ALGEBRA LOOKSPAM

Evaluate sin [Arccos (-2/3)].

(1/3) square root of 5

If 1 cm = 0.39 in, about how many cm are there in 0.75 in?

1.92

Peter can paint a room in 2 hrs and John can paint the same room in 1.5 hrs. How long can they do it together in minutes?

51.43

If log (base 64) x = 3/2, find x.

512

If e^2x- 3e^x + 2 = 0, find x.

In 2

After paying a commission to his broker of 7% of the sale price, a seller receives P103,000 for his car. How much was the car sold?

P110,753

Juan invested P10,000. Part of it he put in the bank at 5% interest. The remainder he put in bands which pay a 9% yearly return. How much did he invest at 9% interest if his yearly income from the two investments was P6607?

P4,000

The value of a computer is depreciated over 5 years for tax purposes. That is, at the end of 5 years, the computer is worth O. If a business paid P21,000 for a computer how much will it have depreciated after 2 years?

P8,400

What is the greatest factor of 24 and 647?

8

At exactly what time after 5 o'clock will the hour hand and the minute hand be perpendicular for the first time?

B. 5:10 and 54 seconds

Determine the equation that expresses the statement. : F is directly proportional to y. Symbols a, b, c and d are constants.

F=a.y

Find the value of x for which f(x) = cot 2x is discontinuous.

x = π /2

A pendulum 1 m long oscillates through an angle of 100. Find the distance through which the end of the Pendulum swings in going from one extreme position to the other.

π/18m

An Electrical Engineer invested $50,000, part at 6 percent and part at 8 percent. The annual interest on the 6 percent investment was $480 more than that from the 8 percent investment. How much was invested at 8 percent interest?

$18,000

A family's electricity bill averages $80 a month for seven months of the year and $20 a month for the rest of the year. If the family's bill were averaged over the entire year, what would the monthly bill be?

$55

If 1 is added to the difference when 10x is subtracted from -18x, the result is 57. What is the value of x?

-2`

For the 2 functions, f(x) and g(x), tables of values are shown below. What is the value of g(f(3))? (see picture)

-3

The temperature at 6 PM was 39°F. By midnight, it had dropped 40°F. What was the temperature at midnight?

-9°F

If the graph of y = f(x) is transformed into a graph of 2y - 6 = -4 f(x - 3), point (a,b) on the graph of y = f(x) becomes point (A,B) where A and B are expressed as:

.A=a+3, B=-2b+ 3*

A company manufactures industrial laminates (thin nylon-based sheets) of thickness 0.02 in with tolerance of 0.004 in. Solve the inequality involving absolute values that describes the range of possible thickness for the laminate.

0.096 ≤ x ≤0.024

How many liters of water must be added to 1 liter of 35% boric acid solution in order to produce 20% boric acid solution?

0.75 L

Emilio is 1 year 7 months old and Brooke is 2 years 8 months old. How much older is Brooke than Emilio

1 year one month

Find the sum of a geometric progression if there are 4 geometric means between 3 and 729.

1,092

Find the coefficient of the 7th term of the expansion (x + 2y) to the 8th power.

1,792x^2 y^6

The horsepower which a shaft can transmit varies as the cube of the diameter and the angular speed. If a 75-mm diameter shaft transmits 270 hp when turning 1,000 rpm, find the horsepower which can be transmitted by a 125-mm shaft rotating 1,500 rpm.

1,875 hp

four-pound mixture of raisins and nuts is two-thirds raisins. How many pounds of nuts are there?

1.3 pounds

z varies directly as x and inversely as y2. If x = 1 and y = 2 then z = 2. Find z when x = 3 and y = 4.

1.5

z varies directly as x and inversely as y~2. It x2. Find x =1 andy = 2thenz = 2. Find z when x = 3 and y = 4.

1.5

What is the next term in the geometric sequence 16, -4, 9, -9/4, ...?

1/16

What is the value of x in Arctan 3x + Arctan 2x = 45 degrees?

1/6

Bob is 2 years from being twice as old as Ellen. The sum of twice Bob's age and three times Ellen's age is 66. How old is Ellen?

10

If f(x) = (5x + 2) and f(x - 3) + f(x) = 2x, then x is equal to________________

11/8

A boat can travel 10 miles downstream and at the same time can travel 6 miles upstream. If the current of water is 3 mph, find the speed of the boat in still water.

12 mph

Aubrey measured the width of her dining room in inches. It is 150 inches. How many feet wide is her dining

12.5 ft

In a pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there?

14

If Rita can run around the block in 5 times in 20 minutes, how many times can she run around the block in one hour?

