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3 years ago

A square pyramid has a base edge of 2 inches and a slant height of 5 in. Find it’s volume

1 answer:

6 0

Volume of the pyramid is V = (Bh)/3 where B is the base area of the pyramid and h is the height to the pyramid.

B = 2(2) = 4in²
To find h, we need to use the Pythagorean theorem. The height of the pyramid is actually an altitude that drops straight down from the vertex of the pyramid perpendicular to the Base hitting the Base in the center. Therefore, the distance from where the altitude hits the Base and the edge of the Base is equal to 1. We are given the slant height as 5 inches so we can now use the theorem to find the height of the pyramid.
h² + 1² = 5²
h² = 5² - 1²
h² = 25 - 1
h² = 24
$h = \sqrt{24}$
$h=2 \sqrt{6}$
Now we can find the Volume:
V= (Bh)/3
$V= \frac{[4(2 \sqrt{6} )]}{3}$
$V = \frac{8}{3} \sqrt{6}$
This is about 6.5 in³ of volume

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ExtremeBDS [4]

Answer:

it c

Step-by-step explanation:

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3 years ago

PLZZZ HELP DOES ANYONE KNOW HOW TO DO THIS?!?!?<br> Find x and y

yanalaym [24]

According to the figure, I can safely assume that the 10 cm line and 15 cm line are parallel.

Thus, there are two similar triangles, one with the 10 cm bottom and 15 cm bottom, where one triangle is larger by a factor of 15/10 = 3/2

We know that the 8 cm line segment and y both join to create the side of the large triangle.

8cm + y = the side of the large triangle

Multiplying 8cm by 3/2 gives us 12, since we know the large triangle is 3/2 times larger than the smaller one.

8 + y = 12

y = 4 cm

Finding x is going to be a bit different. We know that the 6 cm line and x form the side of the larger triangle, which we know is 3/2 times larger than x.

x + 6cm = ?

The side of the larger triangle is 3/2x, thus

x + 6 = 3/2 x

Subtract both sides by x

6 = 1/2 x

Multiply both sides by 2

12 cm = x

Thus, y = 4 and x = 12.

Let me know if you need any clarifications, thanks!

3 0

3 years ago

3n^2−2n−8 Factoring trinomials II

masya89 [10]

Answer:

(3n + 4) (n-2)

Step-by-step explanation:

Are you asking to factor this 3n^2 - 2n -8 ?

If so the best way to do this problem is with the X method.

top: 3*(-8)

left: factor of 3*-8 right: factor of 3*-8

bottom: -2

try the factors 4 and -6 because 4*-6 = 3 *-8 = -24

Because notice that 4 + -6 = -2

so:

3n^2 -2n - 8 can be rewritten as 3n^2 -6n + 4n - 8

We should first use Distributive property to factor: 3n^2 -6n + 4n - 8

3n^2 -6n + 4n - 8 = 3n (n - 2) + 4(n - 2)

Now we factor by grouping here : (3n + 4) (n-2)

I factored out the group (n-2)

Therefore: (3n + 4) (n-2) = 3n^2 -2n - 8

6 0

3 years ago

Two companies rent boats by the hour. The total cost, in dollars, c, depends on the number of hours, h.

Maurinko [17]

Answer:

A(35)

B(35_20=15

Step-by-step explanation:

same as all above

3 0

3 years ago

An Austrian study was completed to determine if untrained sea lions and sea lionesses could follow various experimenter-given cu

Sholpan [36]

Using the z-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

<h3>What are the hypothesis?</h3>

At the null hypothesis, it is tested if Zwerg cannot correctly follow this type of direction by an experimenter more than 50% of the time, that is:

$H_0: p \leq 0.5$

At the alternative hypothesis, it is tested if Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time, that is:

$H_1: p > 0.5$

<h3>Test statistic</h3>

The <em>test statistic</em> is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are:

$n = 48, \overline{p} = \frac{37}{48} = 0.7708, p = 0.5$

The value of the <em>test statistic</em> is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

$z = \frac{0.7708 - 0.5}{\sqrt{\frac{0.5(0.5)}{48}}}$

$z = 3.75$

Considering a <u>right-tailed test</u>, as we are testing if the proportion is greater than a value, with a <u>significance level of 0.05</u>, the critical value for the z-distribution is $z^{\ast} = 1.645$ .

Since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

To learn more about the z-distribution, you can take a look at brainly.com/question/16313918

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2 years ago