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Solve the following system of equation by using the method of substitution. x + 2y = -1 and 2x – 3y =12

Answers

Answer 1

Answer:

Answer:

x = 3

y = -2

Step-by-step explanation:

x + 2y = -1

2x – 3y =12

Using substitution means that in one equation you solve for a variable. In this case, the first equation would be easier to solve for x since there are no coefficients.

x = -2y - 1

Now, we plug in the value of x into the second equation, and solve for y.

2 (-2y - 1) - 3y = 12

-4y - 2 - 3y = 12

-7y - 2 = 12

-7y = 14

y = -2

Since we have a numerical value of y, we can use it to solve for x by plugging it into one of the original equations.

x + 2(-2) = -1

x - 4 = - 1

x = 3

If you'd like to check the answer, plug in both values you got to the original equations!

I hope this helps!

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Answers

Answer:

A. distributive property

Which expression best represents the cube

Answers

Step-by-step explanation:

The following is a list of perfect Cubes

13 = 1

23 = 8

33 = 27

43 = 64

53 = 125

63 = 216

73 = 343

83 = 512

93 = 729

103 = 1000

If a variable with an exponent has an exponent which is divisible by 3 then it is a perfect cube. To get the cube root, we simply divide the exponent by 3. For example x9 is a perfect cube, its cube root is x3 . x11 is not a perfect cube.

According to a recent study, 9.2% of high school dropouts are 16- to 17-year-olds. In addition, 6.2% of high school dropouts are white 16- to 17-year-olds. What is the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old?

Answers

Answer:

Step-by-step explanation:

So, out of a 100% students that drop out, 9,2% is in the range of 16-17 years of age. The conclusion would be, $(92)/(1000)$ would express the probability of randomly picking a dropout that belong in this set of 16-17 year olds.

Notice that I put "1000" because I want a 0,0092 as a multiplier, because in probability, that represents "9,2%". You actually awnt to always put 100, because that's 100%, but this is just a trick, writing 9,2/100 still works.

Now, for the second bit of information you want to also include that "6,2% white students", which is a subset of the set of 16-17 year olds. and that's a probability, in of itself. Thus, you multiply these two probabilities.

What you want to plug, in your calculator, the follwing expression:

$(9,2)/(100) (6,2)/(100)$

This will give you a number, which you'll have to multiply by 100, to obtain the answer for your problem!

Final answer:

The probability that a randomly selected dropout aged 16 to 17 is white, given the provided statistics, is 67.39%.

Explanation:

The student is asking a question related to conditional probability in the field of Mathematics. The question prompts us to find out the probability that a randomly selected high school dropout in the age range of 16 to 17 is white. To find the answer, we use the following formula:

P(A|B) = P(A ∩ B) / P(B)

Where:
P(A|B) is the probability of event A happening given that event B has occurred.
P(A ∩ B) is the probability of both event A and event B happening together.
P(B) is the probability of event B happening.

From the problem statement, we know that P(B), the percentage of dropouts who are 16-17 years old, is 9.2%. Also, P(A ∩ B), the percent of dropouts who are both white and 16-17 years old, is given as 6.2%. We are supposed to find P(A|B), the probability that a dropout is white given that they are 16-17 years old.

Therefore, by substituting these values into the formula, we get:

P(A|B) = 6.2% / 9.2% = 67.39%

Rounded to two decimal places, the answer is 67.39%. So, there is approximately a 67.39% chance that a random high school dropout aged 16-17 is white.

Learn more about Conditional Probability here:

brainly.com/question/32171649

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In? gambling, the chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For? example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is? 3, the odds of winning are 2:3(Note; if the odds of winning are 2/3, the propability of sucess is2/5)The odds of event occuring are 1:6. Find (a) the propability that the event will occur,(b) propability that the event will not occur.

(a)The propability that event will occur is....(TYPE AN INTEGER OR DECIMAL ROUNDED TO THE NEAREST THOUSANDTH AS NEEDED.)

(b)The propability thet the event will not occur is...(TYPE AN INTEGER OR DECIMAL ROUNDED TO THE NEAREST THOUSANDTH AS NEEDED)