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105 Cards in this Set
- Front
- Back
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When going to the next smaller unit move decimal to the right
When going to the next larger unit move decimal to the left |
5.23 cm - 52.3 mm
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Any power to zero is 1.
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10 to the power of o = 1
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19 decimeters to millimeters
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19 deci x 10cm/1dm x 10 million/ 1cm
= 1900mm |
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Density=Mass/Volume
Density=People/mi squared |
Density= grams/ cm squared
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Percent to Decimal
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47%= 47/100 = .47
2%= 2/100 = .02 813%= 813/100 = 8.13 |
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Percent to Fraction
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45%= 45/100= 1/20
2%= 2/100= 1/50 525%= 525/100 = 21/4 = 5 1/4 |
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Convert Decimal to Percent
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.38 = 100% x .38 = 38%
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absolute change
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new value - orginal
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relative change
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absolute change/ orginal value x 100%
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You purchase a shirt w/ pre-tax of $21.00. Sales tax rate is 6%. Final cost?
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shirt + tax= total
$21 x .06 = $1.26 $21.00 + $1.26 = $22.26 total = $22.26 |
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A shirt is on sale at 44% off. The regular price is $539. What is the sales price before tax?
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reg price- $539
savings- 44% $539 - 44% of 539 .44 x 539 = 237.16 $539 - $237.16 = $301.84 |
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Your recipt shows you paid $19.35 for a cd, tax included. Sales tax rate is 7.5%. What is pre tax price?
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100% cd + 7.5% cd = $19.35
100% + 7.5% 107.5% + cd = $19.35 1.075 /1.075 x cd = 19.35/ 1.075 = $18.00 |
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Interest rate increases from 3% to 4%. What is absolute change?
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4% - 3% = 1 percentage point
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Interest rate increases from 3% to 4%. What is the relative change?
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1/3 = 0.33 x 100% = 33.3 %
The relative interest rate increased by 33 and 1/3% |
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Place value
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singular (1)
10 100 1,000 10,000 100,000 1,000,000 10,000,000 |
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26,000 students
How many significant digits? |
2 significant digits.
Implies a measurement to 1,000 people 2.6 x 10 to the 4 |
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13.80 seconds
How many sig. digits? |
4 signficant digits
1.380 x 10 seconds |
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0.000203 meter
How many sig digits? |
3 signficant digits
implied precision to one millionth meters |
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450,000 years
How many sig. digits? |
2 signficant digits.
implied precision to 10,000 years |
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Scientfic Notation
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Must be a number between 1 and 10
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$700 billion
correct or incorrect? |
incorrect
$7.0 x 10 to the 11 power |
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12 million
correct or incorrect? |
incorrect
1.2 x 10 to the 7 power |
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Convert from ordinary to scientfic by moving and counting decimal point until it lies after nonzero digit.
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The power is positive if decimal moved left
The power is negative if decimal moved right |
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1330
in scientfic notation |
1.330 x 10 to the 3 power
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.00000345
convert to scientfic notation |
3.45 x 10 to the - 6 power
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To move from scientfic to ordinary move to right if power is positive
move to left if power is negative |
1.7842 x 10 to the 3 power
1784.2 |
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2.111 x 10 to the 7 power
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21,110,000
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9.2 x 10 to the - 4 power
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.00091
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Estimation
How how is 1000 feet? |
Compare it to a building.
Assume each story is 10 feet. 1000feet x 1 story/ 10 feet = 100 story building so 1,000 feet is roughly equavilent to a 100 story building |
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Accuracy
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How closley a measurement approximates a true value. An accurate measurement is very close to the true value.
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Precision
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Describes the amount of detail in a measurement.
Hint: Usually measurements (measured to inch or feet) |
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Your true height is 62.50 inches.
