DIFFERENTIAL EQ; ADMATH; PROBAB

Equal volumes of different liquids evaporate at different but constant rates. If the first is totally evaporated in 6 weeks and the second in 5 weeks, when (week) will the second be 1/2 the volume of the first? A. 27/7 B. 30/7 C. 33/7 D. 29/7

B. 30/7

Find the area of the polygon with vertices at 2+31, 3+1, -2- 4i, — 4 — i, — 1+ 2i. A. 47/5 B. 47/2 C. 45/2 D. 45/4

B. 47/2

A cask containing 20 gallons of wine was emptied on one-fifth of its content and then 13 filled with water. If this is done 6 times, how many gallons of wine remain in the cask? A. 5.121 B. 5.243 C. 6.554 D. 5.343

B. 5.243

Determine the sum of the infinite series: S = (0.9) + (0.9)^2 + (0.9)^3+ (0.9)^n + A. 7 B. 9 C. 6 D. 8

B. 9

If sinx = 2, find cos4x. A. -j15√3 B. 97 C-156√3 D. 26

B. 97

Find the value of x in xy + xz = -8 xy + z = 1 xz + yz = -3 A. 1 B. 2 C. 3 D. 4

B. 2

Find the probability of getting eleven by throwing a pair of dice once. A. 1/18 B. 1/12 C. 1/21 D. 1/15

A. 1/18

A club of 40 executives, 33 like to smoke Marlboro, and 20 like to smoke Philip Morris. How many like both? A. 13 B. 10 C. 11 D. 12

A. 13

The table shows the number CD players sold in a small electronics store in the years 1989-1999 as follows; YEAR CD PLAYERS SOLD 1989 545 1990 675 1991 665 1992 665 1993 600 1994 550 1995 680 1996 560 1997 545 1998 560 1999 695 What was the average rate of change of sales between 1989 and 1999? A. 15 CD players/year C. 70 CD players/year D. 695 CD players/year B. 150 CD players/year

A. 15 CD players/year

7. Express the power (1+i)^8 in rectangular form. A. 16 B. 8i C. 1-i D. - 6

A. 16

A tank initially holds 100 gal of salt solution in which 50 lbs. of salt has been dissolved. A pipe fills the tank with brine at the rate of 3gpm containing 2 lbs. of dissolve salt per gallon. Assuming that the mixture is kept uniform by stirring a drain pipe draws out of the tank the mixture of 2gpm. Find the amount of salt in the tank at the end of 30 minutes. A. 171.24 lbs. B. 124.11 lbs. C. 143.25 lbs. D. 105.22 lbs.

A. 171.24 lbs.

A box contains 9 red balls and 6 blue balls. If two balls are drawn in succession, what is the probability that one of them is red and the other is blue? A. 18/35 B 18/37 C. 16/35 D. 16/37

A. 18/35

A box contains 9 red balls and 6 blue balls. If two balls are drawn in succession, what is the probability that one of them is red and the other is blue? A. 18/35 B. 18/37 C. 16/35 D. 16/37

A. 18/35

The sum of the cube of the consecutive numbers from 1 to 30 is A. 216,225 B. 215,325 C. 217,186 D. 216,961

A. 216,225

A man wishes to buy a place of land worth 15 million pesos. If it were possible for him to save one peso for the first day, two pesos on the second day, 4 pesos on the third day and so on. In how many days would he save enough money to buy the land? A. 25 B. 23 C. 24 D. 27

A. 25

An audience of 450 persons is seated in a row having the same number of persons in each row. If 3 more persons seat in each row, it would require 5 rows less to sear the audience. How many rows were there originally? A. 30 B. 27 C. 18 D. 20

A. 30

The sum of the ages of two boys is four times the sum of the ages of a certain number of girls. Four years ago, the sum of the ages of the girls was one eleventh of the sum of the ages of the boys and eight years hence, the sum of the ages of the girls will be one half that of the boys. How many girls are there? A. 4 B. 5 C. 6 D. 3

