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VladimirAG [237]
3 years ago
15

What is the area of this figure? Enter your answer in the box below.​

Mathematics
1 answer:
viva [34]3 years ago
8 0

Answer:

A = 81 m²

Step-by-step explanation:

The formula for area of the parallelogram is

 A = LH         where L is the length of the base, and H is the height

L is given as 9, and H is given as 5, so

 A = (9)(5) = 45 m²

The are of the triangle is

 A = (1/2)bh         where b is the base and h is the height

b is given as 9.  Its's 9 because that side of the parallelogram is parallel to the base of the parallelogram and is also equal in measure.  The height of the triangle is give as 8, so the area is..

 A = (1/2)(9)(8)

       A = 36  m²

The total area is

45 m² + 36 m² = 81 m²

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Answer:

a) 64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

b) The hardness distribution is not given. But you would have to find s when n = 39, then the probability would be 1 subtracted by the pvalue of Z when X = 51.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n trials, the mean is \mu*n and the standard deviation is s = \sigma\sqrt{n}

In this question:

n = 48, \mu = 48*5 = 240, s = 4\sqrt{48} = 27.71

These values are in minutes.

(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?

From 6:50 PM to 11 PM there are 4 hours and 10 minutes, so 4*60 + 10 = 250 minutes. This probability is the pvalue of Z when X = 250. So

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

By the Central Limit Theorem

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

Z = \frac{250 - 240}{27.71}

Z = 0.36

Z = 0.36 has a pvalue of 0.6406

64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51?

The hardness distribution is not given. But you would have to find s when n = 39(using the standard deviation of the population divided by the square root of 39, since it is not a sum here), then the probability would be 1 subtracted by the pvalue of Z when X = 51.

5 0
2 years ago
V(j+y)=61y+82<br> please solve!!!!<br> need help
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Get y by itself...

y= -(jV-82)/(V-61)


4 0
3 years ago
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