A tape measuer that can be read to nearest 1/8 inch gives you a height of 62 3/8 inches. A laser reading to 0.05 inches gives you a reading of 62.90 inches. Which is the more accurate? |
measured - true
62 3/8 - 62.50 62.375 - 62.50 = - 0.125 inches masured- true 62.90 - 62.50= .40 inches Add another 0 to .40 to make them comparable (same number of digits) .400 is bigger than .125 therefore .125 (tape measuer) is more accurate |
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Your true height is 62.50 inches.
A tape measuer that can be read to nearest 1/8 inch gives you a height of 62 3/8 inches. A laser reading to 0.05 inches gives you a reading of 62.90 inches.Which is more precise? |
tape measure - 1/8 inch
laser - .50 inch make them same unit with same number of digits. 0.25 and .050. .050in (the laser) is more precise because it is being measured to a smaller inch. |
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What is the rounding rule for addition and subtraction?
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Round your ANSWER to same precision of the LEAST precise number. Dont Round Until End.
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Round and find precise number.
15. - 12. 63 |
15. - 12.63 = 27.63
The least precise number is 15 because it has less digits and is not as specfic. Therefore round it to 28 |
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Round and find precise number
23,500 - 10,000 |
23,500 - 10,000 = 33,500
23,500 has 3 sig. digits 10,000 has 1 sig. digit Therefore 10,000 is least precise. Therefore round to 30,000 |
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Rounding rule for multiplication and division.
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Round answer to same number of significant digits a measurement w/ fewest sig. digits.
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Round answr and find least precise.
The perimeter of a rectangle 12.25 ft by 22 ft. |
12.25 + 12.25 + 22 + 22 = 68.90 feet
22 is least precise because it has less sig. digits. Therefore round to 69 feet. |
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A book written in 1975 states oldest ruins are 2,000 years old. How old are they now in 2005? Round to least precise.
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2,000 - 1975 = 30
2,000 + 30 = 2,030 years 2,000 is least precise because the book states they round the ruins to nearest 1,000 years. Therefore round to 2,000 years |
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The government in a town of 82,000 people plans to spend $41.5 million this year. Assuming the money must be from taxes, what average amount must be collected from each resident. Round to least precise.
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82,000 people $41.5 million
part/whole $41.5 million/ 82,000 people = $506.10 per person 41,500,000 - 3 sig. digits 82,000- 2 sig. digits Therefore 82,000 is least precise. Round to $510.00 |
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Find number of sig. digits and implied precision.
450,000 years |
2 sig. digit.
Implied precision to 10,000 years |
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Find number of sig. digits and implied precision.
0.000203 meters |
0.000203 meter.
also 2.03 x 10 to the -4 power 3 sig. digits. Implied precision to one millionth metter. |
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A testing service makes an error that causes scores for students all to be too low by 50 points. Is this a systematic error or random error?
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systmematic
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Digital scale shows you weigh 112.7 pounds but you actually weigh 146 pounds. Is the scale fairly accurate or fairly precise?
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Find asbolute and relative error.
measured - true value 112.7 lbs - 146 lbs = - 33.3 lbs. The scale was off by 33.3 lbs. Therefore the scale was fairly precise but not very accurate. |
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Find random and systematic errors.
Times in a swim meet. |
Systematic error: Malfunction with stop watch or computer device
Random:Human error if fails to press stop stop watch right when the swimmer finishers. |
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You need a 48 in board but you cut it to 47.5 inches. Find absolute and relative error.
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measured - actual
47.5 - 48 = - 0.5 absolute error: Off by 0.5 of an inch - 0.5in/48in x 100% = - 1.04% Relative error: Measurment off by 1.04% |
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Assumptions.
I want to run for mayor and my plan is to go to all 300,000 households and spend a few minutes talking with each member. IS this possible to do in a year? |
Assume you talk for 3 min. to each person
Assume there are 3 people per house 300,000 households x 3min/1person x 3people/1householf x 1hr/60 min =45,000 hours x 1day/24 hours = 45,00/24 = 1,875 days. This is impossible because it would take more than 365 days (one year) |
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I have seen 10 to the 50 power commercials on tv.
Is this a rational assumption? |
asume you watch 1hr of tv everday
-assume 4 commercials/hr Im 19 - assume 10 to the 50 in 19 years 19years x 365dys/1yr x 1hr/1day x 4commercials/1hr = 27,740 commercials Compare 27,740 to 10 to the 50 power. Clearly 10 to the 50 power is too large to be a rational assumption. |
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Convert to scientfic notation.
0.0045 |
(make number between 1-10)
4.5 x 10 to the - 3 (negative because decimal is moving to left) |
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Convert to scientfic notation
624.87 |
6.2487 x 10 to the 2 power
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Solve for scientfic notation
(4 x 10^3) + (5 x 10 ^2) |
(4 x 10^3) + (5 x 10 ^2)=
(4,000) + (500) = 4,500 =4.5 x 10^3 |
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Solve for scientfic notation
(9 x 10^13) / (3 x 10^10) |
(9 x 10^13) / (3 x 10^10)
switch (9 x 3) / (10^13 +10) 9/3 x 10^13/ 10^10 (subtract powers of ten in division) 3 x 10^3 |
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Convert to scientfic notation
0.000001 meter |
0.000001 meter
move decimal to the left 10 ^ - 6 meter |
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Make assumptiond. If it takes 2,930 miles to walk from NY to California, is it possible for a person to do this in one year?
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Assume i can walk 30 miles/day
365 days in a year 30ml/1day x 365days/1yr = 10,950 miles/year If i can walk 10,950 miles in a year its possible to walk 2,930 miles in a year |
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Total number of words in the textbook.
Find order of magnitude. Order of magnitude is when your using assumptions, not accurate measurement. |
Assume 782 pages
Assume 300 words per page 782 x 300 = 234,600 The total number of words in the book is on the order of 234,600 |
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There are roughly 130 milllion birds worldwide. How many births are there per minute?
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130/1yr x 1yr/365dy x 1dy/24hr x 1hr/60min = 247.3 birds born per minute
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Explain difference bweteen percent and percentage point.
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Percenatge point expresses absolute change from orginal value to its current value while a percent expresses relative difference
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Ive decreased my calorie intake by 125% which has helped me lose weight. Make assumptions. Deciede if true or false.
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assume you consume 200 calories/day
125% of 200 1.25 x 200 = 250 calroies False, your consuming more calories. |
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I have a 60% average on assignments. I want to make my course average a 70% by getting an 80% on final which is worht 25%
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25% final 75% left make decimals
.25 .75 .25 x 80 = 20 towards final .75 x 60 = 45 towards final 20 + 45 = 65 False, you would average a grade of 65% not 70% |
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Finf final cost of car. Pre tax it is $19,200. Sales tax rate is 7.2%
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pretax- 19,200
sales tax- 7.2% car + tax = final cost 19,200 + 7.2% of 19,200 = total 7.2% of 19,200 = .072 x 19,200 = 1,382.30 19,200 + 1,382.40 = $20,582.40 final |
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Your dinner bill is $42.50. You leave $50. What percent tip did you leave?
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$50.00 - $42.50 = $7.50
7.25/42.50 x 100 = 17.6% |
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123 varsity student athletes in graduating class of 569 students. Express first number as percentage of the second.
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123 people/569 class = 0.21616 x 100% = 21.6%
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Glass of wine has 12% alcohol by volume. 0.5 ounces of alchol, how much wine does glass hold?
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12%/ounce = total
12%=.12 total/part .5/.12 =4.17 volume of wine is 4.17 ounces |
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A typical glass of wine is 20 grams of alcohol. A 110lb woman w/ 4 liters (4,000ml) of blood, she drinks 2 glasses of wine. Find her blod alcohol content.
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20g x 2 = 40 grams of alcohol
40grams/ 4,000ml = 0.01g/ml 0.01 g/ml x 100ml/100= 1.0g/100ml=BAC legal limit is .08. She is over |
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Is a temperature of 105 Celsuius boiling hot? Put in farenheight
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F= 1.8 (105) + 32
F = 221 F Yes |
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10^5 x 10^ -3
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10^5 + - 3 = 10^2
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10^2 - 10^1
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10^2= 100
10^1= 10 100-10 = 90 |
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A boat is moving at 30 nautical miles pr hour. What is its speed in miles per hour. There are 6076.1 ft in one nautical mile. There are 5280ft in one mile.
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30 nautical/1 hr x 6076.1ft/1 nautical mile x 1mile/5280ft =
34.523 miles/hr |
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84 quarts in liters
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84 quarts x 0.9464L/1 quart = 79.4976 L
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Convert 15 degress celsuis to farinheight
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F = 1.8 (15) + 32
F = 59 degress |
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Convert 75 degress farenheight to celsius.
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c = (75-32)/1.8
c =23.8 |
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One square foot in inches.
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12 inches in 1 foot
12ft x 12ft = 144144 square inches |
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The bed if a truck if 3.5 ft deep, 12 feet long, and 5 ft wide. What is the area?
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area = length x width
60 = 12 x 5 area = 60 ft squared |
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The bed if a truck if 3.5 ft deep, 12 feet long, and 5 ft wide. What is the volume of the truck?
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volume = area x depth
v= 60ft x 3.5ft v= 210ft cubed |
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2/3 x 1/4
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2/12= 1/6
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1/4 + 3/8
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1/4 x 2
2/8 + 3/8 = 5/8 |
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Put decimal into fraction.
4.1 |
41/100
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Put decimal into fraction
4.01 |
401/100
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Put fraction into decimal
3/8 |
0.375
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Put fraction into decimal
23/6 |
3.83333
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Bottled water costs 0.75 euro per liter in Paris. What is the price in US dollars per quart. One quart = 0.9464 liter
1 euro = $1.46908 |
0.75 euro/1 liter x $1.46908/1 Euro x .9464 liter/ 1 quart =$1.04
$1.04/quart |
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You work 40 hours per week and are paid $13.50 per hour. If you work 52 weeks in a year, how much wil you earn?
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40hrs/ 1wk x $13.50/1hr x 52wks/1yr = $28,080 per year
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What has the greater population density? Hawii has a population of 1.3 million and an area of 6425 miles squared. Arizonia has a popilation of 5.2 million and an area of 113,609 miles squared.
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density = people/ miles squared
Hawaii = d = 1.3million/6425 ml^2 d= 202.33people/mi^2 Arizonia= 5.2million/113,609 miles^2 d= 4573.84 people/miles^2 Arizona has a greater population density |
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Are these two units interchangable?
USCS - 1/16 inch Metric- 0.5 millimeter |
Easiest way is to convert 1/16in. to decimal
1/16= 0.0625 inches 0.5 mm 0.0625in/1 x 2.540cm/ 1in x 1000mm/100cm 1/16in= 1.5875 mm Mo they are not interchangable because it is alot larger than 0.5mm. |
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The initial population of a town is 15,600 and it grows with a doubling time of 8 years. What wiill the population be in 12 yrs? in 24 yrs?
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new value= initial x 2 ^ (t/doubling)
=15,600 x 2 ^(12/8) =44,123 after 12 yr 15,600 x 2 ^ (24/8) = 124,800 after 24 yrs |
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In 2006 the population was 6.5 billion. If the doubling time is sixty yrs what will the population be in 2016?
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= 6.5 billion x 2 ^ (10/60)
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The production of a gold mine is decling by 6% per year. If its annual production is 4000 kg, what will its production be in 15 yrs?
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half life= 70/percemt
70/6= 11.6 half life 4,000 x (1/2) ^ (15/11.6) = 1,632.3 kg after 15 years |
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Suppouse it cost $15 to fill a gas tank in 1985. How much would it have been to fill the same tank in 1965?
cpi 1965- 55.0 cpi-1985- 210.9 |
(55.0/210.9) x $15.00
= $3.91 |
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Suppouse you needed $45,000 to maintain a paticular style of living in 1981. How much would you need in 1995 to maintain it?
