MATH SET B

From past experience it is known 90 percent of one year old children can distinguish their mothers voice of a similar sounding female. A random sample of 20 one year's old are given this voice recognize test. Find the probability that at least 3 children didn't recognize their mother's voice. A. 0.677 C. 0.729 B. 0.323 D. 0.271

B. 0.323

How many different combinations of 5 students can be drawn from a class of 25 students? A. 48680 C. 56820 B. 53130 D. 42050

B. 53130

Find the circumference of the circle x>> + y>> -12x + 10y + 15 = 0 A. 24.6 C. 42.6 B. 62.4 D. 64.2

C. 42.6

In what quadrant will θ terminate if csc is positive and sec is negative? A. I C. II B. III D. IV

C. II

Convert to rectangular coordinates the point having cylindrical coordinates (2, D/3,-3) A. (1, sqrt 3, -3) B. (sqrt 3, 1, -3) C. (-1, sqrt 3, -3) D. (1, -sqrt 3, -3)

A. (1, sqrt 3, -3)

A line has a y-intercept of 12 and a slope of 2. What is the abscissa of a point on the line whose ordinate is 6? A. -3 C. 6 B. 3 D. -6

A. -3

In a small town, the average daily temperature in April follows a normal distribution with a mean of 65 ½ F and a standard deviation of 5 ½ F. Imagine a local festival is scheduled for April 14th. The organizers are concerned about the comfort of attendees and decide to provide heated tents if there's a high chance of the temperature dropping below 60 ½ F during the event. What is the probability that the temperature on April 14th will be below 60 ½ F? A. 0.1587 C. 0.3413 B. 0.8413 D. 0.4331

A. 0.1587

Evaluate the integral of x ln x from 1 to 2 A. 0.636 C. 0.363 B. 0.633 D. 0.336

A. 0.636

At a local pet adoption center for dogs and cats, it is known that if a person adopts a pet, there is a 0.45 probability that it will be a cat and a 0.55 probability that it will be a dog. If a cat is adopted, the probability that it is female is 0.60. If a dog is adopted, the probability that it is female is 0.35. An adopted pet is selected at random and is found to be male. What is the probability that the adopted pet is a dog? A. 0.67 C. 0.72 B. 0.56 D. 0.8

A. 0.67

If verse sin θ = 0.524, what is the value of θ in rad? A. 1.07 C. 1.53 B. 2.3 D. 1.20

A. 1.07

Find the principal root of (1 +𝑖)^(2−𝑖) A. 1.4900 + 4.1257𝑖 B. 1.4900 − 4.1257𝑖 C.4.1257 + 1.4900𝑖 D. 4.1257 − 1.4900 𝑖

A. 1.4900 + 4.1257𝑖

Fencing is limited to 20 ft. in length. What is the maximum rectangular area that can be fenced in using two perpendicular comer sides an existing wall? A. 100 ft2 C. 85 ft2 B. 125 ft2 D. 150 ft2

A. 100 ft2

Find the height of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm. A. 11.55 C. 10.63 B. 15.36 D. 13.25

A. 11.55

A triangle has variable sides x, y, z subject to the constraint such that the perimeter P is fixed to 18 cm. What is the maximum possible area for the triangle? A. 15.59 cm2 C. 20.68 cm2 B. 18.68 cm2 D. 25.64 cm2

A. 15.59 cm2

How many positive real roots are in the polynomial 3x4 - x3 + 2x>> + x +1 =0 A. 2 or 0 C. 3 or 1 B. 2 or 1 D. 1 or 0

A. 2 or 0

What is the differential equation of the family of parabolas having their vertices at the origin and this foci on the x-axis? A. 2y dx + x dy = 0 B. 2x dx - y dy = 0 C. x dy + y dx = 0 D. dy/dx - x = 0

A. 2y dx + x dy = 0

Find the fourth proportional to 7, 9 and 28 A. 36 C. 22 B. 35 D. 32

A. 36

Find the area of the surface which is part of the plane x/2 + y/3 + z/6 =1 A. 3√14 C. 7 B. √11 D. √14

