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# Algebra

### A lottery has one \$2000 prize, two \$1000 prizes

I need help in figuring out how to do this math problem. I've worked on the equation multiple times and can't seem to figure it out. The question again is: A lottery has one \$2000 prize, two \$1000 prizes, and ten \$500 prizes. Two thousand tickets are sold at \$5 each. Find the expectation if a person buys two tickets.

### A tennis club offers two payment options:

5) A tennis club offers two payment options: Option1: \$35 monthly fee plus \$4/hour for court rental Option 2: No monthly fee but \$6.50/hour for court rental. Let x = hours per month of court rental time. a) Write a mathematical model representing the total monthly cost, C, in terms of x for the following: Option 1: C=_

### Algebra: Calculating Parabolas

Please see the attached file for the fully formatted problem. If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 96 ft/s, its height after t s is given by.............h(t) = -16t^2 + 96t + 5. How long does it take the ball to return to the ground ?

### Word problem - rabbits

Raising rabbits. Before Roland sold two female rabbits, half of his rabbits were female. After the sale, only onethird of his rabbits were female. If x represents his original number of rabbits, then (x-2)/3 = x/2 - 2 Solve this equation to find the number of rabbits that he had before the sale.

### Solve by substitution

I need detailed explaination on each problem Solve by substitution...Indicate whether each system is independent, dependent or inconsistent. x = 1/8y -1 y = 1/4x + 39 Solve by addition x-2y=-1 -x+5y=4 3x +5y=-1 x-2y=11

### High School Math Problems/Sequences using sigma

Need help solving problem numbers 6,8,9,10,11, 12,13,14,15,16 and show work. I fxed the attachment to my self and save it. Please let me know if you can open file This sttachment may be better 6.What is the tenth term of the geometric progression ½, -1, 2, -4? 8.Which series is represented by &#8721;_(i=1)^4&#9618

### Profit Maximization and Profit Function

Q2. A firm's profit function is given by: Profit = 108 + 2X^2 -4 XY + 3Y^2 - 8X - 12Y Determine: (a) the values of X and Y that maximize profit. (b) the maximum value of profit. I've taken the 1st derivate for X & Y, solves for x and equated these two against each other and and get X = 10. Plug this X value in and I get Y

### Functions and Population Growth

Pick a country of your choice that is experiencing population growth. Using the Library, web resources, and/or other materials to find the most recent population count of the country you have chosen and the population growth rate of that country. Use that growth rate to approximate the population in the year 2012. Solve the prob

### Your group will develop four different population scenarios for a town. As a group, you will decide on the name of the town and the initial population. You will graph the function for each population scenario and use your model to make some decisions about the population.

MTH133 Unit 4 Group Project - A Name: Your group will develop four different population scenarios for a town. As a group, you will decide on the name of the town and the initial population. You will graph the function for each population scenario and use your model to make some decisions about the population. 1) 1) De

### Inductive Reasoning and Estimation

These are a total of 18 mixed problems all ranging from inductive reasoning to estimation. I need help coming to the conclusion. Please help me answer these study questions and show me step by step how to get the answer and how to check if the answer is correct.

### Graph Equations for Factoring

A) without solving the equation or factoring, detemine the solution(s) to the equation, x^2+4x-5=0, using only the graph. answer and explain how you obtained your answer(s) by looking at the graph: b) does this function have a maximum or a minimum? answer: explain how you obtained your answer by looking at the graph.

### Calculate the future value of \$2000 in 5 years at an interest rate of 5% per year.

6. Calculate the future value of \$2000 in 5 years at an interest rate of 5% per year. \$6,245.97 \$3,221.02 \$3,257.79 \$2,552.56 \$2,145.48 7. Calculate the future value of \$2000 in 10 years at an interest rate of 5% per year. \$6,245.97 \$3,221.02

### Mixture problem

Ziggy's Famous Yogurt blends regular yogurt that is 3% fat with its no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no-fat yogurt should be mixed to obtain 60 pounds of low-fat yogurt?

### Arithmetic problems

Please show all steps taken to arrive at your answers as it is possible. Problem # 1. Reduce this fraction to lowest terms. 121/132 Problem #2. Identifying the Properties Name the property that justifies this equation. 77. x². 5 = 5x² Problem #3 Addition and Subtraction of Real Numbers: Please Evaluate.

