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SAT Practice Test 2015. If h hours and 30 minutes is equal to 450 minutes, what is the value of h?
There are 60 minutes in one hour. Thus, in h hours there are h*60 minutes; and in h hours and 30 minutes there are (h*60+30) minutes.
This total should equal 450 minutes:
h*60+30=450
h*60=420
h=7 hours
Answer: 7
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SAT Practice Test 2015. A project manager estimates that a project will take x hours to complete, where x > 100. The goal is for the estimate to be within 10 hours of the time it will actually take to complete the project. If the manager meets the goal and it takes y hours to complete the project, which of the following inequalities represents the relationship between the estimated time and the actual completion time?
A) x + y < 10
B) y > x + 10
C) y < x - 10
D) -10 < y - x < 10
If the manager met the goal, the difference between the number of hours the project takes, y, and the number of hours the project was estimated to take, x, should be between -10 and 10.
Thus, -10 < y - x < 10.
Answer: D
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SAT Practice Test 2015. The distance traveled by Earth in one orbit around the Sun is about 580,000,000 miles. Earth makes one complete orbit around the Sun in one year. Of the following, which is closest to the average speed of Earth, in miles per hour, as it orbits the Sun?
A) 66,000
B) 93,000
C) 210,000
D) 420,000
The speed in miles per year is: 580,000,000 miles / year.
Since there are 365 days in a year, the speed in miles per day is:
580,000,000 miles / 365 days = 1,589,041 miles / day
Since there are 24 hours in a day, the speed in miles per hour is:
1,589,041 miles / 24 hours = 66,210 miles / hour
Answer: A
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SAT Practice Test 2015. A function f satisfies f(2)=3 and f(3)=5. A function g satisfies g(3)=2 and g(5)=6. What is the value of f(g(3))?
A) 2
B) 3
C) 5
D) 6
It is given that g(3)=2. Thus, f(g(3))=f(2)
And it is given thar f(2)=3. Thus, f(g(3))=3
Answer: B
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SAT Practice Test 2015. A musician has a new song available for downloading or streaming. The musician earns 0.09 dollars each time the song is downloaded and 0.002 dollars each time the song is streamed. Which of the following expressions represents the amount, in dollars, that the musician earns if the song is downloaded d times and streamed s times?
A) 0.002d + 0.09s
B) 0.002d - 0.09s
C) 0.09d + 0.002s
D) 0.09d - 0.002s
For each time the song is downloaded the musician earns 0.09 dollars. If the song is downloaded d times, the musician wil earn 0.09d.
For each time the song is streamed the musician earns 0.002 dollars. If the song is streamed s times, the musician wil earn 0.002s.
Thus the total amount in dollars the musician will earn is 0.09d + 0.002s
Answer: C
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SAT Practice Test 2015. The sales manager of a company awarded a total of 3000 dollars in bonuses to the most productive salespeople. The bonuses were awarded in amounts of 250 or 750 dollars. If at least one 250 dollar bonus and at least one 750 dollar bonus were awarded, what is one possible number of 250 dollar bonuses awarded?
These are the possible combinations for a total of 3000 dollars in bonuses:
One 750 dollar bonus, and nine 250 dollar bonus;
Two 750 dollar bonus, and six 250 dollar bonus;
Three 750 dollar bonus, and three 250 dollar bonus.
Answer: 3, 6, or 9
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SAT 2015 Test. A landscaping company estimates the price of a job, in dollars, using the expression 60 + 12nh, where n is the number of landscapers who will be working and h is the total number of hours the job will take using n landscapers. Which of the following is the best interpretation of the number 12 in the expression?
A) The company charges 12 dollars per hour for each landscaper.
B) A minimum of 12 landscapers will work on each job.
C) The price of every job increases by 12 dollars every hour.
D) Each landscaper works 12 hours a day.
In the given equation 60 is a fixed price and nh is the total number of hours of work done
when n landscapers work h hours. Therefore, the price increases by 12 dollars per hour for each landscaper.
Answer: A
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SAT 2015 Test. A local television station sells time slots for programs in 30-minute intervals. If the station operates 24 hours per day, every day of the week, what is the total number of 30-minute time slots the station can sell for Tuesday and Wednesday?
Two days have a total of 48 hours, or 96 30-minute time slots.
Answer: 96
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SAT 2015 Test. The posted weight limit for a covered wooden bridge in Pennsylvania is 6000 pounds. A delivery truck that is carrying x identical boxes each weighing 14 pounds will pass over the bridge. If the combined weight of the empty delivery truck and its driver is 4500 pounds, what is the maximum possible value for x that will keep the combined weight of the truck, driver, and boxes below the bridge’s posted weight limit?
