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2 years ago

How do i solve 3v + 1 + 7v = -12

Mathematics

2 answers:

Pie2 years ago

6 0

Answer:

Answer:

v=-13/10

Step-by-step explanation:

Our equation: $3v+1+7v=-12$

So, lets solve this step by step:

Step #1 - We first need to combine like terms. This means to combine the vs together. Once we combine them, we get:

$10v+1=-12$

Step #2 - Now we iscolate the variable(which in this case is v). To do this we subtract the 1 to the other side of the equation. Once we subtract the 1 to the -12, we get:

$10v=-13$

Step #3 - Finally, we must get rid of the coefficent. To do this, we divide the 10 in front of the v by 10. What we do on one side, we must do on the other, which means we must also divide the -13 by 10 as well. Now we get our answer:

$v = -\frac{13}{10}$

Hope this helps! :3

riadik2000 [5.3K]2 years ago

4 0

Answer:

-1.3

Step-by-step explanation:

3v+1+7v=-12 equation

10v+1=-12 combine like terms

10v=-13 subtract 1 from both sides

v=-1.3 divide by 10

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(a) Null Hypothesis, $H_0$ : $\mu \leq$ 3.50 mg

Alternate Hypothesis, $H_A$ : $\mu$ > 3.50 mg

(b) The value of z test statistics is 2.50.

(c) We conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.

(d) The p-value is 0.0062.

Step-by-step explanation:

We are given that Green Beam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a mean of 3.59 mg of mercury. Assuming a known standard deviation of 0.18 mg.

Let $\mu$ = average mg of mercury in compact fluorescent bulbs.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 3.50 mg {means that the average mg of mercury in compact fluorescent bulbs is no more than 3.50 mg}

Alternate Hypothesis, $H_A$ : $\mu$ > 3.50 mg {means that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean mg of mercury = 3.59

$\sigma$ = population standard deviation = 0.18 mg

n = sample of bulbs = 25

So, test statistics = $\frac{3.59-3.50}{\frac{0.18}{\sqrt{25} } }$

= 2.50

The value of z test statistics is 2.50.

Now, P-value of the test statistics is given by;

P-value = P(Z > 2.50) = 1 - P(Z $\leq$ 2.50)

= 1 - 0.9938 = 0.0062

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Therefore, we conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.

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