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2 years ago

William is planning to cover one side of the roof of his barn with solar panels.

Mathematics

1 answer:

marishachu [46]2 years ago

8 0

Answer:

5 i think

Step-by-step explanation:

to start you need to find the total area the side of the roof he plans to cover which is 360 feet.

16x2 + 20x2 = 72

so lets just say thats the total area of one solar panel then you could just divide 360 feet by 72 feet to get...

5. so i guess william needs 5 solar panels

i could be spouting nonsense rn.. so sorry if im wrong

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A selective college would like to have an entering class of 950 students. Because not all students who are offered admission acc

pogonyaev

Answer:

a) The mean is 900 and the standard deviation is 15.

b) 100% probability that at least 800 students accept.

c) 0.05% probability that more than 950 will accept.

d) 94.84% probability that more than 950 will accept

Step-by-step explanation:

We use the normal approximation to the binomial 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

(a) What are the mean and the standard deviation of the number X of students who accept?

$n = 1200, p = 0.75$ . So

$E(X) = np = 1200*0.75 = 900$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1200*0.75*0.25} = 15$

The mean is 900 and the standard deviation is 15.

(b) Use the Normal approximation to find the probability that at least 800 students accept.

Using continuity corrections, this is $P(X \geq 800 - 0.5) = P(X \geq 799.5)$ , which is 1 subtracted by the pvalue of Z when X = 799.5. So

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

$Z = \frac{799.5 - 900}{15}$

$Z = -6.7$

$Z = -6.7$ has a pvalue of 0.

1 - 0 = 1

100% probability that at least 800 students accept.

(c) The college does not want more than 950 students. What is the probability that more than 950 will accept?

Using continuity corrections, this is $P(X \geq 950 - 0.5) = P(X \geq 949.5)$ , which is 1 subtracted by the pvalue of Z when X = 949.5. So

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

$Z = \frac{949.5 - 900}{15}$

$Z = 3.3$

$Z = 3.3$ has a pvalue of 0.9995

1 - 0.9995 = 0.0005

0.05% probability that more than 950 will accept.

(d) If the college decides to increase the number of admission offers to 1300, what is the probability that more than 950 will accept?

Now n = 1300. So

$E(X) = np = 1300*0.75 = 975$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1200*0.75*0.25} = 15.6$

Same logic as c.

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

$Z = \frac{949.5 - 975}{15.6}$

$Z = -1.63$

$Z = -1.63$ has a pvalue of 0.0516

1 - 0.0516 = 0.9484

94.84% probability that more than 950 will accept

5 0

3 years ago

The measures of the angles of XYZ are in the ratio 1:4:10. What are the measures of the angles?

Elanso [62]

Answer:the angles are 12 degrees, 48 degrees and 120 degrees.

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees.

The measures of the angles of XYZ are in the ratio 1:4:10. The total ratio is the sum of the proportion of each angle. It becomes

1 + 4 + 10 = 15

Therefore, the measure of the first angle would be

1/15 × 180 = 12 degrees

Therefore, the measure of the second angle would be

4/15 × 180 = 48 degrees

Therefore, the measure of the third angle would be

10/15 × 180 = 120 degrees

6 0

3 years ago

4/5 of 75 shared in ratio 2:3

Vika [28.1K]

4/5*75=60
ratio will be 24:36

4 0

3 years ago

Read 2 more answers

Jane has a circular garden with a diameter of 16 feet if one bag of fertilizer covers 30 ft.² how many bags will she need to cov

AleksAgata [21]

Answer:

She need 7 bags to cover the garden

Step-by-step explanation:

Diameter of circular garden = 16 feet

Radius of circular garden = $\frac{16}{2} = 8 feet$

Area of circular garden = $\pi r^2 = \frac{22}{7} \times 8^2 =200.96ft^2$

30 sq.feet covered by no. of bags = 1

200.96 sq.feet covered by no. of bags = $\frac{200.96}{30}=6.69$

Hence She need 7 bags to cover the garden

5 0

3 years ago

Can some one help me i need it done by today

lapo4ka [179]

Answer:

Number 9: 1.25 miles

Step-by-step explanation:

In total Brian hiked 16 miles

In total Christine hiked 14.75

So, 16 - 14.75 = 1.25

Overall, Brian hiked 1.25 more miles than Christine.

7 0

2 years ago