Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1525. What was the rate charged per hour by each mechanic if the sum of the two rates was $130 per hour?
1st car has fuel efficiency of 15 miles per gallon. Second car has fuel efficiency of 40 miles per gallon. during a week the two cars combined went a total of 1225 miles with a total gas consumpton of 40 gallons. How many gallons were consumed by each car?
Let X be a complete metric space. If F_n is a sequence of nonempty closed subsets of X such that F_n+1 is contained in F_n and the limit as n-->infinity of the diameter(F_n) = 0, show that the interesection of all F_n is nonempty.
The number N, in millions, of the hearing impaired individuals of age x can be approxiamted by N= -0.00006x^3 + .006x^2 -0.1x +1.7. Approximate to the nearest million the number of impaired individuals of ages 50 and 60. age 50 = age 60 =
1. The Starship USS Enterprise is travelling in a straight flight path through the Delta Quadrant to investigate the Sontaran Nebula when its sensors detect a disturbance in the fabric of the space-time continuum. Captain Jean Luc Picard orders Lt. Commander Data to reverse course. However, as Data does this, the effect of the
Q1. Lisa can shovel snow from her driveway in 35 min. Bill can do he same job in 50 min. How long would it take lisa and bill to shovel the driveway if they worked together. Q2. Kathy bicycles 6 KM/h faster than Carlos. In the same time it takes Carlos to bicycle 45 km, Kathy can bicycle 63 km. How fast does each bicyclist
Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes a station at 9:10 am. If train B passes the same station at 9:25 am, at what time will train B catch up to train A?
In 1991, the life expectancy of males was 72.5, in 1996 it was 74.7 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991. E(t)=_____t + _____ Round to nearest tenth Use the function to predict the life expectancy in 2005 E(14)=_____ Round to nearest tenth.
1. Add 8/r-2 + 8/r+2 2. Simplify by removing factors of 1 w^2-4/2-w 3. Solve x-6/x+6=2/5 4. Simplify by removing factors of 1 80v^6x^7/50v^2x^2 5. Simplify if possible 5/49z^3+1/35z^2 6. Solve 5-y/8-y=3/y-8 7. Find all numbers which the rational is undefined - 8. Multiply and simplify 9x^7/8r^6*64r^8/81
Please show all the steps for easier understanding. Problem #1 A vacuum pump removes 15% of the air that is in a container at the beginning of a stroke. If m_r is the mass of air in the container after the rth stroke: (i) Express m_2 and m_3 in terms of the original mass m_0. (ii) How many strokes are required to obtai
You have a total portfolio of $20,000 to either invest in stocks, invest in bonds, or save in a money market. You want to have at least two times more money in stocks than in bonds. You estimate that stocks will provide 2 times more money this year than money markets. Lastly, you want to have $4,000 less in money market than
Is (-2,6) a solution to 7x + 3y=4 AND 8x + 7y = 26 Solve the system of equations by graphing. If the system is inconsistent or the equations are dependent, state that Solve using the addition (elimination) method. Solve using the addition (elimination) method Solve using the substitution method Solve using the substitution
Please show all the work. If n is a (fixed) positive integer what is the number of solutions (x,y) (with x and y positive integers) to the equation 1/x + 1/y = 1/n . Carefully explain your reasoning.
Monica and Marty are llamas at petting zoo. They like to count the visitors that pet them. Total of 105 people pet both Monica and Marty. 2.5 times as many people pet Monica as Marty. How many people petted Monica and how many petted Marty. Amy was soaking poor feet. Together Amy and Marcus walked total 10.5 miles. Amy walked
I do a fair flip of a fair coin until I get heads for the first time. If I get heads for the first time on the nth throw, Sally pays me 2^n dollars. How much does she pay me on average? Solve by simulation (least squares)
As a salesperson at Kim's Furniture, Yolanda has a choice between two options for receiving monthly pay. With one option, she receives a base salary of $412 and gets an additional 20% commission on the sales she makes. With the other option, she doesn't receive a base salary but gets 24% commission on the sales she makes. What a
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $49,345., and the variable costs will be $9.75 per book
Here is the question: A small city contains 2500 people. If the population doubles every 25 years. How large will the population be in 225 years?
1. If a < b, then -a > -b. Why? 2. What is the inherent meaning and justification of cross-multiplication as it applies to solving an inequality? 3. How can you differentiate between a function and an equation? 4. Give an example of a mixture type of problem along with the answer.
I need help figuring this problem out. find the average weight in pounds of a type of bird of your choice. Use the rational exponent equation L = 2.43 * W^0.3326 to estimate the wingspan L in feet of the bird that weighs W pounds (Rockswold, 2006). Include in your post the type of bird and the average weight and show the calc
1.Maria invests $5000 which compounds daily over 8 years. When she withdraws the money she has $6205.51 whta was her interest rate? 2. Consider an investment of $10,000 at 6.8% interest for 20 years. Fiind the amount if it was compounded quarterly.
Part 1. Computation of Indices Below is information on food items for the years 2000 and 2004. Item 2000 2004 Price Quantity Price Quantity Margarine (pound) $0.81 18 $0.89 27 Shortening (pound) 0.81 5 0.94 9 Milk (½ gallon) 1.44 70 1.43 65 Potato chips 2.91 27 3.07 33 A. Compute a simple price index for each of
For the quadratic function f(x) = x2 + 6x â?" 7, I have to give the coordinates of the x-intercept(s), y-intercept(s), and vertex of the parabola. If the parabola has a maximum or minimum, I have to give its coordinates.
First Part: What is the discriminant? Explain what information the discriminant gives us and why this information is important. What does the discriminant tell us about the graph of a quadratic equation? Second Part: What is a parabola and where does it come from? What important information is given by the vertex of a p
If I wanted to have $150,000.00 when I retire in 10 years and I'm investing into a high yield bond that pays 7% compounded annually, what do I have to invest today to achieve my goal? Tell me the formula and solve the equation.
1) Find the equation of the line that is perpendicular to the line x-3y+16=0 and passes through the point (1,7). 2) Suppose the graph f(x) is given, describe how the graph of the function f(x-2)+3 can be obtained.
Please help me solve this congruence: 21x = 4 (mod 76). I do not know how to reduce/change mods like when they go from 8x = 6 (mod 14) to x=6 mod 7. I do not understand this, so please describe every single step in your solution when you do stuff like that. I do know how to find the GCD of 2 numbers so you do not need to t
10. Provide an appropriate response. If a system has four inequalities, the number of corner points of the feasible region must be? . a. at least three, but not more than four b. exactly four c. exactly three d. at least one, but not more than four
Last year Ottoâ??s garden was square. This year he plans to make it smaller by shortening one side 5 feet and the other 8 feet. If the area of the smaller garden will be 180 square feet, then what was the size of Ottoâ??s garden last year?
Write a system of two equations in two unknowns for each problem. Solve each system by substitution. See Examples 8 and 9. 92. Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest