Given:
μ = 89 ng/ml, population mean
σ = 23 ng/ml, population standard deviation
Random variable, x = 100
To test P(x < 100), calculate the z-score.
z = (x-μ)/σ = (100 - 89)/23 = 0.4783
From standard tables, obtain
P(x < 100) = 0.6838 = 68.4%
Answer: 68.4%
f(h(x))= 2x -21
Step-by-step explanation:
f(x)= x^3 - 6
h(x)=\sqrt[3]{2x-15}
WE need to find f(h(x)), use composition of functions
Plug in h(x)
f(h(x))=f(\sqrt[3]{2x-15})
Now we plug in f(x) in f(x)
f(h(x))=f(\sqrt[3]{2x-15})=(\sqrt[3]{2x-15})^3 - 6
cube and cube root will get cancelled
f(h(x))= 2x-15 -6= 2 x-21
X² - 14x + 33 = 0 is in the form ax² + bx + c = 0. We will need this for the second step.
Subtract 33 from both sides
x² - 14x = - 33
Divide the b term by 2 and then square the result. Then add that to both sides.
- 14 / 2 is - 7. (- 7)² = 49. Add that to both sides
x² - 14x + 49 = - 33 + 49
Combine the constants and factor the trinomial
(x - 7)² = 16
Square root both sides
x - 7 = +/- 4
or
x - 7 = - 4 and x - 7 = 4
You have to place a plus-minus statement because (- 4)² and 4² both equal 16.
Now we solve for x in each equation. Add 7 to both sides to isolate our variable.
x = 3 and x = 11
Answer:
If Aiden wanted to spend the same amount as Diane, then he would have 1 hour to paint his windows. He would spend $105 and take 1 hour.
Answer:
angle ABE = 55 degrees
Step-by-step explanation:
(3x-8) + (x+14) = 90
4x+6 = 90
4x = 84
x = 21
angle ABE = 3(21)-8 = 55
