APES Unit 1-9 Review Math Questions

Subtract the following: (2.8 x 10^-4) - (1 x 10^-2)

= (2.8 x 10^-4) -> 0.00028 = (1 x 10^-2) -> 0.01 = (0.00028) - (0.01) = -0.00972 = -9.72 x 10^-3

Find the average of the following numbers: 124, 456, and 785

= 124 + 456 + 785 = 1,365 = 1,365/3 = 455

Express each of the following in standard form: 2.71 x 10^4

= 27,100

A water tank holds 500 gallons and is 35% full. How many gallons are in the tank?

= 35% -> 0.35 = 500 x 0.35 = 175 gallons

Divide 900 by 36,000

= 900/36,000 = 0.025

Place the following numbers in scientific notation Twenty Three Thousand

= twenty three thousand -> 23,000 = 2.3 x 10^4

UNIT 5

Land & Water Use

UNIT 3

Populations

Convert 1200 watts to kw (kilowatts)

1.2 kw (kilowatts)

Divide 45.5 by 10

45.5÷10 = 4.55

Convert 60 gram to milligram

60,000 milligram

If the concentration of mercury in a water supply changes from 65 ppm to 7 ppm, what is the percentage change in mercury concentration?

= ((7-65)/65) x 100 = -58/65x 100 = -0.8923076 x 100 = -89.230769% = -90% is the percent change in mercury concentration

On average 1 kg of corn contains 3 x 103 kcal and a single hectare can produce 1.2 x 104 kg of corn per year. If a person ate half of their 2,000 kCal/day diet from corn and corn products, approximately how many people can a single hectare of corn feed in 30 days?

= (1000 kCal/1 day) x (30 days/1) = 30,000 kCal = (4 x 107 kCal/1 hectare) x (1 person/30,000 kCal) = 1,333 people

Multiply and divide the following: (2 x 10-3)(9 x 10-3)

= (2 x 10^-3) -> 0.002 = (9 x 10^-3) -> 0.009 = (0.002)(0.009) = 0.000018 = 1.8 x 10^-5

Add the following: (2 x 10^5) + (3 x 10^3)

= (2 x 10^5) -> 200,000 = (3 x 10^3) -> 3,000 = (200,000) + (3,000) = 203,000 = 2.03 x 10^5

On average 1 kg of corn contains 3 x 103 kcal and a single hectare can produce 1.2 x 104 kg of corn per year. How much kcals of corn are produced in a hectare of land each year?

= (3 x 103 kCal/1 kg) x (1.2 x 10^4 kg/1 hectare) = 4 x 107 kCal per hectare

On average 1 kg of corn contains 3 x 103 kcal and a single hectare can produce 1.2 x 104 kg of corn per year. How many kcals of corn is produced in the US each year?

= (4 x 107 kCal/ 1 hectare) x (96 million/1) = 4 x 1015 kCal

The number of km2 of Wilderness area increased from 4.0 X 104 to 6.0 X 104 in a decade. What is the percent increase?

= (6x104)- (4x104)(4x104)x 100 = (2x104)(4x104)x 100 = 0.5 x 100 = 50% Increase

Multiply and divide the following: (7.1 x 10^-5)(6 x 10^-6)

= (7.1 x 10^-5) -> 0.000071 = (6 x 10^-6) -> 0.000006 = (0.000071)(0.000006) = 0.0000000004 = 4 x 10^-10

Multiply and divide the following: (7.1 x 10^6)/(2 x 10^1)

= (7.1 x 10^6) -> 7,100,000 = (2 x 10^1) -> 20 = 7,100,000/20 = 355,000 = 3.55 x 10^5

On average 1 kg of corn contains 3 x 103 kcal and a single hectare can produce 1.2 x 104 kg of corn per year. The US grows corn on 96 million hectares of corn each year. How many kg of corn is produced each year in the US?

= (96 x 10^6 hectares/1 year) x (1.2 x 10^4 kg/1 hectares) = 1.152 x 1012 = 1.2 x 10^12 kg per year

Radon has a half-life of 3.8 days. After 7.6 days, 6g remain. What was the mass of the original sample?

