161-$405= $864

Alycia spent $864 on entertainment and food. Now, you have to find the percent of her income that this amount represents:

($864/$2,700)*100= 32%

According to this, the answer is that the percent of her income that was spent on entertainment and food is 32%.

8 0

3 years ago