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1 year ago

6

Find the value of x in the given figure of a triangle

1 answer:

Luba_88 [7]1 year ago

5 0

In the triangle ABE

step 1

Find out the measure of angle AEB

m by form a linear pair

mm

step 2

Find out the measure of angle ABE

m by alternate interior angles

step 3

Find out the measure of angle x

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

msubstitute given values

x+100+30=180

x=180-130

<h2>x=50 degrees</h2>

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A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

<em>So, the 95% confidence interval is (46.4, 53.6)</em>

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

<em>So, the 95% confidence interval is (47.9, 52.1)</em>

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

<em>Notice that the margin of error decreases when the sample size increases.</em>

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3 years ago

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matrenka [14]

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Step-by-step explanation:

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3 years ago

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There are 100 pieces of candy in a

PIT_PIT [208]

Answer:

d

Step-by-step explanation:

because 100*9 is 900

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2 years ago

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Solve the system of equations given below

Fantom [35]

$y-15=3x \\-2x+5y=-3 \\ \\-2x+y-15=0 /\cdot2 \\-2x+5y-3=0 /\cdot(-2) \\ \\-4x+2y-30=0 \\4x-10y+6=0 \\ \\-8y-24=0 \\\boxed{y=-3} \\ \\-3-15=3x \\\boxed{x=-6}$

The answer is C. (-6, -3)

Hope this helps.

r3t40

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3 years ago

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A computer uses 239 watts per hour. how many watts would it uses if it is on for 8 days.

madam [21]

45888
239 watts per hour x 24 hours x 8 days

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3 years ago