Solve for Z (This should be another easy question, + there are answers you can choose from)

How do i solve systems of equations by elimination?

Vera_Pavlovna [14]

Say you had this problem:

-4x - 2y= -12
4x +8y = -24

First you would have to cancel out one part of the equation to get on variable alone. In this case it's easy it would be -4x and 4x. So then you would cancel those out.

Now we have

-2y= -12
8y =-24

so then you just add them all up

6y=-36

Next you just divide both sides by 6
so then you answer for y would be -6.

Next you would choose one of your equations and plug the -6 in.

So it would be

-4x -2 (-6) =-24

So you would times negative 2 by negative 6, which would be positive 12. Since a negative times a negative equales a positive.

-4x + 12= -24

Next you would minus 12 on both sides.

-4x + 12=-24
- 12 = -12

The 12's would cancel out and then you just minus -24 by -12 which you would ended up just plusing them together because a negative plus a negative equales a negative. Or a negative minus a negative number would end up adding them up.

-4x= -36

Next you would get x alone and how you would do that is you would divide -4 in both sides which would cancel them -4 out then it would be divided by -36.

So it would look like this.

-4x= -36
-4 -4

So negative 36 divided by negative 4 is 9.

So your final answer would be

y= -6
x= 9

I hope I explained to you properly how to do systems of equations by elimination.

8 0

3 years ago

For the pair of points, find the slope of the line that passes through both points. (1,1) and (5,7)

zvonat [6]

Answer: 3/2

Step-by-step explanation:

$\frac{7-1}{5-1}=\frac{6}{4}=\frac{3}{2}$

5 0

2 years ago

Of all the registered automobiles in a city, 12% fail the emissions test. Fourteen automobiles are selected at random to undergo

postnew [5]

Answer:

a) 0.1542

b) 0.7685

c) 0.2315

d) No, it is not unusual

Explanation:

The procedure to make the test meets the requirements of binomial experiments because:

there are two possible mutually exclusive outputs: fail the test, or pass the test.
the probability of each event remains constant during all the test (p=12% = 0.12, for failing the test, and 1-p = 88% = 0.88, for passing the test)
each trial (test) is independent of other trial.

Solution

(a) Find the probability that exactly three of them fail the test.

You want P(X=3)

Using the equation for discrete binomial experiments, the probability of exactly x successes is:

$P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}$

Substituting C(n,x) with its developed form, that is:

$P(X=x)=\dfrac{n!}{x!\cdot (n-x)!}\cdot p^x\cdot (1-p)^{(n-x)}$

Thus, you must use:

x = 3 (number of automobiles that fail the emissions test)
n = 14 (the number of automobiles selected to undergo the emissions test),
p = 0.12 (probability of failing the test; this is the success of the variable on our binomial experiment)
1 - p = 0.88 (probability of passing the test; this is the fail of the variable on our binomial experiment)

$P(X=3)=\dfrac{14!}{3!\cdot (14-3)!}\cdot 0.12^3\cdot 0.88^{11}=0.1542$

(b) Find the probability that fewer than three of them fail the test.

The probability that fewer than three of them fail the test is the probability that exactly 0, or exactly 1, or exactly 2 fail the test.

That is: P(X=0) + P(X=1) + P(X=2)

Using the same formula:

$P(X=0)=\dfrac{14!}{0!\cdot 14!}\times 0.12^0\cdot 0.88^{14}$

$P(X=0)=0.1670$

$P(X=1)=\dfrac{14!}{1!\cdot 13!}\cdot 0.12^1\cdot 0.88^{13}$

$P(X=1)=0.3188$

$P(X=2)=\dfrac{14!}{2!\cdot 12!}\codt0.12^2\cdot 0.88^{12}$

$P(X=2)=0.2826$

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.7685

(c) Find the probability that more than two of them fail the test.

The probability that more than two of them fail the test is equal to 1 less the probability that exactly 0, or exactly 1, or exactly 2 fail the test:

P( X > 2) = 1 - P( X = 0) - P(X = 1) - P(X = 2)

P X > 2) = 1 - [P(X=0) + P(X = 1) + P(X = 2)]

P (X > 2) = 1 - [0.7685]

P (X > 2) = 0.2315

(d) Would it be unusual for none of them to fail the test?

Remember that not failing the test is the fail of the binomial distribution. Thus, none of them failing the test is the same as all of them passing the test.

You can find the probability that all the automibles pass the emission tests by multiplying the probability of passing the test (0.88) 14 times.

Then, the probability that none of them to fail the test is equal to:

$(1-p)^{14}\\\\(0.88)^{14}=0.1671$

That means that the probability than none of the automobiles of the sample fail the test is 16.71%.

Unusual events are usually taken as events with a probability less than 5%. Thus, this event should not be considered as unusual.

5 0

3 years ago

A company borrowed $25,000 at 3.5% and was charged $2,625 in interest. How long was it before the company repaid the money?

nirvana33 [79]

Hello

3 years. Since no mention of compounding was made I will assume that it's 3.5% simple interest. So first, let's calculate what percent of the entire loan was interest. Just a simply matter of division. 2625 / 25000 = 0.105 = 10.5% Now lets' divide the percentage of the loan that was paid in interest by the interest rate. 10.5% / 3.5% = 3 So the company took 3 years to repay the loan.
Have a nice day

5 0

4 years ago

Read 2 more answers

Please help! Will be marking brainliest!

Ludmilka [50]

Answer:

integer and rational

Step-by-step explanation:

5 0

3 years ago