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If the two pumps are started together, at what time will the two pumps have emptied 50% of the water in the swimming pool? It takes pump (B) 6 hours to empty the same swimming pool. It takes pump (A) 4 hours to empty a swimming pool. The length of side AB isįor the remainder of the division of x 3 - 2x 2 + 3kx + 18 by x - 6 to be equal to zero, k must be equal to In a triangle ABC, angle B has a size of 50 o, angle A has a size of 32 o and the length of side BC is 150 units. If 2 television sets are selected at random from the 10, what is the probability that 1 of them is defective? It is known that 3 out of 10 television sets are defective. What is the period of the function f(x) = 3 sin 2(2x + Pi/4)? The range of the function f(x) = -|x - 2| - 3 is If the committee is selected at random, what is the probability that it has an equal number of male and female teachers? If ax 3 + bx 2 + c x + d is divided by x - 2, then the remainder is equalĪ committee of 6 teachers is to be formed from 5 male teachers and 8 female teachers. What value of x makes the three terms x, x/(x + 1) and 3 x/ those of a geometric sequence?Īs x increases from Pi/4 to 3 Pi/4, |sin(2x)| If in a triangle ABC, sin(A) = 1/5, cos(B) = 2/7, then cos(C) = If f(x) = 1 / (x - 2), which of the following graphs is closest to the graph of |f(x)|? Which of the following functions satisfy the condition f(x) = f -1(x)?
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If this cone is cut along the slanted height to make a sector, what is the central angle, in degrees, of the sector? If each data value in the data set is multiplied by 4, then the value of the standard deviation of the new data set is equal toĪ cone made of cardboard has a vertical height of 8 cm and a radius of 6 cm. What is the volume of the region between the two cylinders?Ī data set has a standard deviation equal to 1. The two cylinders have the same height of 20 cm. If x - 1, x - 3 and x + 1 are all factors of a polynomial P(x) of degree 3, which of the following must also be a factor of P(x)?Ī cylinder of radius 5 cm is inserted within a cylinder of radius 10 cm. What is the smallest positive zero of function f(x) = 1/2 - sin(3x + Pi/3)? The y coordinates of all the points of intersection of the parabola y 2 = x + 2 and the circle x 2 + y 2 = 4 are given by The area of the circle x 2 + y 2 - 8y - 48 = 0 is The lines with equations x + 3y = 2 and -2x + ky = 5 are perpendicular for k = What is the equation of the horizontal asymptote of function What is the smallest distance between the point(-2,-2) and a point on the circumference of the circle given by What is the length of vector w given by w = - u - 2 v? Vectors u and v are given by u = (2, 0) and v = (-3, 1). N is another point on the circle so that angle McN has a size of 30°. The circle of equation (x - 3) 2 + (y - 2) 2 = 1 has center c. Which of these graphs is the closest to the graph of If L is a line through the points (2,5) and (4,6), what is the value of k so that the point of coordinates (7,k) is on the line L?įind a negative value of k so that the graph of y = x 2 - 2x + 7 and the graph of y = kx + 5 are tangent? What is the probability that the sum of the two dice is greater than 3?