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3 years ago

I don’t understand how to get x and y

Mathematics

1 answer:

DIA [1.3K]3 years ago

8 0

Answer:

x is approximately 7.97 or 8.0

y is approximately 6.9

Step-by-step explanation:

We have a triangle:

side a = y

side b = 4

side c = x

We can use the trigonometric function tangent which relates opposite and adjacent sides of the triangle in respect with a certain angle.

In this case we'll be using angle of 60º

y is opposite to 60º and 4 is adjacent

$tan=\frac{opposite}{adjacent}$

Solve for opposite;

$opposite=adjacent*tan\\o=4*tan60\\o=6.9$

This is the value of y.

To find x, we can use the pythagorean theorem.

$c^2=a^2+b^2\\c=\sqrt{a^2+b^2} \\c=\sqrt{(4)^2+(6.9)^2} \\c=\sqrt{16+47.61}\\ c=\sqrt{63.61}\\ c=7.97$

7.97 ≅ 8.0

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What is the volume, in cubic inches, of a rectangular prism with a height of 19 inches, a width of 11 inches, and a length of 4

jolli1 [7]

Answer:

836

Step-by-step explanation:

4 times 19 times 11

7 0

2 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%.

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Yuliya22 [10]

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vfiekz [6]

Step-by-step explanation:

I think the answer is:

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