Math Answers

A students' council with 22 members must select 3 students to help run a fundraiser. This is to be done by randomly selecting 3 names from the 22 names available. The council has 3 students from grade 9, 4 students from grade 10, 10 students from grade 11, and the remainder from grade 12. Determine the probability that 2 out of the 3 names are chosen from the same grade

find the limit lim x→0 x^2 cos 1/x.

Write the following as an algebraic expression. Then simplify.

The sum of two consecutive integers if the first integer is x

find the limit lim x→0 x^2 cos 1/x.

prove that the function f given by

f(x)={ 2,if x is irrational

-2,if x is rational

is discontinuous, for all x€R,using the sequential definition of continuity

The proportion of people in a given community who have a certain disease is 0.005. A test

is available to diagnose the disease. If a person has the disease, the probability that the test

will produce a positive signal is 0.99. If a person does not have the disease, the probability

that the test will produce a positive signal is 0.01. If a person tests positive, what is the

probability that the person actually has the disease?

3. Suppose a retailer purchased an item with birr 80 and sold for birr 130. Its fixed cost is birr 10,000 and variable cost other than cost of goods sold is 5%.

Compute

A. Develop the cost equation

B. Find Breakeven point in terms of quantity

{F} Solve the first order linear inhomogeneous differential equation using the Bernoulli method

y^,-(2y/x)=1+(1/x)

{F} 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).

{F} 9.

A) Let U(10)={1,3,7,9} be a group under multiplication modulo 10, what is the order of group?

B) What is the order of group Z of integers under addition?