Math Basics, Percents, Ratios, Rates, Proportions
The number 24 is what percentage of 80?
30%
Data Set A: {1, 2, 3, 4, 5, 6, 7}
Data Set B: {1, 1, 2, 2, 3, 3, 4}
Which data set has a higher mean?
Data Set A
Colors of Marbles in a Bag
| Color | Number |
| Red | 8 |
| Blue | 10 |
| Green | 22 |
| Total | 40 |
The table shows the number of different colors of marbles in a bag. If a marble is chosen at random from the bag, what is the probability that the marble will be blue?
How many solutions exist to the equation shown above?
Exactly 1 (x = 3)
In Science class, Daniel conducted an experiment to learn about evaporation. Daniel measured the height of fluid in a beaker over a period of time. The function f(x) = 39 - 0.18x gives the estimated height, in centimeters (cm), of the fluid in the beaker x days after the start of the experiment. What does 39 represent in this context?
The estimated height, in cm, of the fluid at the start of the experiment
An object travels at a constant speed of 12 centimeters per second. At this speed, what is the time, in seconds, that it would take for the object to travel 108 centimeters?
9 seconds
A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weight more than once. The sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds. Which of the following conclusions is best supported by the sample data?
A) The majority of all fish in the pond weigh less than 2 pounds.
B) The average weight of all fish in the pond is approximately 2 pounds.
C) Approximately 30% of all fish in the pond weight more than 2 pounds.
D) Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.
D) Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.
There are n nonfiction books and 12 fiction books on a bookshelf. If one of these books is selected at random, what is the probability of selecting a nonfiction book, in terms of n?
n / (n + 12)
The function f is defined by f(x) = 3x + 12. For what value of x is f(x) = 27?
x = 5
Safina's regular wage at her job is p dollars per hour for the first 8 hours of work in a day plus 1.5 times her regular hourly wage for work in excess of 8 hours that day. On a given day, Safina worked for 10 hours, and her total earnings for that day were $137.50. What is Safina's regular hourly wage?
$12.50
A park has an area of 11,863,808 square yards. What is the area, in square miles, of this park? (1 mile = 1,760 yards)
3.83 square miles
The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?
A) Mean
B) Median
C) Range
D) Standard deviation
B) Median
A youth symphony orchestra consists of five violinists, three clarinetists, and two bassoonists. The conductor wants to put together a trio of each instrumentalist (that is, a trio with one violinist, one clarinetist, and one bassoonist). How many different possible trios are there?
30
Simplify the following expression:
3 /(6 - 3y) + 1/(y - 4)
-6 / (y - 4)(6 - 3y)
A fish hatchery has three tanks for holding fish before they are introduced into the wild. Ten fish weighing less than 5 ounces are placed in Tank A. Eleven fish weighing at least 5 ounces but no more than 13 ounces are placed in Tank B. Twelve fish weighing more than 13 ounces are placed in Tank C. Which of the following could be the median of the weights, in ounces, of these 33 fish?
A) 4.5
B) 8
C) 13.5
D) 15
B) 8
w = 47.25 (or 189/4)
| ________ | Masses (kilograms) __ |
|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?
x = 2.6
| | State sales tax | No state sales tax |
| State income tax | 39 | 4 |
| No state income tax | 6 | 1 |
To the nearest tenth of a percent, what percent of states with a state-level sales tax do not have a state-level income tax?
13.3%
Solve for t:
0.8t - 0.46 = 8(t - 0.001) + 1.9
t = -0.3267
An economist modeled the demand Q for a certain product as a linear function of the selling price P. The demand was 20,000 units when the selling price was $40 per unit, and the demand was 15,000 units when the selling price was $60 per unit. Based on the model, what is the demand, in units, when the selling price is $55 per unit?
16,250
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
The mean amount of time that the 20 employees of a construction company have worked for the company is 6.7 years. After one of the employees leaves the company, the mean amount of time that the remaining employees have worked for the company is reduced to 6.25 years. How many years did the employee who left the company work for the company?
15.25 years
The table summarizes the distribution of age and assigned group for 90 participants in a study.
| | 0-9 years | 10-19 years | 20+ years | Total |
| Group A | 5 | 17 | 8 | 30 |
| Group B | 6 | 8 | 16 | 30 |
| Group C | 19 | 5 | 6 | 30 |
| Total | 30 | 30 | 30 | 90 |
One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10 years of age?
5/12
The function g is defined by the equation g(x) = -3(5)x. Which of the following equations defines the function h if h(x) = g(x + 3)?
A) h(x) = -27(125)x
B) h(x) = -9(15)x
C) h(x) = -9(5)x
D) h(x) = -375(5)x
D) h(x) = -375(5)x
In New York, Ms. Isabella's eight-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth-grade class size in New York is 26. If the students in Ms. Isabella's class are representative of students in New York's eighth-grade classes and there are 1,800 eight-grade classes in the state, what is the best estimate of the number of eighth-grade students in New York who have fewer than two siblings?
~30,600 students