151 results

feet - Unit of distance measurement, equal to 12 inches

165cm in ft

Using our [URL='http://www.mathcelebrity.com/linearcon.php?quant=165&pl=Calculate&type=centimeter#foot']linear conversion calculator[/URL], we get:
[B]5.41339 feet[/B]

200 feet shorter than the height of a light house

200 feet shorter than the height of a light house
Let the height of a light house be h:
h
200 fee shorter mean we subtract 200 from h:
[B]h - 200[/B]

55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. What is the

55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. What is the length of shadow she will cast?
Set up a proportion of height to shadow length where s is the shadow length of the woman:
55/32 = 5.5/s
[URL='https://www.mathcelebrity.com/prop.php?num1=55&num2=5.5&den1=32&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
s = [B]3.2[/B]

9 workers were hired to harvest potatoes from a field. each is given a plot which is 11*7 feet in si

9 workers were hired to harvest potatoes from a field. each is given a plot which is 11*7 feet in size. what is the total area of the field
The area of each plot is 11*7 = 77
With 9 workers, the total area of the field is:
9 * 77 = [B]693 sq feet[/B]

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6 feet tall. If a person who is 6 feet tall is engaged in a battle with an animal that was proportionally as tall as the person is to the preying mantis, how tall would the animal be?
In terms of inches, [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']6 feet = 72 inches[/URL]
Set up a proportion of height of smaller creature to larger creature where h is the heigh of the animal
1.5/72 = 72/h
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=1.5&num2=72&den1=72&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = 3456 inches
In terms of feet, we have [URL='https://www.mathcelebrity.com/linearcon.php?quant=3456&pl=Calculate&type=inch']3456 inches[/URL] = [B]288 feet[/B]

A 12 feet ladder leans against the side of a house. The bottom of the ladder is 9 feet from the side

A 12 feet ladder leans against the side of a house. The bottom of the ladder is 9 feet from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.
We have a right triangle, where 12 is the hypotenuse. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=9&hypinput=12&pl=Solve+Missing+Side']Using our right triangle calculator[/URL], we get:
side = [B]7.9[/B]

A 15 feet piece of string is cut into two pieces so that the longer piece is 3 feet longer than twic

A 15 feet piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
If the shorter piece is x, the longer piece is 20 - x
We also are given
15 - x = 2x + 3
Add x to each side:
3x + 3 = 15
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B3%3D15&pl=Solve']equation calculator[/URL], we get a shorter piece of:
[B]x = 4[/B]
The longer piece is:
15 - x
15 - 4
[B]11[/B]

A 20 feet piece of string is cut into two pieces so that the longer piece is 5 feet longer than twic

A 20 feet piece of string is cut into two pieces so that the longer piece is 5 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
If the shorter piece is x, the longer piece is 20 - x
We also are given
20 - x = 2x + 5
Add x to each side:
3x + 5 = 20
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B5%3D20&pl=Solve']equation calculator[/URL], we get a shorter piece of:
[B]x = 5
[/B]
The longer piece is:
20 - x
20 - 5
[B]15[/B]

A 3-foot stick casts a shadow of 8 feet. If at the same time a tree casts a shadow of 15 feet, how t

A 3-foot stick casts a shadow of 8 feet. If at the same time a tree casts a shadow of 15 feet, how tall is the tree?
Set up a proportion of height to shadow length where t is the height of a tree:
3/8 = t/15
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=t&den1=8&den2=15&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
t = [B]5.625[/B]

A 5 foot ladder is leaning against a wall. If the bottom of the ladder is 3 feet from the base of th

A 5 foot ladder is leaning against a wall. If the bottom of the ladder is 3 feet from the base of the wall, how high up the wall is the top of the ladder?
The answer is [B]4[/B]. Since we have a right triangle, with special ratio 3-4-5.
The ladder represents the hypotenuse.

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of t

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of the two poles, what is the minimum length of cord you would need?
The difference between the 70 foot and 50 foot pole is:
70 - 50 = 20 foot height difference.
So we have a right triangle, with a height of 20, base of 30. We want to know the hypotenuse.
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=20&side2input=30&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator to solve for hypotenuse[/URL], we get:
hypotenuse = [B]36.06 feet[/B]

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch?