A. 4

Numbers like 12345, 13542, 53412 and 21435 are some of the 120 different arrangements that can be made from the digits 1, 2 ,3 ,4 and 5. If all 120 arrangements are placed in numerical order, what will be the 87t number? A. 43215 B 45312 C. 43521 D. 43251

A. 43215

Find the general solution of the differential equation 7y y' = 5x. A. 5x^2 - 7y^2 = C B. 7y^2 - 10x^2 = C C. 14y^2 - 5x^2 = C D. 7y^2 - 10x^2 = C

A. 5x^2 - 7y^2 = C

__________ of a real number is always positive. A. absolute value B mean C. limit D. standard deviation

A. absolute value

John started his egg farm business. His chickens produce 480 eggs per week. If he sells it at $2 a dozen (let 1 week = 7 days). How much does his chicken produce per week? A. $60 B. $80 C. $45 D. $120

B. $80

Find the rectangular coordinates of the spherical coordinate (2, 4, 2). A. (2, √2 , 0) B. (√Z, √2, 0) C. (√2. 0, √2) D. (√Z, 2, √2)

B. (√Z, √2, 0)

The sum of the n nth roots of a complex quantity is always A. unity B. 0 C. n(real component of a root) D. real comp. of the complex quantity

B. 0

A person draws 3 balls in succession from a box containing 5 red balls, 6 yellow balls and 7 green balls. Find the probability of drawing the balls in the order red, yellow and green. A. 0.3489 B. 0.04289 C. 0.0894 D. 0.3894

B. 0.04289

The time X a student spends learning a computer software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. A student is selected at random. What is the probability that the student spends at least 6 hours learning the software package? A. 0.0918 B. 0.9082 C. 0.4706 D. 0.6293

B. 0.9082

Evaluate In(3+j4) A. 1.46 + j0.102 B. 1.61 + j0.927 C. 1.77 + j0.843 D. 1.95 + j0.112

B. 1.61 + j0.927

What is the Laplace transform of e^-2t A. 1/(s-2) B. 1/(s+2) C. 1/(s-1) D. 1/(s+1)

B. 1/(s+2)

A Manila High School has 85 seniors, each of whom plays on at least one of the school's three varsity sports teams: football, baseball, and basketball. It so happen that 74 are on the football team; 26 are on the baseball team; 17 are on both the football and basketball teams; 18 are on both the baseball and football teams; and 13 are on both the baseball and basketball teams. Determine the number of seniors playing all three sports given that twice this number is members of the basketball team. A. 10 B. 11 C. 22 D. 20

B. 11

A merchant has 3 items on sale. A radio for $50.00, a clock for $30.00 and a flashlight for $1.00 At the end of the day, she has sold a total 100 of the three sale items and has taken in exactly $1,000 on the total sales. How many of each item did she sell? Disregard sales tax. A. 80, 4 and 16 B. 16, 4 and 80 C. 4, 16 and 80 D. 80, 16 and 4

B. 16, 4 and 80

Which of the following is a disadvantage of using the sample range to measures spread or dispersion? A. It produces very small spreads B. The largest of the smallest observation (or both) may be a mistake or an outlier. C. The sample range is not measured in the same units as the data. D. It produces spreads that are too large.

B. The largest of the smallest observation (or both) may be a mistake or an outlier.

Find the Laplace Transform of sinat. A. s/(a2+ s2) B. a/(s2 + a2) C. a/(1-s2) D. a/(s2-a2)

B. a/(s2 + a2)

Find a general solution to the differential equation y" - 2y' + y=xe^x + 4, y(0) = 1, y' (0) = 1 A. y = e^x + xe^x -1/2 e^x In(1 + x^2) + e^x arctanx B. y=-3e^x + 4xe^x +1/6x^3e^x+4 C. y=-3e^x+4xe^x-2/3 xe^2x -2/9e^2x D. y = e^xcosx + e^xsinx + 1/3 e^xcosx Inlcosx + 1/3 xe^2x sinx

