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3 years ago

What is the volume of an equilateral triangular prism?

Mathematics

1 answer:

Nata [24]3 years ago

6 0

Actually, the "slant height" is 4, but the vertical height or "altitude" of the equilateral triangle is not 4

but anyway..... $\bf \begin{array}{cllll}
\textit{height of an equilateral triangle}\\\\
h=\cfrac{s\sqrt{3}}{2}\\
----------\\
\textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}
\end{array}\qquad s=\textit{length of one side}$

and the volume, is the area of the triangle, times the length, so, whatever you get for the area of the triangle * 10

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Given the function g(x) = x2 + 10x + 20, determine the average rate of change of

Dmitrij [34]

A function assigns the values. The average rate of change for the given function g(x) is 1.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

The average rate of change of a function is given by the formula,

Average rate of change, = [f(b)-f(a)]/(b-a), [a,b]

Where a is the lower limit and b is the upper limit.

Given the upper limit for the function is 0, therefore, the value of a is 0, similarly, the value of b is -9. Thus,

a = 0

g(a) = 0²+10(0)+20 = 20

b = -9

g(b) = (-9)²+10(-9)+20 = 11

The average rate of change for the function g(x), can be written as,

$\text{Average rate of change}= \dfrac{g(-9)-g(0)}{-9-0}=\dfrac{11-20}{-9} = 1$

Hence, the average rate of change for the given function g(x) is 1.

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2 years ago

Use the distributive property to write an equivalent expression. 6(12+3)

Rufina [12.5K]

Answer:

Step-by-step explanation:

= 6(12+3)

= 6*12 + 6*3

= 72 + 18

= 90

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3 years ago

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3 years ago

What is the simplest form for 4/3?

shutvik [7]

4/3 in simplest form is 4/3 but in decimal form it would be 1.33333

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3 years ago

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One of the earliest applications of the Poisson distribution was in analyzing incoming calls to a telephone switchboard. Analyst

grandymaker [24]

Answer:

(a) P (X = 0) = 0.0498.

(b) P (X > 5) = 0.084.

(d) P (X ≤ 1) = 0.5578

Step-by-step explanation:

Let X = number of telephone calls.

The average number of calls per minute is, λ = 3.0.

The random variable X follows a Poisson distribution with parameter λ = 3.0.

The probability mass function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,3...$

(a)

Compute the probability of X = 0 as follows:

$P(X=0)=\frac{e^{-3}3^{0}}{0!}=\frac{0.0498\times1}{1}=0.0498$

Thus, the probability that there will be no calls during a one-minute interval is 0.0498.

(b)

If the operator is unable to handle the calls in any given minute, then this implies that the operator receives more than 5 calls in a minute.

Compute the probability of X > 5 as follows:

P (X > 5) = 1 - P (X ≤ 5)

$=1-\sum\limits^{5}_{x=0} { \frac{e^{-3}3^{x}}{x!}} \,\\=1-(0.0498+0.1494+0.2240+0.2240+0.1680+0.1008)\\=1-0.9160\\=0.084$

Thus, the probability that the operator will be unable to handle the calls in any one-minute period is 0.084.

(c)

The average number of calls in two minutes is, 2 × 3 = 6.

Compute the value of X = 3 as follows:

$P(X=3)=\frac{e^{-6}6^{3}}{3!}=\frac{0.0025\times216}{6}=0.09$

Thus, the probability that exactly three calls will arrive in a two-minute interval is 0.09.

(d)

The average number of calls in 30 seconds is, 3 ÷ 2 = 1.5.

Compute the probability of X ≤ 1 as follows:

P (X ≤ 1 ) = P (X = 0) + P (X = 1)

$=\frac{e^{-1.5}1.5^{0}}{0!}+\frac{e^{-1.5}1.5^{1}}{1!}\\=0.2231+0.3347\\=0.5578$

Thus, the probability that one or fewer calls will arrive in a 30-second interval is 0.5578.

5 0

3 years ago