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zaharov [31]
2 years ago
10

Please help for 50 POINTS!!!!

Mathematics
1 answer:
Debora [2.8K]2 years ago
7 0

Solution:

<u>We know that:</u>

  • Sum of interior angles of triangle: 180°
  • Those 2 bars drawn on GH and IH defines that GH = IH.

<u>This means that:</u>

  • The triangle is an isosceles triangle.
  • The bottom two angles are equal.

Equation created: 58 + x + x = 180

<u>Simplify the LHS.</u>

  • 58 + x + x = 180
  • => 58 + 2x = 180

<u>Subtract 58 both sides.</u>

  • 58 - 58 + 2x = 180 - 58
  • => 2x = 122
  • => x = 61

Thus, the measure of ∠GIH is 61°.

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Answer:

The linear regression equation that represents  the set of data is:

y=1083.48+23.73x

The predicted number of new cases for 2013 is 1368.

Step-by-step explanation:

The general form of a linear regression is:

y=a+bx

Here,

<em>y</em> = dependent variable

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<em>a</em> = intercept

<em>b</em> = slope

Compute the values of <em>a</em> and <em>b</em> as follows:

\begin{aligned}        a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} =             \frac{ 6857 \cdot 55 - 15 \cdot 17558}{ 6 \cdot 55 - 15^2} \approx 1083.476 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}        = \frac{ 6 \cdot 17558 - 15 \cdot 6857 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 23.743\end{aligned}

The linear regression equation that represents  the set of data is:

y=1083.48+23.73x

Compute the predicted value of the number of new cases for 2013 (i.e. <em>x</em> = 12) as follows:

y=1083.48+23.73x

  =1083.48+(23.73\times12)\\\\=1083.48+284.76\\\\=1368.24\\\\\approx 1368

Thus, the predicted number of new cases for 2013 is 1368.

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