The answer is B: 1/6 because the probability will be 3/18. Simplified, it's 1/6. Hope this helped!
Answer:
1. 16
2. -4
Step-by-step explanation:
First factor the expression
lim x→1 (x^3 + 5x^2 + 3x-9)/(x-1)
lim x→1 (x-1) (x+3)^2/(x-1)
Canceling the x-1 in the top and bottom
lim x→1 (x+3)^2
Let x=1
lim x→1 (1+3)^2 = 4^2 = 16
2. lim x→0 (x^2 -6x+8) /(x-2)
First factor the expression
lim x→0 (x-4) (x-2) /(x-2)
Canceling the x-2 in the top and bottom
lim x→0 (x-4)
Let x=0
lim x→0 (0-4) = -4
Filling in the table
x -.1 -.01 -.001 .001 .01 .1
f(x) -4.1 -4.01 -4.001 -3.999 -3.99 -3.9
55 + 80 + 95 + 100 +115 +90 =535 actual enrollments. 75 + 80 +85 +90 +95 + 100 = 525 predicted enrollments. 535 - 525 = 10 residuals.
Answer: f(120°) = (√3) + 1/2
Step-by-step explanation:
i will solve it with notable relations, because using a calculator is cutting steps.
f(120°) = 2*sin(120°) + cos(120°)
=2*sin(90° + 30°) + cos(90° + 30°)
here we can use the relations
cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)
sin(a + b) = cos(a)*sin(b) + cos(b)*sin(a)
then we have
f(120°) = 2*( cos(90°)*sin(30°) + cos(30°)*sin(90°)) + cos(90°)*cos(30°) - sin(90°)*sin(30°)
and
cos(90°) = 0
sin(90°) = 1
cos(30°) = (√3)/2
sin(30°) = 1/2
We replace those values in the equation and get:
f(120°) = 2*( 0 + (√3)/2) + 0 + 1/2 = (√3) + 1/2