= 0 days > 1 (half life 1) = 3.8 days > 2 (Half life 2) = 7.6 days (has been cut in have twice) = 6g -> 12g/1st half life ->24g/2nd half life = 24g

Place the following numbers in scientific notation 0.0000483

= 0.0000483 = 4.83 x 10^-5

Express each of the following in standard form: 9.65 x 10^-4

= 0.000965

Express each of the following in standard form: 8.5 x 10^-2

= 0.085

If 35% of a natural area is to be developed, leaving 500 acres untouched, how many acres are to be developed?

= 100% - 35% = 65% = 35% -> 0.35 = 65% -> 0.65 = 0.65/500 acres= 0.35/x = 0.65x/0.65= 175/0.65 = x = 269.230769acres = x= 300 acres

The half-life of Cs-137 is 30.2 years. If the initial mass of the sample is 100g, how much will remain after 120.8 years?

= 100g/2 = 50 = 50g/2 = 25 | 30.2 x 2 = 60.4 | =25g/2 = 12.5 | 60.4 x 2 = 90.6 = 12.5g/2 = 6.25g | 90.6 x 2 = 120.8

Find each percent change to the nearest percent (you may round, if necessary). State if it is a percent increase or a decrease. From 100 km to 125 km

= 125-100/100 x 100 = 25/100 x 100 = 0.25 x 100 = 25% Increase

The Edwards family needs to buy a dishwasher. The new energy-efficient machines use less water and energy, but that they are more expensive. A traditional dishwasher costs $200 whereas the water-efficient machine costs $300. If the cost of electricity is $0.20/kWh, how much money will you save per year owning the energy efficient dishwasher?

= 160 kWh/year x $0.02/kWh = $32 per year

A teenager drinks 480 calories of soda. She also eats another 1920 calories of food that day. What percentage of calories was from the soda?

= 1920 + 480 = 2,400 = 4802,400 x 100 = 20%

With a half-life of 28.8 years, how long will it take 1g of strontium-90 to decay to 250mg?

= 1g -> 1000 mg = 1,000mg -> 500mg -> 250mg = 2 half lives = 28.8 years x 2 = 57.6 years

Solve: (2 x 10^5) x (3 x 10^10)

= 2 x 105-> 200,000 = 3 x 1010-> 30,000,000,000 = (200,000) x (30,000,000,000) = 6,000,000,000,000,000 = 6 x 10^15

A farmer cultivates 2.3x104 acres of land and leaves 5.3 x 103 acres untouched. How many acres does she own?

= 2.3 x 104 + 5.3 x 103 = 28,300 acres

Solve: (2.96 x 10^7) + (1.0 x 10^8)

= 2.96 x 107-> 29,600,000 = 1.0 x 108-> 100,000,000 = (29,600,000) + (100,000,000) = 129,600,000= 1.296 x 10^8

The Edwards family needs to buy a dishwasher. The new energy-efficient machines use less water and energy, but that they are more expensive. A traditional dishwasher costs $200 whereas the water-efficient machine costs $300. The traditional machine uses 20 L of water per load of dishes, and the efficient machine uses 7 L. How many liters would the efficient dishwasher save per year?

= 20 - 7 = 13 saved = 260 loads / 1 year × 13 L/ 1 load = 3,380L per year

Joshua tress in the Mojave Desert occupy 25% of a piece of land. The land has 450 hectares in total. How much land is made up of Joshua Trees?

= 25% -> 0.25 = 450 x 0.25 = 112.5 hectares

The Edwards family needs to buy a dishwasher. The new energy-efficient machines use less water and energy, but that they are more expensive. A traditional dishwasher costs $200 whereas the water-efficient machine costs $300. How many years would you have to own the more efficient dishwasher before you would save money on water compared with the traditional machine? Round to the nearest year.

= 300 - 200 = 100 = $100 x 1 year/$3.38 = 30 years

The Edwards family needs to buy a dishwasher. The new energy-efficient machines use less water and energy, but that they are more expensive. A traditional dishwasher costs $200 whereas the water-efficient machine costs $300. Disregarding the cost savings for water use (#4), how many years would you have to own the more efficient dishwasher before you would save money on energy compared with the traditional machine? Round to the nearest year.

= 300 - 200 = 100 = $100/$32 = 3 years

The Edwards family needs to buy a dishwasher. The new energy-efficient machines use less water and energy, but that they are more expensive. A traditional dishwasher costs $200 whereas the water-efficient machine costs $300. The average cost of water in the United States is $1.00 for every 1000 L. How much money would you save each year by using the more efficient dishwasher?