### 2D heat Equation

Hello, I was wondering if someone could help me with the attached problem. I don't really know how many credits to assign to this. Please contact me if you know how to solve the problem for a different amount of credits and I will consider it. Thank you in advance.

### Percentages and Food Content

Gather three of your favorite packaged foods, perhaps one from each: breakfast, lunch and dinner. Use the model used by the food industry, example and analyze, through the mathematical formula explained, the fat content and protein content from your foods. The written paper should be one page in length and concise in your reas

### Finding the Difference

NOTES: 1. all steps of your solution must be shown and a few words to explain what you did to solve the problem. For instance, if lowest common denominators are required show how you determined the value of the LCD. If factors are removed, show the value of the total factor removed. Please do not just supply an answer.   .

### Diffusion Equations and Boundary Conditions

Hello, I have a test coming up soon and I don't understand how to solve the kind of problem as given below. Please provide some explanation in the solution. Thanks in advance, Eriko Consider  the  diffusion  equation € φt = a 2 φxx + x 3 , −L ≤ x ≤ L with  initial  condition  € φ(x,0) =1

### Finding equations of line

Complete the equation of the line L satisfying each of the following sets of geometric conditions by determining the values of b1 and bo. 1. L has a slope of ¾ and x-intercept of (-4,0), y=b1x+bo b1= bo= 2. L passes through (2,1) and is perpendicular to the line with the equation 3x-2y=5, y=b1x+bo b1= bo= 3. L p

### Partial diff equation

It is given that that a Fourier Cosine series of teh function f(x) is given by (see file) A PDE is given by: u_t = u_xx 0<x>Pi t>0 With boundary conditions: u_x(0,t) = u_x(pi, t)=0 1. Determine all the solutions of the PDE that satisfy these boundary conditions. 2. find teh solution that satisfies in additi

### 1D Heat Equation with Non-Homogenous Boundary Conditions

Please see the attached file for the fully formatted problem. Solve the heat equation u_t =a^2 * u_xx for 0<x<L under the conditions: u(0,t)=1 u(L,t)=2 u(x,0)=0 Solve this problem by converting this problem into a problem with homogeneous boundary conditions. Show that as t approaches infinity the solution ap

### Distance and midpoint functions

Solve for the following items: a. The point on the x-axis that is equidistant (equal distance) from (12,6) and (8,2). b. The distance between the points (6,4) and (18,4). c. The distance between the points (1,4) and (19,6). d. The midpoint between (12, 6) and (18, 4) e. The midpoint between (-6, -8) and (23, 5)

### Functions and Domains

MTH133 Unit 4 - Individual Project Name: 1) State the domain of the following: a) Answer: b) Answer: c) Answer: d) Answer: e) Answer: 2) Suppose the graph of is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph? a)

### Word Problem on coins

Question. Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes than nickles but three times as many quarters as dimes. The total of coins was \$11.40. how many coins of each did Sam find?

### Word Problem Estimation

Please help to find the way to estimate the number of grubs in a lawn, that contains an average of 3.8 grubs per square foot, and the lawn in a rectangular shape measures 60.4 ft by 80.2 ft. What formula do I use?

### Solving for Net Present Value

A company is considering an investment in a machine that costs \$54,000 and would result in cash savings of \$15,000 per year for 5 years. The company's cost of capital is 10%. Compute the Net Present Value.

### Converging and Diverging Sequences

For Xsubn given by formulas establish either the convergence or the divergence of the sequence X=Xsubn Xsubn= n/(n+1) Xsubn= 2n^2+3/(n^2+1) find the limits of the following sequences: lim((2+ 1/n)^2)) lim((-1)^n/(n+2)) lim((n^1/2)-1)/((n^1/2)+1)) lim((n+1)/(n(n^1/2))) establish the convergence and find the limits o

### Description of Demand equation

Demand for pool. Tropical pools seals an above ground model for p dollars each The monthly revenue for this model is given by the formula R(p)= -10.08^2 + 300p. Revenue is the product of the price p and the demand (quantity sold) R(p) = -10.08p^2 + 300p a. Factor out the price on the right hand side of the formula b.

### Generalized quaternion group

Define the generalized quaternion group by the presentation Q_n = < a,b|a^2n=1, b^2=a^n, ab=ba^-1 > for n >=1 Show that |Q_n|=4n Show that Q_1 is cyclic and Q_2 is the quaternion group Show that Q_3 is not isomorphic with either the dihedral group D_6 or the alternating group A_4