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General
8 months ago
Use the roster method to write each of the given sets. For some exercises you may need to consult a reference, such as the Internet or an encyclopedia. (Enter EMPTY for the empty set.) The set of natural numbers x that satisfy x + 4 = 1
General
8 months ago
newborns GENDER QUANTITY WOMAN 95.025 TOTALS 194.933 According to the Table, what is the probability of success for a newborn to be female? What is the probability of failure? If 5 newborns are randomly chosen, what is the probability that 3 of them are female? If 10 newborns are randomly chosen, what is the probability that more than 1 is female?
General
8 months ago
A $20000 loan compounded monthly at 6% p.a. is to be repaid at $300 per month. How long will it take to be paid out fully?
General
8 months ago
result of x in 3(x+5)-2 (3-2x)= 30
General
8 months ago
Find the limit of the function f(x,y)=(x^2-y^2)/(x+y), as (x,y) tends to (2,-2)
General
8 months ago
Proofs. Below, in the first three questions, A and B denote sets. (a)Prove or disprove, using any method, the following statement: |P(A − B)| = 2|A|−|B|, where P(X) is the power-set of X.rove that A − (B ∩ A) = A − B using the set identities as well as the set subtraction law: A − B = A ∩ B. (c)Prove that A − (B ∩ A) = A − B, but this time using definitions only (of sets, set operations, set relations, etc.), . You should NOT use set identities. (d)Prove by induction that for any positive integer n, 4 divides 32n − 1. (e)Is the statement “If √13 ̸ ∈ Q, then √25 ̸ ∈ Q” True or False? Explain your answer in detail (proof something if necessary). You can use the fact that if n is an integer such that 13 divides n2, then 13 divides n. (f) Given the following clauses: (¬P ∨ W ) ∧ (P ∨ Q ∨ T ) ∧ (¬S) ∧ (P ∨ Q ∨ S) ∧ (¬Q ∨ T ) ∧ (¬T ) ∧ (¬W ) Perform the smallest possible resolution refutation, that is, prove the above CNF formula is unsatisfiable (i.e., a contradiction) in the smallest number of steps. (g) Prove by resolution that KB |= φ, where: KB = (¬P ∨ W ) ∧ (P ∨ Q ∨ T ) ∧ (¬S) ∧ (P ∨ Q ∨ S) ∧ (¬T ) ∧ (¬W ) and φ = Q ∧ ¬T Provide a proof showing all the steps of your reasoning.
General
8 months ago
Round to the nearest cent of $65,729.915.
General
8 months ago
A group of friends is going to climb a hill. As they rise, the temperature drops by 1'C every 200 meters, if the temperature was 20'C when they began to rise. What temperature will it be when they have ascended 600 meters?
General
8 months ago
Cooper Hudson's home is assessed at $375,000. The tax rate is 5.1 mills.What is the tax on Coopers home?
General
8 months ago
Dylan bought a new Ford truck for $28,000. Dylan made a down payment of $6000 and paid $390 monthly for 70 months.What the total finance charge?
General
8 months ago
X³-X²-4X+12 Combination of factoring cases
General
8 months ago
Juan-Solez, a prominent painter, takes out a simple discount note for one year from River National Bank for $5,000. The annual rate of Interest is 8%.What is the amount of the discount and the proceeds?
General
8 months ago
With interest of $1,832.00 and a principal of 16,000 for 206 days, use the ordinary Interest method to determine the rate
General
8 months ago
find indicial equation for (x-7)y" - 2x^2y' + 9y=0
General
8 months ago
A potter forms a lump of clay into a cylinder. As you wind it up, the length, L, of the cylinder increases and the radius, r, decreases. If the length of the cylinder is increasing by 0.8 cm per second, find the rate at which the radius is changing when the radius is 2 cm and the length is 11 cm. (Of units ).
General
8 months ago
Using the numbers 09, 15 and 2010, what mathematical equation would give the sum of 23?
General
8 months ago
a) Verify that y = -1/(xc) is a family of one-parameter solutions of the equation differentially`=y2. b) Since f (x, y) = y2 and ∂f/∂y = 2y are continuous everywhere, the region R of Theorem 1.2.1 can be taken as the entire xy-plane. Find a solution from the family of part (a) that satisfies that y(0) = 1. Then find a solution from the family of part (a) that satisfies that y(0) = -1. Find the longest interval I of definition for the solution of each initial value problem. c) Determine the longest interval of definition I for the solution of the initial value problem y`= y2 , y(0) = 0. [Hint: The solution is not a member of the family of solutions in part (a)] .
General
8 months ago
F(x,y)=3x-y/x+2y
General
8 months ago
A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine II per month are 7,170 and 8,230. The time requirements and profit per unit for each product are listed below. A B C Machine I 5 9 12 Machine II 7 8 15 Profit $9 $13 $16 How many units of each product should be manufactured to maximize profit, and what is the maximum profit? Start by setting up the linear programming problem, with A, B, and C representing the number of units of each product that are produced.
General
8 months ago
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