Algebra
A store sells two different-sized containers of a certain Greek yogurt. The storeʼs sales of this Greek yogurt totaled 1277.94 dollars last month. The equation 5.48x + 7.30y = 1277.94 represents this situation, where x is the number of smaller containers sold and y is the number of larger containers sold. According to the equation, what is the price, in dollars, of each smaller container?
5.48 dollars
Factor 256w2 - 676
(16w - 26)(16w + 26)
In triangle XYZ, the measure of X is 24o and the measure of Y is 98o. What is the measure of Z?
58o
There are 170 blocks in a container. Of these blocks, 10% are green. How many blocks in the container are green?
17
This type of function is written in the form f(x)=ax2+bx+c, where a, b, and c are constants.
(1/2)y = 4
x - (1/2)y = 2
The system of equations above has solution (x,y). What is the value of x ?
6
f(x) = (x + 6)(x - 4)
If the given function f is graphed in the xy-plane, where y = f(x), what is the x-coordinate of an x-intercept of the graph?
-6 or 4
What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?
360
Pure beeswax has a density of 0.555 ounce per cubic inch. An online company sells pure beeswax at a price of $8.00 per ounce. What is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company?
4.44
This is the ratio of the adjacent side to the hypotenuse in a right triangle.
What is cosine?
In the system of equations below, a and c are constants.
(1/2)x + (1/3)y = 1/6
ax + y = c
If the system of equations has an infinite number of solutions , what is the value of a ?
3/2
In the xy-plane, a line with equation 2y = 9/2 intersects a parabola at exactly one point. If the parabola has equation y = -4x2 + bx, where b is a positive constant, what is the value of b?
6
x2 + 20x + y2 + 16y = -20
The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?
(-10, -8)
Response Frequency
Strongly favor 56
Somewhat favor 214
Somewhat oppose 104
Strongly oppose 37
A researcher interviewed 411 randomly selected US residents and asked about their views on the use of nuclear energy. The table above summarizes the responses of the interviewees. If the population of the United States was 300 million when the survey was given, based on the sample data for the 411 US residents, what is the best estimate, in millions, of the difference between the number of US residents who somewhat favor or strongly favor the use of nuclear energy and the number of those who somewhat oppose or strongly oppose it? (Round your answer to the nearest whole number.)
94
If logb(x)=y, this equation represents the equivalent exponential form.
What is by = x?
A local transit company sells a monthly pass for $95 that allows an unlimited number of trips of any length. Tickets for individual trips cost $1.50, $2.50, or $3.50, depending on the length of the trip. What is the minimum number of trips per month for which a monthly pass could cost less than purchasing individual tickets for trips?
28
The function f is defined by f(x) = ax + b, where a and b are constants. In the xy-plane, the graph of
y = f(x) has an x-intercept at (2, 0) and a y-intercept at (0, -323). What is the value of b?
-324
Triangle ABC is a right triangle, and sin(B) = 5/13. If side AB has a length of 26 and C is a right angle, what is the length of side BC?
24
Andrew | 2.4 | 2.5 | 3.6 | 3.1 | 2.5 | 2.7
Maria | x | 3.1 | 2.7 | 2.9 | 3.3 | 2.8
Andrew and Maria each collected six rocks, and the masses of the rocks are shown in the table above. The mean of the masses of the rocks Maria collected is 0.1 kilogram greater than the mean of the masses of the rocks Andrew collected. What is the value of x ?
2.6
When a function f(x) is replaced with f(x−h)+k, this is the graphical change that occurs.
What is a horizontal translation?
In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the point (2, 2). If the point (20, w) lies on line k, what is the value of w ?
74
(70n)1/5((70n)1/6)2
For what value of x is the given expression equivalent to (70n)30x, where n > 1?
4/225
A right circular cone has a height of 22 cm and a base with a diameter of 6 cm. The volume of this cone is n(pi) cm3. What is the value of n?
66
A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?
8
This represents how often a trigonometric graph repeats itself within a given frame.
What is frequency?