Questions on Algebra: Unit Conversion answered by real tutors!

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Question 992226: Change the following numbers into there binary equivalents..... 19,39 and 77
Answer by stanbon(69061)   (Show Source):
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Change the following numbers into there binary equivalents..... 19,39 and 77
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19 = 16+2+1 = 2^4 + 2^1 + 1 = 10011
-----
39 = 32+4+2+1 = 2^5+2^2+2^1+1 = 100111
------
77 = 64+8+4+1 = 2^6+2^3+2^2+1 = 1001101
---------------
Cheers
Stan H.
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Question 991484: 5(x-6)=60÷12
Found 2 solutions by ikleyn, EdenWolf:
Answer by ikleyn(988)   (Show Source):
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.
5(x-6) = ,

5(x-6) = 5,

x-6 = 1,

x = 7.

Answer by EdenWolf(454)   (Show Source):
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Question:
Simplify and solve for x.

Question 990897: Suppose U={1,2,3,4,5,6,7,8} and B={2,4,6,8}. What is B?
Answer by MathLover1(11324)   (Show Source):
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if U={1,2,3,4,5,6,7,8} and B={2,4,6,8}, then B is subset of U

Question 989447: If a=4 find the value of 3a

Answer by farohw(153)   (Show Source):
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a = 4 find the value of 3a:
3(4) = 12

Question 987216: A bowling ball is traveling at 15 mi/h when it hits the pins. How fast is the bowling ball traveling in feet per second.
Answer by solver91311(20879)   (Show Source):
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15 miles per hour times 5280 feet per mile times 1/3600 hours per second.

John

My calculator said it, I believe it, that settles it

Question 987009: 10.) Just as you are recovering, your child falls ill. You know that there have been mistakes in your medication dosages, so you hurriedly scan the Internet to make sure that what the doctor is giving your child is safe. The doctor orders 2 things:
A. 150mg of an antibiotic to be given every 6 hrs. Your child weighs 30lb. Your research indicates that 20-40mg/kg/day is recommended dosage. Is this prescription safe for your child? If not, what would the maximum safe dosage be every 6 hours?
B. 15ml of Tylenol3 to be given every 4-6 hrs. Your research indicates that there are 12mg codeine per 5ml of liquid and that the safe dosage is between 0.5 and 1mg/kg/dose every 4-6 hrs. Is this prescription safe for your child? If not, what would the maximum safe dosage be every 4-6 hrs?

Answer by Boreal(1464)   (Show Source):
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The dosage is 600 mg a day, since it is given every 6 hours.
The weight of the child is 13.64 kg
600 mg/day/13.64 kg is the right units and it is 44. That is too high by 10%. I would give 135 mg every six hours, 10% less. The total daily dose would be 540 mg, which is 39.60 mg/kg/day. Alternatively, one could give 150 mg three times a day, or 450 mg/day. That would be 33 mg/kg/day, which would also be suitable.
===========
Each dose should be between 0.5 and 1 mg/kg
15 ml of Tylenol #3 contains 36 mg of codeine, since it is three times 5 ml.
That is 2.64 mg/kg, which is too much by a factor of 2.5 to 5.
The child should get about 20-40% of that amount prescribed or about 5 ml, not 15 ml. That would be 12 mg of codeine per dose, and that would be 0.88 mg/kg/dose.

Question 986992: 2.) Sally Leadfoot was pulled over on her way to Syracuse to Ithaca by an officer claiming she was speeding. The speed limit is 65 mi/hr and Sally had travel 97km in 102 minutes. How fast was Sally's average speed? Does she deserve a ticket?
Answer by solver91311(20879)   (Show Source):
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Maybe, maybe not. If she stopped at a rest area for an hour and had to travel the entire 97 km in 42 minutes, then yes indeed she would have been exceeding the speed limit at some point while she was actually moving. But if she travelled at her average speed or very nearly her average speed for the entire trip, she would have only been going about 35 miles per hour at any given time. Average speed is the total distance traveled by the amount of time it took, even if you stand still or go very slowly for some period of time.

Had the problem read, "...Sally had traveled 97 km in 102 minutes at a constant speed.", then there would have been no ambiguity to this question.

