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2 years ago

What is the measurement of angle 1 plz help me !

Mathematics

1 answer:

Evgen [1.6K]2 years ago

6 0

Answer:

ANGLE 1 = 40°

Step-by-step explanation:

angle 1 = angle 2 ------(alternate interior angles)

2x + 20 = 3x + 10

20 - 10 = 3x - 2x

x = 10.

Angle 1 = 2x + 20 = 2(10) + 20 = 20 + 20 = 40°.

HOPE IT HELPS!!!

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$a)\ \ \bar x_m-\bar x_f=67.03\\\\b)\ \ E=15.7416\\\\c)\ \ CI=[51.2884, \ 82.7716]$

Step-by-step explanation:

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$n_m=41\ , \ \sigma_m=33, \bar x_m=135.67\\\\n_f=37. \ \ ,\sigma_f=20, \ \ \bar x_f=68.64$

#The point estimator of the difference between the population mean expenditure for males and the population mean expenditure for females is calculated as:

$\bar x_m-\bar x_f\\\\\therefore \bigtriangleup\bar x=135.67-68.64\\\\=67.03$

Hence, the pointer is estimator 67.03

b. The standard error of the point estimator, $\bar x_m-\bar x_f$ is calculated by the following following:

$\sigma_{\bar x_m-\bar x_f}=\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}$

-And the margin of error, E at a 99% confidence can be calculated as:

$E=z_{\alpha/2}\times \sigma_{\bar x_m-\bar x_f}\\\\\\=z_{0.005}\times\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\\\=2.575\times \sqrt{\frac{33^2}{41}+\frac{20^2}{37}}\\\\\\=15.7416$

Hence, the margin of error is 15.7416

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$\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}$

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$CI=\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\=(135.67-68.64)\pm 15.7416\\\\=67.03\pm 15.7416\\\\=[51.2884, \ 82.7716]$

Hence, the 99% confidence interval is [51.2884,82.7716]

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2 years ago

For ΔABC, ∠A = 2x - 2, ∠B = 2x + 2, and ∠C = 5x. If ΔABC undergoes a dilation by a scale factor of 1 2 to create ΔA'B'C' with ∠A

Zolol [24]

<h3>Answer:</h3>

A) ∠A = ∠A' = 38° and ∠B = ∠B' = 42°

<h3>Explanation:</h3>

The sum of angles in ∆ABC is 180°, so ...

... (2x -2) + (2x +2) + (5x) = 180

... 9x = 180

... x = 20

and the angles of ∆ABC are ∠A = 38°, ∠B = 42°, ∠C = 100°.

___

The sum of angles of ∆A'B'C' is 180°, so ...

... (58 -x) +(3x -18) +(120 -x) = 180

... x +160 = 180

... x = 20

and ∠A' = 38°, ∠B' = 42°, ∠C' = 100°.

_____

The values of angle measures of ∆ABC match those of ∆A'B'C', so we can conclude ...

... A) ∠A = ∠A' = 38° and ∠B = ∠B' = 42°

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3 years ago