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3 years ago

I need the answer pls help!

Mathematics

1 answer:

valina [46]3 years ago

7 0

Answer:

x = ± 7

Step-by-step explanation:

Given

(2x - 1)(3x + 2) = x + 292 ← expand left side using FOIL

6x² + x - 2 = x + 292 ( subtract x from both sides )

6x² - 2 = 292 ( add 2 to both sides )

6x² = 294 ( divide both sides by 6 )

x² = 49 ( take the square root of both sides )

x = ± 7

That is x = - 7, x = 7

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Simplify the expression. <br><br> -1/2 + 1/6

sukhopar [10]

-1/2 = -3/6

-3/6 + 1/6 = -2/6

-2/6 = -1/3

-1/3 is your answer

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2 years ago

Boris is ordering supplies for his company. He ordered 20 boxes of pencils and 32 boxes of pens. What is the ratio of boxes of p

Allisa [31]

$\frac{boxes \ of \ pens}{boxes \ of \ pencils}=\frac{32}{20}=\frac{8 \times 4}{5 \times 4}=\boxed{\frac{8}{5}} \Leftarrow A$

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2 years ago

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In a certain clinical study, 15% of participants were classified as heavy smokers, 25% as light-smokers, and the rest as non-smo

Natasha_Volkova [10]

Answer:

There is a 28.57% probability that a randomly selected participant who died by the end of the study was a non-smoker.

Step-by-step explanation:

We have the following probabilities:

A 15% probability that a participant is classified as a heavy smoker.

A 25% probability that a participant is classified as a light smoker.

A 100% - 25% - 15% = 60% probability that a participant is classified as a non smoker.

A x% probability that a non smoker dies.

A 3x% probability that a light smoker dies.

A 5x% probability that a heavy smoker dies.

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

This problem is:

What is the probability of the participant being a non-smoker, given that he died?

P(B) is the probability that the participant is a non smoker. So

$P(B) = 0.6$

P(A/B) is the probability that the participant dies, given that he is a non smoker. So:

$P(A/B) = x$

P(A) is the probability that the participant dies:

$P(A) = P_{1} + P_{2} + P_{3}$

$P_{1}$ is the probability that a heavy smoker is selected and that he dies. So:

$P_{1} = 0.15*5x = 0.75x$

$P_{2}$ is the probability that a light smoker is selected and that he dies. So:

$P_{2} = 0.25*3x = 0.75x$

$P_{3}$ is the probability that a non-smoker is selected and that he dies. So:

$P_{3} = 0.60*x = 0.60x$

The probability that a participant dies is:

$P(A) = P_{1} + P_{2} + P_{3} = 0.75x + 0.75x + 0.60x = 2.10x$

The probability of the participant being a non-smoker, given that he died, is:

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.6x}{2.10x} = \frac{0.6}{2.10} = 0.2857$

There is a 28.57% probability that a randomly selected participant who died by the end of the study was a non-smoker.

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2 years ago

Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together the

klasskru [66]

The rate charged per hour by each mechanic was: x = 75 $ / hr and y = 115 $ / hr.

<h3>What is a system of equations?</h3>

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours.

Together they charged a total of $3225.

For this case we have the following variables:

x be the amount of $ / hr that the mechanic obtains 1.

y be the amount of $ / hr obtained by mechanic 2.

An equation to express this would be:

x + y = 190

20x + 15y = 3225

Solving the system of equations we have:

20x + 15(190 -x) = 3225

20x + 2850 - 15x = 3225

5x = 375

x = 75

simililary

y = 190 - x

y = 115

Hence, the rate charged per hour by each mechanic was:

x = 75 $ / hr

y = 115 $ / hr

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