John

My calculator said it, I believe it, that settles it

Question 986990: 1.) Winnipeg is refilling the pool. How many gallons of water will it take if the pool is 50m by 25m by 1.5m? (1 gallon = 3.786 L)(1m cubed= 1000 L)
Answer by josgarithmetic(13975)   (Show Source):

Question 986997: 6.) Your car's gas tank holds 18.6 gallons and is one quarter full. Your car gets 16 miles/gal. You see a sign saying, "Next gas 73 miles.:" Your often wrong brother, who is driving, is sure you'll make it without running out of gas. You're not so sure and need to do some quick figuring. Should you turn around and get gas now or will you make it? Explain in detail your decision.
Answer by macston(4006)   (Show Source):
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.
(18.6 gallons/tank)(1/4 tank)=4.65 gallons
You have 4.65 gallons of gas.
(4.65 gallons)(16 miles/gallon)=74.4 miles
If you match your calculated mileage and your gas gauge is accurate, you should have just enough gas to make it to the station.
.

Question 986988: 4.While in Canada, you rent a car and discover that the speed limit on the highway is 100 km/hr. What is the equivalent value in mi/hr?
Answer by Alan3354(47455)   (Show Source):
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Convert kms to miles.

Question 986993: 4.) Convert 1 ft cubed to m cubed (note: 3.28ft = 1 mi)

5.) Convert 45mi/hr to ft/sec
i need these worked out thanks

Answer by Alan3354(47455)   (Show Source):
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They're conversions.
You can look them up, or do them on your phone.

Question 986055: 3/4 miles= inches
Answer by josgarithmetic(13975)   (Show Source):

Question 985994: What is the unit rate of 50 miles on 2.5 gallons
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(47455)   (Show Source):
Answer by jim_thompson5910(33401)   (Show Source):
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you want the answer in the form "miles per gallon"

The "per gallon" means "ONE gallon"

Divide both parts of the ratio 50 miles:2.5 gallons by 2.5

50/2.5 = 20
2.5/2.5 = 1

So the ratio 50 miles:2.5 gallons reduces to 20 miles:1 gallon.

Answer: The unit rate is 20 miles per gallon. One gallon of gas will allow you to drive 20 miles.

Question 984740: 925 meter per kilogram to feet per pound
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

Just type your question, exactly as you posted it here, into Google.

John

My calculator said it, I believe it, that settles it

Question 981666: Ed weighs 10 kilograms more than his sister Debbie. Their combined weight is 120 kilograms. How many kilograms does Ed weigh?
Answer by JulietG(1712)   (Show Source):
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E + D = 120 (Their combined weight is 120 kilograms.)
E = D + 10 (Ed weighs 10 kilograms more than his sister Debbie)
Substitute the known value of E from the second equation into the first.
(D+10) + D = 120
2D + 10 = 120
Subtract 10 from each side
2D = 110
Divide each side by 2
D = 55
Debbie weighs 55kg and Ed weighs 65kg

Question 980554: I need to mix a cleaning solution that would spray out of a bottle and contain 70% rubbing alcohol to clean lab surfaces. To save cost, it makes sense to add water to some amount of alcohol yet maintain the 70% level. Average spray bottles likely hold about 25 fl ounces or what about 800 ml? What should my solution look like? Thank you. Leann
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(13975)   (Show Source):
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What are your materials? If you add some amount of water to 70% alcohol, then you will obtain a concentration of alcohol LESS THAN 70%.

If you are starting with 100% alcohol and want to add some water to prepare 25 fluid ounces of 70% alcohol, then ...

v, volume of the "pure" alcohol of 100%;
25-v, volume of the water to add;

Find v, and then find 25-v.

Answer by ankor@dixie-net.com(18980)   (Show Source):
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add water to some amount of alcohol yet maintain the 70% level.
Average spray bottles likely hold about 25 fl ounces or what about 800 ml?
What should my solution look like?
:
let x = amt of alcohol to be removed and amt of water to be added
Lets use an amt of alcohol to be 25 oz
25 - x = .7(25)
25 - x = 17.5
-x = 17.5 - 25
-x = -7.5
x = 7.5 oz of alcohol removed and 7.5 oz of water added maintaining a 25 oz bottle

Question 978743: 85 inches to 12 ft/ 1ft to 3ft/1yard to 0.91m/1yard

Answer by Alan3354(47455)   (Show Source):
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Do you have a question?