= 3380L/ 1 year x $1.00/ 1000L = $3.38 per year

Between 1950 and 2000, global meat production increased from 52 billion kilograms to 240 billion kilograms. During this period, the global human population increased from 2.6 billion to 6.0 billion. Use the values from part a to calculate the change in global per capital meat production during this 50-year period as a percentage of the 1950 value.

= 40-20/20x 100 = 20/20x 100 = 1 x 100 = 100% increase

The Edwards family needs to buy a dishwasher. The new energy-efficient machines use less water and energy, but that they are more expensive. A traditional dishwasher costs $200 whereas the water-efficient machine costs $300. The federal standard for energy use in dishwashers is 400 kWh/year. An energy efficient dishwasher will save 40% of that energy use. How much energy will an energy efficient dishwasher use in a year?

= 400 kWh per year x 0.4 = 160 = 400 - 160 = 240 kWh per year

A 48g sample of Germanium-66 is left undisturbed for 10 hours. At the end of that period, only 3.0g remain. What is the half-life of this material?

= 48 -> 24 -> 12 -> 6 -> 3 = 4 half lives = 10 hours/4 half lives = 2.5 hours

The Edwards family needs to buy a dishwasher. The new energy-efficient machines use less water and energy, but that they are more expensive. A traditional dishwasher costs $200 whereas the water-efficient machine costs $300. If the average family washes 5 loads of dishes per week, how many loads does the family wash per year?

= 5 loads/1 week x 52 weeks/1 year = 260 loads per year

In a pasture of grass and other plants, the biomass of insects makes up 5000 kilograms. This is 5% of the total biomass of the pasture. What is the total biomass of the pasture? Set up the problem and solve below:

= 5% -> 0.05 =0.05/ 0.05x = 5,000/0.05 (divide 0.05 to each side) = x = 5,000/0.05 x = 100,000 kg

Express each of the following in standard form: 5.2 x 10^3

= 5,200

Express each of the following in scientific notation: 0.00053

= 5.3 x 10^-4

Find each percent change to the nearest percent (you may round, if necessary). State if it is a percent increase or a decrease. From 70 g to 75 g (round to nearest whole %)

= 5/70x 100 = 0.0714285x 100 = 7.142857 = 7% Increase

Write the following numbers in scientific notation: 550,000,000,000

= 550,000,000,000 = 5.5 x 10^11

Uranium-235 has a half-life of 700 million years. 600kg is stored as a spent fuel-rod at a nuclear power plant. How many billion years will it take to decay to 75kg?

= 600 -> 300 -> 150 -> 75 = 3 half years = 700,000,000 × 3 = 2.1 × 10⁹ years

In another section of the community garden, some members raise chickens, not only for their eggs, but for the manure to fertilize the avocado trees. Each chicken produces 50 kg of manure per year and the garden's chicken coop holds 25 chickens. Each avocado tree needs 10 m^2 of space to grow. Calculate the number of avocado trees that the manure from the chicken coop can fertilize.

= 625 m^2/10 m^2 = 62.5 trees -> 62 = 62 Trees

Carbon-14 has a half-life of 5730 years. Consider a sample of fossilized wood that when alive would have contained 96kg of C-14. It now contains 3000g. How old is the sample?

= 96 -> 48 -> 24 -> 12 -> 6 -> 3kg = 5 half lives = 1 kg -> 1,000g = 3kg -> 3,000 g = 5730 x 5 = 28,650 years

On average 1 kg of corn contains 3 x 103 kcal and a single hectare can produce 1.2 x 104 kg of corn per year. Thirteen percent of the US corn crop is exported to other countries. How many kg is exported?

Answer from #22: 1.2 x 1012 kg per year = 13% -> 0.13 = 1.2 x 10^12 x 0.13 = 1.6 x 10^11 kg per year

UNIT 8

Aquatic & Terrestrial Pollution

UNIT 7

Atmospheric Pollution

UNIT 4

Earth Systems & Resources

UNIT 6

Energy Resources & Consumption

UNIT 9

Global Change

You observe a population of rabbits that has an initial size of 10 individuals (N0 = 10). The intrinsic rate of growth for a rabbit is r = 0.5 (or 50%), which means that each rabbit produces a net increase of 0.5 rabbits each year. Assume the intrinsic rate of growth is 1.0 instead. Calculate the expected population size in 10 years.

