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satela [25.4K]
3 years ago
6

The base of a right rectangular pyramid has length 14 ​cm, width 12 ​cm, and height 13 cm. Describe a cross section that could b

e formed by a horizontal plane that intersects the faces of the pyramid above the base.
Mathematics
1 answer:
lakkis [162]3 years ago
8 0
It would be a RECTANGLE proportional to the base of the pyramid.
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An article written for a magazine claims that 78% of the magazine's subscribers report eating healthily the previous day. Suppos
Schach [20]

Answer:

89.44% probability that less than 80% of the sample would report eating healthily the previous day

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

p = 0.78, n = 675

So

\mu = E(X) = np = 675*0.78 = 526.5

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{675*0.78*0.22} = 10.76

What is the approximate probability that less than 80% of the sample would report eating healthily the previous day?

This is the pvalue of Z when X = 0.8*675 = 540. So

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

Z = \frac{540 - 526.5}{10.76}

Z = 1.25

Z = 1.25 has a pvalue of 0.8944

89.44% probability that less than 80% of the sample would report eating healthily the previous day

8 0
4 years ago
Suppose WX = 4x - 8 and WZ = 2x + 2. Solve for x
podryga [215]

Answer: 5

Step-by-step explanation:

Because the shape is a kite we can tell that WX and WZ are congruent.

So 4x-8 = 2x+2

Add 8 to both sides

4x = 2x+10

Subtract 2x

2x = 10

Divide by 2

x = 5

5 0
2 years ago
How does knowing 8+5=13 help you solve 13-5?​
amid [387]

Answer:

Fact Families

Step-by-step explanation:

They are fact families

8 0
3 years ago
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Consider the following scenario:
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C. The number of times a dessert was offered at a special price.

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15. Oscar wants to rent a boat. The rental shop charges and initial fee of $12 plus $8 per hour to rent the boat. Write a equati
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C=8h+12
the 8h represents the $8 per hour for renting the boat, and h represents however many hours you rent the boat for.  The +12 is the initial $12 fee.  This is in slope intercept form, just using different variables than y=mx+b
5 0
3 years ago
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