A. 3√14

Find the area of the region bounded by the curves y = x>> - 4x and x + y= 0 A. 4.5 C. 6.5 B. 3.5 D. 2.5

A. 4.5

How many four-letter words beginning and ending with a vowel without any letter repeated can be formed from the word "personnel"? A. 40 C.720 B. 180 D. 240

A. 40

What is the LCM of 9 and 15? A. 45 C. 15 B. 3 D. 135

A. 45

Find the acute angles between the two planes 2x - y + z = 8 and x + y + 2z - 11 = 0. A. 60 1/2 C. 50 1/2 B. 30 1/2 D. 40 1/2

A. 60 1/2

How many different signals each consisting of one flag or more hung in a horizontal line, can be formed from a set of 4 different flags. A. 64 C. 81 B. 325 D. 125

A. 64

If the half-life of a substance is 1,200 years, find the percentage that remains after 240 years. A. 87% C. 95% B. 90% D. 81%

A. 87%

Find the area enclosed by the lemniscate r>> = a>> cos 2θ. A. a>> C. a>> / 2 B. 2a>> D. a>> / 4

A. a>>

The polynomial x>> + 4x + 4 is the area of the square floor. What is the length of its side? A. x + 2 C. x +1 B. x - 2 D. x - 1

A. x + 2

What is the x-intercept of the line whose parametric equations are x = 2t - 1 and y = 6t + 11? A. -4/3 C. -14/3 B. -7/3 D. -5/3

C. -14/3

The position of a particle moving along the x-axis at anytime t is given by x(t) = 2t3 - 4t>> + 2t - 1. What is the slowest velocity achieved by the particle. A. 17/4 C. -2/3 B. 3 D. -3/2

C. -2/3

In a hotel it is known that 20% of the total reservation will be cancelled in the last minute. What is the probability that out of 15 reservation that there will be more than 8 but less than 12 will cancelled? A. 0.0084 C. 0.000784 B. 0.0784 D. 0.784

C. 0.000784

The radius of the circle is measured to be 3 cm correct to within 0.02 cm. Estimate the propagated error in the area of the circle. A. 0.283 C. 0.377 cm B. 0.253 cm D. 0.423 cm

C. 0.377 cm

Basket A contains 6 blue balls and 5 red balls and basket B have 4 blue balls and 7 red balls. If a ball is drawn from each basket, what is the probability that they are of the same color? A. 0.425 C. 0.488 B. 0.352 D. 0.634

C. 0.488

If the radius of the sphere is measured as 3 cm with a possible error of 0.01 cm. Find the approximate error in the computed volume. A. 3.25 C. 1.13 B. 2.25 D. 1.25

C. 1.13

A ladder 20 ft long leans against a vertical wall. If the top slides downwards at the rate of 2 fps, how fast the lower end is moving it is 16 ft from the wall? A. 2.5 fps C. 1.5 fps B. 2 fps D. 1.8 fps

C. 1.5 fps

A group of students were asked about there favorite subject in Math. Fifty said they like Algebra, Sixty like Trigo and 65 like Geometry. Twenty like both Algebra and Trigo, fifteen like both Trigo and Geometry and 25 like both Algebra and Geometry. Five like all subjects. Find the probability that the student chosen likes only Algebra assuming that there is no one not liking any subjects? A. 1/10 C. 1/12 B. 2/11 D. 1/5

C. 1/12

Water is running out a conical funnel at the rate of 1 cu in/sec. If the radius of the base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in from the top. A. 1/3pi in/sec B. -1/3pi in/sec C. 1/9pi in/sec D. -1/9pi in/sec

C. 1/9pi in/sec

Three cats can kill 5 rats in a minute. How many minutes will it take for 15 cats to kill 250 rats? A. 15 C. 10 B. 20 D. 8

C. 10

The measure of an angle and its supplement are in the ratio of 3:6. Find the measure of bigger angle in degrees. A. 40 C. 120 B. 80 D. 60

C. 120

Which is not equivalent to 150 degrees? A. 2.62 rad C. 1333.33 mils B. 0.42 rev D. 166.67 grad

