A bag contains 5 milk and 9 dark chocolates.

A boat traveled 27 miles in 2 hours. At this rate, how many miles will the boat travel in

Art [367]

6.75 miles per half hour !!!!!!!

7 0

3 years ago

A ski lift is designed with a total load limit of 20,000 pounds. It claims a capacity of 100 persons. An expert in ski lifts thi

Yanka [14]

Answer:

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n values of a distribution, the mean is $\mu \times n$ and the standard deviation is $\sigma\sqrt{n}$

An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.

This means that $\mu = 200*100 = 20000, \sigma = 30\sqrt{100} = 300$

If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload

Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So

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

$Z = \frac{20000 - 20000}{300}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

1 - 0.5 = 0.5

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

5 0

3 years ago

The town of lantana needs 14,000 for a new playground. Lantana elementary school raised 5,258, Lantana middle school raised 2834

Nutka1998 [239]

Lantana needs $1776 to reach its goal of $14000

5 0

3 years ago

What is the simplified form of the quantity of x plus 6, all over the quantity of x plus 4 + the quantity of x minus 3, all over

Rina8888 [55]

$\frac{x+6}{x+4} +\frac{x-3}{3}$

make denomenators the same

we have
x+4 and 3
times the fraction with x+4 in denomenator with the fraction 3/3
times the fraction with 3 in denomenator with the fraction x+4
we get
$\frac{3x+18}{3x+12} +\frac{x^2+x-12}{3x+12}$
since common denoms, can add them to get
$\frac{3x+18+x^2+x-12}{3x+12}$
$\frac{x^2+4x+6}{3x+12}$
that is simplified

7 0

3 years ago

Select the list that correctly includes all of the coefficients from the problem

matrenka [14]

Answer:

( B.) 6, 1, -2 , -4

Step-by-step explanation:

A coefficient is a number multiplied by a variable. So, in this case let's take a look at the problem.

-2+6y+m-2y+8-4m

Now we have to find the numbers that have a variable next to it

which are 6,m,-2, and -4

(If you are wondering that why m is a coefficient its because it is also known as 1m)

Final answer = 6, 1, -2 , -4

Hope this helps!

7 0

3 years ago