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch?
Using [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']our length converter[/URL], we see that:
7 feet = 84 inches
So $3.36 for 84 inches. We [URL='https://www.mathcelebrity.com/perc.php?num=3.36&den=84&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']divide $3.36 by 84[/URL] to get the cost per inch:
$3.36/84 = [B]0.04 per inch[/B]

a 9-foot rope is cut into two pieces one piece is x feet express the length of the other piece in te

a 9-foot rope is cut into two pieces one piece is x feet express the length of the other piece in terms of x
Piece 1 + Piece 2 = 9
Piece 1 = x
x + Piece 2 = 9
Subtracting x from each side, we get:
x - x + Piece 2 = 9 - x
Cancel the x's on the left side, we get:
Piece 2 = [B]9 - x
[/B]
Check our work:
x + 9 - x ? 9
9 = 9

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purch

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 150 feet.
The area of a rectangle is length * width, so we have:
A = 290 * 150
A = 43,500 sq ft.
Now, to find the number of bags needed for a 300 square feet per bag of fertilizer, we have:
Bags Needed = Total Square Feet of Lawn / Square Feet covered per bag
Bags Needed = 43,500 / 300
Bags Needed = [B]145[/B]

A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height fr

A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. The ball continues to bounce half the height of the previous bounce each time. How far will the ball have traveled when it hits the ground for the fifth time?
Take the top of the bounces one at a time:
[LIST=1]
[*]Ball is dropped 12 feet and it bounces up to 6 feet
[*]Ball drops 6 feet back down and bounces up to 3 feet up
[*]Ball drops 3 feet back down and bounces up to 1.5 feet up
[*]Ball drops 1.5 feet down and bounces up to 0.75 feet up
[*]Return down after Bounce 5 is 0.75 feet down
[/LIST]
[U]Total distance travelled:[/U]
12 + 6 + 6 + 3 + 3 + 1.5 + 1.5 + 0.75 + 0.75
[B]34.5 feet
[MEDIA=youtube]OvDp4Y3vOPY[/MEDIA][/B]

A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-f

A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-fourths the height of the previous bounce. Find the total vertical distance travelled by the all in ten bounces.
The height of each number bounce (n) is shown as:
h(n) = 6(0.75)^n
We want to find h(10)
h(n) = 6(0.75)^n
Time Height
0 6
1 4.5
2 3.375
3 2.53125
4 1.8984375
5 1.423828125
6 1.067871094
7 0.8009033203
8 0.6006774902
9 0.4505081177
10 0.3378810883
Adding up each bounce from 1-10, we get:
16.98635674
Since vertical distance means both [B]up and down[/B], we multiply this number by 2 to get:
16.98635674 * 2 = 33.97271347
Then we add in the initial bounce of 6 to get:
33.97271347 + 6 = [B]39.97271347 feet[/B]

A boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation that rep

A boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation that represents the length y (in feet) of a boa constrictor that is x years old.
8 inches per year = 8/12 feet = 2/3 foot
[B]y = 18 + 2/3x[/B]

A car drives 3 feet the first second, 9 feet in the next second, and 27 feet in the third second. If

A car drives 3 feet the first second, 9 feet in the next second, and 27 feet in the third second. If the pattern stays the same, how far will the car have traveled after 5 seconds, in feet?
Our pattern is found by the distance function D(t), where we have 3 to the power of the time (t) in seconds as seen below:
D(t) = 3^t
The problem asks for D(5):
D(5) = 3^5
[URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=3%5E5&pl=Calculate']D(5)[/URL] = [B]243[/B]

A car travels 71 feet each second.How many feet does it travel in 12 seconds?

A car travels 71 feet each second.How many feet does it travel in 12 seconds?
Distance = Rate * Time
We're given a rate of 71 feet per second and a time of 12 seconds. So we plug this in:
Distance = 71 feet/second * 12 seconds
[URL='https://www.mathcelebrity.com/drt.php?d=+&r=71&t=+12&pl=Calculate+the+missing+Item+from+D%3DRT']Distance[/URL] = [B]852 feet[/B]

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge of 25¢ per square foot for any footage that exceeds 180 sq ft and $1.30 per step for any carpeting on a staircase. A customers cleaning bill was $253.95. This included the cleaning of a staircase with 14 steps. In addition to the staircase, how many square feet of carpet did the customer have cleaned?
Calculate the cost of the staircase cleaning.
Staircase cost = $1.30 * steps
Staircase cost = $1.30 * 14
Staircase cost = $18.20
Subtract this from the cost of the total cleaning bill of $253.95. We do this to isolate the cost of the carpet.
Carpet cost = $253.95 - $18.20
Carpet cost = $235.75
Now, the remaining carpet cost can be written as:
75 + $0.25(s - 180) = $235.75 <-- were s is the total square foot of carpet cleaned
Multiply through and simplify:
75 + 0.25s - 45 = $235.75
Combine like terms:
0.25s + 30 = 235.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B30%3D235.75&pl=Solve']Type this equation into our search engine[/URL] to solve for s, and we get:
s = [B]823[/B]

