A fruit bag contains apples and bananas. If 17 out of 25 of the fruit are apples. What percent are bananas?

Mr. Marcucci received a bonus of $496 from his employer. He has to pay 33% of his bonus to taxes. How much will Mr. Marcucci pay

tiny-mole [99]

Edit: 33% is not $\frac{1}{3}$ , therefore my solution is wrong. The correct answer is 0.33 x 496, which is $163.68

The following is the original solution, which is incorrect.
33% = $\frac{1}{3}$ . Multiply the bonus of $496 by $\frac{1}{3}$ to get the solution of $\frac{496}{3}$ , or 165 and $\frac{1}{3}$

Therefore the solution is $165.33

7 0

3 years ago

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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

2 years ago

I need to show .y work for 132 × 3

Lelechka [254]

Answer:

132 × 3 = 396

Step-by-step explanation:

132 3 × 2 = 6

× 3 3 × 3 = 9

396 3 × 1 = 3

7 0

3 years ago

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−15x + 60 ≤ 105 AND 14x + 11 ≤ −31

almond37 [142]

Answer:

1. -15x + 60 <= 105 2. 14x + 11 <= - 31

Step-by-step explanation:
1. x> = - 3
2. x <= - 3

Isolate the variable by dividing each side by factors that don't contain the variable

5 0

3 years ago

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Determine the x-intercept points of the function h(x) = (x - 5)(x-6)(x + 4).

AlexFokin [52]

Answer:

A.

Step-by-step explanation:

The x-intercepts are the points where the x value is zero. In this case, to find the "zeros" of the function, set each factor to zero. x-5 -> x=5. x-6 -> x=6. x+4 -> x=-4.

7 0

3 years ago