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3 years ago

Solve each equation by factoring 4) 4n? +n - 16=-2

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

4 0

Answer:

n=14/5

Step-by-step explanation:

4n+n-16=-2

We move all terms to the left:

4n+n-16-(-2)=0

We add all the numbers together, and all the variables

5n-14=0

We move all terms containing n to the left, all other terms to the right

5n=14

n=14/5

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Find the possible value of "a" using the distance formula.<br> (4,-1) and (a,5) with d = 10

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Answer:

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Step-by-step explanation:

The distance formula is given by:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

We are given the two points (4, -1) and (a, 5). The distance between them is 10.

Let (4, -1) be (x₁, y₁) and let (a, 5) be (x₂, y₂). Substitute:

$10=\sqrt{(a-4)^2+(5-(-1))^2}$

Solve for <em>a</em>. Square both sides and simplify:

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Simplify:

$64=(a-4)^2$

Take the square root of both sides. Since we are taking an even root, we will need plus/minus. Hence:

$\pm\sqrt{64}=\pm8=a-4$

Solve for <em>a:</em>

<em /> $a-4=8\Rightarrow a=12\text{ or } a-4=-8\Rightarrow a=-4$ <em />

<em />

So, our two possible points are (12, 5) or (-4, 5).

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Nadia wants to estimate the mean driving range for her company's new electric vehicle. She'll sample vehicles and measure each o

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Using the z-distribution, it is found that the smallest sample size required is given by:

B) 7 vehicles.

<h3>What is the margin of error for a z-distribution confidence interval?</h3>

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$M = z\frac{\sigma}{\sqrt{n}}$

In which:

z is the critical value.

$\sigma$ is the population standard deviation.

n is the sample size.

In this problem, we have a 90% confidence level, hence $\alpha = 0.9$ , z is the value of Z that has a p-value of $\frac{1+0.9}{2} = 0.95$ , so the critical value is z = 1.645.

The margin of error and the population standard deviation are given by, respectively:

$M = 10, \sigma = 15$ .

Then, we solve for n to find the needed sample size.

$M = z\frac{\sigma}{\sqrt{n}}$

$10 = 1.645\frac{15}{\sqrt{n}}$

$10\sqrt{n} = 1.645 \times 15$

$\sqrt{n} = 1.645 \times 1.5$

$(\sqrt{n})^2 = (1.645 \times 1.5)^2$

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Rounding up, 7 vehicles have to be sampled, hence option B is correct.

More can be learned about the z-distribution at brainly.com/question/25890103

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