The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches. Men the same age have mean height 69.3 inches with standard deviation 2.8 inches. What are the z-scores for a woman 6 feet tall and a man 5'10" tall? (You may round your answers to two decimal places) z-scores for a woman 6 feet tall: z-scores for a man 5'10" tall:

Answers

Answer 1

Answer:

Answer: The z-scores for a woman 6 feet tall is 2.96 and the z-scores for a a man 5'10" tall is 0.25.

Step-by-step explanation:

Let x and y area the random variable that represents the heights of women and men.

Given : The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches.

i.e. $\mu_1 = 64$ $\sigma_1=2.7$

Since , $z=(x-\mu)/(\sigma)$

Then, z-score corresponds to a woman 6 feet tall (i.e. x=72 inches).

[∵ 1 foot = 12 inches , 6 feet = 6(12)=72 inches]

$z=(72-64)/(2.7)=2.96296296\approx2.96$

Men the same age have mean height 69.3 inches with standard deviation 2.8 inches.

i.e. $\mu_2 = 69.3$ $\sigma_2=2.8$

Then, z-score corresponds to a man 5'10" tall (i.e. y =70 inches).

[∵ 1 foot = 12 inches , 5 feet 10 inches= 5(12)+10=70 inches]

$z=(70-69.3)/(2.8)=0.25$

∴ The z-scores for a woman 6 feet tall is 2.96 and the z-scores for a a man 5'10" tall is 0.25.

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The table represents the start of the division of 8x^4+2x^3-7x^2+3x-2 by the indicated divisor. Find the quotient.

Answers

Answer: 2x² + x - 2 (the first option)

Explanation:

1) Question: divide 8x⁴+2x³-7x²+3x-2 by 4x² - x + 1

2) First term of the quotient

8x⁴ + 2x³ - 7x² + 3x - 2 | 4x² - x + 1
                                       ---------------------
-8x⁴ + 2x³ - 2x²                   2x²
----------------------------------
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3) Second term of the quotient:

8x⁴ + 2x³ - 7x² + 3x - 2 | 4x² - x + 1
                                       ---------------------
-8x⁴ + 2x³ - 2x²                   2x² + x
----------------------------------
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        ----------------------------
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4) third term of the quotient:

8x⁴ + 2x³ - 7x² + 3x - 2 | 4x² - x + 1
                                       ---------------------
-8x⁴ + 2x³ - 2x²                   2x² + x - 2
----------------------------------
           4x³ - 9x² + 3x - 2
          -4x³ + x² -   x
        ----------------------------
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                    8x² - 2x + 2
                 -------------------------
                             0

5) Conclusion: since the remainder is 0, the division is exact and the quotient is 2x² + x - 2

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Answer:

Answer: 2x² + x - 2 (the first option)

Step-by-step explanation:

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Answers

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

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_____
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