Resources

Resources

Weighted averages: word problems

For a college chemistry experiment, students need to prepare a solution containing ethylene glycol. They are each given

20

fluid ounces of a solution containing

2\%

ethylene glycol, to which they will add another solution that contains

12\%

ethylene glycol. How much of the

12\%

solution should they add to obtain a

5\%

ethylene glycol solution?

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Write your answer as a whole number or as a decimal rounded to the nearest tenth.

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A farm supply company in Franklin County has developed its own blend of grains for horses. The blend includes oats, which cost

\$9.40

per kilogram, and feed corn, which costs

\$3.40

per kilogram. Overall, the mixture costs

\$5.80

per kilogram. If a worker at the company is mixing up a batch and starts with

130

kilograms of oats, how many kilograms of corn should he add to make the blend?

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Write your answer as a whole number or as a decimal rounded to the nearest tenth.

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A teaching assistant at a university needs

28\%

acid solution for her class's lab experiment. There isn't any of this concentration in stock, but the lab has

50

22\%

acid solution, as well as a lot of

32\%

acid solution. How much of the

32\%

acid solution should the teaching assistant add to the

22\%

acid solution to obtain a solution with the desired concentration?

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Write your answer as a whole number or as a decimal rounded to the nearest tenth.

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Two friends are making lemonade to sell at their lemonade stand. First, they make

4\,\text{liters}

of lemonade containing

31\%

lemon juice, but that doesn't taste quite right to them. They decide to add some store-bought lemonade that is

26\%

lemon juice until they have a mixture that is

27\%

lemon juice. How much of the store-bought lemonade should they add?

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Write your answer as a whole number or as a decimal rounded to the nearest tenth.

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A landscaping company mixes its own proprietary blend of topsoil that costs

\$29.15

per ton to make. The blend contains soil that costs

\$27.65

per ton and organic compost that costs

\$42.65

per ton. If the company already has

18

tons of soil on hand, how many tons of compost do they need to mix in?

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Write your answer as a whole number or as a decimal rounded to the nearest tenth.

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Latrell works for a company that manufactures liquid dyes for clothing. He currently wants to mix up some

38\%

-concentrated pink dye. He has

54

26\%

-concentrated pink dye, as well as plenty of

46\%

-concentrated pink dye. How many liters of the

46\%

-concentrated pink dye will Latrell need to add to the

26\%

-concentrated pink dye to make a batch with a concentration of

38\%

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Write your answer as a whole number or as a decimal rounded to the nearest tenth.

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A boutique owner sells a salt scrub that is made of a tropical oil blend costing

\$7.95

per ounce and sea salt costing

\$1.45

per ounce. The salt scrub ultimately costs

\$3.40

per ounce. In order to make a new batch of the salt scrub, she just ordered

6

ounces of the tropical oil blend. How many ounces of sea salt will she need to make the salt scrub with the correct proportions?

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Write your answer as a whole number or as a decimal rounded to the nearest tenth.

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16

An area to be landscaped is a sector with a radius of

19

metres and an angle at the centre of

145^{\circ}

. The area is to be covered with turf at

\$ 12.50

per square metre and then top-dressed with soil at

\$ 2.30

per square metre. Find the total cost of the landscaping to the nearest dollar.

Fawzia goes out to lunch. The bill, before tax and tip, was

\$15.55

. A sales tax of

5\%

was added on. Fawzia tipped

13\%

on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.

\$\(52\).\(75\) with a \(25\)\% discount. How much will he pay for it?\ A. \$\(13\).\(19\)\ B. \$\(39\).\(56\)\ C. \$\(5594\)

-7

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1

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4

Volume of cubes and prisms URT

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A triangular prism is

7

9

feet long. It has a triangular face with a base of

5

8

feet. The volume of the prism is

114

55

cubic feet. What is the height of its triangular face?

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5 \mathrm{ft}

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6 \mathrm{ft}

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7 \mathrm{ft}

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8 \mathrm{ft}

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An amount of money is shared between Kofi and Ama in the ratio

3

5

. If Ama received GH¢

4

650

00

, what is Kofi's share?

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930.00

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1550.00

1 \mathrm{mg} / \mathrm{mL}

dilution of NICUmycin in

0.9 \%

NSS is needed for a neonatal patient. NICUmycin is vailable as a

30 \mathrm{mg} / \mathrm{mL}

vial. The order is for

30 \mathrm{~mL}

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a. How many mLs of NICUmycin are needed?

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b. How many mLs of

0.9 \%

NSS are needed?

A food processing plant is preparing frozen mixed vegetables. The mixture contains peas, which cost ₹

94

50

per kilogram, and diced carrots, which cost ₹

72

00

per kilogram. Overall, the mix will cost ₹

87

75

per kilogram. If there are already

260

kilograms of peas prepared, how many kilograms of carrots should the plant workers add?

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Write your answer as a whole number or as a decimal rounded to the nearest tenth. kilograms

Three people who work full-time are to work together on a prooject, but their total time on the project is to be equivalent to that of only one person working fuIl-time. If one of the people is budgeted for one-half of his time to the project and a second person for one- third of her time, what part of the third worker's time should be budgeted to this project?

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13.3\%

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35.2\%

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16.7\%

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18.7\%

The Nutty Professor sells cashews for

\$ 6.80

per pound and Brazil nuts for

\$ 4.90

per pound. How much of each type should be used to make a

38

pound mixture that sells for

\$ 5.75

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Round answers to the nearest pound.

10

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2

25

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A Carnot engine takes in heat at a temperature of

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900\,\text{K}

and releases heat to a reservoir at a temperature of

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480\,\text{K}

. What is its efficiency?

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1.53\%

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2.87\%

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68.3\%

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46.7\%

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Click Submit to complete this assessment.

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Save and Submit

10

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2

25

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A Carnot engine takes in heat at a temperature of

900 \mathrm{~K}

and releases heat to a reservoir at a temperature of

480 \mathrm{~K}

. What is its efficiency?

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1.53 \%

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2.87 \%

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68.3 \%

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46.7 \%

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Click Submit to complete this assessment.

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10

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Save and Submit

Answer the following. Round your answers to the nearest hundredth.

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-308.64^{\circ}

to radian measure.

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\square

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1.7

radians to degree measure.

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\square^\circ

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Submit Assignment

The total operating costs of a monorail are paid using a combination of passenger fares and tax revenue. The farebox recovery ratio is the ratio of passenger fares to total operating costs. A monorail in one city has

\$ 69

million in operating costs per year, and uses

\$ 30

million from tax revenue. To the nearest hundredth, what is the farebox recovery ratio for the city?

A local grocer wants to mix candied pecans, priced at

\$14.00

pound(lb), and candied cashews, priced at

\$10.00

pound(lb). How many pounds of candied cashews must he mix with

8

lbs of candied pecans to make a mixture that costs

\$12.50

lbs? (Round the answer to the nearest tenth of a pound.)

Ayden had a goal of finishing painting at least

80 \%

500

square meters of a house's walls by today. He actually finished painting

415

square meters today.

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Did Ayden meet his goal? Why?

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/

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, Ayden painted

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square meters more

/

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How many pounds of candy that sells for

\$3.25

lb

must be mixed with candy that sells for

\$2.75

lb

20

lb

of a mixture that should sell for

\$3.15

lb

A factory has a batch of hand sanitizer with

50\%

alcohol content. How much pure

(100\%

concentration) alcohol should they include in a

600\text{mL}

bottle to make a

68\%

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\text{mL}

You need to infuse

500\,\text{ml}

8\,\text{hours}

. What will you set your IV pump to deliver in

\text{ml/hr}

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61\,\text{ml/hr}

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63\,\text{ml/hr}

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65\,\text{ml/hr}

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75\,\text{ml/hr}

5

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6

-2

: MathXL for School: Practice & Problem Solving

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18

11

59

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6

2

-12

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Write the number in

2

equivalent forms as a fraction, decimal, or percent.

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9\%

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What is the equivalent decimal?

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(Type a whole number or a decimal.)

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Enter your answer in the answer box and then click Check Answer.

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1

\_(\text{＂rem ＂})^{(\text{＂part ＂})}

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Review Progress

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3

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11

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A bouncy ball is dropped such that the height of its first bounce is

6

75

feet and each successive bounce is

74 \%

of the previous bounce's height. What would be the height of the

6

th bounce of the ball? Round to the nearest tenth (if necessary).

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\square

3636

pounds of strip loin steak. The amount of weight lost from the trim on each pound is

35\%

75\%

more of the steak's weight is lost after cooking it. How many pounds of trimmed, cooked strip loin will the chef have left to serve to the customers?

Dorris is trying to decide between two laser printers. Both have similar features and warranties so price is the determining factor. Printer A costs

\$159

and printing costs are approximately

\$0.004

per page Printer B costs

\$129

and printing costs are approximately

\$0.02

per page. How many pages need to be printed for the cost of the two printers to be the same?

An online furniture store sells chairs for

\$ 200

each and tables for

\$ 600

each. Every day, the store can ship a maximum of

32

pieces of furniture and must sell a minimum of

\$ 12000

worth of chairs and tables. If

15

chairs were sold, determine the minimum number of tables that the store must sell in order to meet the requirements.

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Taylor is working two summer jobs, making

\$ 7

per hour washing cars and making

\$ 16

per hour tutoring. In a given week, she can work a maximum of

17

total hours and must earn no less than

\$ 200

. If Taylor worked

2

hours washing cars, determine the maximum number of whole hours tutoring that she can work and still meet her requirements.

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A circle has a circumference of

113

04

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What is the diameter of the circle? Use

3

14

\pi

and enter your answer as a decimal.

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A circle has a circumference of

1,017.36

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What is the radius of the circle? Use

3

14

\pi

and enter your answer as a decimal.

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Suppose the diameter of a circle is

16

units. What is its circumference?

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3

14

\pi

and enter your answer as a decimal.

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Suppose the diameter of a circle is

4

units. What is its circumference?

