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3 years ago

Ned caught 1/3 pound of fish. Sarah caught 5/12 pound of fish. Jesse caught 1/6 pound of fish. How many in total did they catch?

2 answers:

8 0

They caught: 11/12 pounds of fish
First you need to change them to a same common denominator. Since 3 and 6 already go into 12, you just have to change 1/3 and 1/6 to a denominator with 12.
First you need to change 1/3 to 4/12. By doing that, you do: 1/3x4/4=4/12.
You then have to change 1/6 to 2/12. By doing that, you do: 1/6x2/2=2/12.
Then you just add up all the fractions and simplify: 4/12+2/12+5/12=11/12.
You can't simplify 11/12 any further so you're answer would be:
They caught 11/12 pounds of fish in total.
Hope this helps! :D

cupoosta [38]3 years ago

7 0

Ok so since the largest denominator is 12 we want to get the other denominators the same so it is easier to add together. Multiply 3 by 4 to get a denominator, then multiply 1 by 4 and you'll get 4/12. Then multiply 6 by 2 and then 1 by 2 and you'll get 2/12. Add all 3 of the fractions to get 11/12 pounds of fish. Hope this helps!

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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

A line passes through the point (-8, 6) and has a slope of -5/4.

Margarita [4]

Answer:

y = -5/4x - 4

Step-by-step explanation:

Plug in 6 for y and -8 for x. Then solve for b or "y-intercept". You should get -4

5 0

2 years ago

Read 2 more answers

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