A chalkboard is 3 feet tall and 4 feet long. What is its perimeter

A chalkboard is 3 feet tall and 4 feet long. What is its perimeter
A chalkboard is a rectangle. So the perimeter is:
2l + 2w
Using [URL='https://www.mathcelebrity.com/rectangle.php?l=4&w=3&a=&p=&pl=Calculate+Rectangle']our rectangle calculator[/URL], we get:
P = [B]14[/B]

A cheetah can run 68 mph. How fast is a cheetah in feet per second

A cheetah can run 68 mph. How fast is a cheetah in feet per second
(68 miles / hour) * (1 hour / 3600 seconds) * (5280 feet / 1 mile) = 68 * 5280 feet per 3600 seconds
395040 feet / 3600 seconds
[B]99.73 feet per second[/B]

A cheetah travels at a rate of 90 feet per second. The distance d traveled by the cheetah is a func

A cheetah travels at a rate of 90 feet per second. The distance d traveled by the cheetah is a function of seconds traveled t. Write a rule for the function. How far will the cheetah travel in 25 seconds?
Distance, or D(t) is expressed as a function of rate and time below:
Distance = Rate x Time
For the cheetah, we have D(t) as:
D(t) = 90ft/sec(t)
The problem asks for D(25):
D(25) = 90(25)
D(25) = [B]2,250 feet[/B]

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallp

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallpaper border are needed to wrap around the entire room?
A rectangle has an Perimeter (P) of:
P = 2l + 2w
We're given l = 17 and w = 15. So we have:
P = 2(17) + 2(15)
P = 34 + 30
P = [B]64[/B]

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box?
Since 1 foot = 12 inches, we have:
2 feet 4 inches = 2(12) + 4
2 feet 4 inches = 24 + 4
2 feet 4 inches = 28 inches
We type [URL='https://www.mathcelebrity.com/cube.php?num=28&pl=Side&type=side&show_All=1']cube side = 28[/URL] into our search engine to get:
V = [B]21952 cubic inches[/B]

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?
Area of a cube is length times width:
A = 8 & 3/4 * 6 & 1/2
We need to convert these to improper fractions.
[LIST]
[*]8 & 3/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%263%2F4&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 35/4
[*]6 & 1/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F2&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 13/2
[/LIST]
Multiply the improper fractions together:
A = 35/4 * 13/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=35%2F4&frac2=13%2F2&pl=Multiply']Using our fraction multiplier[/URL], we get:
[B]455/8 sq ft[/B]
If you want to convert this to a mixed fraction, we [URL='https://www.mathcelebrity.com/fraction.php?frac1=455%2F8&frac2=3%2F8&pl=Simplify']type this in our calculator [/URL]and get:
[B]56 & 7/8 sq ft[/B]

A diving board is 10 feet long and 1 foot wide. What is its area?

A diving board is 10 feet long and 1 foot wide. What is its area?
A diving board is a rectangle. And the area of a rectangle is:
A = lw
Plugging in our numbers, we get:
A = 10(1)
A = [B]10 sq feet[/B]

A dog on a 20-foot long leash is tied to the middle of a fence that is 100 feet long. The dog ruined

A dog on a 20-foot long leash is tied to the middle of a fence that is 100 feet long. The dog ruined the grass wherever it could reach. What is the area of the grass that the dog ruined.
The leash forms a circle where the dog can get to.
A = pi(r)^2
A = 3.1415(20)^2
A = 3.1415 * 400
A = 1256 square feet
The fence blocks off half the circle where the dog can move to, so we have a half-circle area:
A = 1256/2
A = [B]628 square feet[/B]

A family room measures 15.6 feet long and 18.4 feet wide. What is the area of the room?

A family room measures 15.6 feet long and 18.4 feet wide. What is the area of the room?
The room is rectangular. So our area A = lw.
Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=15.6&w=18.4&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get:
A = [B]287.04 square feet[/B]

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants t

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation.
Perimeter of a rectangle:
P = 2l + 2w
We have P = 165 and l = x --> x>50 and width y <= 20. Plug these into the perimeter formula
[B]165 = 2x + 2y where x > 50 and y <= 20[/B]

a firefighter must cut a 2,700 foot rope into 75 equal pieces how long will each be

a firefighter must cut a 2,700 foot rope into 75 equal pieces how long will each be
2700/75 = [B]36 feet per piece[/B]

A flea is very small, but can jump very high. For example, a flea that is 1/8 inch tall can jump 12

A flea is very small, but can jump very high. For example, a flea that is 1/8 inch tall can jump 12 inches in height. If a child who is 4 feet tall had the ability to jump like a flea, how high could she jump?
Set up a proportion of height to jump height where j is the jump height of the child:
1/8/12 = 4/j
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=0.125&num2=4&den1=12&den2=j&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
j = [B]384 feet[/B]

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per foot, what is the cost of the fencing for the garden?
Garden is a rectangle which has Perimeter P of:
P = 2l + 2w
l = 3w
P = 2(3w) + 2w
P = 6w + 2w
P = 8w
Width w = n, so we have:
P = 8n
Cost = 8n * 8 = [B]64n dollars[/B]

A helicopter is flying at an altitude of 785 feet. It descends 570 feet, and then ascends 595 feet.

