Radicals
Write the following in radical form
x^(5/9)
What is
9sqrt(x^5)
At the beginning of an environmental study, a forest covered an area of 1500 km2. Since then, this area has decreased by 4.25% each year. Let t represent the number of years since the start of the study. Let y be the area that the forest covers. Write an exponential function showing the relationship of y and t.
What is
y=1500(0.9575)^t
Convert the radian measure to degrees
(12pi)/5
432 degrees
Write a formula for the nth term of the following sequence.
4, -8, 16, -32,...
a_n=4(-2)^(n-1
What correlation would exist between the number of miles driven and the gallons of gas used?
positive
Simply
(1/27)^(-2/3)
What is
9
2,199
Find the exact value of
cot((5pi)/6)
What is
-sqrt3
Solve the following system
y=x^2-3x+2
y=5x-10
(6,20) or (2,0)
The scores of a test are normally distributed. 68% of the scores are between 50 and 70. What is the mean and standard deviation?
mean = 60, std = 10
Simplify
sqrt(2a^5)xxsqrt(12a^4
What is
2a^4sqrt(6a
A study was done for the population of a certain species of fish. Suppose the population size, P(t), after t years is given by the equation below. By what percent does the population change yearly?
P(t)=500(1.032)^t
3.2%
Find the amplitude of
y=3+2/3sin(4x-pi)
What is
2/3
Solve the following system. Round the the nearest hundredth
y=2x^2+4x-1
y=-2x-3
(-2.62, 2.24) or (-0.38, -2.24)
The data points in the following scatter plot show the amount y (in milligrams) of a radioactive substance after decaying for a time x (in days). Use the equation to predict how much of the substance will exist after 15 days. Round to the nearest hundredth.
y=252(0.95)^t
116.75
Solve:
sqrt(x-2)+4=9
What is
27
Solve. Round to the nearest thousandths
7^(x-4)=3^(-6x)
What is 0.912
A path traveled by a roller coaster is given by the equation below, where x represents the horizontal distance (in feet) and y represents the vertical distance (in feet) from the roller coaster's starting point. What is the maximum height?
y=52sin5x+24
?
76 feet
Solve the following system of equations
x-y^2=-9
x^2+y^2=21
(-4, sqrt5), (-4, -sqrt5), (3, 2sqrt3), (3, -2sqrt3)
At a particular high school, 20% of the students participate in student council and 60% of the students participate in sports. If 25% of the students participate in either student council or sports, what is the probability that a student participates in BOTH student council and sports?
55%
Suppose that an object is dropped for a height of h meters and hits the ground at a velocity v meters per second. What is the height the object was dropped from if the velocity is 26.9 meters per second and
v=sqrt(19.6h
36.9 meters
A loan of 15,000 is taken out with 4.5% interest compounded annually. If no payments are made, how long will it take 26, 750? Round to the nearest year.
13 years
What is the exact value of tan(a) if a is an angle in standard position, with terminal side in quadrant 3 such that
sina=-6/7
(6sqrt13)/13
Samuel wants to rent an office space for 4 years. The annual rent is $50,545 and will increase by 6.3% each additional year of the lease. What will the total rent be for the entire 4 year lease? Round to the nearest dollar.
$222,101
A survey was given to adult residents in a particular city. It found that 30% of the residents regularly use public transportation, and 75% of the residents have the ability to drive. 25% of the residents regularly use public transportation AND have the ability to drive.
Find the probability that an adult resident in this city regularly uses public transportation, given that he or she has the ability to drive. Round your answer to the nearest hundredth.
0.33