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3 years ago

Select the correct answer.

Mathematics

2 answers:

My name is Ann [436]3 years ago

7 0

Answer:

Step-by-step explanation:

That was actually trickier than I thought it would be

I was looking for 4(x-4), but 4(x-2)(x+2) also works

diamong [38]3 years ago

6 0

Answer:

4(x - 2)(x + 2) (Answer B)

Step-by-step explanation:

4x^2 - 16 is the difference of two squares, a case in which there is a simple formula to remember: a^2 - b^2 = (a - b)(a + b)

4x^2 - 16 = (2x - 4)(2x + 4)

This can be further simplified: 2(x - 2)(2)(x + 2) = 4(x - 2)(x + 2) (Answer B)

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I got most of them but I need help on those 3

Vadim26 [7]

Using Pythagoras:-

x^2 = 6^2 + (sqrt18)^2
= 36 + 18 = 54

x = sqrt54 = 3 sqrt6

3 0

3 years ago

Find the minimum sample size necessary to be 99% confident that the population mean is within 3 units of the sample mean given t

SVEN [57.7K]

Answer:

The minimum sample size required is 207.

Step-by-step explanation:

The (1 - α) % confidence interval for population mean μ is:

$CI=\bar x\pm z_{\alpha /2}\frac{\sigma}{\sqrt{n}}$

The margin of error of this confidence interval is:

$MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}$

Given:

$MOE=3\\\sigma=29\\z_{\alpha /2}=z_{0.01/2}=z_{0.05}=2.576$

*Use a z-table for the critical value.

Compute the value of n as follows:

$MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\\3=2.576\times \frac{29}{\sqrt{n}} \\n=[\frac{2.576\times29}{3} ]^{2}\\=206.69\\\approx207$

Thus, the minimum sample size required is 207.

3 0

3 years ago

What is (2,7) rotated 90% clockwise

ohaa [14]

Answer:

The required point is, (7, -2)

Step-by-step explanation:

The straight line passing through (0,0) and (2,7) is,

y = $(\frac {7 -0}{2-0}) \times x$

⇒ y = 3.5x --------------(1)

Now, the straight line perpendicular to this line and passing through (0, 0) is

y = $(\frac {-1}{3.5}) \times x$

⇒ 7y + 2x = 0 -------------(2)

Let, (h,k) be the required point.

then, it is on the line 7y + 2x = 0

⇒7k + 2h = 0

⇒k = $(\frac {-2}{7}) \times h$ ------------(3)

Again, distance from (0,0) of (h, k) is same as that of (2,7)

⇒ $h^{2} + k^{2} = 4 + 49 = 53$

⇒ $h^{2} \times (\frac {53}{49})$ = 53 [putting the value of k from (3)]

⇒ $h^{2}$ = 49

⇒h = 7 [since, (h,k) is in 4th quadrant, so,h >0]

So, k = -2 [putting the value of h in (3)]

So, the required point is, (7, -2)

5 0

3 years ago

Which of the following fractions would convert into a repeating decimal

ozzi

Answer: $\frac{2}{9}$

Step-by-step explanation: It is 2/9 because 2/9 converts to 0.222222222...

Hope it helps!

7 0

3 years ago

How many thirds are in 2/9

navik [9.2K]

1 third is in 2/9 because when simplified 2/9 becomes 1/3 being 1 third in 2/9

3 0

3 years ago

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