Math Answers

5. A class in statistics contains 10 students, 3 of whom are 19, 4 are 20, 1

is 21, 1 is 24, and 1 is 26. Let X be the average age of the 2 randomly

selected students and derive the probability function for X.

6. A man has four keys in his pocket and, since it is dark, cannot see which

is his door key. He will try each key in turn until he finds the right one.

Let X be the number of keys tried (including the right one) to open the

door. What is the probability function for X?

7. Suppose a fair die is tossed two times. Let X be the larger of the two

faces that appear. Find px(k).

8. Suppose a particle moves along the x-axis beginning at 0. It moves one

integer step to the left or right with equal probability. What is the probability

function of its position after four steps?

9. Five cards are dealt from a standard 52-card deck. Let Y be the number

of red cards that are dealt. What is the probability function for Y ?

{Fs} The equation for a displacement 𝑠(𝑚), at a time 𝑡(𝑠) by an object starting at a displacement of 𝑠0 (𝑚), with an initial velocity 𝑢(𝑚𝑠 −1 ) and uniform acceleration 𝑎(𝑚𝑠 −2 ) is: 𝑠 = 𝑠0 + 𝑢𝑡 + 1 2 𝑎𝑡 2 A projectile is launched from a cliff with 𝑠0 = 30 𝑚, 𝑢 = 55 𝑚𝑠 −1 and 𝑎 = −10 𝑚𝑠 −2 . The tasks are to: a) Plot a graph of distance (𝑠) vs time (𝑡) for the first 10s of motion. b) Determine the gradient of the graph at 𝑡 = 2𝑠 and 𝑡 = 6𝑠. c) Differentiate the equation to find the functions for: i) Velocity (𝑣 = 𝑑𝑠 𝑑𝑡) ii) Acceleration (𝑎 = 𝑑𝑣 𝑑𝑡 = 𝑑 2 𝑠 𝑑𝑡2 ) d) Use your results from part c to calculate the velocity at 𝑡 = 2𝑠 and 𝑡 = 6𝑠. e) Compare your results for part b) and part d). f) Find the turning point of the equation for the displacement 𝑠 and using the second derivative verify whether it is a maximum, minimum or point of inflection. g) Compare your results from f) with the graph you produced in a).

Find the equation of the line which is perpendicular to 4𝑦=5𝑥−8 and passing through (2,3).

A random sample of size 16 has 53 as mean. The sum of the squares of the deviation

taken from mean is 150. Can this sample be regarded as taken from the population having

56 as mean? Obtained 95% and 99% level of confidence limit of the mean of population

The line 𝑦=𝑥−5 is tangent to the curve 𝑦=𝑥^2−9𝑥−𝑘

Find the value of 𝑘.

𝐴(1,−2) is a point on the circle (𝑥−3)2+ (𝑦+1)2= 5

a. State the coordinates of the centre of the circle and hence find the coordinates of the point 𝐵 where 𝐴𝐵 is the diameter of the circle.

b. 𝐶(2,1) also lies on the circle. Use coordinate geometry to verify that angle 𝐴𝐶𝐵 = 900

Find dy/dx of the function xy² + e^6x y³ = cos(x² + 2) at the point (1,1) by using implicit differentiation. 

The area of a square is increasing at the rate of 28cm² s^-1. Find the increasing rate of the length of a side,x when the area of the square is 49cm² .

Find the conical form of a quadratic form Q(x,y)=2x^2+2y^2-2xy by using an orthogonal transformation hence find nature,rank,index and signature of the conical form?

Two cubical dice are thrown and their scores addes together if X= add is the sum of the scores on the two dice what is P(X is divided by 4)