The quotient of a number and 35 is 100. Create an equation, solve it, and then tell what that number is

Phantasy [73]

% means 100 so, 1.49/100=0.0149

4 0

3 years ago

To make cranberry jam, you need 12 cups of sugar for every 16 cups of cranberries. Find the amount of sugar needed for 4 cups of

Yuri [45]

ANSWER: 3 cups of sugar

3 0

3 years ago

Read 2 more answers

Heather had $89.50 in a bank account. She withdrew $10.25. What was her new balance?

dem82 [27]

Answer:

79.25

Step-by-step explanation:

7 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 $p = 0.93$

Approximating the binomial to the normal.

$E(X) = np = 300*0.93 = 279$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.93*0.07} = 4.42$

The probability that at least 285 rooms will be occupied is 1 subtracted by the pvalue of Z when X = 285. So

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

$Z = \frac{285- 279}{4.42}$

$Z = 1.36$

$Z = 1.36$ has a pvalue of 0.9131.

So there is a 1-0.9131 = 0.0869 = 8.69% probability that at least 285 rooms will be occupied.

8 0

3 years ago

Of the 75% of a group that passed a physical examination only 3/5 passed the additional psychological exam. What fraction of the

Helga [31]

To find the fraction of the grouo that passed both exams, we need to first convert 75% into a fraction:

75%
=75/100
=3/4

We can then mutiply the fraction above by the students who passed the psychological exam:

3/4×3/5
=9/20

Therefore the answer is 9/20.

Hope it helps!

3 0

3 years ago