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IgorLugansk [536]

3 years ago

10

An aquarium has a length of n^ 2 +2 inches, a height of n + 5 inches, and a width of 10 inches. What is the volume, in cubic inc

hes, of the aquarium, in terms of n ?

1 answer:

kodGreya [7K]3 years ago

5 0

The formula of a volume of a rectangle prism:

$V=lwh$

l - length

w - width

h - height

We have

$l=n^2+2;\ w = 10,\ h=n+5$

Substitute:

$V=(n^2+2)(10)(n+5)=(10n^2+20)(n+5)\\\\=(10n^2)(n)+(10n^2)(5)+(20)(n)+(20)(5)\\\\=10n^3+50n^2+20n+100$

<h3>Answer: V = (10n³ + 50n² + 20n + 100) in³</h3>

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The figure shows a plane slicing through a cone. The plane is neither parallel nor perpendicular to the base of the cone, and th

aalyn [17]

<h3>Answer: Ellipse</h3>

==================================================

Explanation:

Imagine that this plane was a saw blade, or a laser, that cut the cone. We would have two pieces and each piece would have a shape of an ellipse on them. The cutting plane would also have the same ellipse shape.

Or you think of the cutting plane as a flat piece of cloth. If we cut everything around the cone, then we would have an ellipse shaped hole as a result.

The reason why we get an ellipse and not a circle is because the plane is angled like that. It needs to be perfectly parallel to the circular base in order to get a circular cross section.

5 0

3 years ago

I have to place them in order.m

julsineya [31]

Answer:

1. 4.5 (9/2)

2. 5.2 (square root of 27)

3. 5.8

4. 6.3 (2pi)

Step-by-step explanation:

The square root of 27 is 5.2, 2pi is 6.3, and 9/2 is 4.5. So the first one is 4.5. The second one is 5.2. The third one is 5.8 and the fourth one is 6.3. I hope this helps! Please mark me brainliest!

7 0

3 years ago

In a random sample of 150 customers of a high-speed Internetprovider, 63 said that their service had been interrupted one ormore

erastovalidia [21]

Answer:

a) The 95% confidence interval would be given by (0.341;0.499)

b) The 99% confidence interval would be given by (0.316;0.524)

c) n=335

d)n=649

Step-by-step explanation:

1) Notation and definitions

$X_{IS}=63$ number of high speed internet users that had been interrupted one or more times in the past month.

$n=150$ random sample taken

$\hat p_{IS}=\frac{63}{150}=0.42$ estimated proportion of high speed internet users that had been interrupted one or more times in the past month.

$p_{IS}$ true population proportion of high speed internet users that had been interrupted one or more times in the past month.

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

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

1) Part a

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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96$

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

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

If we replace the values obtained we got:

$0.42 - 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.341$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.499$

The 95% confidence interval would be given by (0.341;0.499)

2) Part b

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:

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

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

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

If we replace the values obtained we got:

$0.42 - 2.58\sqrt{\frac{0.42(1-0.42)}{150}}=0.316$

$0.42 + 2.58\sqrt{\frac{0.42(1-0.42)}{150}}=0.524$

The 99% confidence interval would be given by (0.316;0.524)

3) Part c

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 $ME =\pm 0.05$ 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)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.42(1-0.42)}{(\frac{0.05}{1.96})^2}=374.32$

And rounded up we have that n=335

4) Part d

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 $ME =\pm 0.05$ 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)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.42(1-0.42)}{(\frac{0.05}{2.58})^2}=648.599$

And rounded up we have that n=649

5 0

3 years ago

A teenager’s heart pumps an average of 7200 L of blood every 24 hours. What is the rate of change of volume of blood?

love history [14]

Answer:

300L per hour

Step-by-step explanation:

The rate of change of volume of blood pumped by the teenager's heart expresses the volume of blood pumped with respect to hour.

Rate of change of volume of blood = $\frac{volume of blood}{time}$

= $\frac{7200L}{24}$

= 300L/hour

The rate of change of volume of blood by the teenager's heart is 300 litres per hour. This implies that his/ her heart pumps 300 litres of blood every hour.

7 0

3 years ago

Find the product.<br> (x2+3x+7)(x^7)=<br><br><br> Please help :)

Nesterboy [21]

Answer: x^9+3x^8+7x^7

Step-by-step explanation:

the ^ mean the exponent

4 0

2 years ago