Question 978738: 85 inches to feet to yard to meter
Found 2 solutions by Theo, rothauserc:
Answer by Theo(5548)   (Show Source):
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i'll round everything to 6 places.
this should get you an answer accurate to 4 decimal places.

use a conversion table to find feet per inch, yards per feet, meters per yard.

the conversion table will tell you:

1 inch = 1/12 feet.
1 foot = 1/3 yards.
1 yard = .9144 meters.

if 1 inch = 1/12 feet, then 85 inches = 85 * 1/12 = 85/12 feet.

if 1 foot = 1/3 yards, then 85/12 feet = 85/12 * 1/3 = 85/36 yards.

if 1 yard = .9144 meters, then 85/36 yards = 85/36 * .9144 = 77.724/36 = 2.159 meters.

you can check your answer by working backwards from meters to yards to feet to inches.

check your conversion tables again:

my conversion tables showed me:

1 meter = 1.09361 yards
1 yard = 3 feet
1 foot = 12 inches

if 1 meter = 1.09361 yards, then 2.159 meters = 2.159 * 1.09361 = 2.361104 yards.

if 1 yard = 3 feet, then 2.361104 yards = 2.361104 * 3 = 7.083312 feet.

if 1 foot = 12 inches, then 7.083312 feet = 7.083312 * 12 = 84.999744 inches.

the answer isn't right on because of rounding.

the most likely culprit is the conversion from meters to yards and yards to meters.

the conversion table lists 1 yard = .9144 meters.
the conversion table lists 1 meter = 1.09361 yards.

if 1 meter = 1.09361 yards, then divide both sides of this equation by 1.09361 to get:
1 meter / 1.09361 = 1 yard.
simplify to get .914403 meters = 1 yard.

the conversion table said that 1 yard = .9144 meters.
there was some rounding being done.
this threw off the confirmation.
we got close to 85 inches but not right on.
if there was no rounding, we would have been right on.

Answer by rothauserc(2272)   (Show Source):
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85/12 = 7.08 feet
7.08 / 3 = 2.36 yards
2.36 * 0.9144 = 2.16 meters

Question 978507: In a recent year, 6.5x10^8 metric tons of wheat were produced in the world. One metric ton is equivalent to 1000 kilograms. A grain of wheat weighs about .000008 kilograms. Find the number of grains of wheat that were produced in the world.

Sorry, i didn't know what category to place it in! But i think it has something to do with scientific notation. Thanks!! :D

Answer by jim_thompson5910(33401)   (Show Source):
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This is a unit conversion problem.

Given: 6.5 x 10^8 metric tons

Abbreviations for units:
KG = kilogram
MT = metric ton

Conversion factor: 1000 KG/1 MT

Multiply by the conversion factor to go from MT to KG

(6.5 x 10^8 MT) * (1000 KG/1 MT) = (6.5 x 10^8)*(1 x 10^3) = 6.5 x 10^11 KG

Notice how the MT units cancel

So, 6.5 x 10^8 MT = 6.5 x 10^11 KG

-------------------------------------------------------
Now use the fact that "A grain of wheat weighs about .000008 kilograms." to do another conversion

Conversion factor: 1 grain/0.000008 KG

Multiply by the conversion factor to go from KG to number of grains

(6.5 x 10^11 KG)*(1 grain/0.000008 KG)
(6.5 x 10^11 KG)*(1 grain/8*10^(-6) KG)
(6.5/8) x (10^11/10^(-6)) grains
(0.8125) x 10^(11-(-6)) grains
(0.8125) x 10^(11+6) grains
(8.125 x 10^(-1)) x 10^(17) grains
8.125 x 10^(-1+17) grains
8.125 x 10^(16) grains

The answer in scientific notation is 8.125 x 10^(16) grains of wheat

Expand that all out, to write into standard form, to get 81,250,000,000,000,000 grains (8125 followed by 13 zeros) of wheat

Note: In words, that large number above is eighty-one quadrillion, two hundred fifty trillion

