What is the simplified of this?

A triangular pyramid with a height of 9 inches has a volume of 63 cubic inches. If the height of the triangular base is 6 inches

Bond [772]

Option D: 21 in is the base length of the triangular base.

Explanation:

Given that a triangular pyramid with a height of 9 inches has a volume of 63 cubic inches.

The height of the triangular base is 6 inches.

We need to determine the base length of the triangular pyramid.

The base length of the triangular pyramid can be determined using the formula,

$Volume =\frac{1}{3} \times Bh$

Substituting $Volume=63$ and $Height=9$ in the above formula, we get,

$63 =\frac{1}{3} \times B(9)$

Simplifying the terms, we get,

$63 =3B$

Dividing both sides by 3, we have,

$21=B$

Thus, the base length of the triangular pyramid is 21 in

Hence, Option D is the correct answer.

3 0

2 years ago

You read online that the probability of being dealt four‑of‑a‑kind in a five‑card poker hand is 1 / 4165. Explain carefully what

Lapatulllka [165]

Answer:

There is about 4,164/4,165 chances of not getting getting a four of a kind. So, it is extremely unlikely or even borderline impossible in that situation to get a four of a kind.

But in the long run, it can be increased only if you keep drawing. So, the awnser would have to be. D

Step-by-step explanation:

A. It does mean that if you are dealt 4165 five‑card poker hands, one will be four‑of‑a‑kind.

B. It does not mean that all will be four‑of‑a‑kind. The probability is actually saying that only on the 4165 the poker hand will you get a four‑of‑a‑kind, not just on any of the 4165 poker hands.

C. The probability is actually saying that in the long run, with a large number of five‑card poker hands, the fraction in which you will be dealt a four‑of‑a‑kind is 1 / 4165.

D. The chance you will be dealt four‑of‑a‑kind is 1 / 4165 only on the first hand. This chance will then increase with each new hand you are dealt until you eventually win

6 0

2 years ago

Which equation represents direct variation? A) y=3x B) yx=3 C)y=3x^2 D) y=3x^3

geniusboy [140]

A) y=3x hope this helps

7 0

3 years ago

How do I figure this out?

Gnoma [55]

Staircase one looks like our normal staircase we have today which looks like it’s easier so staircase two is more difficult to walk up?

But also

staircase one will be harder because it’s just smaller? Shorter and less space for your feet to step on. Staircase two has 1 ft of space for your feet to land on and is a bit higher which seems like normal stairs? But if I go measure my staircase... I don’t think it’s 1 ft... so? Maybe it’s staircase one? I’m sorry if I’m confusing you!!

I don’t think that’s a right or wrong question? Maybe it’s just your opinion? I’m so sorry, I honestly have no clue

7 0

3 years ago

Evaluate the integral. (remember to use absolute values where appropriate. Use c for the constant of integration.) 5 cot5(θ) sin

ozzi

$I=5\int \frac{cos^{4}\theta }{sin\theta }\times cos\theta d\theta \\\\I=5\int \left ( 1-sin^{2}\theta \right )^{2}\times \frac{cos\theta }{sin\theta }d\theta \\put\ \sin\theta =t\\\\dt=cos\theta d\theta \\\\I=5\int\frac{t^{4}+1-2t^{2}}{t}dt\ \ \ \ \ \ \ \ \ \ \because (a-b)^2=a^2+b^2-2ab\\\\I=5\left ( \int t^{3}dt + \int \frac{1}{t} -2\int t \right )dt$

by using the integration formula

we get,

$\\I=5\left ( \frac{t^{4}}{4} +logt -t^{2}\right )\\\\I=\frac{5}{4}t^{4}+5\log t-5t^{2}+c$

now put the value of t=\sin\theta in the above equation

we get,

$\int 5\cot^5\theta \sin^4\theta d\theta=\frac{5}{4}sin^{4}\theta+5\log \sin\theta - 5sin^{2} \theta+c$

hence proved

7 0

2 years ago