N0 = 10 r = 1.0 t = 5 Nt = (10)e(1)(10) = 220264.6579 = 220,265 Rabbits

Find each percent change to the nearest percent (you may round, if necessary). State if it is a percent increase or a decrease. From 3 inches to 10 inches (round)

= 10-3/3 x 100 = 7/3 x 100 = 2.3 x 100 = 233.3 = 233% Increase

Convert 5 km^2 to m^2

5,000,000 m^2

The density of Calcium carbonate (CaCO3) in coral reefs is 2 x 103 kg/m^3. If the CaCO3 in a reef weighs 4 x 108 kg, what is the volume?

Formula: D = m/v D = 2 x 103 m = 4 x 108 v = ? = 2 x 103 = 4 x 108 v = Rearrange formula to v = m/D = v = 4 x 1082 x 103 = 2 x 105 m^3

Between 1950 and 2000, global meat production increased from 52 billion kilograms to 240 billion kilograms. During this period, the global human population increased from 2.6 billion to 6.0 billion. Calculate the per capita meat production in 1950 and 2000

In 1950: = 52 billion kg/2.6 billion = 20 kilograms per person In 2000: = 240 billion/6 billion = 40 kilograms per person

You observe a population of rabbits that has an initial size of 10 individuals (N0 = 10). The intrinsic rate of growth for a rabbit is r = 0.5 (or 50%), which means that each rabbit produces a net increase of 0.5 rabbits each year. What is the size of the rabbit population 1 year from now?

N0 = 10 r = 0.5 (50%) t = 1 Nt = (10)e(0.5)(1) = 16.487 = 16 Rabbits

You observe a population of rabbits that has an initial size of 10 individuals (N0 = 10). The intrinsic rate of growth for a rabbit is r = 0.5 (or 50%), which means that each rabbit produces a net increase of 0.5 rabbits each year. What will it be in 10 years?

N0 = 10 r = 0.5 (50%) t = 5 Nt = (10)e(0.5)(10) = 1484.134 = 1,484 Rabbits

You observe a population of rabbits that has an initial size of 10 individuals (N0 = 10). The intrinsic rate of growth for a rabbit is r = 0.5 (or 50%), which means that each rabbit produces a net increase of 0.5 rabbits each year. What will the size of the population be 5 years from now?

N0 = 10 r = 0.5 (50%) t = 5 Nt = (10)e(0.5)(5) = 121.825 = 122 Rabbits

UNIT 2

The Living World, Biodiversity

UNIT 1

The Living World, Ecosystems

Convert 500 km to meter

500,000 meter

Divide 530.4 by 3.4

530.4÷3.4 = 156

Place the following numbers in scientific notation One Billion

= 1 Billion -> 1,000,000,000 = 1 x 10^9

Farmers in a certain state lose 2.3 x 102 kg of topsoil in a year on average. There are 4.5 x 103 farmers in this state. How much topsoil is lost in this state annually?

= (2.3 x 10^2) x (4.5 x 10^3) = 1,035,000 kg or 1.035 x 10^6 kg

Multiply and divide the following: (2.8 x 10^-6)(4 x 10^-5)

= (2.8 x 10^-6) -> 0.0000028 = (4 x 10^-5) -> 0.00004 = (0.0000028)(0.00004) = 0.0000000001 = 1 x 10^-10

Add the following: (3.27 x 10^4) + (9.8 x 10^3)

= (3.27 x 10^4) -> 32,700 = (9.8 x 10^3) -> 9,800 = (32,700) + (9,800) = 42,500 = 4.25 x 10^4

If cyanide in a stream next to a gold mine increases from 240 ppm to 360 ppm, what percent increase is this?

