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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?
5. The probability that a woman does not know swimming is 2/5. If seven women in a city are
selected at random, find probability that
(i) four women know swimming.
(ii) at least one woman knows swimming
4. A committee of 5 is formed by drawing lots from 8 boys and 6 girls. Find the probability that
the committee will consist of 2 boys and 3 girls.
The price-demand equation and the cost function for the production of HDTVs are
given, respectively, by
x = 7, 500 − 25p and C(x) = 120, 000 + 24x,
where x is the number of HDTVs that can be sold at a price of $p per TV and C(x)
is the total cost (in dollars) of producing x TVs.
(a) Express the price p as a function of demand x, and find the domain of this
function.
(b) Find the marginal cost.
(c) Find the revenue function and state its domain.
(d) Find the marginal revenue.
(e) Find R′
(3, 500) and R′
(4, 200) and interpret these quantities.
(f) Graph the cost function and revenue function on the same coordinate system.
Find the break-even points and indicate regions of loss and profit.
(g) Find the profit function in terms of x.
(h) Find the marginal profit.
(i) Find P′
(1, 500) and P′
(5, 500) and interpret these quantities.
The number of traffic accidents per week in a small city has a Poisson distribution with mean
equal to 1.3. What is the probability of at least two accidents in 2 weeks?
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?
The SSG president claims that the average number of hours the students study their lesson is more than 25 hours per week with standard deviation of 4 hours. The average of 30 students surveyed is 36 hours per week, is there sufficient evidence to reject the SSG president’s claim at �� = 0.10 level of significance?
(a) What is the parameter to be tested?
(b) Is the population standard deviation given?
(c) How many samples do we have in this problem?
(d) What is the given level of significance?
(e) What is the appropriate statistical test to be used?
a.leadership skills test a random sample of 200 school managers were administered a developed leadership skills test. the sample mean and the standard deviation were 78 and 4.2 respectively. in the standardization of the test, the mean was 73 and the standard deviation was 8. test for significant difference using a = 0.05 utilizing the p value method. steps (p-value method)
Given a population of 5000 score with mean μ=86 and σ=10. How many scores are below 56?
Inverse Laplace Transforms
Find L^-1 {F(s)} when F(s) is given by
5. 1/(s+1)(s+2)(s^2+2s+10)
