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3 years ago

Here is a linear equation in two variables: 2x+4y−31=123. Solve the equation, first for x and then for y.

Mathematics

1 answer:

Allushta [10]3 years ago

7 0

Answer:

$x = 77 - 2y$

$y = \frac{77 - x}{2}$

Step-by-step explanation:

Given

$2x + 4y - 31 = 123$

Required

Solve for x and for y

$2x + 4y - 31 = 123$

Add 31 to both sides

$2x + 4y - 31+31 = 123+31$

$2x + 4y = 154$

Solving for x

Subtract 4y from both sides

$2x + 4y - 4y = 154 - 4y$

$2x = 154 - 4y$

Divide by 2

$x = 77 - 2y$

Solving for y

$2x + 4y = 154$

Subtract 2x from both sides

$2x - 2x + 4y = 154 - 2x$

$4y = 154 - 2x$

Divide by 4

$y = \frac{154 - 2x}{4}$

Split

$y = \frac{77 - x}{2}$

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A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y. Corn costs $215 per acre to produce, and cotton costs

tatyana61 [14]

Answer:

The system that represent the scenario is

$x+y\leq500$

$215x+615y\leq 187,500$

The solution in the attached figure

Step-by-step explanation:

Let

x-----> the acres of corn

y----> the acres of cotton

we know that

$x+y\leq500$ ------> inequality A

$215x+615y\leq 187,500$ -----> inequality B

using a graphing tool

the solution is the shaded area in the attached figure

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3 years ago

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ANSWER PLEASE! 14 points if you do

Goshia [24]

The correct answer is C. 2y = 22

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3 years ago

Explain when the median of a data set is a better measure of center than the mean.

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Answer:

The median of a data set is better when you have a term or terms that are not close to the other terms

Step-by-step explanation:

For example:

Say you have the data set

1, 15, 17, 18, 22, 84

The median of these terms would be 17.5

(it is the exact center of the data group)

17 + 18 = 35

35/2 = 17.5

The mean of these terms would be 26.17

(this number is not close to the center because the numbers 1 and 84

are not close enough to the other terms)

1 + 15 + 17 + 18 + 22 + 84 = 157

157/6 = 26.17

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4) Realtor gets 3% commission on sales, sold a $200,000 house, her commission is

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Answer:

6,000

Step-by-step explanation:

200,000 * 0.03 = 6,000

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3 years ago

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You are given the information that P(A) = 0.30 and P(B) = 0.40.

Ad libitum [116K]

Answer:

1.B. No. You need to know the value of P(A and B). 2.C. Yes P(A and B) =0, so P(A or B) = P(A) + P(B).

Step-by-step explanation:

We can solve this question considering the following:

For two mutually exclusive events:

$\\ A_{1}\;and\;A_{2}$

$\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2})$ (1)

An extension of the former expression is:

$\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2}) - P(A_{1} and A_{2})$ (2)

In mutually exclusive events, P(A and B) = 0, that is, the events are independent one of the other, and we know the probability that both events happen at the same time is zero (P(A and B) = 0). There are some other cases in which if event A happens, event B too, so they are not mutually exclusive because P(A and B) is some number different from zero. Notice the difference between OR and AND. The latter implies that both events happen at the same time.

In other words, notice that the formula (2) provides an extension of formula (1) for those events that are not mutually exclusive, that is, there are some cases in which the events share the same probabilities in a way that these probabilities must be subtracted from the total, so those probabilities in common do not "inflate" the actual probability.

For instance, imagine a person going to a gas station and ask for checking both a tire and lube oil of his/her car. The probability for checking a tire is P(A)=0.16, for checking lube oil is P(B)=0.30, and for both P(A and B) = 0.07.

The number 0.07 represents the probability that both events occur at the same time, so the probability that this person ask for checking a tire or the lube oil of his/her car is:

P(A or B) = 0.16 + 0.30 - 0.07 = 0.39.

That is why we cannot simply add some given probabilities without acknowledging if the events are or not mutually exclusive, whereas we can certainly add the probabilities in question when we know that both probabilities are mutually exclusive since P(A and B) = 0.

In conclusion, knowing the events are mutually exclusive does provide extra information and we can proceed to simply add the probabilities of either event; thus, the answers are those in which we need to previously know the value of P(A and B).

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3 years ago