= (360-240)/240 = 0.5 x 100 = 50%

Multiply and divide the following: (4 x 10^4)/(2 x 10^-4)

= (4 x 104) -> 40,000 = (2 x 10-4) -> 0.0002 = 40,000/0.0002 = 200,000,000 = 2 x 10^8

A toxin increases from 12 ppm to 48 ppm. What percent increase is this? Set up the problem below:

= (48 - 12)/ 12 = 3x 100 = 300%

Multiply and divide the following: (5.4 x 10^-1)/(10 x 10^1)

= (5.4 x 10^-1) -> 0.54 = (10 x 10^1) -> 100 = 0.54/100 = 0.0054 = 5.4 x 10^-3

Burning one gallon of gasoline in a car releases approximately 20 pounds CO2 into the atmosphere. One person drives 50,000 miles in a hybrid car that averages 50 miles per gallon (mpg), while another person drives 50,000 miles in an SUV that averages 20 mpg. Over the course of the 50,000 miles, how many fewer pounds of CO2 are released by the 50-mpg car than by the 20-mpg car?

= (50,000 miles/1) x (1gallon/50miles) = (1000gallons/1) x (20lbs/1gallon) = 20,000 lbs = (50,000 miles/1) x (1gallon/20miles) = (2500 gallons/1) x (20lbs/1gallon) = 50,000 lbs = 50,000 lbs - 20,000 lbs = 30,000 lbs

Subtract the following: (9 x 10^11) - (7 x 10^10)

= (9 x 10^11) -> 900,000,000,000 = (7 x 10^10) -> 70,000,000,000 = (900,000,000,000) - (70,000,000,000) = 830,000,000,000 = 8.3 x 10^11

Add the following: (9.06 x 10^5) + ( 3.1 x 10^-2)

= (9.06 x 10^5) -> 906,000 = ( 3.1 x 10^-2) -> 0.031 = (906,000) + (0.031) = 906,000.031 = 9.1 x 10^5

Subtract the following: (9.9 x 10^3) - (3 x 10^2)

= (9.9 x 10^3) -> 9,900 = (3 x 10^2) -> 300 = (9,900) - (300) = 9,600 = 9.6 x 10^3

The Amazon rainforest has 6.8 million square kilometers. In July of 2019 approximately 1,345 square kilometers burned down. Calculate the percent change.

= 6.8 million -> 6,800,000 (initial) = 6,800,000 - 1,345 = 6798655 (final) = ((6,798,655-6,800,000)/6,800,000) x 100 = -13456,800,000 x 100 = -0.019779411764705882352% = -0.020% is the percent change of the square kilometers

Express each of the following in scientific notation: 78,000

= 7.8 x 104

Place the following numbers in scientific notation 70 Trillion

= 70 Trillion -> 70,000,000,000,000 = 7 x 10^13

Solve: (8 x 10^12) - (1.2 x 10^12)

= 8 x 1012-> 8,000,000,000,000 = 6 x 1015-> 6,000,000,000,000,000 = (8,000,000,000,000) - (6,000,000,000,000,000) = 3.96 x 10^7

Find each percent change to the nearest percent (you may round, if necessary). State if it is a percent increase or a decrease. From 45 m to 90 m

= 90-45/45x 100 = 45/45x 100 = 1 x 100 = 100% Increase

Place the following numbers in scientific notation Three Hundred

= Three Hundred -> 300 = 3 x 10^2

These half-life problems require no formula or calculator. "Sketch" out the problem to solve. 23. A 50g sample of radioactive Iodine-131 has a half-life of 8.0 days. After 32 days, how much is left?

= You have to divide 32 by 8 (32/8) in order to know how many times it gets halved. So in this case it is 4 times halved. = 50/2 = 25/2 = 12.5/2 = 6.25/2 = 3.125g

New Zealand has a population of 4.3 million people, a total fertility rate (TFR) of 2.1, and a net migration rate of 2 per 1,000. If the TFR stays the same for the next century, and the net migration rate stays the same as well, when will the population of New Zealand double?

= growth rate = 8600/4,300,000= = 0.002 x 100 = 0.2% = 70/0.2 = 350 years

Calculate the following problems and put your answer in scientific notation. Show the work you enter into your calculator along with the answer. One Ten Thousandth of Three Million

= one ten thousandth of three million -> three hundred = three hundred -> 300 = 3.0 x 10^2

Find each percent change to the nearest percent (you may round, if necessary). State if it is a percent increase or a decrease. From 25 hours to 20 hours

= 20-25/25 x 100 = -5/25 x 100 = -0.2 x 100 = -20% Decrease

There are 5,416 mammal species on Earth. If 25% of mammals are endangered, how many species is this?

