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3 years ago

What is the solution to the following system ?

1 answer:

4 0

3x+3y+6z=9
x+3y+2z=5
3x+12y+12z=18

Step 1: use Eq 2 to solve for x
x+3y+2z=5
x= -3y-2z+5
Step 2: Solve for y unsing Eq 1
3x+3y+6z=9
3y= -3x-6z+9
y= -x-2z+3

Step 3: plug in x= -3y-2z+5 to solve for the value of y
y=-x-2z+3
y= (-1)(-3y -2z +5) - 2z+3
y= 3y+2z-5- 2z+3
-2y= -2
y=1

Step 4: plug y= 1 into the x= equation
x= -3y-2z+5
x= -3(1)-2z+5
x= -2z+2
Step 5:Plug y= 1 and x= -2z+2 into the 3rd equation to solve for z
3x+12y+12z=18
12z= -3(-2z+2)-12(1)+ 18
12z= 6z - 6 - 12 +18
6z= -18+18
6z=0
z=0

Step 6: Plug z in to solve for x
x=-2z+2
x= (-2)(0)+2
x= 2

ANSWER:
x,y,z = 2,1,0
answer choice C

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Answer:

a. $13

b. $3

Step-by-step explanation:

Juan wants to start a lemonade stand to earn money. He needs money to purchase the materials before he can sell the lemonade and earn money. His mother agrees to loan him $10. He makes a list of the items he wants to buy.

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Sugar $3

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3 years ago

A group of 54 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic

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Answer:

$t=\frac{5.25-4.73}{\frac{3.98}{\sqrt{54}}}=0.9601$

P-value

First we find the degrees of freedom given by:

$df = n-1= 54-1=53$

Since is a two-sided test the p value would be:

$p_v =2*P(t_{53}>0.9601)=0.3414$

Step-by-step explanation:

Data given and notation

$\bar X=5.25$ represent the sample mean

$s=3.98$ represent the sample standard deviation

$n=54$ sample size

$\mu_o =4.73$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean differs from 4.73, the system of hypothesis would be:

Null hypothesis: $\mu =4.73$

Alternative hypothesis: $\mu \neq 4.73$

Since we know don't the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{5.25-4.73}{\frac{3.98}{\sqrt{54}}}=0.9601$

P-value

First we find the degrees of freedom given by:

$df = n-1= 54-1=53$

Since is a two-sided test the p value would be:

$p_v =2*P(t_{53}>0.9601)=0.3414$

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