Number & Quantity
Given the function
f(x)=x^3-3x
evaluate the function for x = 1.
-2
(3x^2-5x+1)-(3x^2-2x+6)=?
-3x+5
If f(x)=2x+6 and f(b)=18, then what does b equal?
b=6
Write the following equation in slope-intercept form.
-2x+6y=14
y=1/3x+7/3
A fair coin is flipped five times, and each flip results in tails. What is the probability the coin will land on tails on the sixth flip?
1/2
For a real number m, completely simplify (2m3)4.
16m12
Solve the following for m:
m/4=(m-1)/4
m=4
If the graph of
f(x)=x^2-1
is shifted to the left by 3 units, write the new function.
(x+3)^2-1
A line is the (x,y) coordinate plane has a slope of -5/4 and passes through the point (-3,5). What is the y-intercept of this line?
5/4
A student has 5 different shirts, 3 different pairs of pants, and 2 different pairs of shoes in his closet. How many different outfit combinations (one shirt, one pair of pants, and one pair of shoes) are possible?
30 outfits possible
Simplify as much as possible:
(x-3)/(x+5)+x/5
(x^2+10x-15)/(5x+25)
Last week a student began collecting rare coins. Since then, he has doubled his collection by obtaining 36 more coins than he started with. How many coins are currently in his collection?
72 coins
In the standard (x,y) coordinate plane, the graph of the function
f(x)=3x-5
crosses through the point (q,4). What is the value of q?
q=3
In the standard (x,y) coordinate plane, what are the coordinates of the midpoint of the line segment connecting (2,7) and (5,7)?
(7/2, 7)
If every letter in the alphabet is placed into a bag, that are the odds that you will select a letter found in the word "HAPPY"?
4/26 or 2/13
What is the product of the complex numbers (4i-4) and (-2i+4)?
24i-8
If x-y=-5 and x+y=1, find xy.
xy=-6
Given the functions
f(x)=x+6
and
g(x)=x^2-2
What is the value of f(g(3))?
13
In the (x,y) coordinate plane, a circle is centered at the point (2,5). If the point (4,9) is on the circumference of this circle, then which of the following distances is the radius?
2root()5
During the week the Smiths plan to roof their cabin, there is a 20% change of rain each day. If they plan to roof the cabin on 2 consecutive days, and assuming the chance of rain is independent of the day, what is the probability that it will rain both days?
0.04
Simplify the following expression into a single radical:
(2)^(20/3)/(4)^(5/2)
root(3)(2^5)
The product of two numbers is 20, while their sum is 12. What is the difference of the two numbers?
8
The number of patients seen by a doctor over a day is represented by the function
P(t)=8t-5
where P is the total number of patients seen after t hours. Based on this function, how many patients are seen between hours 5 and 6?
8 patients
If points M, N, P, and Q lie on a line in that order such that N is the midpoint of the line segment MP.
If the length of MN is 14,
the length of NP is 2x, and
the length of PQ is 4x-9,
what is the length of the line segment MQ?
47
The probability of randomly selecting a green marble from a bag is 4/5. If there are 110 marbles in the bag, how many are NOT green?
22