MATHEMATICS COLLEGE

What does -7(x+7)=-56

Answers

Answer 1

Answer:

Answer:

x=1

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve.

Answer 2

Answer:

Answer: x = 1

The way you find x is by dividing both sides of the equation by -7

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What is the y intercept of the line represented by the equation
3x+2y = 6?

Answers

Answer:

Step-by-step explanation:

To identify the y-intercept represented by the given equation, we need to get the equation into slope-intercept from:

$y=mx+b$

$m=slope$

$b=y-intercept$

Start with:

$3x+2y=6$

Subtract $3x$ from both sides of the equation:

$2y=-3x+6$

Divide both sides of the equation by the coefficient of $y$ , which is $2$ :

$y=-1.5x+3$

Identify the y-intercept:

$b=3$

PLEASE HELP!! (3/5) - 50 POINTS -

Answers

Answer:

infinite number of solutions

Step-by-step explanation:

A dependent system is where the two equations are the same line has has an infinite number of solutions

Answer:

$\boxed{\sf D) \ an\ infinite \ number \ of \ solutions}$

Step-by-step explanation:

A dependent system of equations has an infinite number of solutions.

When you graph the system of equations, both the equations represent the same line and have an infinite number of solutions.

I WILL GIVE 5 STAR AND BRAINLIEST IF 2 PEOPLE ANSWER! GIVE A GOOD ANSWER PLZ!!! Jenny is 12 years older than Steve. Five years ago, Jenny was four times older than Steve was then. How old are Jenny and Steve now?

Answers

Answer:

The age of Jenny=21 years

The age of Steve=9 years

Step-by-step explanation:

So... Let's make their age into unknown variables so it's easier to decipher:

Jenny's age: x

Steve's age: y

If 5 years ago Jenny was four times older than Steve the equation would look like:

y+12-4y=-15

First, you add like terms:

y+12-4y=-15

y-4y=-15-12

Now isolate the unknown variable:

3y=-27

y=9

But this was 5 years ago, and Jenny is 12 years older than Steve so add those two together:

9+12=21

Hope this helped!

According to the National Institute of Allergy and Infectious Diseases, 6% of American adults have a food allergy. A large company plans a lunch reception for its 500 employees. Assume that employees are independent. Let the random variable X be the number of company employees who have a food allergy. (a) What are the assumptions/requirements of a Binomial distribution? Does this situation meet all these requirements?
(b) What are the expected value and standard deviation of X (i.e., of the population)?
(c) What is the probability that none of the 500 employees has a food allergy?

Answers

Answer:

a) The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

In this problem, for each person, either they are allergic to some kind of food, or they are not. The probability of a person being allergic is independent of any other people. So this situations meets all these requirements.

b) The expected value is 30 and the standard deviation is 5.31.

c) Close to 0% probability that none of the 500 employees has a food allergy

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have food allergy, or they do not. The probability of an adult having allergy is independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_(n,x)$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$√(V(X)) = √(np(1-p))$

6% of American adults have a food allergy

This means that $p = 0.06$

500 employees.

This means that $n = 500$

(a) What are the assumptions/requirements of a Binomial distribution? Does this situation meet all these requirements?

The requirements is that each trial can only have two outcomes(success/failure), and each trial has the same probability of a success, that is, they are independent of each other.

(b) What are the expected value and standard deviation of X (i.e., of the population)?

$E(X) = np = 500*0.06 = 30$

$√(V(X)) = √(np(1-p)) = √(500*0.06*0.94) = 5.31$

The expected value is 30 and the standard deviation is 5.31.

(c) What is the probability that none of the 500 employees has a food allergy?

This is P(X = 0).

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

$P(X = 0) = C_(500,0).(0.06)^(0).(0.94)^(500) \cong 0$

Close to 0% probability that none of the 500 employees has a food allergy

Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x? StartFraction 5 plus-or-minus 3 StartRoot 11 EndRoot Over 12 EndFraction StartFraction 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction StartFraction 5 plus-or-minus StartRoot 47 EndRoot Over 12 EndFraction StartFraction negative 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction

Answers

The required value of the quadratic function which is determined by the using quadratic formula would be $x = (5\pm√(97))/(12)$ which is the correct answer would be an option (B).