Search & Filtering
Given g(x) = (x + 1)(x^2 − x), g: R → R where R is the set of real numbers.
a) Find the domain and range of the function g. (2 marks)
b) Determine whether the function is injective, surjective, and/or bijective. Justify
your answers. (7 marks)
2. JOY leather, a manufacturer of leather Products, makes three types of belts A, B and C which are processed on three machines M1, M2 and M3. Belt A requires 2 hours on machine (M1) and 3 hours on machine (M2) and 2 hours on machine (M3). Belt B requires 3 hours on machine (M1), 2 hours on machine (M2) and 2 hour on machine (M3) and Belt C requires 5 hours on machine (M2) and 4 hours on machine (M3). There are 8 hours of time per day available on machine M1, 10 hours of time per day available on machine M2 and 15 hours of time per day available on machine M3. The profit gained from belt A is birr 3.00 per unit, from Belt B is birr 5.00 per unit, from belt C is birr 4.00 per unit. What should be the daily production of each type of belt so that the profit is maximum?
a) Formulate the problem as LPM
b) Solve the LPM using simplex algorithm.
c) Interpret the shadow prices
Let Q and R be any two sets given, prove that [Q̅ ∪ (Q − R)][overlined] = Q ∩ R.
the mean score and the standard score in the statistics test are repectively equal to 80 and 2.5, whereas in the pre calculus test they are respectively equal to 70 and 2. if vince got a score of 85 in statistics and a score of 75 in pre-calculus, in which subject is her standing better assuming normality on both subject?
A box contain 10 black marble, 8 white marble and 6 yellow marble. If a ball is drawn at random, what is the probability of getting black marble and white marble?
A food manufacturing company produces oatmeal cookies that have a sugar content that
is approximately normally distributed. The mean sugar content is 1.1 grams with a standard
deviation of 0.15 gram. Determine the probability that a random sample of 10 oatmeal cookies
will have an average sugar content of greater than 1.2 grams.
Each time Caroline goes shopping she decides whether or not to buy fruit.
The probability that she does buy fruit is 0.4.
Independently, she then decides whether or not to buy a CD, with a probability of 0.3 that she does buy a CD.
Work out the probability that she buys fruit or buys a CD or both.
Use any appropriate method in finding the indicated solution of the following differential
equations.
[2𝑥𝑦 cos(𝑥2) − 2𝑥𝑦 + 1]𝑑𝑥 + [𝑠𝑖𝑛(𝑥2) − 𝑥2]𝑑𝑦 = 0
Box A box B both contain the numbers 1,2,3 and 4 contrast the probability mass function and draw the histogram of the sum when one number from each box is take at a time with replacement
two coins are tossed let T the number of tails that occurs determine the values of the random variable T
