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Tresset [83]
2 years ago
11

How to find the altitude Of A Trapezoid Without Knowing The Area

Mathematics
1 answer:
Rudik [331]2 years ago
3 0
A=1/2 (b1+b 2)(h) is the area of a trapezoid
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The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 104 inches, and a standard
dsp73

Answer:

91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

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}}

In this problem, we have that:

\mu = 104, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2

What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

This is the pvalue of Z when X = 106.8. So

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

By the Central Limit Theorem

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

Z = \frac{106.8 - 104}{2}

Z = 1.4

Z = 1.4 has a pvalue of 0.9192

0.9192 = 91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

8 0
3 years ago
The endpoints of PQ are P(2, 0) and Q (4, 2). Find the coordinates of midpoint PQ.
lawyer [7]

Answer:

Step-by-step explanation:

Parameterize the ellipse as (acos∙,bsin∙). Take points P:=(acosp,bsinp) and Q:=(acosq,bsinq) on the ellipse, with midpoint M:=(P+Q)/2.

If |PQ|=2k, then

a2(cosp−cosq)2+b2(sinp−sinq)2=4k2

The coordinates of M are

xy==a2(cosp+cosq)b2(sinp+sinq)

4 0
3 years ago
Need help with this quiz asap due by today
drek231 [11]

Answer:

5

Step-by-step explanation:

So first you need to what is over the four. 6x2=12/4. Okay so what does that equal? 12/4=3. Now we need to solve the first equation.  3+5=8. And the last part. 8-3=5

4 0
2 years ago
Read 2 more answers
12. Algebra There are 92 students in the third and fourth grades at Johnsonville Elementary. Of these, 47 are in fourth grade. W
Fudgin [204]

x + 47 = 92.   <--- x represents the number of 3rd graders

x +47-47 = 92-47

x=45

There are 45 third grader. Hope this helped!

4 0
3 years ago
Read 2 more answers
A rectangular prism has the dimensions 8 feet by 3 feet by 5 feet. What is the surface area of the prism?
raketka [301]

Answer:

A=158

Step-by-step explanation: SA = 2 × l × w  +  2 × l × h  +  2 × w × h

8 0
2 years ago
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