What is the area of a circle with a radius of 5 cm?
Not Answered
A)
5
π
cm
2
B)
10
π
cm
2
C)
25
π
cm
2
D)
50
π
cm 2 A jar contains 8 red marbles, 6 blue marbles, and 4 green marbles. If one marble is chosen at random, what is the probability it is blue?
Not Answered
A)
1
18
B)
2
9
C)
1
4
D)
1
3
Which of the following is equivalent to the expression
(
3
2
)
×
( 3 4 ) ?
Not Answered
A)
3
6
B)
3
8
C)
9
4
D)
9
8
A recipe requires
4
cups of flour for every
3
cups of sugar. If a baker uses
12
cups of flour, how many cups of sugar does the baker need?
Not Answered
A)
3
cups
B)
6
cups
C)
8
cups
D)
9
cups
How many integers between 1 and 25 (inclusive) meet both of the conditions given in the statements below?
m ∠ Q , and ∠ C and ∠ R are right angles. If A B
=
Q R , then which of the following must be true?
√
2
2
units
D)
m
∠
A
a ( − 2 b ) , then which of the following is equivalent to 8 φ 3 ?
Not Answered
A)
−
52
B)
−
48
C)
−
24
D)
24
What is the slope of the line with the following equation?
3 x − 5
Not Answered
A)
−
5
B)
−
1
3
C)
3
D)
5
Antonio and Samir both work exactly three out of five weekdays. Based on that information, which of the following cannot be true?
Not Answered A) Antonio and Samir might work on the same days of the week. B) Antonio and Samir might work on all different days of the week. C) Antonio works on Monday. D) Samir does not work on Friday. Given the inequality | x − 3 | < k , for which of the following values of k does the solution set for x exist but not contain 7 ?
10 What is the value of x in the geometric sequence below?
16 ,
x ,
144 ,
432 ,
. . .
Not Answered
A)
24
B)
32
C)
48
D)
64
A sphere has a surface area of
324
π
cm 2 . Which of the following must be TRUE?
I. The sphere has a diameter of 9
cm . II. The sphere has a volume of 972 π
cm 3 . III. The largest cross section of the sphere has an area of 81 π
cm 2 .
Not Answered A) II only B) I and III only C) II and III only D) I, II, and III A scientist arrives at her lab to find that 24 out of 250 samples have been improperly stored. If she is able to salvage 12 of the improperly stored samples, what percent of the total number of samples was she not able to salvage?
Not Answered
A)
4
.
8
%
B)
5
.
3
%
C)
9
.
6
%
D)
10
.
6
%
Let's solve each question one by one.
Area of a Circle: The area ( A ) of a circle is given by the formula: [ A = \pi r^2 ] For a radius ( r = 5 ) cm: [ A = \pi (5^2) = 25\pi , \text{cm}^2 ] Answer: C) ( 25\pi , \text{cm}^2 )
Probability of Choosing a Blue Marble: Total marbles = ( 8 + 6 + 4 = 18 ). Probability of choosing a blue marble: [ P(\text{blue}) = \frac{6}{18} = \frac{1}{3} ] Answer: D) ( \frac{1}{3} )
Equivalent Expression: [ \left( \frac{3}{2} \right) \times \left( \frac{3}{4} \right) = \frac{3 \times 3}{2 \times 4} = \frac{9}{8} ] Answer: D) ( \frac{9}{8} )
Cups of Sugar Needed: The ratio of flour to sugar is ( 4:3 ). If the baker uses ( 12 ) cups of flour: [ \text{Sugar needed} = \frac{3}{4} \times 12 = 9 , \text{cups} ] Answer: D) 9 cups
Integers Divisible by 5 with 2 Digits: The two-digit integers divisible by 5 between 1 and 25 are ( 10, 15, 20 ). There are 3 such integers. Answer: B) 3
Triangles Congruence: Since ( m\angle A = 45^\circ ) and ( m\angle B = m\angle Q ), and both triangles are right triangles, they are similar but not necessarily congruent unless the sides are equal. Answer: A) ΔABC and ΔPQR are congruent. (This is not necessarily true without additional information, so the correct answer is not clear without more context.)
Operation φ: Given ( a \phi b = a(-2b) ): [ 8 \phi 3 = 8(-2 \times 3) = 8(-6) = -48 ] Answer: B) -48
Slope of the Line: The slope-intercept form of a line is ( y = mx + b ), where ( m ) is the slope. Here, ( m = 3 ). Answer: C) 3
Work Days of Antonio and Samir: If they both work exactly three days, they can work on the same days or different days. However, if they work on all different days, that would mean they would need to work on 6 different days, which is impossible since there are only 5 weekdays. Answer: B) Antonio and Samir might work on all different days.
Inequality Solution Set: The inequality ( |x - 3| < k ) means ( 3 - k < x < 3 + k ). For the solution set to not contain 7, we need ( 3 + k \leq 7 ) or ( k \leq 4 ). Answer: C) ( k = 4 )
Value of x in the Geometric Sequence: The ratio between consecutive terms is constant. The ratio from ( 16 ) to ( x ) is the same as from ( x ) to ( 144 ): [ \frac{x}{16} = \frac{144}{x} \implies x^2 = 16 \times 144 \implies x^2 = 2304 \implies x = 48 ] Answer: C) 48
Sphere Surface Area: The surface area ( S ) of a sphere is given by ( S = 4\pi r^2 ). Setting ( 4\pi r^2 = 324\pi ): [ r^2 = 81 \implies r = 9 \implies \text{diameter} = 18 , \text{cm} ] Volume ( V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (9^3) = 972\pi , \text{cm}^3 ). The largest cross-section area is ( \pi r^2 = 81\pi , \text{cm}^2 ). All statements are true. Answer: D) I, II, and III
Percent of Samples Not Salvaged: Total samples = 250, improperly stored = 24, salvaged = 12. Not salvaged = ( 24 - 12 = 12 ). Percent not salvaged: [ \frac{12}{250} \times 100 = 4.8% ] Answer: A) 4.8%
If you have any further questions or need clarification on any of the answers, feel free to ask!