B. y=-3e^x + 4xe^x +1/6x^3e^x+4

Find a general solution to the differential equation y " - 2y + y = xe^2x A. y = C1 e^x + C2 xe^x -1⁄2 e^x In(1 + x^2) + ex arctanx B. y=C1e^x + C2xe^x + xe^x -2e^x C. y = C1e^x + C2xe^x - 2/3 xe^2x -2/9e^2x D. y = C1 e^xcosx + C2e^xsinx + 1/3 e^xcosx Inlcosx + 1/3 xe^2x sinx

B. y=C1e^x + C2xe^x + xe^x -2e^x

The angular velocity of a rotating rigid body about an axis of rotation is given by w = 41 + j 2k. Find the linear velocity of a point P on the body whose position vector relative ot a point on the axis of rotation is 21-3j +k. A. 5i8j- 4k B. -51-8j-4k C.-5i-8j-14k D. 5i-8j-14k

C. -5i-8j-14k

A project activity can be done by 25 men in 60 days. At the end of the 5th day, 6 men were laid off. At the start of the 33rd day, 12 more men were hired to finish the job. How many days is the project advanced/ delayed? A. 0.81 advanced B. 0.81 delayed C. 0.19 advanced D. 0.19 delayed

C. 0.19 advanced

From past experience, it is known 90% of one-year old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Find the probability at least 3 children do not recognize their mother's voice. A. 0.222 B. 0.500 C. 0.323 D. 0.122

C. 0.323

A piece of paper is 0.03 inches thick. Each time the paper is folded in half, the thickness is doubled. If the paper is folded in half 12 times, how thick to the nearest foot, would the paper be? A. 1.2 ft B. 5.3 ft C. 10.24 ft D. 4.24 ft

C. 10.24 ft

A basketball coach has a total of 10 players. In how many ways can he field a team of 5 players if the team captain is always included? A. 42 B. 70 C. 126 D. 25

C. 126

There are 13 teams in a tournament. Each team is to play with each other only once. What is the minimum number of days can they all play without any team playing more than one game in any day? A. 11 B. 12 C. 13 D. 14

C. 13

In how many ways can a student going abroad accompanied by 3 teachers selecting from 6 teachers? A. 16 B. 24 C. 20 D. 12

C. 20

In the chemical processing of a certain mineral, the fate of change of the amount of mineral present varies as the amount of the mineral remaining. If after 8 hours, 100 pounds of mineral have been reduced to 70 pounds, what quantity of the mineral will remain after 24 hours? A. 53.2 B. 43.4 C. 34.3 D. 25.3

C. 34.3

In the chemical processing of a certain mineral, the rate of change of mne amount of mineral present varies as the amount of the mineral remaining. If after 8 hours, 100 pounds of mineral have been reduced to 70 pounds, what quantity of the mineral will remain after 24 hours? A. 53.2 B. 43.4 C. 34.3 D. 25.3

C. 34.3

9 liters of wine are taken from a container full of wine. It is then filled with water. Then 9 liters of the mixture are taken and the container is again filled with water. If the ratio of the quantity of the wine now in the container to the quantity of the water in it is 16/9, what is the capacity of the container? A. 60 L B. 54 L C. 45 L D. 36 L

C. 45 L

A steel ball is 120°C cools in 20 min to 80°C in a room 25°C. Find the temperature of the ball after half an hour. A. 40.96°C B. 45.98°C C. 66.85°C D. 55.86°C

C. 66.85°C

In the vicinity of a bonfire, the temperature T in degrees at distance of x meters from the center of the fire was given by; T =762,500/x^2 + 300 At what range of distances from the fire's center was the temperature less than 500 deg. C? A. More than 45 meters B. More than 30 meters C. More than 35 meters D. More than 20 meters

C. More than 35 meters

Solve (x + y)dy = (x − y)dx A. x^2+y^2 = C B. x^2 + 2xy + y^2 =C C. x^2-2xy - y^2 = C C. x^2-2xy + y^2 = C

C. x^2-2xy - y^2 = C

Find all differential equation of the family of line's passing through the origin. A. x dx + y dy = 0 B. x dy-y dx = 0 C. ydx + x dy = 0 D. y dx-x dy = 0

