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irina1246 [14]
3 years ago
15

You have a 20 - ounce bottle of juice. You pour out 1/4 of the bottle to share with a friend. If you pour out 3 ounces for yours

elf,what fraction of the 20 ounces will be left in the bottle?
Mathematics
1 answer:
kramer3 years ago
4 0

Answer:

3/5

Step-by-step explanation:

You have a 20 ounce bottle. You pour out 1/4 of it.

20 x 1/4 = 20/4 = 5   You pour out 5 ounces.

20 - 5 = 15 ounces

If you pour out 3 ounces for yourself,  15 - 3 = 12

what fraction of the 20 ounces (original or total amount) will be left in the bottle?

12 ounces is left after pouring out 1/4 of the bottle for your friend and 3 ounces for yourself. 20 ounces was the total amount you first had in the bottle. The fraction that is left is calculated by dividing the amount left (12) by the total (20)

12/20  BUT each number can be divided by/reduced by 4, so dividing each number by 4  (12/4 = 3, 20/4 =5) gives 3/5.

3/5

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The data given below contain the state cigarette tax​ (in $) for all 20 regions of a country.
g100num [7]

Answer:

(a) \bar x= 1.583 -- Population Mean

(b) s = 1.032 --- Population standard deviation

(c) See Explanation

Step-by-step explanation:

Given:

Cigarette tax for 20 regions

Solving (a): The population mean

This is calculated as:

\bar x = \frac{\sum x}{n}

\sum x = 1.36 + 1.70 + 2.50 + 0.45 + 1.18 + 0.64 + 3.46 + 0.57 + 2.00 + 0.80 + 1.60 +0.98 + 0.36 + 2.24 + 4.35 + 0.62 + 2.70 + 1.78 + 1.53 + 0.84

\sum x = 31.66

n = 20

So, we have:

\bar x= \frac{31.66}{20}

\bar x= 1.583

Solving (b): The population standard deviation

This is calculated as:

s = \sqrt{\frac{\sum( x - \bar x)^2}{n}

\sum (x -\bar x)^2 = (1.36 - 1.583)^2 + (1.70 - 1.583)^2+ (2.50 - 1.583)^2+ (0.45 - 1.583)^2+ (1.18 - 1.583)^2+ (0.64 - 1.583)^2+ (3.46 - 1.583)^2+ (0.57 - 1.583)^2+ (2.00 - 1.583)^2+ (0.80 - 1.583)^2+ (1.60 - 1.583)^2+(0.98 - 1.583)^2+ (0.36 - 1.583)^2+ (2.24 - 1.583)^2+ (4.35 - 1.583)^2+ (0.62 - 1.583)^2+ (2.70 - 1.583)^2+ (1.78 - 1.583)^2+ (1.53 - 1.583)^2+ (0.84- 1.583)^2

\sum (x -\bar x)^2 = 21.29222

So:

s = \sqrt{\frac{21.2922}{20}

s = \sqrt{1.06461}

s = 1.032

Solving (c):

Population mean tells the average amount while the standard deviation represents the spread from the calculated mean

Option (4) is correct

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Answer:

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Step-by-step explanation:

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