15

In a certain electrical project, 12 electricians are needed to finish it the project in 17 days. After 11 days, 5 electricians quit the work due to sickness and are not replaced until 4 days. How many more electricians should be added to complete the job on time?

15

The sum of two integers is 36, and the difference is 6. What is the smaller of the two numbers?

15

The table shows the number CD players sold in a small electronics store in the years 1989-1999 as follows; (SEE PICTURE)

15 CD players/year

At how many minutes after 3:00 PM will the minute hand of a clock overtakes the hour hand?

16 4/11

If 10"x4, find the valve of 10^2x+1.

160

Ben is two years away from being twice Ellen's age. The sum of twice Ben's age and Thrice Ellen's age is 66. Find Ben's age now.

18

A chemist mixed a solution that was 34% acid with another solution that was 18% acid to produce 30-ounce solution that was 28% acid. How much of the 34% acid solution did he use?

18.75

A man left from Manila for Baguio City past 9 AM. Between 4 to 5 hours, he arrived at Baguio and noticed that the minute and hour hands of his wrist watch interchanged in position. At what time did the man arrive in Baguio?

1:45.73 PM

If the sum of the roots of the equation kx~2 - 2x - k - 10 = 0 is 1, find the value of k.

2

A and B can do a piece of work in 3 days, B and C in 4 days, while A and C in 2.5 days. In how many days can all of them do the work together?

2.03

Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards.

2.04 mils

A wall "h" meters high is 2 m away from the building. The shortest ladder that can reach the building with one end resting on the ground outside the wall is 6 m. How high is the wall in meters?

2.24

Joy is 10 percent taller than Joseph and Joseph is 10 percent taller than Tom. How many percent is Joy taller than Tom?

21 percent

In how many minutes after 10 o'clock will the hands of the clock be opposite each other for the first time?

21.81

Which of the following is not a multiple of 11?

221

Find the sum of all odd integers between 100 and 1,000.

247,500

A contractor has a manpower of 50 men and of the same capacity at work on a job in 30 days, the working day being 8 hours, but the contract expires in 20 days, how many workers should the contractor add?

25

What is the fourth proportional to 6, 10 and 15

25

Find two numbers whose sum is 50 and with largest possible product.

25 , 25

Maria is 10 years older than Jake, who is 16 years old. How old is Maria?

26 years old

At the city park, 32% of the trees are oaks. If there are 400 trees in the park, how many trees are NOT oaks?

272

If x — 1 is a factor of x2 + kx — 4, then k has the value of_____________.

3

When 5x76 - 4x"4 —- 7x3 + 2x - 3 is divided by (x + 1), what is the remainder?

3

How many positive real roots are there in the polynomial x^4-4x^3+7x²-6x-18 = 0.

3 or 1

How many positive real roots are there in the polynomial: x^4-4x^3+7x^2-6x-18=0

3 or 1

Find the coefficient of term involving x^8 in the expansion (x^2 + 2/x)^16.

3,294,720

If Nanette cuts a length of ribbon that is 13.4 inches long into 4 equal pieces, how long will each piece be?

3.35 m

Liza thought she had the exact money to buy 10 chocolate bars. However the price per bar had increased by 50 centavos. Consequently, she was able to buy only 8 bars and had P2 left. How much money did Liza have?

30

What is the sum of the exponents of the binomial expansion (x^2 + y^4) to the 10th power.

330

A snack machine accepts only 5-centavo coins. Chocolate bars cost 25c each, packages of peanuts cost 75c each and a can of cola costs 50c. How many 5-centavo coins are needed to buy 2 chocolate bars, one pack of Peanuts and a can of soda?

35

A weight of 60 pounds rest on the end of an 8-foot lever is 3 feet from the fulcrum. What weight must be placed on the other end of the lever to balance the 60-pound weight?

36 pounds

A man is running around a circular track 200 m in circumference. An observer uses a stopwatch to time each lap, obtaining the data as follows: (see picture) What is the average speed from 68 sec and 168 sec?

4 m/s

Mon and Mila can restock an aisle at the supermarket in 1 hour working together. Working alone, Mon can restock an aisle in 1.5 hours and Mila in 2 hours. If they work together for two hours, and then work separately for another two hours, how many aisles will they have completed?

4.33

Joseph gave 1/4 of his candies to Joy and Joy gave 1/5 of what she got to Tim. If Tim received 2 candies, how many candies did Joseph have originally?

40

In a certain factory, the ratio of the number of male to female workers is 2:3. If one hundred new female workers are hired, the number of female workers will increase to 65% of the total number of workers. Find the number of female workers in the factory.