= 25% -> 0.25 = 0.25 x 5,416 = 1,345 species

Some members of a community garden in California want to plant an orchard to earn some extra income. After researching, they decided to plant avocado trees. Avocado saplings (baby trees) cost $20 each. It takes 3 years for avocado trees to reach maturity and bear fruit, but after they do, each tree will produce $125 worth of fruit. The community garden is made of 50 members and their goal is to sell $250 per capita each year. Calculate the total number of trees that all the garden members will need in total in their orchard to meet the goal.

= 250 dollar per capita/125 dollars worth of fruit = (2 trees/1 person) x 50 people = 21 x 50 = 100 trees

A carmaker improved the mpg of a model of car from 22 to 32. What percent change is this? (round to nearest whole %)

= 32-22/22 x 100 = 10/22 x 100 = 0.45 x 100 = 45.45 = 45% Increase

An old Honda Civic can go 348 miles on average before it runs out of gas. its tank holds 12 gallons of gas. What is the car's mpg? (miles per gallon)

= 348miles/12gallons = 29 miles per gallon

Americans recycle about 35% of their solid waste (trash). If an average American generates about 2 kg of waste every day, how much of that waste is recycled per year?

= 35% -> 0.35 = (2kg/1day) x (365days/1 year) = (750kg/year) x 0.35 = 255.5 kg

Twenty percent of a forest is cut down. The forest area is 35,000 hectares. How many hectares of trees are left?

= 35,000 x 0.8 = 28,000 hectares

What is 45% of 1800?

= 45% -> 0.45 = 0.45 x 1,800 = 810

A 48g sample of Germanium-66 is left undisturbed for 10 hours. At the end of that period, only 3.0g remain. What is the half-life of this material?

= 48/2 = 24/2 12/2 = 6/2 = 3 = Since it had to be halved 4 times in order to get 3.0g, then we have to divide 4 by 10 (hours). = 4/10 = 2.5

In another section of the community garden, some members raise chickens, not only for their eggs, but for the manure to fertilize the avocado trees. Each chicken produces 50 kg of manure per year and the garden's chicken coop holds 25 chickens. Calculate the mass of the manure produced per year by the chicken coop.

= 50 kg x 25 chickens = 1,250 kg

Calculate the following problems and put your answer in scientific notation. Show the work you enter into your calculator along with the answer. Five Hundred Billion times Thirty Five Thousand

= 500,000,000,000 x 35,000 = 17,500,000,000,000,000 = 1.75 x 10^16

Some members of a community garden in California want to plant an orchard to earn some extra income. After researching, they decided to plant avocado trees. Avocado saplings (baby trees) cost $20 each. It takes 3 years for avocado trees to reach maturity and bear fruit, but after they do, each tree will produce $125 worth of fruit. The community garden is made of 50 members and their goal is to sell $250 per capita each year. Calculate the cost of the water for all the trees each year.

= 52 dollars x 100 = 5,200 dollars

Some members of a community garden in California want to plant an orchard to earn some extra income. After researching, they decided to plant avocado trees. Avocado saplings (baby trees) cost $20 each. It takes 3 years for avocado trees to reach maturity and bear fruit, but after they do, each tree will produce $125 worth of fruit. The community garden is made of 50 members and their goal is to sell $250 per capita each year. After subtracting the cost of water, calculate the profit will each person make each year.

= 52 dollars/1 tree x 2 trees/1 person = 104 dollars per person = 250 - 104 = 146 dollars

Calculate the percentage growth rate for a country with a population of 6 million: in a year in which it had 100,000 births, 70,000 deaths, 30,000 immigrants, and 50,000 emigrants.

= 6 Million -> 6 x 10^6 = growth rate = (100,000 births + 30,000 immigrants) - (70,000 deaths + 50,000 emigrants) =(130,000) - (120,000) = 10,000/6 x 106 x 100 = 0.016 x 100 = 0.16666666666666 = 0.17%

A gas engine is 6% efficient. What portion of a 12-gallon tank of gas is wasted?

