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3 years ago

10.Which of the following is HCF of 2x^2-18 and x^2-2x-3?

Mathematics

1 answer:

Vika [28.1K]3 years ago

7 0

Answer: x - 3

Step-by-step explanation:

Factor:

2x^2 - 18

1. Factor out 2: 2(x^2 - 9)

2.Factor x^2 - 9 into (x-3)(x+3): 2(x - 3)(x + 3)

*Notice that x^2 - a^2 can always be factored into (x-a)(x+a)

where a is a constant so in this case, a is 9 which is also 3^2

so x^2 - 9 can be factored into (x - 3)(x + 3)

x^2 - 2x - 3

1. Think what two numbers multiplied together is -3 and added together is 2

-> 3 and -1 since 3(-1) = -3 and 3+ (-1) = 2

2. Factor x^2 - 2x -3 into (x - 3)(x + 1)

Therefore, since both 2x^2 - 18 and x^2 - 2x -3 do not have another common factor besides x - 3, x - 3 is the HCF of 2x^2 - 18 and x^2 - 2x -3.

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An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by th

butalik [34]

Answer:

a) A sample size of 5615 is needed.

b) 0.012

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

99.5% confidence level

So $\alpha = 0.005$ , z is the value of Z that has a pvalue of $1 - \frac{0.005}{2} = 0.9975$ , so $Z = 2.81$ .

(a) Past studies suggest that this proportion will be about 0.2. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015.

This is n for which M = 0.015.

We have that $\pi = 0.2$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.015 = 2.81\sqrt{\frac{0.2*0.8}{n}}$

$0.015\sqrt{n} = 2.81\sqrt{0.2*0.8}$

$\sqrt{n} = \frac{2.81\sqrt{0.2*0.8}}{0.015}$

$(\sqrt{n})^{2} = (\frac{2.81\sqrt{0.2*0.8}}{0.015})^{2}$

$n = 5615$

A sample size of 5615 is needed.

(b) Using the sample size above, when the sample is actually contacted, 12% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?

Now $\pi = 0.12, n = 5615$ .

We have to find M.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$M = 2.81\sqrt{\frac{0.12*0.88}{5615}}$

$M = 0.012$

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3 years ago

What is the end behavior of the graph of the polynomial function y = 10x9 – 4x?

scoray [572]

Answer:

See below.

Step-by-step explanation:

The value of the highest degree ( x^9) is 9 - odd.

So this well rise from negative infinity on the left and rise to positive infinity on the right - or, putting it in a different way, fall to the left and rise to the right.

4 0

3 years ago

Read 2 more answers

The output is ten less then the input x

mart [117]

Y=X-10

Step-by-step explanation:

Step 1:

Let X be the input and Y be the output variable

Given: The output is 10 less than the input

Step 2:

Y=X-10 be the require function