Algebra
Scientists collected fallen acorns that each housed a colony of the ant species P. ohioensis and analyzed each colony's structure. For any of these colonies, if the colony has x worker ants, the equation y = 0.67x + 2.6, where 20 ≤ x ≤ 110, gives the predicted number of larvae, y, in the colony. If one of these colonies has 58 worker ants, which of the following is closest to the predicted number of larvae in the colony?
A. 41
B. 61
C. 83
D. 190
A. 41
The function f(t) = 40,000(2)t/790 gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
A. 2
B. 790
C. 1580
D. 40,000
B. 790
Which expression represents the result of increasing a positive quantity W by 43%?
A. 1.43w
B. 0.57w
C. 43w
D. 0.43w
A. 1.43w
An angle has a measure of 9π/20 radians. What is the measure of the angle in degrees?
81
y - 9x = 13
5x = 2y
What is the solution (x,y) to the given system of equations
A. (5/2,1)
B. (1, 2/5)
C. (-2, -5)
D. (-5, -2)
C. (-2,-5)
7x2 - 20x - 32 = 0
What is the positive solution to the given equation?
4
In a bag, there are 7 red, 4 white, 33 blue, and 33 yellow cubes. If one of these cubes is selected at random, what is the probability of selecting a cube that is neither blue nor yellow?
A. 6/7
B. 7/11
C. 1/3
D. 1/7
D. 1/7
In triangle ABC, the measure of angle A is 54°, the measure of angle B is 90°, and the measure of angle C is (k/2)°. What is the value of k?
A. 36
B. 45
C. 72
D. 108
C. 72
If 46 = 16 + 2(x - 8), what is the value of 2(x - 8)?
A. 16
B. 23
C. 30
D. 38
C. 30
Which expression is equivalent to h15q7/hsq21 , where h > 0 and q > 0?
A. h10/q14
B. h3/q3
C. h10q14
D. h3q3
A. h10/q14
An object has a mass of 168 grams and a volume of 24 cubic centimeters. What is the density, in grams per cubic centimeter, of the object?
A. 7
B. 144
C. 192
D. 4,032
A. 7
A right circular cylinder has a volume of 432 cubic centimeters. The area of the base of the cylinder is 24 square centimeters. What is the height, in centimeters, of the cylinder?
A. 18
B. 24
C. 216
D. 10,368
A. 18
Figure A and figure B are both regular polygons. The sum of the perimeter of figure A and the perimeter of figure B is 63 inches. The equation 3x + 6y = 63 represents this situation, where x is the number of sides of figure A and y is the number of sides of figure B. Which statement is the best interpretation of 6 in this context?
A. Each side of figure B has a length of 6 inches
B. The number of sides of figure B is 6
C. Each side of Figure A has a length of 6 inches
D. The number of sides of Figure A is 6
A. Each side of figure B has a length of 6 inches
What is the solution to the given equation
A. 7
B. 9
C. 16
D. 63
C. 16
The population of City A increased by 7% from 2015 to 2016. If the 2016 population is k times the 2015 population, what is the value of k?
A. 0.07
B. 0.7
C. 1.07
D. 1.7
C. 1.07
A square is inscribed in a circle. The radius of the circle is 20√2 / 2 inches. What is the side length, in inches, of the square?
A. 20
B. 20√2 / 2
C. 20√2
D. 40
A. 20
A salesperson’s total earnings consist of a base salary of x dollars per year, plus commission earnings of 11% of the total sales the salesperson makes during the year. This year, the salesperson has a goal for the total earnings to be at least 3 times and at most 4 times the base salary. Which of the following inequalities represents all possible values of total sales s, in dollars, the salesperson can make this year in order to meet that goal?
A. 2x ≤s ≤3x
B. 2/0.11X ≤s≤ 3/0.11X
C. 3X ≤s≤ 4x
D. 3/0.11X ≤s≤ 4/0.11X
B. 2/0.11X ≤s≤ 3/0.11X
f(x) = 9,000(0.66)x
The given function f models the number of advertisements a company sent to its clients each year, where x represents the number of years since 1997, and 0 ≤ x ≤ 5. If y = f(x) is graphed in the xy-plane, which of the following is the best interpretation of the y-intercept of the graph in this context?
A. The minimum estimated number of advertisements the company sent to its clients during the 5 years was 1708.
B. The minimum estimated number of advertisements the company sent to its clients during the 5 years was 9,000.
C. The estimated number of advertisements the company sent to its clients in 1997 was 1708.
D. The estimated number of advertisements the company sent to its clients in 1997 was 9,000.
D. The estimated number of advertisements the company sent to its clients in 1997 was 9,000.
For a baobab tree habitat in South Africa, a scientist randomly selected 50 baobab trees that were 17 years old and randomly assigned them to two groups. Each group was subjected to a different watering pattern for 2 consecutive years to observe whether the watering pattern affects the trees’ growth rate. Based on the design of the study, what is the largest group to which these results can be applied?
A. All the 50 baobab trees that were selected in this habitat
B. All the baobab trees that were 19 years old in this habitat
C. All the baobab trees that were 17 years old in South Africa
D. All the baobab trees that were 17 years old in this habitat
D. All the baobab trees that were 17 years old in this habitat
A rectangle is inscribed in a circle, such that each vertex of the rectangle lies on the circumference of the circle. The diagonal of the rectangle is twice the length of the shortest side of the rectangle. The area of the rectangle is 1,089√3 square units. What is the length, in units, of the diameter of the circle?
66