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Algebra

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

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

Question About Quadratic Function

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

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

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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?

The vertex of a parabola

Since our projectile travels at a constant rate of 340 ft / sec in the horizontal direction, we have, using the formula D = RT, that our horizontal distance x = 340 t, giving t = x / 340 Our above equation h(t) can now be converted into h(x), as follows h(x)=-16*(x/340)^2+340*x/340 giving h(x)=-x^2/7225+x Wha

Projectile Prediction

Civil War Artillery Piece Part 1 We have a mortar which is fired at a 45 deg angle. It has an initial velocity component of 340 ft / sec in both the vertical as well as horizontal directions. We have, then, that our equation of height above ground as a function of time t is h(t) = -16t2 + 340t What is the ordered pair which

Normal subgroup

Let N be a normal subgroup of G, a in G, and C the conjugacy class of a in G. a) Prove that a in N if and only if C is contained in N. b) If C_i is any conjugacy class in G, prove that C_i is contained in N or the intersection of C_i and N is empty. c) Use the class equation to show that |N| = |C_1| + ...+ |C_k|, where C_1, .