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4 years ago

Rob peeled 125 oranges in 5 hours. At that rate, how many oranges would he peel in 12 minutes?

Mathematics

2 answers:

marin [14]4 years ago

6 0

Answer:

$\boxed {\tt 5 \ oranges}$

Step-by-step explanation:

Let's set up a proportion.

$\frac{oranges}{minutes} =\frac{oranges}{minutes}$

He can peel 125 oranges in 5 hours. First, let's find the minutes in 5 hours.

There are 60 minutes in 1 hour, so multiply 60 and 5 (60*5=300). There are 300 minutes in 5 hours.

$\frac{125 \ oranges}{300 \ minutes}=\frac{oranges}{minutes}$

We don't know how many oranges he can peel in 12 minutes. So we say he can peel x oranges in 12 minutes.

$\frac{125 \ oranges}{300 \ minutes}=\frac{x \ oranges}{12 \ minutes}$

$\frac{125 \ }{300 \ }=\frac{x \ }{12 }$

Solve for x by isolating it. x is being divided by 12. The inverse of division is multiplication. Multiply both sides of the proportion by 12.

$12*\frac{125 \ }{300 \ }=\frac{x \ }{12 \ }*12$

$12*\frac{125 \ }{300 \ }=x$

$12*0.416666667=x$

$5=x$

Rob can peel 5 oranges in 12 minutes.

vlabodo [156]4 years ago

6 0

Answer:

5 oranges in 12 minutes

Step-by-step explanation:

$125 \div 5 = 25$

$25 \div 60 = 0.41$

$0.41 \times 12 = 5$

what i did here was I took the original amount (125), divided it by 5 which is 25 oranges per hour

1 hr = 60 mins

then I divided 25 oranges by 60 mins, then times it by 12 to get 5 around 5 oranges in 12 minutes.

You might be interested in

3,10,24,52 what is the pattern

Sloan [31]

Multiply 2 and then add 4 each time

3 x 2 = 6 + 4 = 10
10 x 2 = 20 + 4 = 24
24 x 2 = 48 + 4 = 52

hope this helps

7 0

4 years ago

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 golden rectangle has side lengths in the ratio of about 1 to 1.62. To the nearest tenth, what is length of the shorter side of

olga55 [171]

Answer: The length of the shorter side of a golden rectangle is about 24.7 inches.

Step-by-step explanation:

Given : A golden rectangle has side lengths in the ratio of about 1 to 1.62.

Since 1.62 > 1 , so

$\dfrac{\text{Length of shorter side}}{\text{Length of longer side}}=\dfrac{1}{1.62}$

If the length of the longer side is 40 inches , then we have

$\dfrac{\text{Length of shorter side}}{\text{40 inches}}=\dfrac{1}{1.62}\\\\ \Rightarrow\ \text{Length of shorter side}=\dfrac{1}{1.62}\times \text{40 inches}\\\\ \Rightarrow\ \text{Length of shorter side}=24.6913580247\approx24.7\text{ inches}$