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Construct the Tabular Representation and Histogram Representation of the following probability distribution:
1. In a class of 100 students, 80 students passed in all subjects, 10 failed in one subject, 7 failed in two subjects and 3 failed in three subjects. Find the probability distribution of the variable for number of subjects a student from the given class has failed in.
2. The probability of landing on 1 is 0.25. The probability of landing on 2 is 0.75. Let X be the sum of the two spins. Construct a probability distribution for the random variable x.
For a certain type of fluorescent light in a large building, the cost per bulb of replacing bulbs all at once is much less than if they are replaced individually as they burn out. It is known that the lifetime of these bulbs is normally distributed, and that 60% last longer than 2500 hours, while 30% last longer than 3000 hours.
a) What are the approximate mean and standard deviation of the lifetimes of the bulbs?
If the light bulbs are completely replaced when more than 20% have burned out, what is the time between complete replacements
Say 40% of the class is female. What is the probability that 6 of the first 10 students walking in will be female?
Two functions f : R → R and g : R → R are defined by f(x) = 5x3 + 1 and g(x) = 2x − 3 for all x ∈ R.
Determine the inverse of (f -1 ◦ g) and (g ◦ f )(2) and ( f ◦ g)(2).
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)
In the following problems, perform the operations and simplify as much as possible.
a. (x2 + 2x)/(3x2 – 18x + 24) ÷ (x2 – x – 6)/(x 2 – 4x + 4)
b. (x2 + 6x + 9)/x/(x + 3)
c. 1/(3x – 1) + x/(x2 – 9)
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 .
- If a student randomly guesses at five multiple-choice questions, find the probability that the student gets exactly three correct. Each question has five possible choices.
- Say 40% of the class is female. What is the probability that 6 of the first 10 students walking in will be female?
Find Larange’s interpolating polynomial passing through set of points
(0,2) (2,-2),(3,-1),Use it to find
at x = 2
A company manufactures and sells x televisions per month. If the cost and the
revenue functions (in dollars) are
C(x) = 72, 000 + 60x and R(x) = 200x − x2/30,
respectively, with 0 ≤ x ≤ 6, 000, what will the approximate changes in revenue and
profit be if the production is increased from 1, 500 to 1, 505? from 4, 500 to 4, 505?
#339914 on Dec 2023