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2 years ago

Find the length of the third side. If necessary, write in simplest radical form.

Mathematics

1 answer:

AleksandrR [38]2 years ago

8 0

Answer:

Step-by-step explanation:

This is a right triangle, and so the Pythagorean Theorem applies. The legs of this triangle are 3√3 and 3; squaring these gives us 9(3) = 27 and 9. Then, this Theorem gives us the length of the hypotenuse as

h^2 = 27 + 9, or h^2 = 36, so that h, the length of the hypotenuse, must be 6.

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If you invest $1,500 today in a bank that gives you a 5 percent annual interest rate, which of these items can you buy in two ye

Andre45 [30]

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3 years ago

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If f(x) = x^2 - 2x and g(x) = 6x + 4, for what value of x does (f + g)(x) = 0?

larisa86 [58]

Answer:

x = -2

Step-by-step explanation:

$f(x) =x^2 -2x\:\: and \:\: g(x) = 6x + 4\\(f+g)(x) = f(x) + g(x) \\(f+g)(x) = x^2 -2x+ 6x + 4\\(f+g)(x) = x^2+4x + 4\\(f+g)(x) = (x+2)^2\\ 0 = (x+2)^2...[\because (f+g)(x) =0]\\0 = x+2\\\therefore x = -2$

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3 years ago

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The mass of a pencil is 5.44 g. The mass of a crayon is 2.145 g.

Salsk061 [2.6K]

Answer:

3.295g

Step-by-step explanation:

5.44g-2.145g=3.295g

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2 years ago

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An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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2 years ago

Find one-eight of the sum of 18 and the product of 6 and 1

4vir4ik [10]

Answer: 3

Step-by-step explanation:

The question is to calculate one-eight of the sum of 18 and the product of 6 and 1. This will be:

= 1/8 [18 + (6 × 1)]

= 1/8 [18 + 6]

= 1/8 × 24

= 3

The answer is 3.

8 0

3 years ago