A car travels 420 miles in 7 hours. If the rate remains the same, how far does it travel in 11 hours?

mr. morris has a class of 14 students. he can spend $24 on each student to buy math supplies for the year. he first buys all the

Natali [406]

Hello!

First of all let's divide and find how much each calculator cost.

95.2/14=$6.80

Now we will subtract from 24.

24-6.8= 17.2

Mr. Morris has $17.2 left to spend on each student.

I hope this helps!

4 0

2 years ago

Read 2 more answers

A statistician calculates that 8% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the

hichkok12 [17]

Answer:

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

A statistician calculates that 8% of Americans own a Rolls Royce.

This means that $p = 0.08$

Sample of 595:

This means that $n = 595$

Mean and standard deviation:

$\mu = p = 0.08$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.08*0.92}{595}} = 0.0111$

What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?

Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.

Probability the proportion is less than 5%:

P-value of Z when X = 0.05. So

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

By the Central Limit Theorem

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

$Z = \frac{0.05 - 0.08}{0.0111}$

$Z = -2.7$

$Z = -2.7$ has a p-value of 0.0035

2*0.0035 = 0.0070

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

8 0

3 years ago

Jordan invests £16200 into his bank account

atroni [7]

Answer:

18225

Use the formula: .

A = final amount

P = initial amount invested

r = annual interest rate

t = time (in years)

Insert all values in appropriate places.

Simplify.

A=16200(1+(0.025)(6))

6 0

2 years ago

What is the angle that is half of its own complement?

Cerrena [4.2K]

If you have an angle and want to know its complement, you subtract it from 90 degrees. What angle, when subtracted from 90 degrees, gives the same value?

90 - x = x

The supplement of x is the angle that you add to x to make 180 degrees. In other words, 180 - x = the supplement of x.

4 0

3 years ago

4.5/18 = x/100 <br> What is x?

USPshnik [31]

Answer:
x=25

Explanation:
Using the method of cross multiplication and division set up like so,
(100•4.5)/18 will give you 25.
4.5•100=450
450/18=25

5 0

2 years ago