The net for a triangular prism consists of
2 identical triangles, here all nets have sides 5,12, and 13.
3 rectangles, all with a common dimension: the height H=14 of the prism.

Each of the 3 rectangles should have dimensions
H=14 plus one of the following:
each of 5, 12, 13 corresponding to one side of the base (triangle).

So the dimensions of the rectangles are
5x14, 12x14, 13x14

And dimensions of the triangles are
5,12 and 13.

The total surface area is therefore
(5+12+13)*14 + 2*(5*12/2)
=420+60
=480.

There is only one net that satisfies this condition.

8 0

3 years ago

Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old. How large a sample size

julsineya [31]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

For this case we can use as estimator for the proportion $\hat p =0.5$ , since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

8 0

3 years ago

Wen takes a job with a starting salary of $100,000 for the first year. she earns a 3% increase each year. what does s5 represent

steposvetlana [31]

$S_{n} = \frac{ a_{1}(1- r^{n}) }{1-r}$ $a_{1} = 100000, r=1.03, n=5$
$S_{5} = \frac{100000(1- 1.03^{5}) }{1-1.03} = \frac{100000(-.159)}{-.03} =530,000$

So after 5 years she is making $530,000.

Hope that helps

8 0

3 years ago

Read 2 more answers

Pampered Pooch charges $5 for one hour of Doggy Daycare $10 for two hours and fifteen dollars for 3 hours what is the rate chang

DochEvi [55]

Answer:

$5 difference in rate at each step or change in hours.

Step-by-step explanation:

4 0

3 years ago