All categories

3 years ago

Work out the unknown angles. Give reasons for each answer.

Mathematics

1 answer:

zalisa [80]3 years ago

8 0

A)

Because the sum of angles in a triangle must equal 180° we can say:

62+α+90=180

α+152=180

α=28°

b)

Since all sides have equal length, all angles must have equal measure. (This is an equilateral triangle). And again, because the sum of the angle must be 180° we can say:

b+b+b=180

3b=180

b=60°

You might be interested in

Find the measure of a A. 44 B. 88 C. 46 D. 90

Rina8888 [55]

<h3>Answer: Choice A. 44</h3>

====================================================

Explanation:

Since we have a circle, the segments extending from the center outward to the edge of the circle are radius segments. Any two radii of the same circle are the same length. The triangle on the left with the 92 degree angle is isosceles. Any isosceles triangle has exactly two side lengths that are the same, which leads to the base angles being the same as well.

For the triangle on the left with angles a,b,92, the base angles are 'a' and 'b'. So a = b.

For any triangle, the angles add to 180

a+b+92 = 180

a+a+92 = 180 ... Replace b with 'a'

2a+92 = 180

2a = 180-92

2a = 88

a = 88/2

a = 44

angle b is also 44 as well

a+b+92 = 44+44+92 = 180

4 0

4 years ago

Read 2 more answers

construct a 90% confidence interval of the population proportion using the giver information x=74 n=150

FrozenT [24]

Answer:

The 90% confidence interval of the population proportion is (0.43, 0.56).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population proportion <em>p</em> is:

$CI=\hat p\pm z_{\alpha/2}\ \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The information provided is:

<em>X</em> = 74

<em>n</em> = 150

Confidence level = 90%

Compute the value of sample proportion as follows:

$\hat p=\frac{X}{n}=\frac{74}{150}=0.493$

Compute the critical value of <em>z</em> for 90% confidence level as follows:

$z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645$

*Use a <em>z</em>-table.

Compute the 90% confidence interval of the population proportion as follows:

$CI=\hat p\pm z_{\alpha/2}\ \sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.493\pm 1.645\times \sqrt{\frac{0.493(1-0.493)}{150}}\\\\=0.493\pm 0.0672\\\\=(0.4258,\ 0.5602)\\\\\approx (0.43,\ 0.56)$

Thus, the 90% confidence interval of the population proportion is (0.43, 0.56).

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=6%20%5Csqrt%7B2%7D%20%20-%204%20%5Csqrt%7B3%7D%20%20%2B%20%20%7C3%20%5Csqrt%7B8%7D%20-%208%20%

natima [27]

Answer:

8√3 ≈ 13.86

Step-by-step explanation:

6√2 - 4√3 + | 3√(2²•2) -8√3 | + 2√2²•3

Every 2² get our from the square root and loses the ² :

6√2 -4√3 + | 2•3√2 -8√3 | + 2•2√3

Solve the multiplications and taking of the | | , the signal inside it changes:

6√2 - 4√3 +8√3 -6√2 +4√3

Now you group the similar terms and solve the possible operations:

6√2 - 6√2 +4√3 - 4√3 + 8√3

8√3 ≈ 13.86

3 0

3 years ago

Read 2 more answers

Identify the lines that are perpendicular

Ilia_Sergeevich [38]

Second and fourth lines are perpendicular.

3 0

4 years ago

The class scores of a history test have a normal distribution with a mean Mu = 79 and a standard deviation Sigma = 7. If Opal’s

e-lub [12.9K]

Using the normal distribution, we got that expression for the z-score of her test score is

$z= \frac{72-29}{7} \\\\z=-7/7\\\\z=-1$

<h3>What is Normal Probability Distribution?</h3>

it's a type of probability distribution which is symmetric about the mean, it gives data near the mean are more frequent than data far from the mean.

Given that mean = $\mu=79$