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# Algebra

### Average Monthly Goals by the End of Summer

A student at Brown U wants to become his own employer by using his car as a taxi for the summer. It costs the student \$120.00 a month to insure his car for the 4 months of summer. He estimates to spend \$440.00 per month on gas. If he lives at home and has no other expenses and charges an average of \$12.00 per fare, how many fare

### Breakeven point problem is featured.

Background: Your boss has asked you to come up with a price model for one of the cell phone models that your company produces. In the model, costs and length of service are directly related. You are also asked to examine the profit formula based on selling a certain number of the phones to determine profitability based on how ma

### Distance calculation is depicted.

A surveyor want to know the appoximate width of a river. Using a small telescope, he or she measures the parallax of a tree on the other side of the river to be 4 degrees. The baseline he or she uses to obtain this parallax is 100 yds long. How many feet wide is the river?

How do you compute the intercepts of a quadratic function? What is the number of x- and y-intercepts that quadratic functions may have? What is the meaning of axis in regards to a quadratic function?

### Height of the elevator shaft

A worker (on earth) dropped a screwdriver from the top of an elevator shaft. Exactly 5 seconds later he heard the sound of the screwdriver hitting the bottom of the shaft. How tall is the elevator shaft?

### Branch and Bound Implicit Enumeration

Use Implicit Enumeration to solve the following 0-1 IP. MAX Z=3X1+X2+2X3-X4+X5 ST 2X1+X2-3X4<=1 X1+2X2-3X3-X4+2X5=>2 Xi=0 or 1 Please show enumeration tree. If a node is fathomed, indicate why it is fathomed. Provide the sequence of problems solved, eg. P1->P3->P4. Clearly indicate what the optimal solution

### A Discussion On Effective Yields

Find the effective yields, to the nearest hundredth of a percent, of an investments at 7.25% compounded quarterly and at 7.35% compounded semi annually. a. 12.66% and 12.72% b. 4.38% and 4.40% c. 4.97% and 4.99% d. 7.45% and 7.49% e. 11.17% and 11.23%

### Cost Model with Joint Equation

the cost of labor varies jointly as the number of workers and the number of days that they work. if it costs \$1450 to have 16 people work for 7 days, how much will it cost to have 20 people work for 13 days? a. \$3367 b. \$3380 c. \$3385 d. \$3388 e. \$3395

### Formulate an equation in standard form

Write the equation of the line that contains the indicated pair of points. express the final equation in standard form. (2,5), (8,12). a. 7x + 6y=16 b. 7x + 6y =-16 c. x - y = 16 d. 7x - 6y = 16 e. 7x - 6y = -16

### Algebra Questions and Systems of Equations

1. Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged \$ 123.00 for 3 days and 300 miles, while Mary was charged \$ 216.00 for 5 days and 600 miles. What does Best Rental charge per day, for mileage? 2. There were 44,000 people at a ball game in Los Angeles. The day's receipts

### Calculation of Measures Of Central Tendency

Question: What is the middle? If we have student scores of 4.0, 3.7, 3.7, 3.7, 1.0 the average would be 3.2 while the median and the mode would both be 3.7. Is one of them really in the middle? How dispersed is this list? That is, how much do the scores vary from the middle? Now, look at a routine you do everyday at work. Which

### Find initial velocity for a basketball shot to succeed

Determine initial velocity for a basketball thrown from a given height to pass through a hoop at a know height and horizontal distance away from the overhand shooter, according to a parabolic model.

### Intercompany Transactions

X-Beams Inc. owned 70% of the voting common stock of Kent Corp. During 2006, Kent made several sales of inventory to X-Beams. The total selling price was \$180,000 and the cost was \$100,000. At the end of the year, 20% of the goods were still in X-Beams' inventory. Kent's reported net income was \$300,000 in 2006 and in 2007.

### the definition of quaternion group

(a) Show that the relations a^4 = 1, b^2 = a^2 and b^(-1)ab = a^(-1) define a group of order 8. (It is called the "quaternion group".) (b) Show that this group is not isomporphic to Î"4 (also of order 8). Please see the attachment for more precise text description.

