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    Algebra

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    Quadratic Reciprocity Law

    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.

    Standard Deviation and Mean: Phony Data

    For any data set of n values with standard deviation s, every value must be within s √n - 1 of the mean. A statistics teacher reports that the test scores in her class of 17 students had a mean of 75.0 and a standard deviation of 5.0. Kelly, the class's self-proclaimed best student, claims that she received a grade of 97. Cou

    Minimum Cost Problems for Company C

    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

    Capacitor, Source Voltage and Maximum Charge

    If a capacitor with a capacitance of 0.000005 farads is wired in a circuit with a total resistance of 5000 ohms (the standard unit of electrical resistance), how long must the capacitor be wired to a source voltage to reach 50% of its maximum charge? (Hint: Begin by expressing q as 0.5Q)

    Displacement and Velocity Equation

    In science, we calculate the displacement of an object (how far it travels) and the velocity of an object (how fast it is moving) using the Displacement Equation and the Velocity Equation: {See attachment}. Where is the displacement of the object, measured in meters t is the amount of time that we analyze the movement of

    Equation Variables: Black Hole

    I am trying to find the formulas for each of the following variables using the Schwarzschild Radius of the black hole Cygnus which is 6966.67 m (if I calculated correctly) a) the Universal Gravitational Constant for this black hole - b) the mass of the collapsed black hole - c) the speed of light for the black hole.

    Quadratic equations - plots

    1. Draw the graph of the equation and label its vertex: y = x^2-3 2. Draw the graph of the equation and label its vertex: y = -4x^2 + 8x + 13

    Word Problem : Application of Sums of Odd and Even Numbers

    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

    Word Problem : Medical Insurance Co-Payments

    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

    Expressions Represented with Graphs

    A building block has the dimensions height Xcm, width (3+X) cm, depth Xcm What espression, in terms of x, would represent the total surface area (A) of the block? Put the expression into the simplest terms. Draw a graph, estimate a value for x, which will give a surface area of 175.5 cm squared. Check your extimate of

    Word Problem : Speed and Distance

    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.

    Find the Area of the Quadrilateral FGKH

    Thea area of triangle ABC is 64 sq. in. DE is parallel to FG is parallel HK is parallel to BC. AD=DF=FH=HB Find the area of the Quadrialateral FGKH. See the attached file.

    Formula to determine variable of gross profit %

    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

    Solve

    Solve: 2x-2y=-5 6x-6y=-3

    Graph: -6y>-24

    I am not sure how to do the following problem and would like to know how to do it. Graph: -6y>-24 That is negative six y is less than negative 24.

    Word Problem : Distance and Speed

    A man walking his dog along a straight country road spots a friend one mile away. His dog sprints ahead to greet her. When the dog reaches her it turns back to the man. when it reaches him it sprints back to the woman. The process continues until the two people meet. If each person walks at 2 MPH and the dog runs at 8 mph, how f