Search & Filtering
1.The average number of field mice per acre in a 5-acre wheat field is estimated to be 10. Find the probability that fewer than 6 field mice are found
(a) on a given acre;
(b) on 2 of the next 3 acres inspected.
Let the function f : R → R and g : R → R be defined by f(x) 2x + 3 and g(x) = -3x + 5.
a. Show that f is one-to-one and onto.
b. Show that g is one-to-one and onto.
c. Determine the composition function g o f
d. Determine the inverse functions f -1 and g -1 .
e. Determine the inverse function (g o f) -1 of g o f and the composite f -1 o g -1
Every continuous function is differentiable.
True or false with full explanation.
Let f : R → R be defined by f(x) = (x3 + 1)/2
a. Prove that f is bijective
b. Determine f-1 (x) and f o f o f-1
For sets A = {-3, -2,…,3} and B = {0, 1,…,10} B’ = {0, 1, 4, 5, 8, 9} and C = {1, 2,…,10}, let f : A → B and g : B’ → C be functions defined by f(n) = n2 for all n ∈ A and g(n) = n + 1 for all n ∈ B’.
a. Show that the composition g o f : A → C is defined
b. For n"\\in" A, determine (g o f)(n)
Solve the inequalities. Give your answer in interval notation, and indicate the answer geometrically on the real-number line.
a) t + 6 ≤ 2 + 3t
b) 3(2 – 3x) > 4(1 – 4x)
Determine the digit 100 places to the right of the decimal point in the decimal representation 7/27. (Apply Polya’s Strategy)
A small firm manufactures and sells litre cartons of non-alcoholic cocktails, X and
Y, which sell for $1 and $1.25, respectively. Each is made by mixing fresh orange, pineapple, and apple juices in different proportions. X consists of one part orange, six parts pineapple and one part apple. Y consists of two parts orange, three parts pineapple and one part apple. The firm can buy up to 300 litres of orange juice, up to 1125 litres of pineapple juice and up to 195 litres of apple juice each week at a cost of $0.72, $0.64 and $0.48 per litre, respectively. Find the number of cartons of X and Y that the firm should produce to maximise profits. You may assume that non-alcoholic cocktails are so popular that the firm can sell all that it produces.
Directions: From the given situation, (a) state the null and alternative hypotheses, (b) compute the test statistic, (c) determine the critical value and sketch the rejection region and non-rejection region in the normal curve.
1. The cahier of a fast-food restaurant claims that the average amount spent by customers for dinner is Php 120.00. A sample of 50 customers over a month was randomly selected and it was found out that the average amount spent for dinner was Php 122.50. Construct the critical regions using a 0.05 level of significance to conclude that the average amount spent by customers is more than Php 120.00. Assume that the population standard deviation is Php6.50.
Activity 1: Draw Me
Directions: Given the following information, construct the rejection region. Show the solution in a step-by-step procedure.
1. H0 : = 84
Ha : 84
m= 87, s= 10, n = 35, alpha= 0.05
2. H0 : = 45
Ha : < 45
m= 40, s = 12, n = 32, alpha= 0.01
#333702 on Dec 2022