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cpi new / cpi orginal
195.3/90.9 = 2.15 45,000 x 2.15 = 96,750 You would need $97,000 to maintain yr style of living. |
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Find the inflation rate from 2002 to 2006
new-orginal/original x 100% cpi 2005 - 195.3 cpi 2002- 179.9 |
195.3 - 179.9 / 179.9 x 100%
= 8.6% inflation rise |
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pg. 266 # 48
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= $6, 296.48
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pg. 197 # 38
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see hw sheet
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You drive an average of 550 miles a week in a car that gets 22 miles a galloon. With gasoline priced at 2.29 a galloon, what would be the difference in total weekly cost for gasoline if you started driving an SUV that gets 15 miles a galloon.
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old: 550 miles/22 mpg x 2.29
= $57.25/ wk on gas SUV: 550 miles/15 mpg x 2.29 =$83.97/ wk on gas =If you started driving the SUV you would be spending $26.72 more a week on gas. |
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The final cost for a pair of boots is $88.83. The local sales tax rate is 4.5%. What was the labeled pre tax price of the boots?
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final- 88.83
tax- 4.5% pretax- ? 100% of boots + 4.5% of boots = 88.83 104.5% = 1.045 1.045/1.045 = 88.83/1.045 = $85.00 $85.00 |
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IS the following an example of a random or systematic error? In a wrriten survey, people sometimes make errors in filling out a questionaire.
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random
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What is the annual interest rate of 21% unpaid balance on $900?
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21/100 = 0.21 of 900 = 189
$189.00 = annual interest rate |
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You invest $5,000 in an account that pays simple interest of 6.5% for 20 yrs. What will you have after 20 yrs?
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a = 5,000 + (5,000 x .065) x 20
a = $11,500 |
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The number of students at Wilson High School has increased by 50 in each of the past four yrs. If the student population was 750 four years ago, what is it today. What type of growth is it?
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It is linear growth because it increased by same absolute amount each yr.
4 x 50 = 200 students from 750 to 950. |
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The price of milk has been rising with inflation at 3% per year. If the price of a gallon of milk was $2 a year ago, what is it now?
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The price is a percent so it is exponentail growth.
0.03 x $2= $0.06 making the price $2.06 |
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Suppouse yr bank acccount has a doubling time of 13 yrs. By what factor does yr balance increase in 50 yrs?
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2^ (50yr/13yr) = 2^ 3.8462
= 14.382 For example, if u start w/ a balance of $1,000 in 50 yrs 1,000 x 14.382 = 14,382 |
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World population was about 6.0 billion in 2000 and was growing at a rate of 1.4% per year. What is the doubling time at this growth rate?
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Use approximte doubling time formula because the growth rate is less than 15%
70/percent= 70/1.4= 50 yr doubling time |
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In 1950, the birth rate was 3.7 births per 100 people and the death rate was 2.0 deaths per 100 people. By 1975, the births had fallen to 2.8 births and deaths to 1.1 deaths. Contrast growth rates.
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1950: 3.7/100 - 2.0/100 = 1.7%
1975: 2.8/100 - 1.1/ 100 = 1.7% Growth rate remained unchanged |
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The 1989 San Franscio earthquake in which 90 people were killed had a magnitude 7.1. Calcuate the enegry released in joules.
E = (2.5 x 10^4) x 10^ (1.5 m) |
(2.5 x 10^4) x 10^ (1.5 x 7.1) =
1.1 x 10^15 joules |
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What is the hydrogen ion concentration of acid rain with a pH of 6
[H+] = 10 ^ - pH |
10 ^ -2 mole per liter
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In terms of hyrdogen ion concentration compare a pH 2 to pH 6
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10 ^ -2 / 10 ^ - 6
= 10 ^ - 2 + 6 =10 ^ 4 |
