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3 years ago

Find the value of x.A. 4B. 5C. 6D. 9

Mathematics

1 answer:

lubasha [3.4K]3 years ago

7 0

Answer:

C. 6

Step-by-step explanation:

You can try the answers to see which satisfies the Pythagorean theorem:

A. 4² +7² = 16+49 ≠ 117

B. 5² +8² = 25 +64 ≠ 117

C. 6² +9² = 36 +81 = 117 . . . . this (C) is the correct choice

and, for completeness, ...

D. 9² +12² = 81 +144 ≠ 117

_____

Working out

You can also actually work the problem. The Pythagorean theorem tells you ...

x² + (x+3)² = (√117)²

2x² +6x +9 = 117

2x² +6x = 108 . . . . subtract 9

x² +3x = 54 . . . . . . divide by 2

x(x +3) = 54 . . . . . . factor

Now, you can compare to your memorized times tables, where you find 6×9 = 54, so you know that x=6.

In case times tables are a challenge, you can continue to complete the square:

x² +3x +1.5² = 54 +1.5²

(x +1.5)² = 56.25 = 7.5² . . . . write as squares

x = 7.5 -1.5 = 6 . . . . . . . . . . . square root, subtract 1.5

The value of x is 6.

_____

The other solution to the quadratic equation is x=-9, but negative segment lengths make no sense. We acknowledge, then ignore, that extraneous solution.

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If h(x)=4x^2-16 we’re shifted 7 units to the right and 3 units down what would the new equation be

attashe74 [19]

Answer:

4(x-7)^2 - 19

Step-by-step explanation:

Shifting 7 units to the right: 4(x-7)^2 - 16.

3 units down: 4(x-7)^2 - 16 - 3, or 4(x-7)^2 - 19

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3 years ago

1. What is the marginal distribution of individuals who are underweight?

Katena32 [7]

Answer:

Step-by-step explanation:

You have to divide the TOTAL underweight which is 130, into the total of individuals which is 1000. 130/1000= 0.13 or 13.0%

Answer C.

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3 years ago

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12 is what percent of 24? What percent of 35 is 7? What percent of 90 is 9? 20 out of 60 is what percent?

irinina [24]

Answer:

12 is 50% of 24

7 is 20% of 35

9 is 10% of 90

20/60 is 33.33%

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2 years ago

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Tracy McKinney is a disc jockey at radio station WMMM. Her annual salary is $52,750. What is her monthly salary?

attashe74 [19]

Okay, so since her annual salary is $52,750 (the amount she gets a year, all twelve months combined) you're trying to find how much she gets monthly. That would mean we would have to divide her annual salary by 12 to find her monthly salary.

$52,750 ÷ 12 = 4,395.8333333333333

And since that's a (bothersome) repeating decimal, we're going to have to round it. Once rounded, you would get $4,395.83. That is her monthly salary.

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3 years ago

There are 4 people at a party. Consider the random variable X=’number of people having the same birthday ’ (match only month, N=

yulyashka [42]

Answer:

S = {0,2,3,4}

P(X=0) = 0.573 , P(X=2) = 0.401 , P(x=3) = 0.025, P(X=4) = 0.001

Mean = 0.879

Standard Deviation = 1.033

Step-by-step explanation:

Let the number of people having same birth month be = x

The number of ways of distributing the birthdays of the 4 men = (12*12*12*12)

The number of ways of distributing their birthdays = 12⁴

The sample space, S = { 0,2,3,4} (since 1 person cannot share birthday with himself)

P(X = 0) = $\frac{12P4}{12^{4} }$

P(X=0) = 0.573

P(X=2) = P(2 months are common) P(1 month is common, 1 month is not common)

P(X=2) = $\frac{3C2 * 12P2}{12^{4} } + \frac{4C2 * 12P3}{12^{4} }$

P(X=2) = 0.401

P(X=3) = $\frac{4C3 * 12P2}{12^{4} }$

P(x=3) = 0.025

P(X=4) = $\frac{12}{12^{4} }$

P(X=4) = 0.001

Mean, $\mu = \sum xP(x)$

$\mu = (0*0.573) + (2*0.401) + (3*0.025) + (4*0.001)\\\mu = 0.879$

Standard deviation, $SD = \sqrt{\sum x^{2} P(x) - \mu^{2}} \\SD =\sqrt{ [ (0^{2} * 0.573) + (2^{2} * 0.401) + (3^{2} * 0.025) + (4^{2} * 0.001)] - 0.879^{2}}$

SD = 1.033

4 0

4 years ago