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2. Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the output
((￢p ∨￢r) ∧￢q) ∨ (￢p ∧ (q ∨ r)) from input bits p, q, and r.
Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the output
(p ∧￢r) ∨ (￢q ∧ r) from input bits p, q, and r.
A political campaign manager wishes to survey a number of voters to estimate the proportion of those who are in favor of his candidate. If a previous survey shows that 55% of registered voters plans to vote for his candidate, what is the minimum sample size required to make his survey accurate with a 95% confidence level and a margin of error of 2.5%?
According to a report, 67.4% of murders are committed with a firearm. (a) If 200 murders are randomly selected, how many would we expect to be committed with a firearm? (b) Would it be unusual to observe 147 murders by firearm in a random sample of 200 murders? Why?
A manufacturer of apple phone charges claims that only 4% of his production is defective. In a random sample of 120 items, the defect rate is 4.99%. At the 1% level of significance, test the manager's claim.
i. State the null and alternative hypotheses for the test. [2]
ii. Calculate the value of the test statistic for this test. [2]
iii. Determine the critical region(s) for this test. [2]
iv. State the conclusion of this test. Give a reason for your answer. [3]
A bottled water company has found in the past that 2% of their bottled water does not meet the company’s high standards. As such periodic samples are taken and tested for their quality. If from the last batch a sample of 12 bottles are taken and tested, determine the probability:
i. Carefully defining the random variable of interest [1]
ii. What is the probability distribution? State the values of the parameters [2]
iii. Justifying the suitability of the probability distribution identified in part (ii) [4]
iv. Calculate the probability that at most 2 bottles do not meet the company’s Standards [4]
v. The expected number of bottles that do not meet the company’s standards. [2]
vi. The amount of sodium sulfate, in mg, found in the bottled water follows a normal distribution with a mean 13mg and a standard deviation of 2.5mg. It is known that 76% of the bottles have a mean that is more than x mg. Find the value of x
The 1500 students weight are normally distributed with a mean of 50kg with the standard deviation of S-5 lbs?
A. How many students are less than 46kg
B. How many students are heavier than 113.5lbs
Find the equation (formula) of a circle with radius r and center C(h,k) and if the Center of a circle is at (3,-1) and a point on the circle is (-2,1) find the formula of the circle.
Find the equation (formula) of a sphere with radius r and center C(h, k, l) and show that x2 + y2 + z2 - 6x + 2y + 8z - 4 = 0 is an equation of a sphere. Also, find its center and radius.
1. a. Construct a truth table for (p ↔ q) and (p → q) ^ (q → p).
b. Determine whether these compound propositions are logically equivalent.
2. Let R(x, y): x² + y² = 1. Find the truth values of the propositions R(2 3 , 6 4 ) and R(3 5 , 7 4 ) .
3. Let P(x, y, z): x + y = z, where x, y and z are all real numbers.
a. Express the quantifications ∀x∀y∃z P(x, y, z) and ∃z∀x∀yP(x, y, z) as statements.
b. Find the truth value of the quantifications ∀x∀y∃z P(x, y, z) and ∃z∀x∀yP(x, y, z).
c. Determine whether both quantifications are logically equivalent.
According to a survey, 32% of drivers tailgate other vehicles before passing them (thinking it will incite them to speed up). Consider 45 drivers selected at random. Use a normal approximation to find the probability that:
(a) at least 17 drivers tailgate? (Use only 3 decimal places)
(b) more than 9 but less than 25 drivers tailgate? (Use only 3 decimal places) ans_a is 0.251
#340153 on Dec 2023