module 1
The function f(t) = 60,000(2)t/410 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?
410
The function f is defined by f(x)= -3x+60. What is the value of f(x) when x = -8
84
For the function q, the value of q(x) decreases by 45% for every increase in the value of x by 1. If q(0)=14, which equation defines q?
A) q(x) = 0.55(14)x
B) q(x) = 1.45(14)x
C) q(x) = 14(0.55)x
D) q(x) = 14(1.45)x
C) q(x) = 14(0.55)x
The length of each edge of a box is 29 inches. Each side of the box is in the shape of a square. The box does not have a lid. What is the exterior surface area, in surface inches, of this box without a lid?
4205
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 1089√3 square units, what is the length, in units, of the diameter of the circle?
66
Which expression is equal to (7x3+7x) - (6x3-3x)?
A) x3 + 10x
B) -13x3 + 10x
C) -13x3 + 4x
D) x3 + 4x
A) x3 + 10x
In right triangle RST, the sum of the measures of angle R and angle S is 90 degrees. The value of sin(R) is (√15 : 4). What is the value of cos(S)?
√15 : 4
A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube NOT taken up by the sphere? ( volume of sphere: V=(3/4)πr3 )
A) 149,796
B) 164,500
C) 190,955
D) 310,800
A) 149,796
The function f is defined by f(x) = (1.84)x/4. The equation can be rewritten as f(x) = (1 + p/100)x, where p is a constant. Which of the following is the closest value of p?
A) 16
B) 21
C) 46
D) 96
A) 16
The perimeter of an equilateral triangle is 624 centimeters. The heights of this triangle is k√3 centimeters, where k is a constant. What is the value of k?
104
A producer is creating a video with a length of 70 minutes. The video will consist of segments that are 1 minute long and segments that are 3 minutes long. Which equation represents this situation, where x represents the number of 1-minute segments and y represents the number of 3-minute segments?
A) 4xy = 70
B) 4(x+y)=70
C) 3x + y= 70
D) x + 3y = 70
D) x + 3y = 70
Each year, the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?
A) decreasing exponential
B) decreasing linear
C) increasing exponential
D) increasing linear
C) increasing exponential
(5/4)x + (7/4) = py + (15/4)
In the given system of equations, p is a constant. If the system has no solution, what is the value of p?
Which quadratic equation has no real solutions?
A) x2 + 14x - 49 = 0
B) x2 - 14x + 49 =0
C)5x2 - 14x - 49 = 0
D)5x2 - 14x + 49 = 0
D) 5x2 - 14x + 49 = 0
The positive number a is 2241% of the sum of the positive numbers b and c, and b is 83% of c. What percent of b is a?
4941%
r = 5
A bowl contains 20 ounces of water. When the bowl is uncovered, the amount of water in the bowl decreases by 1 ounce every 4 days. If 9 ounces of water remain in this bowl, for how many days has it been uncovered?
44
A grove has 6 rows of birch trees and 5 rows of maple trees. Each row of birch trees has 8 trees 20 feet or taller, and 6 trees shorter than 20 feet. Each row of maple trees has 9 trees 20 feet or taller and 7 trees shorter than 20 feet. A tree from one of these rows will be selected at random. What is the probability of selecting a maple tree, given that the tree is 20 feet or taller?
9/164
6 + 7r = pw
7r - 5w = 5w + 11
In the given system of equations, p is a constant. If the system has no solution, what is the value of p?
p = 10
the function f is defined by f(x) = ax2+bx+c, where a,b, and c are constants. The graph of y = f(x) in the xy plane passes through the points (7;0) and (-3;0). If a is an integer greater than 1, which of the following could be the value of a + b?
A) -6
B) -3
C) 4
D) 5
A) -6
A chemist combines water and acetic acid to make a mixture with a volume of 56 milliliters (mL). The volume of acetic acid in the mixture is 10 mL. What is the volume of water, in mL, in the mixture? (Assume that the volume of the mixture is the sum of the volumes of water and acetic acid before they were mixed)
46
in triangle ABC, the measure of angle A is 54 degrees. B is a right angle and the measure of angle c is (k/2) degrees. What is the value of k?
72
A) 3x2 + 7x + 14b
B) 3x2 + 28x + 14b
C) 3x2 + 42x + 14b
D) 3x2 + 49x + 14b
D) 3x2+49x+14b
For an electric field passing through a flat surface perpendicular to it, the electric flux of the electric field through the surface is the product of the electric field's strength and the area of the surface. A certain flat surface consists of two adjacent squares, where the side length, in meters, of the larger square is 3 times the side length, in meters, of the smaller square. An electric field with strength 29.00 volts per meter passes uniformly through this surface, which is perpendicular to the electric field. If the total electric flux of the electric field through this surface is 4640 volts * meters, what is the electric flux, in volts * meters, of the electric field through the larger square?
4176
A circle has center G, and points M and N lie on the circle. Line segments MH and NH are tangent to the circle at points M and N, respectively. If the radius of the circle is 168 millimeters and the perimeter of quadrilateral GMHN is 3856 millimeters, what is the distance, in millimeters, between points G and H?
1752