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3 years ago

Find the value of each variable

Mathematics

1 answer:

ohaa [14]3 years ago

6 0

9514 1404 393

Answer:

11. x = 13, y = 13√2

12. x = 8, y = 4√3

13. x = 14√3, y = 7√3

14. x = y = 11√2

15. x = 12√2, y = 12, z = 12√3

Step-by-step explanation:

The ratios of side lengths in the "special" triangles are (shortest to longest)

1 : 1 : √2 . . . . . isosceles right triangle

1 : √3 : 2 . . . . 30°-60°-90° triangle

These ratios make answering these questions much easier.

11. 13 : x : y = 1 : 1 : √2

x = 13, y = 13√2

12. 4 : y : x = 1 : √3 : 2

x = 8, y = 4√3

13. y : 21 : x = 1 : √3 : 2

y = 21/√3 = 7√3

x = 14√3

14. x : y : 22 = 1 : 1 : √2

x = 22/√2 = 11√2

x = y = 11√2

15. Let 'a' represent the altitude. Then we have ...

a : z : 24 = 1 : √3 : 2

a = 12, z = 12√3

and ...

a : y : x = 1 : 1 : √2

y = 12, x = 12√2

_____

Additional comment

It is worth remembering that 1/√n = (√n)/n. This is useful when you have to divide by √2 or √3 in the above problems.

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5x - 3y - 10 = 0 --> -3y=-5x+10
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x = (56-25)/8 = 31/8
So the solution point is at (31/8, 25/8)

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3 years ago

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Sandra wants to make gift baskets. She needs 1.3 pounds of flour to make cupcakes and 1.7 pounds of flour to make pies. About

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Answer:

A: 18 pounds

Step-by-step explanation:

The answer would be 18 pounds because if you take the amount needed to make the cupcakes and multiply it by the number of baskets Sandra wants to make (1.3 x 6 = 7.8) and then add it to how much flour is needed for 6 baskets of pies (1.7 x 6 = 10.2). So when you add the amount of flour needed for 6 baskets of pies and cupcakes the answer is 18 pounds.

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A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the

kolbaska11 [484]

The probability that the sample proportion will be less than 0.04 is 0.8995 or 89.95%.

The true proportion (p) is given to be 0.03.

Therefore, Mean (μ) = p = 0.03.

The standard error of sampling distribution can be calculated using the formula σ = √[{p(1 - p)}/n], where n, is the sample size, that is, n = 476.

Therefore, σ = √[{0.03(1 - 0. 03)}/476] = 0.00782.

Since, np = 14.28 and n(1 - p) = 461.72 are both greater than 5, we assume the sample is normally distributed.

Since, we are asked to find the probability that the sample proportion is less than 0.04, we using our calculator, enter as following:

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Learn more about probability of sampling distributions at

brainly.com/question/15520013

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2 years ago

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3 years ago

Change the fraction 7/12 to a decimal. Round your answer to the nearest thousandth

alina1380 [7]

Just divide.

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It's 3, so we round down to 0.583.

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