= 6% -> 0.06 = 12 x 0.06 = 0.72 wasted

Calculate the following problems and put your answer in scientific notation. Show the work you enter into your calculator along with the answer. 6 Billion divided by 35 Trillion

= 6,000,000,000/35,000,000,000,000 = 0.0001714285 -> 0.0002 = 2x 10^-4

Calculate the following problems and put your answer in scientific notation. Show the work you enter into your calculator along with the answer. Six Thousand divided by 300 billion

= 6,000/300,000,000,000 = 0.00000002 = 2 x 10^-8

Find each percent change to the nearest percent (you may round, if necessary). State if it is a percent increase or a decrease. From 12 L to 6 L

= 6-12/12x 100 = -612x 100 = -0.5 x 100 = -50% Decrease

Solve: (6.0 x 10^6) ÷ (3.0 x 10^4)

= 6.0 x 106-> 6,000,000 = 3.0 x 104-> 30,000 = (6,000,000) ÷ (30,000) = 200= 2.0 x 10^2

In 1987, the population of Black Footed Ferrets in the world was 18 individuals. By 1989 through captive breeding, the number rose to 120. What percent change is this?

120-18/18 x 100 102/18 x 100 = 5.6 x 100 = 566.6 = 567%

Convert 14,000 milliliter to liter

14 liter

New Zealand has a population of 4.3 million people, a total fertility rate (TFR) of 2.1, and a net migration rate of 2 per 1,000. How many people will New Zealand gain next year as a result of immigration?

2/1000= x/4,300,000 1000x/1000= 1000x = 8,600,000 x = 8,6000 people

Express each of the following in scientific notation: 0.00000016

= 1.6 x 10^-7

10% of a barrel of oil is turned into plastic. A barrel of oil contains 42 gallons. How many gallons are NOT turned into plastic?

= 100% - 10% = 90% -> 0.90 = 42 x 0.90 = 37.8 gallons

In another section of the community garden, some members raise chickens, not only for their eggs, but for the manure to fertilize the avocado trees. Each chicken produces 50 kg of manure per year and the garden's chicken coop holds 25 chickens. Manure can be worked into the soil at about 2kg/m^2. Calculate the area that can be fertilized by the chickens' manure.

= 12/50 kg^2 = 625 m^2

Some members of a community garden in California want to plant an orchard to earn some extra income. After researching, they decided to plant avocado trees. Avocado saplings (baby trees) cost $20 each. It takes 3 years for avocado trees to reach maturity and bear fruit, but after they do, each tree will produce $125 worth of fruit. The community garden is made of 50 members and their goal is to sell $250 per capita each year. Each avocado tree needs 40 L of water per day during the dry season (120 days per year) and 2 L of water per day during the rainy season (200 days per year). The community garden must buy water from the water agency at $0.01 per liter. Calculate how much it will cost per year to water each tree.

= 120 days/1 x 40 L/1 day = 4800 L = 200 days/1 x 2 L/1 day = 400 L = 4,800 + 400 = 5,200 L/1 tree x 0.01 dollars/1 L = $52 per Tree

Write the following numbers in scientific notation: 10. 15 million

= 15 Million -> 15,000,000 = 1.5 x 10^7

A 2500-hectare piece of wild chaparral was bought by a developer to turn into homes. The developer built homes on 1000 hectares and left the rest untouched. What was the percent decline in wild chaparral?

= 1500-2500/2500 x 100 = -1000/2500 x 100 = -0.4 x 100 = -40% which mean it decreased by 40%

A new construction site releases dust particles that measure 2 micros (2x10-6 meters). Six hundred thousand particles are released each hour. What is the total length of the particles released in an hour? In a day? In a year?

= 2 x 10-6 x 600,000 = 1.2 meters per hour = 1.2 m/1 hour x 24 = 28.8 meters per day = 28.8 x 365 = 10512 meters per year

Express each of the following in scientific notation: 250

= 2.5 x 10^2

Solve: (2.96 x 107) + (1.0 x 107)

= 2.96 x 107-> 29,600,000 = 1.0 x 107-> 10,000,000 = (29,600,000) + (10,000,000) = 39,600,000= 3.96 x 10^7

Some members of a community garden in California want to plant an orchard to earn some extra income. After researching, they decided to plant avocado trees. Avocado saplings (baby trees) cost $20 each. It takes 3 years for avocado trees to reach maturity and bear fruit, but after they do, each tree will produce $125 worth of fruit. The community garden is made of 50 members and their goal is to sell $250 per capita each year. Calculate the cost to buy all the avocado trees.

= 20 Dollars x 100 = $2,000