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free/or 0.5$ |
| m66261 | A beam of light enters a medium such as water or smog with initial intensity I0. Its intensity decreases depending on the thickness (or concentration) of the medium. The intensity I at a depth (or concentration) of x units is given by
I = I0e-mx.
The constant m (the Greek letter "mu") is called the coefficient of absorption, and it varies with the medium. For sea water, μ = 1.4.
a) What percentage of light intensity I0 remains in sea water at a depth of 1 m? 3 m? 5 m? 50 m?
b) Plant life cannot exist below 10 m. What percentage of I0 remains at 10 m? |
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| m66262 | A bicycle sells for a retail price of b dollars from an online store. The wholesale price of the bicycle is w.
a. Express the markup algebraically.
b. Express the percent increase of the markup algebraically. |
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| m66264 | A blouse that is size x in Japan is size s(x) in the United States, where s(x) = x - 3. A blouse that is size x in the United States is size t(x) in Australia, where t(x) = x + 4. Find a function that will convert Japanese blouse sizes to Australian blouse sizes. |
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| m66266 | A bridge with a semielliptical arch spans a river as shown here. What is the clearance 6 ft from the riverbank? |
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| m66268 | A bungee jumper always rebounds 60% of the distance fallen. A bungee jump is made using a cord that stretches to 200 ft.
a) After jumping and then rebounding 9 times, how far has a bungee jumper traveled upward (the total rebound distance)?
b) About how far will a jumper have traveled upward (bounced) before coming to rest? |
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| m66270 | A cable TV/Internet/phone provider charges Janet $90 per month for all three services. In addition, Janet s monthly bill for cell phone calls and text messages averages $77 per month.
a. What does Janet pay annually for these services?
b. What is her average cost per day for these services? Round to the nearest cent. |
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| m66274 | A car averages 56 mi/h on a trip.
a. Write an equation that shows the relationship between distance, rate, and time for this situation.
b. Let time be the independent variable and distance be the dependent variable. Draw and label the graph of this equation.
c. Use the graph to determine approximately how far this car would travel after 14 hours.
d. Use the graph to determine the approximate length of time a 500-mile trip would take. |
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| m66275 | A car dealership has 30 ft of dividers with which to enclose a rectangular play space in a corner of a customer lounge. The sides against the wall require no partition. Suppose the play space is x feet long.
(a) Express the area of the play space as a function of x.
(b) Find the domain of the function.
(c) Using the graph shown below, determine the dimensions that yield the maximum area. |
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| m66276 | A car is originally worth $34,450. It takes 13 years for this car to totally depreciate.
a. Write the straight line depreciation equation for this situation.
b. How long will it take for the car to be worth half its value?
c. How long will it take for the car to be worth $10,000? Round your answer to the nearest tenth of a year. |
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| m66277 | A car is originally worth $43,500. It takes 12 years for this car to totally depreciate.
a. Write the straight-line depreciation equation for this situation.
b. How long will it take for the car to be worth one quarter of its original price?
c. How long will it take for the car to be worth $20,000? Round your answer to the nearest tenth of a year. |
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| m66278 | A car leaves four skid marks each 50 feet in length. The drag factor for the road is 0.9. Let x represent the braking efficiency.
a. What is the range of values that can be substituted for x?
b. Let the speed be represented by the variable y and x represent the braking efficiency. Write the skid speed equation in terms of x and y.
c. Graph the skid speed equation using the braking efficiency as the independent variable and the skid speed as the dependent variable.
d. Use your graph to estimate the skid speed for braking efficiencies of 20%, 40%, 60%, 80%, and 100%. |
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| m66279 | A car originally sold for $25,900. It depreciates exponentially at a rate of 8.2% per year. Nina put $10,000 down and pays $550 per month to pay off the balance. After how many years will her car value equal the amount she paid for the car to that point? What will that value be? |
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| m66280 | A carpenter is cutting a 3-ft by 4-ft elliptical sign from a 3-ft by 4-ft piece of plywood. The ellipse will be drawn using a string attached to the board at the foci of the ellipse.
a) How far from the ends of the board should the string be attached?
b) How long should the string be?
The eccentricity of an ellipse is defined as e = c / a. For an ellipse, 0 < c < a, so 0 < e < 1, when e is close to 0, an ellipse appears to be nearly circular. When e is close to 1, an ellipse is very flat. |
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| m66281 | A carpet installer uses 46 ft of linen tape to bind the edges of a rectangular hall runner. If the runner is w feet wide, express its area as a function of the width. |
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| m66284 | A CD storage rack is sold to stores at a wholesale price of $18.
a. If a store has a $13 markup, what is the retail price of the CD rack?
b. Find the percent increase of the markup to the nearest percent. |
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| m66287 | A Central Railway freight train leaves a station and travels due north at a speed of 60 mph. One hour later, an Amtrak passenger train leaves the same station and travels due north on a parallel track at a speed of 80 mph. How long will it take the passenger train to overtake the freight train? |
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| m66288 | A certain appliance requires 225 watts when it is switched on. How much would it cost to run for m minutes, at a cost of d dollars per kilowatt-hour? Express your answer algebraically. |
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| m66289 | A certain appliance uses w watts to run. If you run it for m minutes, and the cost per kilowatt-hour is c, the cost of running the appliance for m minutes is given by the formula
Find the cost of running an appliance that requires 500 watts for 25 minutes at a cost of $0.125 per kWh. Round to the nearest cent. |
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| m66290 | A certain area of forest is populated by two species of animal, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as F1 and F2. For one year, each member of species A requires 1 unit of F1 and 0.5 unit of F2. Each member of species B requires 0.2 unit of F1 and 1 unit of F2. The forest can normally supply at most 600 units of F1 and 525 units of F2 per year. What is the maximum total number of these animals that the forest can support? |
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| m66295 | A city swimming league determines that the cost per person of a group swim lesson is given by the formula
C(x) = (60 + 2x) / x,
Where x is the number of people in the group and C(x) is in dollars. Find C-1(x) and explain what it represents. |
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