### Best Fit Line/Linear Regression/Trend Line

1) Global climate change has affected mountain glaciers all over the world. At Cornwall Glacier on Mount Shasta in California, scientists have measured the retreat of the glacier from 1858 through 1994. The data from 1858-1994 is plotted on the graph below, using the location in 1994 as the 0 km point. 2) Construct a best fi

### Working with real data is assessed.

Carbon dioxide is a greenhouse gas in the atmosphere that may raise average temperatures on Earth. The burning of fossil fuels could be responsible for the increased levels of carbon dioxide. If current trends continue, future concentrations of atmospheric carbon dioxide in parts per million (ppm) could reach the levels shown i

### The geometric series

6. Let k > 0 be a constant and consider the important sequence {kn}. It's behaviour as n ® ¥ will depend on the value of k. (i) State the behaviour of the sequence as n ® ¥ when k = 1 and when k = 0. (ii) Prove that if k > 1 then kn ® ¥ as n ® ¥ (hint: let k = 1 + t where t > 0 and use th

### Examine poverty rates in the next several years.

The following table gives the percentage of the U.S. population living below the poverty level for the period from 1990 to 2002. (Source: World Almanac and Books of Facts 2004, page 382.) Year % of U.S. Population Living Below Poverty Level 1990 13.5 19

### Decision-making information

One challenge we face on a daily basis in business is calculating decision-making information when we only know part of the information. We may need to know how much we need to determine how changes in our sales will affect our bottom line. If we know our Fixed Costs (FC), our Variable Costs per unit (VCu), our Price per unit (P

### Investing for Retirement

A college student invests \$8000 in an account that pays interest annually. If the student would like this investment to be worth \$1,000,000 in 45 years, what annual interest rate would the account need to pay?

### Graphing distance as a function of time

A woman walks at a constant rate for 10 seconds. For the next 5 seconds the woman speeds up to a run. After running at a steady rate for 5 more seconds, the woman stops for 5 seconds. It then takes the woman 5 seconds to run back to where she started. Graph the position of the woman as a function of time. Be sure to label your g

### Financial Sustainability of Room Prices

Problem: Room Prices Ten rooms are rented at rates of \$80.00 (USD) and \$120.00 (USD) per night. The total collected for the 10 rooms is \$920.00 (USD). (a) Write a system of linear equations whose solution gives the number of each type of room rented. Be sure to state what each variable represents. (b) Solve the syste

Write a word problem involving a quadratic function. How would you explain the steps in finding the solution to someone not in this class? Problem: My garden is 18 ft long and 15 ft. wide. I like to decrease the length by x feet and increase the width by the same number of feet. The equation A = (18-x)(15+x) = 270 + 3x - x^

### Euclidean domain

Let R be a Euclidean domain such that delta (a + b) is less than or equal to max{ delta (a), delta (b)} for all non zero a, b in R. Prove that q and r in the definition of Euclidean domain are unique.

### Quadratic Congruence and Primitive Roots

1. If g is a primitive root of p, show that two consecutive powers of g have consecutive least residues. That is, show that there exists k such that g^(k+1)=g^k+1(mod p) (Fibonacci primitive root) 2. Show that if p=12k+1 for somek , then (3/p)=1 3. Show that if a is aquadratic residue (mod p) and ab=1(mod p) then b is a qu

### Solving for the Right Triangle

Solve for right triangle | c= 4.48 | | | ------------------------------------------| b=4.48 A= B= a=

### Working with Real Data

WORKING WITH REAL DATA Directions: Form a group of 2 to 4 people. Select someone to record the groupâ??s responses for this activity. All members of the group should work cooperatively to answer the questions. If your instructor asks for your results, each member of the group should be prepared to respond. AIDS Cases

### Per-Capita Death Rate for Fish

In a fish farm, fish are harvested at a constant rate of 2500 fish per year. The per-capita death rate for the fish is 0.2 fish per year and the per-capita birth rate is 0.7 fish per year. (i) Derive a difference equation to describe the population of the fish. (ii) Solve this difference equation and determine the steady state

### Determine the interest on your loan

Â??Looking for an attractive loan for the car of your dreams? Well, you have to look no more. Come in and show us your car deal. We will match any car loan and reduce the interest rate by 1%, with our â??simple interest car loanâ?. No down payment needed, and no trade-ins. Our loans must have a minimum interest rate of .5

### Interest Compounded Monthly: Example Problem

Suppose \$1,200 is invested into an account bearing 5.23% interest, compound monthly. Write an equation that will give the amount A in the account after t years. What would be the amount if compound daily, quarterly and continuously?