If the combined weight of the empty delivery truck and its driver is 4500 pounds, the truck can carry no more than 1500 pounds.
Since each box weighs 14 pounds, the maximum number of boxes the truck can carry is:
$b=1500/14=107.1$
Answer: x=107
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SAT 2015 Test. Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?
If Wyatt husks 12 dozen ears of corn per hour, it will take him 6 hours to husk 72 dozen ears of corn.
If Wyatt husks 18 dozen ears of corn per hour, it will take him 4 hours to husk 72 dozen ears of corn.
Answer: Any number of hours between 4 and 6, inclusive.
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SAT 2015 Test. Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P=108-23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?
A) Kathy will complete the repairs within 108 days.
B) Kathy starts each week with 108 phones to fix.
C) Kathy repairs phones at a rate of 108 per hour.
D) Kathy repairs phones at a rate of 108 per day
At the beginning of the week (day 0), the number of phones left to fix is: $P_0=108-23.0=108$. Therefore, 108 in the equation means that Kathy starts each week with 108 phones to fix.
Answer: B
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SAT 2015 Test. On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?
A) 9mp
B) 20mp
C) 5m+4p
D) 4m+5p
Armand sent m text messages each hour for 5 hours. Therefore the total number of messages Armand sent was m.5.
Tyrone sent p text messages each hour for 4 hours. Therefore the total number of messages Tyrone sent was p.4.
The total number of messages is: $m.5+p.4$
Answer: C
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SAT Practice Test. When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?
A. $p=0.44d+0.77$
B. $p=0.44d+14.74$
C. $p=2.2d-1.1$
D. $p=2.2d-9.9$
At 9 feet, the pressure is 18.7 pounds per square inch.
At 14 feet, the pressure is 20.9 pounds per square inch.
So the pressure increases (20.9-18.7) as the depth increases (14-9) feet. The ratio is $\frac{20.9-18.7}{14-9}=0.44$
Now lets calculate the pressure when depth equals zero:
$p_0=p_9-9.(0.44)$, where $p_9$ is the pressure at 9 feet.
$p_0=18.7-3,96$
$p_0=14,74$
The pressure at any depth will be the pressure at $d=0$ plus $0.44$ times the depth. That is,
$p=14.74+0.44d$
Answer: B
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SAT Practice Test. The toll rates for crossing a bridge are 6.50 dollars for a car and 10 dollars for a truck. During a two hour period, a total of 187 cars and trucks crossed the bridge, and the total collected in tolls was 1,338 dollars. Solving which of the following systems of equations yields the number of cars, x, and the number of trucks, y, that crossed the bridge during the two hours?
A. $x+y=1,338$
$6.5x+10y=187$
B. $x+y=187$
$6.5x+10y=1,338/2$
C. $x+y=187$
$6.5x+10y=1,338$
D. $x+y=187$
$6.5x+10y=1,338/2$
There will be one equation for the total number of vehicles crossing the bridge, and one equation for the total collected in tolls.
The number of cars plus the number of trucks should equal 187: $x+y=187$.
The collected tolls from cars (6.5x) plus the collected tolls from trucks (10y) should equal 1,338: $6.5x+10y=1,338$.
Answer: C
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SAT Practice Test. The gas mileage for Peter’s car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car’s gas tank has 17 gallons of gas at the beginning of a trip. If Peter’s car travels at an average speed of 50 miles per hour, which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins?
A. $f(t)=17-\frac{21}{50t}$
B. $f(t)=17-\frac{50t}{21}$
C. $f(t)=\frac{17-21t}{50}$
D. $f(t)=\frac{17-50t}{21}$
If the car consumes 1 gallon every 21 miles, in 50 miles it will consume $\frac{50}{21}$ gallons.
Therefore, after one hour driving at 50 miles per hour, the tank will have $17-\frac{50}{21}$ gallons remaining (17 is how many gallons there were at the tank at the beginning of the trip).
After two hours driving at 50 miles per hour, the tank will have $17-\frac{50}{21}-\frac{50}{21}=17-\frac{50.2}{21}$ gallons.
After t hours driving at 50 miles per hour, the tank will have $17-\frac{50t}{21}$ gallons.
Answer: B
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SAT Practice Test. The recommended daily calcium intake for a 20 year old is 1,000 milligrams (m g). One cup of milk contains 299 milligrams of calcium and one cup of juice contains 261 milligrams of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20 year old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?