420

A certain two-digit number is equal to five times the sum of its digit. If 9 were added to the number, its digits would be reversed. Find the number?

45

Parcel charges of a courier company are as follows: P40 for the first 2 kilograms P15 for each of the succeeding kilogram weight of parcels With these rates, what amount would be charged on a parcel weighing 30kg.

460

If 3x² is multiplied by the quantity 2x^3y raised to the 4th power, what would this expression simplify to?

48x^94y to the 4th power

Melissa is four times as old as Jim. Pat is 5 years older than Melissa. If Jim is "y" years old, how old is Pat?

4y + 5

The square of a number added to 25 equals 10 times the number. What is the number?

5

The boys take a 12-foot board and rest it on a large rock to make a teeter-tooter. If the boys sit on opposite ends of the board and weighs 50 pounds and 70 pounds, respectively, how far from the fulcrum will the 70-pound boy be if they balance?

5 feet

A boat has a speed of 15 mph in still water. It travels downstream from point A to point B in two-fifths of an hour. It goes back upstream from point B to point C, which is 2 miles downstream from point A, in three-fifths of an hour. Find the rate of the current.

5 mph

Seven people are at the beach for a clambake. They have dug 12.6 pounds of clams. They eat the following amounts of clams: 0.34 pounds, 1.6 pounds, 0.7 pounds, 1.265 pounds, 0.83 pounds, 1.43 pounds, 0.49 pounds. How many pounds of clams are left?

5.945 pounds

Which ratio best express the following: five hours is what percent of a day?

5/24=x/100

A coin collector has a collection of silver coins worth $205. There were five times as many guarters as half-dollars and 200 fewer dimes than quarters. How many quarter coins did the collector have?

500

Rick can paint a room in an hour and a half and James can paint the same room in 2 hours. How many minutes will it take them to paint the room if they do it together?

51

Which of the following equations has roots which are reciprocal of the roots of the equation 2x^3-3x-5=0

5x^2 + 3x - 2 = 0%

If log of (x + 2) base 2 + log of (x — 2) base 2 equals 5, solve for x.

6

Two trains leave the same city at the same time, one going east and the other going west. If one train is travelling at 65 mph and the other at 72 mph, how many hours will it take for them to be 822 miles apart?

6

The geometric mean and the arithmetic mean of two numbers are 8 and 10 respectively. What is the harmonic mean?

6.4

If Jim and Jerry together they can finish a job in 4 hours. If working alone takes Jim 10 hours to finish the job, how many hours would it take Jerry to do the job alone?

6.7

If Jim and Jerry work together they can finish a job in 4 hours. If working alone takes Jim 10 hours to finish the job, how many hours would it take Jerry to do the job alone?

6.7

The electric power which a transmission line can transmit is proportional to the product of its design voltage and the current capacity, and inversely as the transmission distance. A 115-kilovolt line rated at 100 amperes can transmit 150 megawatts over 150 kilometers. How much power in megawatts can a 230-kilovolt line of 150-ampere capacity transmit over 100 kilometers?

675

During his major league career, Hank Aaron hit 38 more home runs than Babe Ruth hit during his career. Together they hit 1,524 home runs. How many home runs did Babe Ruth hit?

740 home runs

A ball is dropped from a height of 18 meters. On each rebound it rises 2/3 of the height from which it last fell. What distance has it travelled at the instant it strikes the ground for the fifth time?

75.78

Toby, a Golden Retriever, gained 5.1 pounds this month. If Toby now weights 65.1 pounds, what is the percent increase in Toby's weight?

8.5%

If container A holds 8 gallons of water, and container B holds 12% more than container A, how many gallons of water does container B hold?

8.96

Find the sum of the first five terms of the geometric progression if the 3rd term is 144 and the 6th term is 486.

844

Find the sum of the first five terms of the geometric progression if the third term is 944 and the sixth term is 486.

844

A jar of coins totaling $4.58 contains 13 quarters and 5 nickels. There are twice as many pennies as there are dimes. How many dimes are there?

9

A ball bounces 2/3 of the altitude from which it falls. Suppose the ball is dropped from a height of 18 ft. How far will it travel before coming to rest?

90 ft

In the vicinity of a bonfire, the temperature T in deg C at distance of x meters from the center of the fire was given by: (see pictures) At what range of distances from the fire's center was the temperature less than 500 deg C?

More than 35 meters

If log 2 = a, log 3 = b, log 5 = c, then log (7.5)=_______?

b+c-a

Listed below are functions each denoted g(x) and each involving a real number x, constant c > 1. If f(x) = 2x, which of these functions yield the greatest valve for f(g(x), for all x > 1?

g(x) = ex