Answer:
both measured would be 25 and 19
Step-by-step explanation:
If we consider "a" as the edge length, and "D" the cube's diagonal, we have that the square cube's diagonal is equal to the edge length's square plus the side diagonal (d) square (Pythagoras theorem)
a² + d² = D²
And since:
d² = a² + a²
Clearing a, we have:
a² = D²-d²
<span>a² = D²-2a²
</span><span>3a² = D²
</span>
a = √(<span>
D²/3)</span>
Surface area is equal to 6·a², so the surface area will be 6·(D²/3) =
2D²The volume is a³, so the volume will be √(D²/3)³ = √
(![D^{6}](https://tex.z-dn.net/?f=%20D%5E%7B6%7D%20)
<span>/3</span>³<span>) =
D</span>
³/√27
Answer:
0.1827
Step-by-step explanation:
Given mean of exponential distribution = 100
==> 1/χ = 100 ==> χ = 1/100 ==> χ = 0.01
PDF of χ , f(x) = χe^(-χx), x ≥ 0
===> f(x) = 0.01e^(-0.01x), x ≥ 0
Now we find the probability that the demand will exceed 170 cfs during the early afternoon on a randomly selected day
P(X>170) = <em>∞∫170 </em>f(x)dx
P(X>170) = <em>∞∫170 </em>0.01 e^(0.01x) dx
P(X>170) = [e^(-0.01x) / -0.01]^<em>∞ </em><u>base</u> 170
P(X>170) = -1 [e^-∞ - e^-0.01*170]
P(X>170) = e^-1.7
P(X>170) = 0.1827
The probability that the demand will exceed 170 cfs during the early afternoon on a randomly selected day is 0.1827
For this case, we have that by definition, the proportions can be expressed in different ways. Example, if we have a dog and three cats:
75%: It's percentage
0.75: In decimal (75% are cats)
: In fraction. (There are
of cats)
: Using ":" to separate sample values. (For every three cats there is a dog)
Care should be taken with the proportions, always multiplying the numbers in the proportion by the same value.
Example:![3: 1 = 3 * 2: 1 * 2 = 6: 2](https://tex.z-dn.net/?f=3%3A%201%20%3D%203%20%2A%202%3A%201%20%2A%202%20%3D%206%3A%202)
Answer:
Care should be taken with the proportions, always multiplying the numbers in the proportion by the same value.
It's easy, just plug the values requested in n & solve:
A(n)=4+(n-1)(8)
second, n=2 ==> A₂ = 4 +(2-1)(8) = 12
fourth, n=4 ===> A₄ = 4 +(4-1)(8) = 20
tenth, n=10 ==> A₁₀ = 4 + (10-1)(8) = 72
This an Arithmetic progression:
with 1st term a₁ =4 & d ( common difference) =8