C. 1333.33 mils

Find the probability that a couple with 4 children will have at least one boy. A. 1/2 C. 15/16 B. 1/16 D. 2/3

C. 15/16

The cable of suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally. The distance between towers is 150m., the points of the cable on the towers are 22m above the roadway, and the lowest point on the cable is 7 m above the roadway. Find the vertical distance to the cable from a point in the roadway 15 m from the foot of the tower. A. 9.6 m C. 16.6 m B. 18.8 m D. 12.8 m

C. 16.6 m

The volume of a hemisphere of radius 2 m is A. 14.67 m3 C. 16.76 m3 B. 67.04 m3 D. 33.52 m3

C. 16.76 m3

A line segment 167 in long is divided into three parts, the length of which are in the ratio 2:6:8. Find the length of the shortest part. A. 20 C. 22 B. 21 D. 23

C. 22

Given the polar curve r = 2 cos 2θ, find the area. A. D/4 C. 2D B. D/2 D. D

C. 2D

51. What is the height of the right circular cone having a slant height of 3.162 m and a base diameter of 2 m? A. 1 C. 3 B. 2 D. 4

C. 3

A substance decreases at a rate which is inversely proportional to the amount present. If 12 units of the substance are present initially and B units are present after 2 days, how long will it take the substance to disappear? A. 1.6 days C. 3.6 days B. 2.5 days D. 4.6 days

C. 3.6 days

An ellipse has an eccentricity of 1/3. Find the distance between the two directrix if the distance between the foci is 4. A. 18 C. 36 B. 30 D. 24

C. 36

What is the sample variance of the following set of numbers? 5,6,8,10,13,14,15,20,21,22 A. 36.87 C. 38.27 B. 35.32 D. 37.36

C. 38.27

The angles of elevation of the top of the tower at two points 30 m and 80 m from the foot of the tower, on a horizontal line are complementary. What is the height of the tower? A. 46 m C. 49 m B. 47 m D. 48 m

C. 49 m

A parabolic arch has a width of 18m across the bottom. At a vertical distance of 3m above the bottom, the width across the arc is 12m. What is the height of the arch in meters? A. 6.2 m C. 5.4 m B. 3.8 m D. 6.2 m

C. 5.4 m

How many arithmetic means will be inserted between 2 and 42 so that the sum of the added mean is equal to 138. A. 5 C. 6 B. 7 D. 8

C. 6

Given A = 5i + 3j and B = 2i + kj where k is a scalar, find k such that A and B are parallel. A. 6 C. 6/5 B. 3 D. 3/5

C. 6/5

A steel ball at 110 deg C cools in 8 min to 90 deg C in a room temp of 30 deg C. Find the temperature of the ball after 20 min. A. 38.97 deg C B. 48.97 deg C C. 68.97 deg C D. 58.97 deg C

C. 68.97 deg C

Two dice are thrown, what is the probability the sum is a composite number? A. 5/12 C. 7/12 B. 6/12 D. 8/12

C. 7/12

An unnoticed mechanical failure has caused one-fourth of a machine shop's production of 10000 pistol firing pins to be defective. A random sample of 25 firing pins was drawn from the population. What is the mean that it is not defective? A. 2500 C. 7500 B. 5000 D. 5500

C. 7500

Find the area bounded by the curve y>> = 16x and x>> = 16y A. 96.35 C. 85.33 B. 102.34 D. 89.63

C. 85.33

A laboratory has a 75-gram sample of radioactive materials. The half-life on the material is 10 days. What is the mass of the laboratory's sample remaining after 30 days? A. 15.385 C. 9.375 B. 12.635 D. 10.325

C. 9.375

Which of the following is the inverse Laplace transform of s(s>>+27)/(s>>+9)^2 ? A. cos(3t)-3t sin(3t) B. sin(3t)-3t cos(3t) C. cos(3t)+3t sin(3t) D. sin(3t)+3t cos(3t)

C. cos(3t)+3t sin(3t)

If the length of the rectangle is decreased by 10% and the width increased by 10%, what is the percentage change of the area? A. decreased by 10% B. increased by 1% C. decreased by 1% D. increased by 10%

