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3 years ago

Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.

Mathematics

2 answers:

Varvara68 [4.7K]3 years ago

6 0

Answer:

The answer is step 3

Step-by-step explanation:

It is because Ernesto didn't distribute correctly, he only distributed 3 to the y and not the 7.

lukranit [14]3 years ago

5 0

The answer is Step 3: 3y + 7 _ 2y = 8.

Ernesto made a mistake in the step 3 because he did not multiply 3 and 7.
The correct order of steps is:

Step 1: x = y + 7
Step 2: 3(y + 7) - 2y = 8
Step 3: 3y + 3·7 - 2y = 8
Step 4: y + 21 = 8
Step 5: y = - 13

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75 is what percent of 100?

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Answer:

75 is 75% of 100

Step-by-step explanation:

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The equation for the cross-section of a parabolic satellite TV dish is stated below, measured in inches. How far is the focus fr

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The coordinates of the focus are (h,k+1/4a)(h,k+1/4a)

y=1/38*x^2
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so if we put values to find focus
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3 years ago

An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 m

SVETLANKA909090 [29]

Answer:

a) $y=-6.254 x +75.064$

b) r =-0.932

The % of variation is given by the determination coefficient given by $r^2$ and on this case $-0.932^2 =0.8687$ , so then the % of variation explained by the linear model is 86.87%.

Step-by-step explanation:

Assuming the following dataset:

Monthly Sales (Y) Interest Rate (X)

22 9.2

20 7.6

10 10.4

45 5.3

Part a

And we want a linear model on this way y=mx+b, where m represent the slope and b the intercept. In order to find the slope we have this formula:

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

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:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=278.65-\frac{32.5^2}{4}=14.5875$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=696.9-\frac{32.5*97}{4}=-91.225$

And the slope would be:

$m=\frac{-91.225}{14.5875}=-6.254$

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

$\bar x= \frac{\sum x_i}{n}=\frac{32.5}{4}=8.125$

$\bar y= \frac{\sum y_i}{n}=\frac{97}{4}=24.25$

And we can find the intercept using this:

$b=\bar y -m \bar x=24.25-(-6.254*8.125)=75.064$

So the line would be given by:

$y=-6.254 x +75.064$

Part b

For this case we need to calculate the correlation coefficient given by:

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

$r=\frac{4(696.9)-(32.5)(97)}{\sqrt{[4(278.65) -(32.5)^2][4(3009) -(97)^2]}}=-0.937$

So then the correlation coefficient would be r =-0.932

The % of variation is given by the determination coefficient given by $r^2$ and on this case $-0.932^2 =0.8687$ , so then the % of variation explained by the linear model is 86.87%.

6 0

4 years ago

The object below is made up of two rectangular prisms. What is the VOLUME, in cubic feet, of the object

faltersainse [42]

Answer:

60ft³

Step-by-step explanation:

you have to divide the object into smaller, more manageable objects

ill divide it into:

2x2x8 and 7x2x2

the formula for finding volume is l*w*h

the first one is 32

the second one is 28

28 + 32 = 60

6 0

3 years ago