A. $299.m+261.j\geq1,000$
B. $299.m+261.j>1,000$
C. $\frac{299}{m}+\frac{261}{j}\geq1,000$
D. $\frac{299}{m}+\frac{261}{j}>1,000$
In $m$ cups of milk there are $m.299$ mg of calcium.
In $j$ cups of juice there are $j.261$ mg of calcium.
If one drinks $m$ cups of milk AND $j$ cups of juice, the total intake of calcium will be $m.299+j.261$ mg of calcium.
The question requires that the 20 year old "meet or exceed" the recommended daily calcium intake. Therefore, the total intake should be greater than or equal to the recommended daily calcium intake:
$m.299+j.261\geq1,000$
Answer: A
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SAT Practice Test.
$\frac{1}{x}+\frac{2}{x}=\frac{1}{5}$.
Anise needs to complete a printing job using both of the printers in her office. One of the printers is twice as fast as the other, and together the printers can complete the job in 5 hours. The equation above represents the situation described. Which of the following describes what the expression $\frac{1}{x}$ represents in this equation?
A. The time, in hours, that it takes the slower printer to complete the printing job alone
B. The portion of the job that the slower printer would complete in one hour
C. The portion of the job that the faster printer would complete in two hours
D. The time, in hours, that it takes the slower printer to complete $\frac{1}{5}$ of the printing job
If the slower printer takes x hours to complete the job, in one hour it will complete the portion $\frac{1}{x}$ of the job.
The second printer is twice as fast as the first one. Therefore, in one hour, it will complete the portion $\frac{2}{x}$ of the job.
The two printers together will complete in one hour $\frac{1}{x}+\frac{2}{x}$ of the job. This expression should equal $\frac{1}{5}$ of the job, because it is given that the two printers together take 5 hours to complete the job.
So the terms in the equation represent the portion of the job that the first ($\frac{1}{x}$), the second ($\frac{2}{x}$) and the sum of the two printers ($\frac{1}{5}$) complete in one hour.
Answer: B
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SAT Practice Test. If $\frac{2}{a-1}=\frac{4}{y}$ (the fraction whose numerator is 2, and whose denominator is a, minus 1, equals, the fraction whose numerator is 4 and whose denominator is y), where $y\neq0$ (y does not equal zero) and $a\neq1$ (a does not equal 1), what is y in terms of a?
A. $y=2a-2$ (y equals 2 a, minus 2).
B. $y=2a-4$ (y equals 2 a, minus 4).
C. $y=2a-\frac{1}{2}$ (y equals 2 a, minus one half).
D. $y=\frac{1}{2}a+1$ (y equals one half a, plus 1).
$\frac{2}{a-1}=\frac{4}{y}$
$2y=4(a-1)$
$y=2(a-1)$
$y=2a-2$
Answer: A
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SAT Practice Test. If $y=x^3+2x+5$ (y equals x cubed, plus 2 x, plus 5) and $z=x^2+7x+1$ (z equals x squared, plus 7 x, plus 1), what is $2y+z$ (2 y plus z) in terms of x?
A. $3x^3+11x+11$ (3 x cubed, plus 11 x, plus 11).
B. $2x^3+x^2+9x+6$ (2 x cubed, plus x squared, plus 9 x, plus 6).
C. $2x^3+x^2+11x+11$ (2 x cubed, plus x squared, plus 11 x, plus 11).
D. $2x^3+2x^2+18x+12$ (2 x cubed, plus 2 x squared, plus 18 x, plus 12).
$2y+z=2(x^3+2x+5)+(x^2+7x+1)$
$2y+z=2x^3+4x+10+x^2+7x+1$
$2y+z=2x^3+x^2+11x+11$
Answer: C
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SAT Practice Test. If $a^{-\frac{1}{2}}=x$ (a, to the power of negative one half, equals x), where $a>0$ (a is greater than zero) and $x>0$ (x is greater than zero), which of the following equations gives a in terms of x?
A. $a=\frac{1}{\sqrt{x}}$ (a, equals the fraction 1 over the square root of x)
B. $a=\frac{1}{x^2}$ (a, equals the fraction 1 over x squared)
C. $a=\sqrt{x}$ (a, equals the square root of x)
D. $a=-x^2$ (a, equals negative x squared)
Answer:
$2y+z=2(x^3+2x+5)+(x^2+7x+1)$
$2y+z=2x^3+4x+10+x^2+7x+1$
$2y+z=2x^3+x^2+11x+11$
Answer: C
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