Please do number 11 for me.

Mathematics

1 answer:

dezoksy [38]3 years ago

4 0

Rule-3 angles of a triangle =180 degrees . One angle is a right angle which is 90 degrees so the remaining 2 must equal 90 so the equation is so 90=(15x)+(8x-2) and now we just have to solve what is the value of x.
First we move -2 to the other side of the equation as +2 so we get 92=15x+8x next we put the 15x and 8x together and get 23 so 92=23 times x. So we divide 92 by 23 and the value of x is 4

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A5cm x 11 cm rectangle sits inside a circle with radius of 12 cm.

never [62]

Answer:

397.16 cm²

Step-by-step explanation:

Area of the circle = πr²

3.14 * 144 = 452.16

452.16 - (11 x 5 ) = area shaded region

452.16 - 55 = 397.16

If my answer is incorrect, pls correct me!

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-Chetan K

5 0

3 years ago

kicyunya [14]

Answer:

8.69% probability that at least 285 rooms will be occupied.

Step-by-step explanation:

For each booked hotel room, there are only two possible outcomes. Either there is a cancelation, or there is not. So we use concepts of the binomial probability distribution to solve this question.

However, we are working with a big sample. So i am going to aproximate this binomial distribution to the normal.

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:

A popular resort hotel has 300 rooms and is usually fully booked. This means that $n = 300$

About 7% of the time a reservation is canceled before the 6:00 p.m. deadline with no pen-alty. What is the probability that at least 285 rooms will be occupied?

Here a success is a reservation not being canceled. There is a 7% probability that a reservation is canceled, and a 100 - 7 = 93% probability that a reservation is not canceled, that is, a room is occupied. So we use $p = 0.93$