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3 years ago

Evaluate: tan(-120 degrees).

1 answer:

8 0

-120° = -2π/3 radians.

Tangent is defined as Opposite/Adjacent or Sine/Cosine in a unit circle. So, if you have memorized the unit circle,

sin(-2π/3) = √3/2
cos(-2π/3) = -1/2

So, tan(-2π/3) would be:
$\frac{ \frac{ \sqrt{3} }{2} }{ \frac{-1}{2} } = \frac{ \sqrt{3} }{2}* -\frac{2}{1}$

Simplify, and you get:
$-\frac{2 \sqrt{3} }{2} = - \sqrt{3}$

And, so, tan(-2π/3) = -√3

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Samuel makes a dozen of mini cupcakes using 5/8 cups of sugar, 3 cups of chocolate chips and 1/2 cup of butter. If each cupcak

baherus [9]

I don't what form of measurement to use (like grams, cusp, etc.) but I'm pretty sure it'd be cups

I think it's 5/96 or .05208333

So, 5/8 is .625. Dividing that up in throwing it into 12 cupcakes.

8 0

3 years ago

(6^2)^4 simplify expression

grin007 [14]

Answer:

1679616

Step-by-step explanation:

6 0

3 years ago

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.

6 0

3 years ago

Hello Please help me.

olga55 [171]

Answer:

Step-by-step explanation:

1) D

2) B

3) no solution

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3 0

3 years ago

Combine like terms to simplify.<br><br> 2. 3v + w +8 - 2n

AURORKA [14]

3v + w +8 - 2n
<span>
Simplifying 3v + w + 8 + -2n

Reorder the terms: 8 + -2n + 3v + w

Hopes it helped!</span>

4 0

3 years ago