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bija089 [108]
3 years ago
13

How many ways can Carlos choose 2 pizza toppings from a menu of 4 toppings if each topping can only be chosen once?

Mathematics
1 answer:
Ahat [919]3 years ago
3 0

Answer:

30 different ways

Step-by-step explanation:

Hi

for the first topping she can choose 1 of 6 items

so she has 6 choices

and then the second topping she has 5 choices as each topping can only be chosen once

so it comes 6 * 5 = 30

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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
How to solve for x where (2^x)*x =n?
Molodets [167]
Tough call.  
You may have to use Newton's Method or something like that.
Graph y=2^x and then graph n/x on the same set of axes.  You may have to assign some arbitrary value to n to make this work.  From the graph you can read off the approximate coordinates of the point of intersection.
4 0
2 years ago
3. Why does it tako 3 copies of; to show the same amount as 1 copy of ?? Explain your answer in words
Amanda [17]
Because 3/6 is equal to 1/2.
You multiply the 1 (in 1/2) by 3, and the 2 (in 1/2) by 3 to get 3/6. You need to have a common denominator, and 6 was the common denominator.
7 0
2 years ago
Colby made $66.50 for mowing 7 lawns. Let x represent the number of lawns mowed and y represent the amount of money earned. Writ
Amanda [17]

Answer:

x = 9.5y

Step-by-step explanation:

7 lawns = $66.50

1 lawn = $66.50 ÷ 7

          = $9.50

You now know that for one lawn mowed, the amount of money earned is $9.50. Thus:

1x = 9.5y

x = 9.5y

6 0
2 years ago
What do I do steps? please help
skad [1K]
Area = Length x Width

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Can you work out the something using mental math?
8 0
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