Question 978236: 12. Using numbers with units, write an algebraic equation which converts 3.2 gallons to quarts. Carry out the calculation.
Answer by josgarithmetic(13975)   (Show Source):

Question 978235: 11. Write an algebraic expression in w hich you multiply gallons by a factor composed of other units to give a result in quarts.
Answer by jim_thompson5910(33401)   (Show Source):
You can put this solution on YOUR website!
Let
x = number of gallons
y = number of quarts

There are 4 quarts in a gallon. Think "quart" as in "quarter". So you will multiply the gallon amount by the factor "4 quarts/1 gallon". The "gallon" unit in the denominator will cancel with the original "gallon" unit.

This is what it will look like as an equation

So if you know the amount of gallons (x), you can use that equation to find the amount of quarts (y).

Question 978227: 8. Using units (not numbers), write an algebraic equation in which you m ultiply grams by a factor composed of other units to give a result in kilograms. (HINT: grams x ????
= kilograms)

Answer by josmiceli(13716)   (Show Source):
You can put this solution on YOUR website!
[ grams ] x [ kg / gram ] = [ kg ]

Question 974649: F(x)= 5X+15
Answer by Alan3354(47455)   (Show Source):
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F(x)= 5X+15
===================
ok then.
Thx for letting us know.

Question 972327: A boy is t years old, his father is ten years older than twice his son's age. How old is the father?
Answer by stanbon(69061)   (Show Source):
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A boy is t years old, his father is ten years older than twice his son's age. How old is the father?
======
boy = t yrs
---
father = 2t+10
---------------------
Cheers,
Stan H.
---------------

Question 972300: How do you convert something with a radius of 10 feet that makes 6 revolutions/minute to inches per minute? Thank you
Answer by Edwin McCravy(13211)   (Show Source):
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1 revolution's distance in feet = 2*pi*r = 2*pi*10 ft = 20pi ft.

1 revolution's distance in inches = 20pi*12 = 240pi inches

6 revolution's distance in inches = 1440pi inches

6 revolution's distance in inches/minute = 1440pi inches/minute

Edwin

Question 971906: Please, help me convert 30cm to m
Answer by Alan3354(47455)   (Show Source):
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Please, help me convert 30cm to m
---------
That's a tough one.
= 30 cm*(1 m/100 cm)
= 0.3 meters

Question 965124: Not sure if "topic": selection is correct.
how do you figure out the smallest and largest possible perimeters of an area:
i.e. (1) A picture frame has an area of 48 sq inches. What is the largest possible perimeter of the pic frame? (2) A backyard has an area of 64 sq feet. What is the smallest possible perimeter of the backyard?

Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(13975)   (Show Source):
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Question 1 is a rectangular shape that can be analyzed. Question 2 shape is unspecified so is incomplete.

x and y dimensions of the rectangle.
p for perimeter:
and
-

The only method for minimizing or maximizing the perimeter seems to be derivatives.

Finding extreme values, set derivative to zero. Continue other steps.

Denominator cannot be zero, and for derivative be zero, the NUMERATOR must be equated to zero.

, the positive value only.
-

-
and from the original area equation, obviously , making the area shape as a SQUARE shape. The values for MINIMUM perimeter.

Note that you will find this is for MAXIMUM area. Check about the area equation and you should find no minimum.

Here is a graph for the PERIMETER equation, in one or either variable, here being , which shows a MINIMUM for the perimeter:

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
how do you figure out the smallest and largest possible perimeters of an area:
i.e. (1) A picture frame has an area of 48 sq inches. What is the largest possible perimeter of the pic frame?
There is no largest perimeter. It can be 1 by 48 --> 98
Or 0.01 by 4800 --> 9600.02
Or 0.0001 by 480000, etc
--------------------
(2) A backyard has an area of 64 sq feet. What is the smallest possible perimeter of the backyard?
Minimum for a rectangle is a square, 8 by 8 --> 32 ft.
A circle is the minimum, solve for r, then for C.

