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2 years ago

A side of the triangle below has been extended to form an exterior angle of 164". Find

Mathematics

1 answer:

Arada [10]2 years ago

3 0

Given:

Measure of exterior angle = 164°

The measure of opposite interior angles are x° and 53°.

To find:

The value of x.

Solution:

According to the Exterior Angle Theorem, in a triangle the measure of an exterior angles is always equal to the sum of measures of two opposite interior angles.

Using Exterior Angle Theorem, we get

$x^\circ+53^\circ=164^\circ$

$x^\circ=164^\circ-53^\circ$

$x^\circ=111^\circ$

$x=111$

Therefore, the value of x is 111.

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Lesha wants to prove that the measures of the 3 angles in a triangle always have a sum of 180°. She decided to prove

levacccp [35]

Answer:

Step-by-step explanation:

Reflecting it across the lines will bring the triangle on to the other triangles. This will show that when the triangle goes under a transformation such as reflection, the angles will stay the same.

5 0

2 years ago

Suppose monthly rental prices for a one-bedroom apartment in a large city has a distribution that is skewed to the right with a

omeli [17]

Answer:

a) Nothing, beause the distribution of the monthly rental prices are not normal.

b) 1.43% probability that the sample mean rent price will be greater than $900

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

(a) Suppose a one-bedroom rental listing in this large city is selected at random. What can be said about the probability that the listed rent price will be at least $930?

Nothing, beause the distribution of the monthly rental prices are not normal.

(b) Suppose a random sample 30 one-bedroom rental listing in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the probability that the sample mean rent price will be greater than $900?

Now we can apply the Central Limit Theorem.

$\mu = 880, \sigma = 50, n = 30, s = \frac{50}{\sqrt{30}} = 9.1287$

This probability is 1 subtracted by the pvalue of Z when X = 900.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{900 - 880}{9.1287}$

$Z = 2.19$

$Z = 2.19$ has a pvalue of 0.9857

1 - 0.9857 = 0.0143

1.43% probability that the sample mean rent price will be greater than $900

8 0

3 years ago

What value of n makes this expression equals to 6 <br> 3n-(2+n)

coldgirl [10]

N = 4
(3)(4)-(2+4) = 12 - 6 = 6

6 0

2 years ago

A chess club with 55 members is electing a new president. Lucy received 33 votes. What percentage of the club members voted for

bonufazy [111]

You would put it up into proportions so 33 over 55 equals x over 100. Then you would cross multiply so 55x=3300. Then you would divide 3300 by 55 and get 60%.

4 0

2 years ago

Solve 2csc^2x-2cscx-1=0 <br> for 0° ≤ x ≤ 360°

umka21 [38]

Answer:

Step-by-step explanation:

2 csc²x-2 csc x-1=0

$\frac{2}{sin^2x} -\frac{2}{sin x} -1=0\\multiply~by~sin^2x\\2-2sin~x-sin^2x=0\\sin^2x+2sinx-2=0\\sin ~x=\frac{-2 \pm\sqrt{2^2-4*1*(-2)} }{2*1} \\=\frac{-2 \pm\sqrt{4+8} }{2} \\=\frac{-2 \pm\sqrt{4*3} }{2} \\=\frac{-2 \pm2\sqrt{3} }{2} \\=-1\pm\sqrt{3} \\|sin~x| \le ~1\\so~sin~x=-1+\sqrt{3} \\sin~x=\sqrt{3} -1\\x=sin^{-1}(\sqrt{3} -1) \approx 47.06^\circ,180-47.06\\or~x=47.06^\circ,132.94^\circ$

6 0

2 years ago