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3

14

\pi

and enter your answer as a decimal.

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\square

To take a taxi, it costs

\$ 3.00

plus an additional

\$ 2.00

per mile traveled. You spent exactly

\$ 20

on a taxi, which includes the

\$ 1

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How many miles did you travel?

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35 \%

3 \%

hydrogen peroxide solutions. They need an

8 \mathrm{~L}

container with a

12 \%

concentration of hydrogen peroxide.

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How much of the

3 \%

hydrogen peroxide solution should they include in the container?

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30 \%

concentration of cobalt chloride in

90 \mathrm{~g}

of a water and cobalt chloride solution.

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What mass, in grams, of water has to evaporate to have a

40 \%

concentration of cobalt chloride?

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A seasoning blend is

4 \%

onion powder, by mass.

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How much pure onion powder should they include in a

72 \mathrm{~g}

bottle to make the final blend have

20 \%

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Katlego mixed a paint hue that is

40 \%

60 \%

yellow. She has

3 \mathrm{~mL}

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What volume, in milliliters, of pure yellow paint should Katlego add to have a hue that is

70 \%

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\mathrm{mL}

100 \mathrm{~mL}

of a strong toothpaste with a

1.1 \%

concentration of sodium fluoride. They have a weaker toothpaste with a

0.3 \%

concentration of sodium fluoride.

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What volume, in milliliters, of the weaker toothpaste would Ujarak need to add to the strong toothpaste to create a blend with a

0.8 \%

concentration of sodium fluoride?

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\mathrm{mL}

A factory has a batch of hand sanitizer with

50 \%

alcohol content.

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(100 \%

concentration) alcohol should they include in a

600 \mathrm{~mL}

bottle to make a

68 \%

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\mathrm{mL}

The bacteria in a Petri dish culture are self-duplicating at a rapid pace.

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The relationship between the elapsed time

t

, in minutes, and the number of bacteria,

B(t)

, in the Petri dish is modeled by the following function.

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B(t)=10 \cdot 2^{\frac{t}{12}}

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How many bacteria will make up the culture after

120

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Round your answer, if necessary, to the nearest hundredth.

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Katya is a ranger at a nature reserve in Siberia, Russia, where she studies the changes in the reserve's bear population over time.

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The relationship between the elapsed time

t

, in years, since the beginning of the study and the bear population

B(t)

, on the reserve is modeled by the following function.

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B(t)=5000 \cdot 2^{-0.05 t}

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In how many years will the reserve's bear population be

2000

? Round your answer, if necessary, to the nearest hundredth.

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A large brine tank containing a solution of salt and water is being diluted with fresh water.

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The relationship between the elapsed time,

t

, in hours, after the dilution begins, and the concentration of salt in the tank,

S(t)

, in grams per liter

(\mathrm{g} / \mathrm{l})

, is modeled by the following function.

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S(t)=500 \cdot e^{-0.25 t}

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What will the concentration of salt be after

10

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Round your answer, if necessary, to the nearest hundredth.

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1

After the closing of the mill, the town of Sawyerville experienced a decline in its population.

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The relationship between the elapsed time,

t

, in years, since the closing of the mill, and the town's population,

P(t)

, is modeled by the following function.

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P(t)=12,000 \cdot 2^{-\frac{t}{15}}

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In how many years will Sawyerville's population be

9000

? Round your answer, if necessary, to the nearest hundredth.

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Olivia has taken an initial dose of a prescription medication.

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The relationship between the elapsed time

t

, in hours, since she took the first dose, and the amount of medication

M(t)

, in milligrams (

\mathrm{mg}

), remaining in her bloodstream is modeled by the following function.

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M(t)=50 \cdot e^{-0.75 t}

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How many milligrams of the medication will be remaining in Olivia's bloodstream after

6

hours? Round your answer, if necessary, to the nearest hundredth.

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\mathrm{mg}

Harper uploaded a funny video of her dog onto a website.

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The relationship between the elapsed time,

d

, in days, since the video was first uploaded, and the total number of views,

V(d)

, that the video received is modeled by the following function.

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V(d)=4^{1.25 d}

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How many views will the video receive after

6

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Round your answer, if necessary, to the nearest hundredth.

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Yasemin deposited

\$ 1000

into a savings account.

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The relationship between the time,

t

, in years, since the account was first opened, and Yasemin's account balance,

B(t)

, in dollars, is modeled by the following function.

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B(t)=1000 \cdot e^{0.03 t}

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How many years will it take for Yasemin's account balance to reach

\$ 1500

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Round your answer, if necessary, to the nearest hundredth.

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Carlos has taken an initial dose of a prescription medication.

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The relationship between the elapsed time

t

, in hours, since he took the first dose, and the amount of medication,

M(t)

, in milligrams (

\mathrm{mg}

), in his bloodstream is modeled by the following function.

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M(t)=20 \cdot e^{-0.8 t}

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In how many hours will Carlos have

1 \mathrm{mg}

of medication remaining in his bloodstream?

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Round your answer, if necessary, to the nearest hundredth.

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