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erma4kov [3.2K]
3 years ago
12

-4m + 2n = 6 -4m + n = 8 solve for and x and y steps

Mathematics
1 answer:
hammer [34]3 years ago
5 0

<u><em>I am doing this problem assuming that you mean to solve for m and n as x and y do not exist in this system of equations.</em></u>

<u><em /></u>

-4m+2n=6

-4m+n=8

We can see that the coefficient of x for both equations are -4; therefore, elimination with subtraction is possible.

<u>First equation - second equation</u>

n=-2

<u>Then substitude back in to solve for m</u>

-4m+(-2)=8

4m=10

m=5/2

Therefore the answer is

n= - 2

m= 5/2

I hope this helped and if you have any questions please ask.

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Let X denote the length of human pregnancies from conception to birth, where X has a normal distribution with mean of 264 days a
Kaylis [27]

Answer:

Step-by-step explanation:

Hello!

X: length of human pregnancies from conception to birth.

X~N(μ;σ²)

μ= 264 day

σ= 16 day

If the variable of interest has a normal distribution, it's the sample mean, that it is also a variable on its own, has a normal distribution with parameters:

X[bar] ~N(μ;σ²/n)

When calculating a probability of a value of "X" happening it corresponds to use the standard normal: Z= (X[bar]-μ)/σ

When calculating the probability of the sample mean taking a given value, the variance is divided by the sample size. The standard normal distribution to use is Z= (X[bar]-μ)/(σ/√n)

a. You need to calculate the probability that the sample mean will be less than 260 for a random sample of 15 women.

P(X[bar]<260)= P(Z<(260-264)/(16/√15))= P(Z<-0.97)= 0.16602

b. P(X[bar]>b)= 0.05

You need to find the value of X[bar] that has above it 5% of the distribution and 95% below.

P(X[bar]≤b)= 0.95

P(Z≤(b-μ)/(σ/√n))= 0.95

The value of Z that accumulates 0.95 of probability is Z= 1.648

Now we reverse the standardization to reach the value of pregnancy length:

1.648= (b-264)/(16/√15)

1.648*(16/√15)= b-264

b= [1.648*(16/√15)]+264

b= 270.81 days

c. Now the sample taken is of 7 women and you need to calculate the probability of the sample mean of the length of pregnancy lies between 1800 and 1900 days.

Symbolically:

P(1800≤X[bar]≤1900) = P(X[bar]≤1900) - P(X[bar]≤1800)

P(Z≤(1900-264)/(16/√7)) - P(Z≤(1800-264)/(16/√7))

P(Z≤270.53) - P(Z≤253.99)= 1 - 1 = 0

d. P(X[bar]>270)= 0.1151

P(Z>(270-264)/(16/√n))= 0.1151

P(Z≤(270-264)/(16/√n))= 1 - 0.1151

P(Z≤6/(16/√n))= 0.8849

With the information of the cumulated probability you can reach the value of Z and clear the sample size needed:

P(Z≤1.200)= 0.8849

Z= \frac{X[bar]-Mu}{Sigma/\sqrt{n} }

Z*(Sigma/\sqrt{n} )= (X[bar]-Mu)

(Sigma/\sqrt{n} )= \frac{(X[bar]-Mu)}{Z}

Sigma= \frac{(X[bar]-Mu)}{Z}*\sqrt{n}

Sigma*(\frac{Z}{(X[bar]-Mu)})= \sqrt{n}

n = (Sigma*(\frac{Z}{(X[bar]-Mu)}))^2

n = (16*(\frac{1.2}{(270-264)}))^2

n= 10.24 ≅ 11 pregnant women.

I hope it helps!

6 0
3 years ago
Scott took out a 4-year car loan for $5,500. He paid back a total of $7,370. What interest rate did he pay for this loan?
elena-14-01-66 [18.8K]
Amount of car loan taken by Scott = $5500
Amount of loan paid back by Scott = $7370
Then
Amount of money paid as interest by Scott = (7370 - 5500) dollars
                                                                     = 1870 dollars
Then
Percentage of interest given for the car loan = (1870/5500) * 100
                                                                       = 1870/55
                                                                       = 34 percent
So Scott had to pay a total interest rate of 34% in the four years.I hope the procedure is simple enough for you to understand and solve future problems.
7 0
3 years ago
There are 35 men and 25 women on a bus. If 20 married couples leave the bus, the number of men is how many times the number of w
Angelina_Jolie [31]

Answer:

3

Step-by-step explanation:

15 men would be left

5 women would be left

6 0
3 years ago
What is 4.4 divided by 2.727
zlopas [31]
1.613 jus use a calculator
5 0
3 years ago
Solve the system of equations by elimination <br> 3x+4y=31<br> 2x-4y=-6
ANEK [815]
3x + 4y = 31
2x - 4y = -6

*The +4 and -4 in the center of the equation cancel out because 4-4 = 0*

3x = 31
2x = -6
------------

*add like terms*

3x + 2x = 5x

31 - 6 = 25

So now you should have this written on your paper ... > 5x = 25

*Divide by 5 on each side*

5x = 25
_      _
5      5

x = 5
5 0
3 years ago
Read 2 more answers
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