Numbers and Algebra
Simplify the following expression:
ln(5e)x
x(ln5 + 1)
or
xln5 + x
State the domain of the function:
y = 1 / (x2 - 4)
x != 2 and -2
What is the period of the function:
y = 3sin(2x - 1) + 4
pi radians or 180 degrees
The next two days both have an independent 30% chance to rain. What is the probability that it rains on the second day but not on the first?
0.21 or 21%
What is the limx->4(x2 + x - 20)/(x - 4)
9
An arithmetic sequence has a common difference of -6 and the first term is 15.
What is the 12th term?
-51
Write the following function in vertex form:
y = 2x2 - 12x + 4
y = 2(x - 3)2 - 14
Calculate the distance between two points in space:
P1 (0, 4, -2)
P2 (1, -1, 8)
Give your answer in exact form (simplified)
3 * sqrt(14)
A carnival game gives you 1, 5, and 10 points for hitting progressively harder targets. If your chance at hitting these targets are 25%, 10% and 5%, what is the expected amount of points you get for one attempt?
1.25 points
Write the derivative with respect to x for:
f(x) = 3esin(x)
f'(x) = 3cos(x)esin(x)
Mr. C currently has $300 in a savings account. The account gives 2% interest compounded quarterly. How much money did Mr. C have in the account 4 years ago?
$276.99
The amount, A, of carbon-14 present in a plant t years after its death can be modeled by A0e-kt . At the time of death, a plant had 100 units of carbon-14. The time taken for half of the original amount of carbon-14 to decay is 5730 years.
Find k
ln2 / 5730
V = (1/12)*pi * h3
Steph Curry is a career 42% 3-point shooter in the NBA. If he takes 9 attempts in a game, what is the probability that he makes at least 4 of them?
What is the area under the curve f(x) = cosx + 1
bounded by the x-axis and the y-axis from x = 0 to pi
pi