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3 years ago

Find the value of x. Round to the nearest tenth.

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

5 0

Answer: 76.5

Step-by-step explanation:

Interior angles of a triangle = 180 degrees so then you do 180-27 to get 153. Then 153 divided by 2 = 76.5

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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

2 years ago

Jeanette purchase a concert ticket on a website the original price of the ticket was $75 she used a coupon code to receive 20% d

Radda [10]

Answer:

10%

Step-by-step explanation:

20%=20/100=0.20

75$x.0.20=15$

The price when she received a 20% discount was:

75$-15$=60$

Then, the web site applied a 10% service fee to the discounted price, so you have:

10/100=0.10

75$x0.10=7.5$

60$+7.5$=67.5$

So, if 75$ is the 100% of the price, what percentage represents 67.5$?

75$--------100%

67.5$------x

x=67.5 x 100/75

x=90%

Then,

100%-90%=10%

3 0

2 years ago

Directions: Select ALL the correct answers.

dybincka [34]

Answer:

b, that each player loaded onto the truck is

proportional to the number of minutes. m. spent loading boxes.

• Cory loaded twice as many boxes as Alonzo.

The equation that represents the number of boxes Cory loaded is

b = 2m.

Step-by-step explanation:

hope this helps

7 0

2 years ago

What is the answer? im trying to figure it out and its hurting my head

Naya [18.7K]

7x-99=2x+1
5x=100
x=20

mark me brainliest if the answer is correct, thank you in advance :)

3 0

3 years ago

What is the image point of (1,-1)(1,−1) after a translation left 4 units and down 5 units?

DENIUS [597]

Answer:

The new point would be (-3,-6)

Step-by-step explanation:

To solve this it is nice to graph the first point at (1,-1). Then move the point left 4 units, making x -3. and then 5 units down, which would make y -6.

8 0

3 years ago