Answer:
1 1/2
Step-by-step explanation:
SO first convert into mixed
1 15/30
Now simplify
1 1/2
IF YOU DONT WANT MIX AND LEAVE AS IMPROPER
3/2
The value of K for which f(x) is a valid probability density function is 1/4.
<h3>How to solve for the value of K</h3>


![K[\frac{2^2}{2} -0]+[K[4(4-2)-(\frac{4^2}{2} -\frac{2^2}{2} )]=1](https://tex.z-dn.net/?f=K%5B%5Cfrac%7B2%5E2%7D%7B2%7D%20-0%5D%2B%5BK%5B4%284-2%29-%28%5Cfrac%7B4%5E2%7D%7B2%7D%20-%5Cfrac%7B2%5E2%7D%7B2%7D%20%29%5D%3D1)
open the equation
![K\frac{4}{2}+K[8 - (\frac{16}{2} -\frac{4}{2} )] = 1\\](https://tex.z-dn.net/?f=K%5Cfrac%7B4%7D%7B2%7D%2BK%5B8%20-%20%28%5Cfrac%7B16%7D%7B2%7D%20%20-%5Cfrac%7B4%7D%7B2%7D%20%29%5D%20%3D%201%5C%5C)
![2K+K[\frac{4}{2} ]=1](https://tex.z-dn.net/?f=2K%2BK%5B%5Cfrac%7B4%7D%7B2%7D%20%5D%3D1)
2K + 2K = 1
4K = 1
divide through by 4
K = 1/4
Read more on probability density function here
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Answer:
a. AB = 3.4 ft
b. AE = 1.6 ft
Step-by-step explanation:
SOH CAH TOA reminds you of the relationship between trig functions and right triangle sides.
a. Cos = Adjacent/Hypotenuse
cos(28°) = BE/BA = 3 ft/BA
Multiplying by BA and dividing by cos(28°), you get ...
BA = (3 ft)/cos(28°) ≈ 3.4 ft
___
b. Tan = Opposite/Adjacent
tan(28°) = AE/BE = AE/(3 ft)
Multiplying by 3 ft, you get ...
AE = (3 ft)·tan(28°) ≈ 1.6 ft
Answer:
4, 8, 16, 32, 64
Step-by-step explanation:
The nth term of a geometric sequence is
= a₁
Given
a₇ = 256 and a₁₀ = 2048 , then
a₁
= 256 → (1)
a₁
= 2048 → (2)
Divide (2) by (1)
= 
r³ = 8 ( take the cube root of both sides )
r =
= 2
Substitute r = 2 into (1)
a₁ ×
= 256
a₁ × 64 = 256 ( divide both sides by 64 )
a₁ = 4
Then
a₁ = 4
a₂ = 2a₁ = 2 × 4 = 8
a₃ = 2a₂ = 2 × 8 = 16
a₄ = 2a₃ = 2 × 16 = 32
a₅ = 2a₄ = 2 × 32 = 64