C. decreased by 1%

A given function f(t) can be represented by a Fourier series if it A. is periodic B. is singled valued C. is periodic, single valued and has a finite number of maxima and minima in any one period D. has a finite number of maxima and minima in any one period

C. is periodic, single valued and has a finite number of maxima and minima in any one period

What kind of graph is r = 2 sec θ? A. circle C. line B. parabola D. ellipse

C. line

If B2 - 4AC = 0. The conic is called. A. circle C. parabola B. ellipse D. hyperbola

C. parabola

The conic having an eccentricity equal to 1 is. A. circle C. parabola B. ellipse D. hyperbola

C. parabola

The equation y>> = cx is the general solution of A. y'= 2y/x C. y'= y/2x B. y'= 2x/y D. y'= x/2y

C. y'= y/2x

The temperature is recorded at 60 airports in a region. The average temperature is 67 degrees Fahrenheit with standard deviation of 5 degrees. What is the z-score for a temperature of 68 degrees? A. 0.1 C. 0.3 B. 0.2 D. 0.4

B. 0.2

Find the 12th term of the harmonic progression 1, 1/3, 1/5 A. 1/9 C. 1/1/7 B. 1/23 D. 1/2

B. 1/23

Find all values of z for which e^4z=i. A. 1/6 pi + ½ kD i B. 1/8 pi + ½ kD i C. -1/6 pi + ½ kD I D. -1/8 pi + ½ kD i

B. 1/8 pi + ½ kD i

A bus leaves Manila at 12NN for Baguio 250 km away travelling an average of 55 kph. At the same time, another bus leaves Baguio for Manila traveling 65 kph. At what distance from Manila they will meet. A. 124.36 km C. 120.36 km B. 114.58 km D. 118.54 km

B. 114.58 km

A solid has a circular base of radius 20 cm. find the volume of the solid if every plane section perpendicular to a certain diameter is an equilateral triangle. A. 25,425 cm3 C. 16,448 cm3 B. 18,475 cm3 D. 20,470 cm3

B. 18,475 cm3

Find the moment of inertia, with respect to x-axis of the area bounded by the parabola y>>=4x and the line x=1.. A. 4.12 C. 3.16 B. 2.13 D. 5.18

B. 2.13

The difference of the squares of two numbers is 157. The square of their difference is equal to 25. Find the greater number. A. 15 C. 25 B. 20 D. 18

B. 20

By stringing together 9 differently colored beads, how many different bracelets can be made? A. 362,880 C. 40,320 B. 20,160 D. 181,440

B. 20,160

Find a (dot) b if /a/ = 26 and /b/ = 17 and the angle between them is pi/3. A. 338 C. 212 B. 221 D. 383

B. 221

Mark was twice as old as Daryl was when Mark was as old as Daryl is now. If Mark is 36 years old now, how old is Daryl now? A. 18 C. 27 B. 24 D. 30

B. 24

How soon after 8 o'clock will the hands of the clock be at right angle? A. 21.82 min C. 40 min B. 27.27 min D. 43.63 min

B. 27.27 min

If the tangent of angle A is equal to the square root of 3, angle A in the third quadrant, find the square of the tangent of A/2. A. 2 C. 4 B. 3 D. 5

B. 3

Find the area bounded by the curves r = 4 / (1 + cos θ) and cos θ = 0 A. 4/3 C. 8/3 B. 32/3 D. 16/3

B. 32/3

The volume of the sphere is 36D cu. m. The surface area of this sphere in sq. m. is: A. 24D C. 12D B. 36D D. 16D

B. 36D

Given f(x) = (x + 3)(x - 4) + 4 when divided by (x - k), the remainder is k. Find k. A. 2 C. 3 B. 4 D. 5

B. 4

Solve for the radius of curvature of the curve y = x3 at point (1,1). A. 6.12 C. 6.32 B. 5.27 D. 4.36

B. 5.27

The cost per hour of running a boat is proportional to the cube of the speed of the boat. At what speed will the boat run against a current of 4kph in order to go a given distance most economically. A. 8 kph C. 4 kph B. 6 kph D. 12 kph

