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3 years ago

14. Divide and write the fraction or mixed number in its simplest form:1/4÷3/8

Mathematics

1 answer:

sasho [114]3 years ago

3 0

Answer:

<em>1/4 ÷ 3/8 = </em><em>2/3</em>

Step-by-step explanation:

When dividing fractions, you have to take the reciprocal of the second fraction, then multiply from there. The reciprocal of a fraction is basically flipped. So then, 1/4 ÷ 3/8 becomes 1/4 x 3/8. Multiplying fractions should be pretty straight forward as you just need to multiply numerator (top number of a fraction) with numerator and vice versa for the denominators (bottom number of a fraction).

So then you get: (1 x 8)/(3 x 4) = 8/12. Then you just simplify it by dividing the numerator and denominator by their greatest possible factor, which in this case is 4. So then, (8 ÷ 4)/(12 ÷ 4) = 2/3.

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If there are 80 toys in a shop, 40% of them are for boys. 50% of the boy's toys and 50% of the girl's toys are made by the shop

lana [24]

Answer: 8 more girl toys than boy toys

Step-by-step explanation:

First you need to find out how many of the toys are for boys and girls.

———————————————

80 * 40 = 80 * 0.4 = 32

32 toys are for boys

———————————————

80 - 32 = 48

48 toys are for girls

———————————————

Now find 50% of the boy and girl toys.

32 * 50% = 32 * 0.5 = 16

48 * 50% = 48 * 0.5 = 24

———————————————

Now subtract the number of girl toys by the number of boy toys to find out how many more were made for girls than boys.

24 - 16 = 8

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3 years ago

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Prove that 25^11−5^19 is divisible by 31.

SCORPION-xisa [38]

Answer:

Divisible by 3 is the answer

Step-by-step explanation:

First get everything to have the same base of 5

25^11 - 5^19

(5^2)^11 - 5^19

5^(2*11) - 5^19

5^22 - 5^19

Now factor out the GCF 5^19 to get

5^22 - 5^19

5^(19+3) - 5^(19+0)

5^19*5^3 - 5^19*5^0

5^19(5^3 - 5^0)

5^19(125 - 1)

5^19*(124)

At this point, we factor the 124 into 31*4 to end up with this full factorization: 5^19*31*4

Therefore, 25^11 - 5^19 is equivalent to 5^19*31*4

Since 31 is a factor of the original expression, this means the original expression is divisible by 31.

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3 years ago

The plan for the Thorne’s backyard play area, shaped like a trapezoid, is shown. The area of the play area is 286.56 square feet

lorasvet [3.4K]

The length of material needed for the border is the perimeter of the backyard play area

<h3>How to calculate the length of material needed </h3>

The area of the play area is given as:

$Area = 286.56$

The area of a trapezoid is calculated using:

$Area = 0.5 * (L1 + L2) * H$

Where L1 and L2, are the parallel sides of the trapezoid and H represents the height.

The given parameter is not enough to solve the length of material needed.

So, we make use of the following assumed values.

Assume that the parallel sides are: 25 feet and 31 feet long, respectively.

While the other sides are 10.2 feet and 8.2 feet

The length of material needed would be the sum of the above lengths.

So, we have:

$Length = 25 + 31 + 10.2 + 8.2$

$Length = 74.4$

Using the assumed values, the length of material needed for the border is 74.4 feet

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brainly.com/question/17297081

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2 years ago

What is 55 plus 65 plus 60

jasenka [17]

Answer:

180

Step-by-step explanation:

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3 years ago

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In March 2015, a Nielsen global online survey "found that consumers are increasingly willing to pay more for socially responsibl

Veseljchak [2.6K]

Answer:

For this case the parameter of interest is given by:

$p$ who represent the true proportion of respondents said that they were willing to pay more for products and services from companies who are committed to positive social and environmental impact

For this case we have an estimation given for this parameter. The estimation comes from a sample of 30000 people selected in 60 countries and they got:

$\hat p = 0.66$

This value represent the best estimator for the true proportion since is an unbiased estimator of the real parameter:

$E(\hat p) = p$

Step-by-step explanation:

For this case the parameter of interest is given by:

$p$ who represent the true proportion of respondents said that they were willing to pay more for products and services from companies who are committed to positive social and environmental impact

For this case we have an estimation given for this parameter. The estimation comes from a sample of 30000 people selected in 60 countries and they got:

$\hat p = 0.66$

This value represent the best estimator for the true proportion since is an unbiased estimator of the real parameter:

$E(\hat p) = p$

For this case if we want to test if the population proportion is equal to an specified value we can use the one sample z test for a proportion:

Null hypothesis: $p=p_0$

Alternative hypothesis: $p \neq p_o$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

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3 years ago

14. Divide and write the fraction or mixed number in its simplest form:1/4÷3/8​

14. Divide and write the fraction or mixed number in its simplest form:1/4÷3/8