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Total Cost Equations

1. Allen bought 20 stamps at the post office in 37¢ and 20¢ denominations. If the total cost of the stamps was $7.06, how many 37¢ stamps did Allen buy? 2. The profit on a watch is given by P = x2 - 5x - 9 and where x is the number of watches sold per day. How many watches were sold on a day when there was a $15 loss?

Solve by the Substitution Method

1) Solve by the substitution method 7x+5y=-12 -8x+y=54 What is the solution of the system? ( use an ordered pair. Use N if there is no solution) 2) Soybean meal is 18% protein; cornmeal is 9% protein. How many pounds of each should be mixed to gather in order to get 360 lb mixture that is 11% protein? a. How many pounds

Completing the Square Method with Conics

Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic. 1) x2 + 12x - y + 30 = 0 Find the equation of the parabola determined by the given information. 2) Vertex at the origin, focus at (0, 3) Find the equation of the hyperbola. 3) Vertices at (0, 8) and (0, -8), fo

Quick Mix Boxer Food Company

The Quick Mix Boxer Food Company wishes to introduce a package of dog treats which contains two new flavors of dog biscuits; liver and chicken which must meet certain nutritional requirements. The liver flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the chicken flavored biscuits contain 1 unit

Describe transformations on graph

State the placement of the horizontal asymptote and y-intercept after the transformation. For example, left 1 or rotated about the y-axis are descriptions. a) g(x)=e^x-5 description of transformation: equation(s) for the horizontal asymptote(s): y-intercept in (x,y) form: b) h(x)=-e^x description of transformation: equat

Sound Intensity and Loudness

Part 1 "Loudness" is measured in decibels, DB. I = I0 * 10 DB/10 (also typed as I =I0*10^(DB/10)) gives the intensity, I, of sound, where I0 is the intensity of the threshold of sound, or the sound that can barely be perceived. Using the library, web resources, and/or other materials,find the measure, in decibels, of a sound

Maximizing the Area of a Rectangle

Part 1: The equation A=(LP)/2-L^2, gives the area of a rectangle of perimeter P and length L. Suppose that you have 600 feet of fencing which you plan to use to fence in a rectangular area of land. Choose any two lengths for a rectangle and find the corresponding area for each using the given equation. Include units and show all

Annual Inflation Rate Calculation

Find the most recent report of the annual inflation rate of a country of your choice as well as the type of currency used in that country. The equation S=C(1+r/100)^5 is to find the inflated cost S, in 5 years, of an item, good or service, where C is the current price of that item in that country's currency and where the inflati

Transformation of graphs

Please see an attachment. 1) Describe the transformations on the following graph of f(x) = e^x . State the placement of the horizontal asymptote and y-intercept after the transformation. For example, left 1 or rotated about the y-axis are descriptions. a) g(x) = e^x - 2 b) h(x) = - e^x 2) Describe the transformations

Approximation of Pi Using Inscribed Polygons: Archimedes

Archimedes found his approximation to Pi by inscribed polygons. Start with a circle of radius 1 and a suitable starting polygon and solve for an inscribed polygon of 96 sides. Next, start with a unit circle and appropriate inscribed regular polygon to approximate Pi using a regular inscribed n-gon with 4096 sides.

Using the Karush-Kuhn Condition

1. Consider the LP Max z=c1x1+2x2+c3x3 Subject to x1 + 5x2+a1x3 ≤ b1 X1-5x2+a2x3≤ b2 X1, x2, x3 ≥ 0 The optimal tableau for this LP is 1 d1 2 1 0 30 0 d2 -8 -1 1 10 ------------------------------------ 0 d3 -7 d4 0 z - 150 Without u

Writing Multi-Step Word Problems

I need to write 3 multi-step word problems with answers. One must use percentages, one must use exponents and the third can be any type. I have to include the process for solving each of the problems. The word problems don't have to be very difficult.

Speed and distance word problems

1.The speed at which light travels is approximately 3.0 × 105 kilometers per second. How far will light travel in 1.5 × 101 seconds? 2. The distance from Earth to the planet Jupiter is approximately 4.5 × 108 miles. If a spaceship traveled at a speed of 2.5 × 104 miles per hour, how many hours would it take the spaceshi

Some algebra questions involving rates

Gaining and losing weight are matters of caloric accounting: Calories in the food you eat minus Calories that you spend in activity. One pound of human body fat contains approximately 3,500 Calories. Based on information provided: Running 7 minute miles burns 979 calories per hour. Swimming at 2mph burns 408 calories per

Factor completely

Factor completely: 4k2 + 12k + 9 a. ( 2k - 9 )( - 3k + 1) b. ( 2k + 3 )2 c. ( 2k - 3 )2 d. ( 2k + 3 )( 2k - 3) Question 2 Factor completely: x2 - 100 a. ( x + 10 )( x - 12 ) b. ( x + 10 )( x + 10 ) c. ( x - 10 )( x - 10 ) d. ( x + 10 )( x - 10 )

Horizontal and Vertical Asymptotes

1. How do you determine the vertical asymptotes, given the equation of a rational function? Illustrate with an example. Why can't the graph of that function cross the assymptote? Describe what happens to the graph of a function as the value of the independent variable approaches its vertical asymptote. 2. How do you determin

Quadratic Equations Word Problems

Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?

Population decline model

Population decline modeled by a rational equation P = P Suppose instead that the Population decline modeled by a rational equation P = P Suppose instead that the town experiences population decline that can be modeled by the following: P=P0/t+1 where t is the number of years from 2010.he town experiences population decline tha

Linear Trend - Population growth

Choose the amount of population growth each year = example 350 (Hint: Choose a whole number for your growth rate, rather than a percent.) a) Fill in the following chart: Year (t) Population (P) t=0 P = 350 (2010) t=1 (2011) t=2 (2012) t=3 (2013) t=6 (2016) b) Find a linear equation in the form P

Wonderful Position for Selected Job

1. Word problems seem to daunt practically everyone. Discuss why they seem intimidating to you (or why not, if they don't). Do you believe that most of the problems we face in our daily life are word problems? Examples? 2. You are in the wonderful position of having to select a job from one of two offers you have just recei

Telephone plan word problem

You need to choose between two telephone plans for local calls. Plan A charges $25 per month for unlimited calls. Plan B charges a monthly fee of $ 13 with a charge of $0.03 per local call. How many local telephone calls in a month make plan A the better deal?

Measurements, Conversions and Area

Measurements and Calculations When making measurements, round each measurement to the nearest 1/4 foot. Part 1-Walls Calculate how much paint you will need to paint the walls of this room. To properly paint the walls, you will need to put one coat of primer paint and two coats of finish paint. For each calculation, briefly

Solve: Average Miles per Gallon

Question: In a family there are two cars. The sum of the average miles per gallon obtained by the two cars in a particular week is 50. The first car has consumed 20 gallons during that week, and the second has consumed 25 gallons, for a total of 1175 miles driven by the two cars combined. What was the average gas mileage obtaine