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11111nata11111 [884]

1 year ago

11

In a parallelogram PQRS, if angle P = (2x+25) degrees and angle Q = (3x-5) degrees, then write the measures of angle S and angle

R.

1 answer:

krek1111 [17]1 year ago

6 0

Consecutive angles of a parallelogram are supplementary, so:

$2x+25+3x-5=180\\5x+20=180\\5x=160\\x=32$

This means $m\angle P=2(32)+25=89^{\circ}$ and that $m\angle Q=3(32)-5=91^{\circ}$ .

Since opposite angles of a parallelogram are congruent,

$\boxed{m\angle S=91^{\circ}, m \angle R=89^{\circ}}$

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Question 1(Multiple Choice Worth 4 points)

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3 years ago

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vfiekz [6]

Answer:

$\displaystyle y=-0.927x+13.63$

Step-by-step explanation:

<u>Simple Linear Regression </u>

It a function that represents the relationship between two or more variables in a given data set. It uses the method of the least-squares regression line which minimizes the error between the estimate function and the real data.

Let's compute the best-fit line for the data

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$y=\{14,11,4,2,1\}$

First, we find the sums

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$\displaystyle \sum y=14+11+4+2+1=32$

Then, we compute the averages values

$\displaystyle \bar{x}=\frac{39}{5}=7.8$

$\displaystyle \bar{y}=\frac{32}{5}=6.4$

We will also compute the sums of the cross-products and the sum of the squares

$\displaystyle \sum xy=(1)(14)+(5)(11)+(6)(4)+(12)(2)+(15)(1)=137$

$\displaystyle \sum x^2=1^2+5^2+6^2+12^2+15^2=1+25+36+144+225$

$\displaystyle \sum x^2=431$

We will compute Sxy and Sxx

$\displaystyle S_{xy}=\sum xy-\frac{\sum x\ \sum y}{n}$

$\displaystyle S_{xy}=137-\frac{(39)(32)}{5}$

$\displaystyle S_{xy}=-117.6$

$\displaystyle S_{xx}=\sum x^2-\frac{(\sum x)^2}{n}$

$\displaystyle S_{xx}=431-\frac{39}{5}^2=126.8$

The slope of the linear regression function is given by

$\displaystyle m=\frac{S_{xy}}{S_{xx}}=\frac{-117.6}{126.8}=-0.927$

The y-intercept ot the linear function is

$\displaystyle b=\bar{y}-b\bar{x}=6.4-(-0.927)(7.8)$

$\displaystyle b=13.63$

Thus the best-fit line is

$\displaystyle y=-0.927x+13.63$

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