B. 6 kph

An equilateral triangle has side of 8 inches. What is its height? A. 6.32 in C. 5.66 in B. 6.93 in D. 6.56 in

B. 6.93 in

From the top of the hill the angle of depression of the top and bottom of a flag pole 10m. high at the foot of the hill are observed to be 40 deg and 45 deg, respectively. Find the height of the hill. A. 42.15 C. 52.15 B. 62.15 D. 72.15

B. 62.15

Find the volume obtained if the region bounded by y = x>> and y = 2x is rotated about the x axis. A. 34D/15 C. 54D/5 B. 64D/15 D. 14D/5

B. 64D/15

The cross product of vector A = 4i + 2j with vector B = 0. The dot product A·B = 30. Find B. A. 6i - 3j C. 3i + 6j B. 6i + 3j D. 3i - 6j

B. 6i + 3j

Water is pouring into a swimming pool. After t hours there are t t + galloons in the pool. At what rate is the water pouring into the pool when t= 9 hours? A. 5/9 gph C. 5/6 gph B. 7/6 gph D. 5/8 gph

B. 7/6 gph

Find the Laplace transform off(t) = e raised to (3t + 1) A. e / (s + 3) B. e / (s - 3) C. e / (s squared + 3) D. e / (s squared - 3)

B. e / (s - 3)

93. Solve dy/dx = 4y divided by x(y3) A.𝑥3𝑦4 = 𝐶𝑒𝑦 C. 𝑥4𝑦2 = 𝐶𝑒𝑦 B. 𝑥4𝑦3 = 𝐶𝑒𝑦 D. 𝑥3y2 = 𝐶𝑒𝑦

B. 𝑥4𝑦3 = 𝐶𝑒𝑦

Find the centroid of the triangle whose vertices are (2, 3), (- 4 6) and (2, -6). A. (1,1) C. (0,1) B. (1,-1) D. (1,0)

C. (0,1)

Find the location of the focus of the parabola x>>+4y−4x−8=0. A. (-2,-2) C. (2,-2) B. (-2,2) D. (2,2)

D. (2,2)

Find the area of the triangle whose vertices are (4,2,3), (7,2,4) and (3,-4,6). A. 15.3 C. 12.54 B. 13.5 D. 12.45

D. 12.45

If the distance between the points (8, 7) and (3, y) is 13. What is the value of y that is positive? A. 5 C. 13 B. 9 D. 19

D. 19

The growth rate of the energy consumption of a country is 7.5%. In how many years will the energy be quadrupled? A. 16.5 C. 15 B. 20.5 D. 19.2

D. 19.2

There are five main roads between the cities A and B, and four between B and C. In how many ways can a person drive from A to C and return, going through B on both trips without driving on the same road twice? A. 32 C. 120 B. 210 D. 240

D. 240

A particle moves on a straight line with a velocity v = (4 - 2t)3 at time t. Find the distance traveled from t = 0 to t = 3.

D. 34

A motorboat weighs 32000 lb and its motor provides a thrust of 5000 lb. Assume that the water resistance is 100 pounds for each foot per second of the speed v of the boat. Then 1000 𝑑𝑣/𝑑𝑡 = 5000 - 100 v. If the boat starts from the rest, what is the maximum velocity that it can attain? A. 20 ft/s C. 40 ft/s B. 25 ft/s D. 50 ft/s

D. 50 ft/s

Evaluate the limit: limit(x>> - 16)/(x - 4) as x approaches to 4 A. 1 C. 4 B. 2 D. 8

D. 8

Find the volume of the solid revolution obtained by revolving the region bounded by y=x-x 2 and the x axis about the x axis. A. D/15 C. D/60 B. D/45 D. D/30

D. D/30

Find the general solution of y' - 2y = -8x>> A. y = 4x^2 + ce^(2x) B. y = 3x^2 + 4x + 2 + ce^(2x) C. y = 4x^2 + 4x + 2 + ce^(x) D. y = 4x^2 + 4x + 2 + ce^(2x)

D. y = 4x^2 + 4x + 2 + ce^(2x)