可汗学院
1.Vendors at a craft fair pay $45 to rent a table for the day. Benjamin rents a table at the craft fair and sells 8 ounce jars of jam for $7.95 per jar. If it costs Benjamin $2.75 to make each container of jam, which of the following equations best models his profit, p, from one day at the craft fair if he sells n jars of jam?
A. p=5.20n
B. p=7.95n
C. p=5.20n-45
D. p=7.95n-45
Correct answer: C
2.John manufactures household furniture. His start-up costs, including tools, plans, and advertising, total $5000. Labor and materials for each piece of furniture total $350, and his production costs are the sum of his start-up costs plus the cost of labor and materials. If John makes f pieces of furniture, what will be his production costs, c, in dollars?
A.f=350c+5000
B.c=350f+5000
C.f=5000c+350
D.c=5000f+350
Correct answer: B
3.The number of problems assigned as homework by a savvy math professor is a function of the length of the class on a particular day, which is either 45 minutes, 90 minutes, or 135 minutes. He first multiplies the number of minutes by 4 and then divides that number by 9. Finally, he subtracts 12 from that amount. Which of the following functions best represents the number of math problems the professor assigns depending on the length of the class, t, in minutes?
A. f(t)=94t−12
B. f(t)=94(t−12)
C. f(t)=12−94t
D. f(t)=12+94t
Correct answer: A
4.Imani's grandmother's house is 5 miles west of her own house down Main Street. While at her grandmother's, Imani decides to ride her bike farther west down Main Street at 10 miles per hour. Which equation best describes the distance, d, in miles, Imani is from home after t hours?
A.d=5+10t
B.d=5−10t
C.d=5t+10
D.d=5t−10
Correct answer: A
5.Hiroto spends $68 on e-books and paperback books combined. Each e-book he buys costs $5, and each paperback book he buys costs $12. If Hiroto buys x e-books and y paperback books, which of the following equations best models the situation?
A.5x+12y=68
B.12x+5y=68
C.17(x+y)=68
D.17xy=68
Correct answer: A
6.A construction company's fees include a flat daily charge to come to a work site, in addition to a constant hourly rate. Any fractional hours are charged at that fraction of the hourly rate. Additionally, if a job takes less than 10 hours to complete, it is completed in one day. According to these rules, a 3.5 hour job would cost $250 and an 8 hour job would cost $475. If the construction company completes a job in one day, which of the following functions best models the cost, c, in dollars, for an h hour job?
A.c(h)=50h
B.c(h)=60h
C.c(h)=50h+75
D.c(h)=60h+10
Correct answer: C
7.From 2005 to 2013, the population of Belize has been increasing by approximately 7,500 people per year. The population of Belize in 2010 was 308,595. If t stands for years since 2005, which of the following functions best models the population, p, of Belize during this time period?
A.p(t)=271,095+7,500t
B.p(t)=308,595+7,500t
C.p(t)=346,095+7,500t
D.p(t)=−14,728,905+7,500t
Correct answer: A
8.In a political science class, test scores were determined to be 20 times the number of hours, h, the student studied plus 3. Which of the following functions best describes a student’s test score depending on the number of hours, h, that the student studied?
A.f(h)=3h+20
B.f(h)=20h
C.f(h)=60h
D.f(h)=20h+3
Correct answer: D
9.A 300-room hotel collects $75 per occupied room and does not collect any money for vacant rooms. Which of the following functions best represents how many dollars, d, the hotel generates given the number of vacant rooms in the hotel, v?
A.d=75(300−v)
B.d=75(300+v)
C.d=300(75−v)
D.d=300(75+v)
Correct answer: A