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# Algebra

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### Assessing Positive Numbers

(Not necessarily whole numbers). Explain why we can write a=m_1b+r1 where m_1 is a non-negative integer and 0 less than or equal to r_1 less than b. Why are m_1 and r_1 unique? Continuing in this fashion, we can next write b=m_2r_1+r_2 with 0 less than or equal to r_2 less than r_1 and m_2 a non-negative integer. This procedure

### Expressing the common interest formula

Find the amount that should be set aside today to yield the desired future amount. Future amount needed = 13,000 Interest rate = 4% Compounding period = quarterly Investment time = 4 years The present value is ___? (round to the nearest cent as needed).

### Height Radicals

1. The time (sec) it takes for an object to fall from a height of h(ft) is expressed by the following equation: h = 16t^2 a. Solve this equation for t. b. A penny dropped from the top of the Prudential Tower takes 7.34 seconds to hit the ground; how tall is the tower?

### Linear relations problem: Worldwide HIV infections

In 2004, there were an estimated 39 million HIV infections worldwide with an annual infection rate of 4.9 million. (a) Solve the equation graphically and find the slope's intercept form of a line that approximates the cumulative number of HIV infections in millions during year x, where x = 2004. (b) Estimate the number of HIV

### Word Problem for Possible Vacation Destinations

Use the five steps for problem solving to answer the following question. Please show all of your work. The Hansons are considering two possible vacation destinations. A trip out west will cost \$1075 in total airfare plus an average of \$450 per day in expenses. A trip south will cost \$1500 in total airfare plus an average of \$

### MATH133 Unit 5 Individual Project -A

See the attachment for full description. 1) Solve a) e^0.05t = 1600 b) ln(4x) = 3 c) log2 (8 - 6x) = 5 d) 4 + 5e^-x = 9 2) Describe the transformations on the following graph of f(x) = log(x). State the placement of the vertical asymptote and x-intercept after the transformation. For example, vertical shift up 2 or ref

### Interest Rates and Compound Interest

If a bank is advertising that a new person can open an account with a 3 3/4 interest rate compounded annually and you invests \$5000in an account at this rate and makes no deposits or withdrawals find the amount of money you will have to the nearest cent after three years can you give me step by step help to solving this question

### Graphs are emphasized.

1. Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center points. a. Y = 3X2 b. (X-1)2 + (Y-8)2 = 16 c. (X+2)2 + (Y-4)2 = 36 d. Y = X2 + X 2. Find the equation for each of the following i

### Label as arithmetic or geometic sequence.

A person hired a firm to build a CB radio tower, the firm charges \$100.00 for labor for the first 10 feet, after that the cost of the labor for each succeeding 10 feet is \$25.00 more than the preceding 10 feet. That is, the next 10 feet will cost \$125.00 the next 10 feet will cost \$ 150.00 etc. How much will it cost to build a

### Arithmetic Sequence - Apply the proper formula where applicable.

A company decides to fine it workers for parking violations on its property. The first offense carries a fine of \$25.00 the second offense is \$30.00 the third offense is \$35.00 and so on. what is the fine for the eight offense? Please show your work and whether you use arithmetic sequence or a geometric sequence and use the p

### Algebra Questions about Graphing

1)A)Fine the slope of the line that passes through the given points B)Find the standard form of the equation of the line (7,3) and (7,0) 2)Use point by point plotting to sketch the graph of the equation y=x-3 3)The equation below specifies a function. Determine whether the function is linear, constant or neither 9x+8y=5

### Word Problems Explanation

1. There are two small containers and one large container that together hold 12 cups of liquid. The large container minus one small container equals 3 cups of liquid therefore how many cups of liquid does each container hold? (solve using equation) 2. A man ordered 4 times as many boxes of ballpoint pens as boxes of felt tip

### 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?

### Analysis Of Quadratic Function

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