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mihalych1998 [28]
3 years ago
5

If -4 is added to a number and them sum is doubled, the result is -16 less than the number. find the number.

Mathematics
1 answer:
mote1985 [20]3 years ago
4 0
Let the number be x
(-4+x)×2 = x-(-16)
-8-2x=x+16
-2x-x=16+8
-3x=24
x=24÷-3
x=-8
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Step-by-step explanation:

For simplicity I will substitue x for β.

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Then it's just simple algebra to cancel till the 3rd step where we used another identity derived from the Pythagorean Theorem.

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Write the equation of line in slope-intercept form. Line parallel to y=0.5x+3 that passes through the point (−9,12)
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A line parallel to the given one will have the same slope, 0.5. For the purpose here, it is convenient to start with a point-slope form of the equation, then simplify. For slope m and point (h, k), the equation of the line can be written as

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Area = length x width

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Area = (x - 5)(x - 5 + 22)

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- Now you have to simplify the second parenthesis:

Area = (x - 5)(x + 17)

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Area = x^2 + 17x - 5x - 85

- Simplify by collecting like terms :

Area = x^2 + 12x - 85

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Now you have your answer as:

x^2 + 12x - 85 feet^2

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if you roll a fair 6-sided die 9 times, what is the probability that at least 2 of the rolls come up as a 3 or a 4?
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Using the binomial distribution, it is found that there is a 0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.

For each die, there are only two possible outcomes, either a 3 or a 4 is rolled, or it is not. The result of a roll is independent of any other roll, hence, the <em>binomial distribution</em> is used to solve this question.

Binomial probability distribution

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
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  • p is the probability of a success on a single trial.

In this problem:

  • There are 9 rolls, hence n = 9.
  • Of the six sides, 2 are 3 or 4, hence p = \frac{2}{6} = 0.3333

The desired probability is:

P(X \geq 2) = 1 - P(X < 2)

In which:

P(X < 2) = P(X = 0) + P(X = 1)

Then

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

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P(X = 1) = C_{9,1}.(0.3333)^{1}.(0.6667)^{8} = 0.117

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P(X < 2) = P(X = 0) + P(X = 1) = 0.026 + 0.117 = 0.143

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.143 = 0.857

0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.

For more on the binomial distribution, you can check brainly.com/question/24863377

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