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3 years ago

Use the figure below and determine the angle measures. what is the measure of angle G?

Mathematics

1 answer:

bogdanovich [222]3 years ago

8 0

Answer:

Step-by-step explanation:

First we want to understand the Base Angles Theorem

The Base Angles Theorem tells us that the base angles or the two bottom angles of an isosceles triangle are congruent.

Using this theorem, we can say that angle A and angle G are congruent meaning m∠A = m∠G. We can then write both of them as x.

We can create the equation ∠N + ∠A + ∠G = 180 degrees.

Knowing ∠N and knowing ∠A + ∠G = 2x, we can rewrite the equation into

90 + 2x = 180

We can then solve for x,

90 + 2x - 90 = 180 - 90

2x = 90

2x / 2 = 90 / 2

x = 45 degrees

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Answer:

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Have a lovely rest of your day/night, and good luck with your assignments! ♡

~ ren ⚘

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3 years ago

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4 years ago

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3 years ago

A random sample of 60 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact te

pentagon [3]

Answer:

The 95% confidence interval on the true proportion of helmets of this type that would show damage from this test is (0.169, 0.397).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 60, \pi = \frac{17}{60} = 0.283$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.283 - 1.96\sqrt{\frac{0.283*0.717}{60}} = 0.169$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.283 + 1.96\sqrt{\frac{0.283*0.717}{60}} = 0.397$

The 95% confidence interval on the true proportion of helmets of this type that would show damage from this test is (0.169, 0.397).

6 0

3 years ago