Question 963022: Use unit multiplier to convert $15 per hour to cents per minute. Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! Use unit multiplier to convert$15 per hour to cents per minute.
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$15 = 1500 cents 1 hour = 60 minutes Question 959154: a) The perimeter of a rectangular field is 120 meters. Its length is 10 meters more than its width. Find the length and width of this rectangle? b) Going for a long trip, Joshua drove for 3 hours and had lunch. After lunch he drove for 4 more hours at a speed that is 10 km/h more than before lunch. The total trip was 600 km. i. What was his speed before lunch? ii. What distance did he drive after lunch? can i have the solution as well. Thanks Answer by rothauserc(2272) (Show Source): You can put this solution on YOUR website! a) Perimeter(P) = 2l +2w where l is length and w is width we are given l = w +10, therefore 2(w+10) + 2w = 120 2w +20 +2w = 120 4w = 100 w = 25 and length is 35 meters and width is 25 meters b) we use the formula rate * time = distance, let r be Joshua's rate before lunch and r+10 is his rate after lunch, therefore 3r + 4(r+10) = 600 3r +4r +40 = 600 7r = 560 r = 80 i) Joshua's speed before lunch is 80 km per hour ii) after lunch, 4(r+10) = 4(80+10) = 360 km Joshua travels 360 km after lunch Question 956848: Accelaration of an object due to gravity is 32feet per second squared, what is accelaration due to gravity in inches per second squared. Answer by macston(4006) (Show Source): Question 956134: A company profits in the year 2000 were 1.5 million dollars. The same company had 10 million dollars in profits in 2013. What is the percent increase in profits from the year 2000 to the year 2013? Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! A company profits in the year 2000 were 1.5 million dollars. The same company had 10 million dollars in profits in 2013. What is the percent increase in profits from the year 2000 to the year 2013? ----- Quantity Increase:: 10-1.5 = 8.5 million Percent Increase:: 8.5/1.5 = 5.667 = 566.67% ------------------------ Cheers, Stan H. --------------- Question 956133: If there are 5280 ft per mile convert 13,600 feet to miles Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! If there are 5280 ft per mile convert 13,600 feet to miles ------------------- You have 2 numbers. Hint: Miles are longer than feet. Question 956117: If there are 2.54 cm per inch convert 271 feet to centimeters Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! If there are 2.54 cm per inch convert 271 feet to centimeters ----------- = 271 ft * 12 in/ft * 2.54 cm/inch ----- Notice how the units cancel if you do it right. Question 955592: The area of a rectangle 18 X -12 in.² write an expression that represents the length of the rectangle Answer by josgarithmetic(13975) (Show Source): You can put this solution on YOUR website! More than one answer. What other information? The area expression has more than one factorization. Question 952404: 190g white flour to cups if 1 cup flour is 125g Answer by macston(4006) (Show Source): You can put this solution on YOUR website! 190 g(1cup/125g)=1.52 cups ANSWER 190 g is 1.52 cups. Question 952485: 2.5qt/min=__gal/h Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! 2.5qt/min=__gal/h ----- 2.5 (quarts/minute)*(1 hr/60 min)*(1 gallon/4 quarts) ====== = (2.5*1*1)/(1*60*4)(gallons/hour) ---- = (2.5/240)(gal/hr) --- = 0.0104 (gal/hr) ----------- Cheers, Stan H. ========= Question 952481: 45mi/h=____Ft/s Convert each unit rate using dimensional analysis Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! 45mi/h=____Ft/s ------------ 45(miles/hour)*(1 hr/3600 sec)(5280 ft/1 mile) ==== = (45*1*5280)/(1*3600*1)(ft/sec) ----- = 66 (ft/sec) -------------- Cheers, Stan H. ----------- Question 951882: The area of a rectangular piece of metal is 30 square centimeters. The piece is 4 centimeters wide. How long is it? Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! The area of a rectangular piece of metal is 30 square centimeters. The piece is 4 centimeters wide. How long is it? ========================= Area = L*W Question 951179: A case of soda contains 24 cans. If a case of soda costs$15.97, how much does each can cost?
Please show the set up.

Answer by rfer(15570)   (Show Source):
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15.97/24=0.665

Question 950906: How do you covert 100 miles per hour to miles per minute ?
Answer by josgarithmetic(13975)   (Show Source):
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The "miles" part stays unchanged.