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3 years ago

P=1/4q+8 make q the subject

Mathematics

1 answer:

Daniel [21]3 years ago

6 0

Answer:

q = 4p - 32

Step-by-step explanation:

P = 1/4q + 8

Making q the subject

P - 8 = 1/4q

Divide both sides by 1/4

q = (p - 8) ÷ 1/4

= (P - 8) × 4/1

= 4p - 32

q = 4p - 32

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Assume you have noted the following prices for books and the number of pages that each book contains. Book Pages (x) Price (y) A

belka [17]

Answer:

a) $y=0.00991 x +1.042$

b) $r^2 = 0.7503^2 = 0.563$

c) $r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

Step-by-step explanation:

Data given

x: 500, 700, 750, 590 , 540, 650, 480

y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50

Part a

We want to create a linear model like this :

$y = mx +b$

Wehre

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

And:

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

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

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=2595100-\frac{4210^2}{7}=63085.714$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=30095-\frac{4210*49}{7}=625$

And the slope would be:

$m=\frac{625}{63085.714}=0.00991$

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

$\bar x= \frac{\sum x_i}{n}=\frac{4210}{7}=601.429$

$\bar y= \frac{\sum y_i}{n}=\frac{49}{7}=7$

And we can find the intercept using this:

$b=\bar y -m \bar x=7-(0.00991*601.429)=1.042$

And the line would be:

$y=0.00991 x +1.042$

Part b

The correlation coefficient is given by:

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

For our case we have this:

n=7 $\sum x = 4210, \sum y = 49, \sum xy = 30095, \sum x^2 =2595100, \sum y^2 =354$

$r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

The determination coefficient is given by:

$r^2 = 0.7503^2 = 0.563$

Part c

$r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503$

4 0

3 years ago

Lucy wants to be exempt from her semester exam. In order for that to happen, she has to average an 85 over 3 test grades. Her fi

anastassius [24]

Answer:

<em>Grades to be scored in 3rd exam = 88</em>

Step-by-step explanation:

Given that average of 3 numbers is 85.

First two numbers are 81 and 86.

To find:

3rd number so that average is 85

Solution:

Let the third number = $x$

Formula for average is:

$Average = \dfrac{Sum\ of\ numbers}{Total\ count\ of\ numbers}$

Here, sum of numbers = $81+86+x =167+x$

Total count of numbers = 3

$85 = \dfrac{167+x}{3}\\\Rightarrow x=255-167\\\Rightarrow \bold{x=88}$

<em>Grades to be scored in 3rd exam = 88</em>

8 0

3 years ago

A painter earns $15 per hour. What is the minimum number of hours he must work to earn at least $200? Write an inequality to rep

IRISSAK [1]

So you know that he earns $15 per hour so we can write that as 15h, h = # of hours worked

We also know he has to earn AT LEAST $200, so putting all this together we form the inequality(=< means less than or equal to): 15h =< 200

so now we have to solve for h (number of hours worked):

15h =< 200

(divide both sides by 15)

h =< 13 1/3

So, the painter must work a minimum of 13 and 1/3 hours to earn at least $200.

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2 years ago

Read 2 more answers

Please check what i have Quickly

RUDIKE [14]

Break the figure into a triangle and a rectangle.

The triangle has a base of 6 and a height of 3, so the area is 6*3/2 = 18/2 = 9
The rectangle has a length of 5 and a height of 6, so 6*5 = 30 is the area of the rectangle.

The total area is 30+9 = 39

Answer: 39

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4 years ago

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How many solutions are there to the equation below? -46 = 3x + 7x

horsena [70]

-46=3x+7x
-46=10x
X= 10/(-46)
X=-5/23

Therefore, the equation only has one solution

8 0

3 years ago

P=1/4q+8 make q the subject​

P=1/4q+8 make q the subject