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3 years ago

A bucket is being filled at a rate of 5/6 gallon in 1/4 minute. What is the unit rate in gallons per minute?

Mathematics

2 answers:

mojhsa [17]3 years ago

6 0

Answer:

3 1/3 gallons per minute

Step-by-step explanation:

We can use ratio's to solve this problem. We will put gallons on top and time on the bottom

5/6 gallons x gallons

-------------------- = -------------

1/4 minute 1 minute

Using cross products

5/6*1 = 1/4 x

Multiply by 4 on each side

5/6 * 4 = 1/4 *4 x

20/6 = x

Dividing the top and bottom by 2

10/3 =x

Changing this back to a mixed number

3 goes into 10 3 times with 1 left over

3 1/3 gallons per minute

Annette [7]3 years ago

3 0

Answer:

10/3 gallons/minute

Step-by-step explanation:

There are 4 quarters in 1, so four quarter-minutes in one minute.

The the number of gallons going into buckets in one minute will be 4 times the number in 1/4 minute:

... 4 × 5/6 gal = 20/6 gal = 10/3 gal

This is the quantity per minute, so the unit rate is

... 10/3 gal/min

____

Alternate solution

You are asked for the rate in gallons per minute. In this context, "per" means "divided by", so you find the desired quantity by dividing gallons by minutes.

... (5/6 gal)/(1/4 min) = (5/6×4/1) gal/min = 10/3 gal/min

_____

Comment on dividing fractions

You're generally taught one or two ways to divide fractions:

invert the denominator and multipy: (5/6)/(1/4) = (5/6)×(4/1) = 20/6 = 10/3.
express both over a common denominator, then lose the denominator: (5/6)/(1/4) = (10/12)/(3/12) = 10/3

Please note that if you invert and multiply after doing the adjustment in the second method, you would have (10/12)×(12/3) = (10/3)×(12/12) = 10/3. That is, the denominators cancel. It's just another way to think about the quotient of fractions.

There's actually a third method you can use, but you need to be really careful.

3. Express both fractions using the same numerator, then invert the result after losing the numerator: (5/6)/(1/4) = (5/6)/(5/20) = 20/6 = 10/3. Again, this is a variation that takes advantage of cancellation after "invert and multiply."

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There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f

Ann [662]

Answer:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The estimated population proportion for this case is:

$\hat p = \frac{350}{500}=0.7$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.