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3 years ago

Solve the system shown.

Mathematics

1 answer:

krek1111 [17]3 years ago

3 0

1. Rewrite the system:

x+12y=68 (i)
x=8y-12 (ii)

2. Let's substitute the equation (ii) into the equation (i):

x+12y=68
(8y-12)+12y=68

3. Then, you have:

8y-12+12y=68

4. When you clear "y", you have:

20y-12=68
20y=68+12
20y=80
y=80/20
y=4

5. You already have the value of "y". Now, you must substitute this value into the equation (ii):

x=8y-12
x=8(4)-12
x=32-12
x=20

6. Therefore, the result is:

x=20
y=4

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When outliers are removed how does the mean change?

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The answer to this question is the mean increases by 3.

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3 years ago

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Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final c

Black_prince [1.1K]

Answer:

The test statistic value Z = 4.64 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

Test the claim that the proportion of all children in the town who suffer not from asthma is 11%

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 167

Given data In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma.

Sample proportion

$p^{-} = \frac{x}{n} = \frac{37}{167} = 0.2215$

Given Population proportion 'P' = 11% = 0.11

Step(ii) :-

Null Hypothesis : H₀ : p = 11

Alternative Hypothesis H₁: p≠11

Test statistic

$Z = \frac{p^{-} -P }{\sqrt{\frac{P Q}{n} } }$

$Z = \frac{0.2215 -0.11 }{\sqrt{\frac{0.11 X 0.89}{167} } }$

Z = 4.64

step(iii)

Critical value Z = 1.96

The calculated value Z = 4.64 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

Conclusion:-

Test the claim that the proportion of all children in the town who suffer not from asthma is 11%

4 0

3 years ago

6. Solve the the following system of equations: 4y+2x=14 2y+2x=10

Inessa05 [86]

4y+2x=14 ==> multiply this 1st equation by (-1) => -4y-2x=-14
Now add it up to the 2nd equation
-4y-2x=-14
2y+2x=10
-------------- And now add them up
-2y +0x=-4
==> -2y=-4==> 2y = 4 & y=2
Last step: plug y into any equation & you will find x=3

3 0

3 years ago

Solve for y in x+0.25y=1.5

IRISSAK [1]

Answer:

Y=-4x+6

Step-by-step explanation:

Step 1: Add -x to both sides.

X+0.25y+-x=1.5+-x

0.25y=-x+1.5

Step 2: Divide both sides by 0.25.

0.25y/0.25=-x+1.5/0.25