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3 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

Jlenok [28]3 years ago

4 0

Answer:

The solution would be (-19, 40)

Step-by-step explanation:

In order to solve this system by substitution, simply take the value of y in the first equation and use it in place of y in the second. This will allow you to solve for x.

5x + 2y = 15

5x + 2(-3x - 2) = 15

5x - 6x - 4 = 15

-x - 4 = 15

-x = 19

x = -19

Now that we have the value of x, we can find the value of y.

y = -3x - 3

y = -3(-19) - 3

y = 43 - 3

y = 40

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Alina [70]

9514 1404 393

Answer:

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Step-by-step explanation:

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3 years ago

A city council consists of seven Democrats and five Republicans. If a committee of four people is selected, find the probability

Hoochie [10]

Answer:

The probability of selecting two Democrats and two Republicans is 0.4242.

Step-by-step explanation:

The information provided is as follows:

A city council consists of seven Democrats and five Republicans.
A committee of four people is selected.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!\times (n-k)!}$

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${12\choose 4}=\frac{12!}{4!\times (12-4)!}=495$

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${7\choose 2}=\frac{7!}{2!\times (7-2)!}=21$

Compute the number of ways to selected two Republicans as follows:

${5\choose 2}=\frac{5!}{2!\times (5-2)!}=10$

Then the probability of selecting two Democrats and two Republicans as follows:

$P(\text{2 Democrats and 2 Republicans})=\frac{21\times 10}{495}=0.4242$

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2 years ago

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