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3 years ago

Can you help me with the first two questions?

Mathematics

2 answers:

melisa1 [442]3 years ago

7 0

$1.\\\$55\ 000-\$1\ 000=\$54\ 000\\\\\$54\ 000:2=\$27\ 000\\\\\\Answer:B$

$2.\\-4(x-11)=16\\\\-4\cdot x-4\cdot(-11)=16\\\\-4x+44=16\ \ \ /:(-4)\\\\-4x:(-4)+44:(-4)=16:(-4)\\\\x-11=-4\\\\Answer:G$

marta [7]3 years ago

7 0

Question #1:
Since it is unknown how much they paid for the original painting, we'll use x to represent that. 2x+1000 is equal to 55,000, so that is our equation.
2x+1000=55,000
2x=54,000
x=27,000
The Leungs originally paid $27,000 (answer choice B)

Question #12:
-4(x-11)=16
Apply the distributive property.
-4x+44=16
-4x=--28
x=7
Since x=7, let's figure out which answer choice can be possible by subsituting the x in each answer choice with 7.
Answer choice F: Does 7-11=4? No, so this answer can't be correct.
Answer choice G: Does 7-11=-4? Yes! This answer is correct.
Answer choice H: Does -28-11=16? No, so this answer can't be correct.
Answer choice I: Does -28+44=64? No, so this answer can't be correct.
It is answer choice G.

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1 rod was left over.

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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

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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

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

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Therefore there is no solution or it is inconsistent

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