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4 years ago

15. The volume of a rectangular pyramid

Mathematics

1 answer:

max2010maxim [7]4 years ago

5 0

Answer:

Its height is 24.71 centimeters.

Step-by-step explanation:

Given:

The volume of a rectangular pyramid is 10,500 cubic centimeters.

It has a length of 15 centimeters and a width of 85 centimeters.

Now, to find the height.

Let the height be $h.$

Volume of rectangular pyramid = 10,500 cubic centimeters.

Length (l) = 15 centimeters.

Width (w) = 85 centimeters.

Now, to get the height by putting formula:

$Volume=\frac{l\times w\times h}{3}$

$10500=\frac{15\times 85\times h}{3}$

$10500=\frac{1275h}{3}$

Multiplying both sides by 3 we get:

$31500=1275h$

Dividing both sides by 1275 we get:

$24.71 =h\\\\h=24.71\ centimeters.$

Therefore, its height is 24.71 centimeters.

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While conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modem

Kitty [74]

Answer:

We conclude that this is an unusually high number of faulty modems.

Step-by-step explanation:

We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.

The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.

Let p = population proportion.

So, Null Hypothesis, $H_0$ : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}

Alternate Hypothesis, $H_A$ : p > 0.013 {means that this is an unusually high number of faulty modems}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion faulty modems= $\frac{10}{367}$ = 0.027

n = sample of modems = 367

So, the test statistics = $\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }$

= 2.367

The value of z-test statistics is 2.367.

Since, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that this is an unusually high number of faulty modems.

6 0

3 years ago

Which of the following inverse functions are defined for x=-1/2? Select all thst apply.

daser333 [38]

All but the last one I think but don't quote me

4 0

3 years ago

Read 2 more answers

Can you please explain this?

Leni [432]

Answer:

The question is giving you pairs of points in space which can be used to define lines. It is then asking you to determine if the lines defined by those points are parallel, perpendicular, or neither.

Step-by-step explanation:

Two key things you need to know to solve this is that the lines will be parallel if their slopes are the same, and perpendicular if one slope is the negative reciprocal of the other (i.e. $s_{1} = -s_{2}^{-1}$ )

Let's start with question 11. You are given two pairs of points, each of which describes a distinct line:

(3,5)-(1,1) and (0, 2)-(5, 12)

To find the slope of each pair, take the vertex with the lesser x co-ordinate, and subtract it from the vertex with the greater x co-ordinate. That will give us a valid Δx and Δy to get the slope.

In the first pair, 3 > 1, so we'll subtract the second point from the first:

$s = \Delta y / \Delta x\\s = \frac{5 - 1}{3 - 1}\\s = 4/2\\s = 2$

So the first pair of vectors describe a line with a slope of 2. Let's look at the other pair:

$s = \Delta y / \Delta x\\s = (12 - 2) / (5 - 0)\\s = 10 / 5\\s = 2$

That also gives us a slope of 2, meaning that the two lines are parallel.

This same process will need to be done for the other three questions. We can't answer questions 12 or 14 here, as the last point is cut off on the edge of the image. For question 3 though, one line has a slope of 7/3, and the other 3/7. That puts them in the "neither" category, as one is not the negative reciprocal of the other, but instead the positive reciprocal.

6 0

3 years ago

If there are 624 calories in 3 servings, how many calories are in 1 serving?

zlopas [31]

Answer:

208 carlories each serving

7 0

3 years ago

Read 2 more answers

PLEASE LITTERALLY HELP ME!!! IM STRUGGLINGGGG!!!

tangare [24]

Answer: