You are opening up a restaurant, initial cost of opening the restaurant is $80,000, plus $4,000 monthly expenses. Estimate f(x)=xsquared - x + 5 to be the anticipated monthly profit of the restaurant in hundreds of dollars during the xth month of business. To break even your total profit from the opening of the restaurant must
The waste hauling company profits are stated as the difference between revenue and costs. That is P(x) = R(x) - C(x), where x is the number of tons processed. Find the maximum profit and the number of tonnage which must be processed in order to yield the maximum profit for each of the following: a) R(x) = 5x; C(x) = 0.0001x2
#4. Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). a. What are the 16 outcomes in the sample space? b. Which outcomes are in the event that exactly three of the selected mortgages are fixed rate? c. Which outcomes are in the event that all four mortgages are of the same type?
1. Let N1(p) denote the number of pairs of integers in [1, p - 1] in which the first is a quadratic residue and the second is a quadratic nonresidue modulo p. Prove that N1(p) = (1/4) (p - ( - 1)^((p - 1)/2)) 2. Let N2(p) denote the number of pairs of integers in [1, p - 1] in which the first is a quadratic nonresidue and the second is a quadratic residue modulo p. Prove that N2(p) = (1/4) (p - 2 + ( - 1)^((p - 1)/2)) 3. Let N3(p) denote the number of pairs of integers in [1, p - 1] in which the first is a quadratic nonresidue and the second is a quadratic nonresidue modulo p. Prove that N3(p) = (1/4) (p - 2 + ( - 1)^((p - 1)/2)) 4. Use the results of theorem 10-4 and corollary 10-1 to construct solutions of x^2 + y^2 =29. 5. Prove ( without assuming corollary 10-1) that, if p is a prime ≡ 1 (mod 4), then there exists positive integers m, x, and y such that x^2 + y^2 =mp, with p ┼ x, p ┼ y, 0 < m < p [ Hint: use the proof of Theorem 11-2]. Theorem 10-4: If p is an odd prime, then ν(p) = (1/8)p + Ep where | Ep| < (1/4)(p)^(1/2) +2. Corollary 10-1: Every prime p ≡ 1(mod 4) is representable as a sum of two squares. Theorem 11-2: For each prime p there exist integers A,B and C, not all zero, such that A^2 + B^2 + C^2 ≡ 0 (mod p).
Theory of Numbers The Distribution of Quadratic Residues Sums of Squares Sums of Four S
1) Find the Shapley- Shubik distribution (in percent) for the system (7: 5,3,2,1,). 2) In a cafeteria every meal has a 5 choice main course, a 3 choice salad, and a 2 choice soup, and a 4 choice dessert. If some one ate a different complete meal every day, how many days could he eat before he would start to repeat a meal?
1. solve 2(3y+4)-5(y-2)=3y-6(y-3) 2. Four more than twice the difference of three times a number and 8 is less than twice the number.
Z/z-2 - 1/z+5 = 7/z squared + 3z - 10
The student-teacher ratio for Stratford High was reported to be 27.5 to 1. If there are 42 teachers, how many students are in the school?
Compute c∫ (e^cosz)(logz)dz where c is the positive oriented circle with center z0=1 and radius 1/2. Please see attached.
In math class we have been assigned to answer the following question: How do you solve an equation? Please provide an example. I know how to solve an equation if it is given to me, but I do not know how to describe how to solve any equation. I hope you can help.
Prove, using the quadratic reciprocity law that (3/p) = 1 if p== 1 or 11 (mod 12) (3/p) = -1 if p==5 or 7 (mod12) for each odd prime p.
With only the small valve open, all of the liquid can be drained from a large vat in 4 hours. With only the large valve open, all of the liquid can be drained in 2 hours. How long would it take to drain the vat with both valves open?
Minimum cost problem: It cost a company C dollars per hour to operate its base base division. an analyst had determined that C is related to the number of base balls produced per hour, x, by the eqauation C = 0.009x^2 - 1.8^2 + 100. What number of balls per hour should be produced to minimize the cost per hour of manufacturing
As Jack finished a section of the novel he was reading, his wife posed a curious question: "Dear, suppose you took the page numbers of the section you just read and added them together. What would you get? Jack summed them rather hastily and said, "Well, I may have to double-check my arithmetic. It's either 412 or 512, I'm not
On the medical insurance policy (such as BCBS), the policy holder may need to make co-payments for percriptions drugs, office visits, and proceduares until total of all co-payments reaches a specific amount. Suppose on the Gattelaro's medical policy that the co-payment for the percription drug is 50% of the cost; the co-payment
Ryan starts jogging home at the rate of 6km/hr. After reaching Harbor Front, he begins jogging back home. Because of fatigue, his speed for the return trip decreases to 4.5km/h and takes 1 hour longer. Determine the total distance that Ryan jogged.
Attached is a spreadsheet with two accounts. Each account has the same retail and invoice. One school has a small enrollment and the other has a larger enrollments. There is a handling fee of $2 per enrollment. There are only two variables that can be changed: brochure cost & incentives. Also, the larger the enrollment, the larg
1: Write the standard form of the equation of the line passing through the point (1,-2) and perpendicular to the line y=-3/2x-2 2: The line through A(-3,-4) and B(-2,Y) is perpendicular to a line with a slope -1/7. Find y
To stay competitive with the fast food restaurant across the street, the Pico de Gallo Restaurante offers a lunch special. Each lunch plate has an .80 charge for beans, rice and guacamole, and each taco oredered costs .75. Senora Taquita, across the street, only charges .35 for the beans, rice and guacamole, but charges .90 fo
Linear Programming / Sensitivity Analysis / Optimization: Please solve in Excel using Solver add-in and also do Sensitivity Report to solve and support answers. The EnergyBoat Company
The Background The EnergyBoat, Inc. produces and distributes high quality motor boat with highly seasonal demand. To handle this seasonality, the company has several options for its supply chain aggregated planning purposes: hiring an additional workers during peak seasons, outsourcing part of the demand to a third party manu
Please see the attached file for the fully formatted problems.
If Bob had $150 more saved he would have five times as much saved as he currently has saved. How much does Bob currently have saved?
Find the deterministic solution for defining the position of a reflective object where the direct path and reflective path are known and the angle between the object and the receiver are also known. Please see the attached file for the diagram.
Please solve the attached equation by squaring. Thank you.
Two mountain bikers started from the ranger station in Rocky Mountain National Park traveling in the same direction on Trail Ridge Road. The first biker left 1 hour earlier than the second and traveled 10 miles/hour. The second biker left later and traveled 15 miles/hour. By 4:00 pm, the second biker had passed the first and was
I would appreciate it if someone could provide the solution to QA1 of the attatched exam paper. SECTION A A1 (a) Give the definitions of the autocovariance and autocorrelation of a time series model. (b) Calculate the autocovariance and autocorrelation function for the time series Y = 3 + Zt + 1/2Zt-1 + 1/5Zt-2, where
By looking at the equation for a rational function, how can you tell if there will be "y-values" which never occur?
1.Determine the equation of the line through (-2, 0) with slope . Write the equation in standard form using only integers as the coefficients. 2.Determine the equation of the line through (0, 9) that is parallel to the line 3x + 5y = 15. Write the equation in slope-intercept form. 3.Determine the equation of the line th
Use the definition to show that the sequence (n-1)/(n+2) (n=1 to infinity) is Cauchy. Please show all steps.