Can two vertical angles form a linear pair?

1 answer:

6 0

Adjacent Angles are two angles that share a common vertex, a common side, and no common interior points. (They share a vertex and side, but do not overlap.) A Linear Pair is two adjacentangles whose non-common sides form opposite rays. ... ∠1 and ∠3 are not vertical angles (they are a linear pair).

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The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are r

Dimas [21]

Answer:

The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

The standard deviation is the square root of the variance. So

$\sigma = \sqrt{0.16} = 0.4$

Then

$M = 1.96*\frac{0.4}{\sqrt{400}} = 0.0392$

The lower end of the interval is the mean subtracted by M. So it is 1.75 - 0.0392 = 1.7108m

The upper end of the interval is the mean added to M. So it is 1.75 + 0.0392 = 1.7892m

The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.

4 0

4 years ago

A rectangular house measuring 50 feet by 24 feet is to have a gravel pathway of constant width built all around it. There is eno

Maksim231197 [3]

First, we determine the area of the rectangular house by multiplying the length by the width. That is,
area of the house = (50 ft)(24 ft) = 1200 ft²
Given that all sides of the house should have the pathway, the length of the house plus the pathway should be 50+2x and the new width would be 24+2x. The new area minus the original area of the house should not be more than 345 ft². Thus, the equation would be,
(50+2x)(24+2x) - 1200 ≤ 345

3 0

3 years ago

What is the slope of the line that passes through the pair of point? (5, 7), (2, 1)

choli [55]

The slope of the line that passes through the pair of point (5, 7), (2, 1) is 2

Solution:

Given that line that passes through the pair of point (5, 7), (2, 1)

To find: slope of the line

The slope of line is given as:

For a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ slope is given as: