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PSYCHO15rus [73]
3 years ago
5

The figure shows two parallel lines PQ and ST cut by the transversals PT and QS.

Mathematics
2 answers:
Sonbull [250]3 years ago
5 0

Answer:

Triangle PQR is similar to triangle TSR because measure of angle 3 equals measure of angle 4 and measure of angle 1 equals measure of angle 5

Step-by-step explanation:

wariber [46]3 years ago
3 0


answer is 

<span>Triangle PQR is similar to triangle TSR because measure of angle 3 equals measure of angle 4 and measure of angle 1 equals measure of angle 5</span>
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True

Step-by-step explanation:

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I want to know 301-200
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301 minus 200? If so, that is 101
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(0,6) (-4,-9)
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Answer:

d=√(16+225)

d=√241

d=15.5

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6 0
3 years ago
Area of a regular polygon with 100 sides and a perimeter of 100 units
babunello [35]
The area is 795.5 sq units.

We first find the apothem, using the formula:
a=\frac{s}{2\tan{(\frac{180}{n})}}

Since there are 100 sides, all sides are equal and the perimeter is 100, the side length, s, is 1:
a=\frac{1}{2\tan{(\frac{180}{100})}}=15.91

Now we find the area of the polygon.  Since there are 100 sides, there will be 100 equal triangles using the center as a vertex.  The formula for the area of a triangle is A=1/2bh; in this case, b is s, the side length, and h is a, the apothem. This gives us:
A=100(1/2)(s)(a) = 100(1/2)(1)(15.91) = 795.5.
5 0
3 years ago
The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 265 minu
pochemuha

Answer:

a) 0.691 = 69.1% probability that a battery lasts more than four hours

b) 25% value = 231

75% value = 299

c) 183 minutes

Step-by-step explanation:

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.

In this problem, we have that:

\mu = 265, \sigma = 50

a) What is the probability that a battery lasts more than four hours?

4 hours = 4*60 = 240 minutes

This is 1 subtracted by the pvalue of Z when X = 240. So

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

Z = \frac{240 - 265}{50}

Z = -0.5

Z = -0.5 has a pvalue of 0.309

1 - 0.309 = 0.691

0.691 = 69.1% probability that a battery lasts more than four hours

b) What are the quartiles (the 25% and 75% values) of battery life?

25th percentile:

X when Z has a pvalue of 0.25. So X when Z = -0.675

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

-0.675 = \frac{X - 265}{50}

X - 265 = -0.675*50

X = 231

75th percentile:

X when Z has a pvalue of 0.75. So X when Z = 0.675

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

0.675 = \frac{X - 265}{50}

X - 265 = 0.675*50

X = 299

25% value = 231

75% value = 299

c) What value of life in minutes is exceeded with 95% probability?

The 100-95 = 5th percentile, which is the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.

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

-1.645 = \frac{X - 265}{50}

X - 265 = -1.645*50

X = 183

8 0
4 years ago
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