C. ydx + x dy = 0

An investor has P 1,100 income from bonds bearing 4% and 5% if the amount at 4% and 5% were interchanged he would eam P 50 more per year. Find the total sum invested. A. ₱ 20,000 B. ₱ 30,000 C.₱ 25,000 D.₱ 35,000

C.₱ 25,000

There are n couples at a party. Each man shakes hands with everyone else except his spouse. No handshakes take place between women. How many handshakes take place? (as a polynomial function of n) A. n! - 1 B. n(n - 1) C. (n-1)(n-2) D. (1/2)(3n^2 - 3n)

D. (1/2)(3n^2 - 3n)

If j = sqrt(-1), the quantity j^5246 is equal to, A. 1 B. -j C. j D. - 1

D. - 1

Write the vector of length 2 and direction 150 degrees in the form ai + bj. A. 1.73i + j B. - 1.73i -j C. 1.73i -j D. -1.73i + j

D. -1.73i + j

Evaluate sin2x if sinx = 2. A. 4 B. -3 C. 6 D. -7

D. -7

In a certain study about 2 pollutants, it is found out that pollutant A has 30% chance of - polluting in a day. Pollutant B has 25% chance of polluting. The 2 pollutants do not pollute on the same day. At any given day, if pollutant A is polluting, what is the probability that Pollutant B is also polluting? A. 30% B. 25% C. 5% D. 0

D. 0

From past experience, it is known 90% of one-year old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Find the probability that all 20 children recognize their mother's voice. A. 0.222 B. 0.500 C. 1.000 D. 0.122

D. 0.122

The time X a student spends learning a computer software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. A student is selected at random. What is the probability that the student spends between 6.5 and 8.5 hours learning the software package? A. 0.0918 B. 0.9082 C.0.221 D. 0.470

D. 0.470

A die is rolled and a coin is tossed. What is the probability that a three and a head will appear? A. 1/4 B 1/2 C. 2/3 D. 1/12

D. 1/12

The Laplace Transforms of t^2e -4t is A. 4s/(s + 4)^4 B. 2s/(s + 4)^5 C. 3/(s + 4)^2 D. 2/(s +4)^3.

D. 2/(s +4)3.

In how many ways can the letters of the word "ENGINEERING" be arranged by taking the letters all at a time? A. 138,600 B. 372,500 C. 288,500 D. 277,200

D. 277,200

The Laplace transform of t^2cos4t A. - 16s/(s2 + 16) B. 8(3s - 16)/(s2 + 16)^3 C .- 81/(s2 + 16) D. 2s(s2 -48)/(s2 + 16)^3

D. 2s(s2 -48)/(s2 + 16)^3

How many possible positive real solutions are there in the polynomial: x^4 4x^3+7x^2-6x-18=0 A. 3 or 0 B. 1 or 2 C. 1 or 0 D. 3 or 1

D. 3 or 1

In how many ways can 5 persons be seated in an automobile having places for 2 in the front seat and 3 in the back seat if only 3 can drive A. 80 B. 36 C. 60 D. 72

D. 72

In how many ways can 2 integers be selected from the integers 1, 2, 3, ... , 100 so that their difference is exactly 7? A. 69 B. 74 C. 81 D. 93

D. 93

A survey was conducted to find out which of the three leading car brands they liked best. The results indicated that 500 liked Honda, 470 liked Toyota, and 430 liked Ford. But of these, 180 liked both Honda and Ford, 140 liked both Honda and Toyota, and 210 liked both Ford and Toyota, Only 60 liked all the 3 car brands. How many persons responded to the survey? A. 910 B. 980 C. 960 D. 930

D. 930

The simplest form of [(n+1)!]2 / [(n!)(n- 1)!] is A. n(n+1) B. n+1 C. n2 D. n(n+1)2

D. n(n+1)2

The Laplace Transform of coshbt is A. s/(b2 + s2 ) B. b/(s2 + b2) C. s/(b2-s2) D. s/(s2 -b 2)

D. s/(s2 -b 2)

In any square matrix, when the elements of any two rows are exactly the same, the determinant is A. negative integer B. positive integer C. unity D. zero

D. zero

Evaluate e^ jtan(π/2) A. e B. 1 C. 0 D. ∞

D. ∞