A helicopter is flying at an altitude of 785 feet. It descends 570 feet, and then ascends 595 feet. Write an expression to represent this situation. Then determine and interpret the sum.
[LIST]
[*]Start at +785 feet
[*]Descend 570 feet means using a minus sign -570
[*]Ascend 595 feet means using a plus sign +595
[/LIST]
[U]Calculate the sum:[/U]
+785 - 570 + 595
[B]+810[/B]

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 2

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 20 feet less than 3 times the width, what are the dimensions of the rectangular plot?
[U]Set up equations:[/U]
(1) 2l + 2w = 800
(2) l = 3w - 20
[U]Substitute (2) into (1)[/U]
2(3w - 20) + 2w = 800
6w - 40 + 2w = 800
[U]Group the w terms[/U]
8w - 40 = 800
[U]Add 40 to each side[/U]
8w = 840
[U]Divide each side by 8[/U]
[B]w = 105
[/B]
[U]Substitute w = 105 into (2)[/U]
l = 3(105) - 20
l = 315 - 20
[B]l = 295[/B]

A hot air balloon at 1120 feet descends at a rate of 80 feet per minute. Let y represent the height

A hot air balloon at 1120 feet descends at a rate of 80 feet per minute. Let y represent the height and let x represent the number of minutes the balloon descends.
Descending means we subtract height, so we have:
[B]y = 1120 - 80x[/B]

A hungry Emperor penguin was swimming 21 feet below sea level. It swam up 9 feet to eat a fish. What

A hungry Emperor penguin was swimming 21 feet below sea level. It swam up 9 feet to eat a fish. What is the position of the penguin now relative to sea level?
21 feet below is written as -21
9 feet up is written as +9
So we have -21 + 9 = [B]-12 or 12 feet below sea level[/B]

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall,

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall, how high up the wall does the ladder reach?
We have a right triangle, where the ladder is the hypotenuse, and we want the measurement of one leg.
Set up the pythagorean theorem with these given items using our P[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=7&hypinput=25&pl=Solve+Missing+Side']ythagorean Theorem Calculator[/URL].
We get Side 1 = [B]24 feet.[/B]

a lion can run 72 feet in one second how far can the lion run in one minute

a lion can run 72 feet in one second how far can the lion run in one minute?
Using our [URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=minute']time conversions calculator by typing [I]1 minute[/I] into our search engine[/URL], we see:
1 minute = 60 seconds
So 72 feet per second * 60 seconds / minute = [B]4,320 feet / minute[/B]

A man is swimming at 10 feet below sea level. Then he descends 1 feet and then ascends 5 feet. What

A man is swimming at 10 feet below sea level. Then he descends 1 feet and then ascends 5 feet. What is the man's new location?
10 feet below sea level is written as -10
He descends 1 foot. Since descending is negative depth, we have:
-10 - 1 = -11
Then he ascends 5 feet, so we add:
-11 + 5 = [B]-6 or 6 feet below sea level[/B]

A mountain with a base 6684 feet below sea level rises 22304 feet. What is the elevation above sea l

A mountain with a base 6684 feet below sea level rises 22304 feet. What is the elevation above sea level of its peak?
Below sea level is written as a negative, so we have:
-6684 + 22304 = [B]15,620 feet above sea level[/B]

A park bench is 6 feet long. Convert the length to inches

A park bench is 6 feet long. Convert the length to inches
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']type in 6 feet into our search engine[/URL]. We get:
6 feet = [B]72 inches[/B]

A plane is flying at an altitude of 45,000 feet. It begins to drop in altitude 3,000 feet per minute

A plane is flying at an altitude of 45,000 feet. It begins to drop in altitude 3,000 feet per minute. What is the slope in this situation?
Set up a graph where minutes is on the x-axis and altitude is on the y-axis.
[LIST=1]
[*]Minute 1 = (1, 42,000)
[*]Minute 2 = (2, 39,000)
[*]Minute 3 = (3, 36,000)
[*]Minute 4 = (4, 33,000)
[/LIST]
You can see for every 1 unit move in x, we get a -3,000 unit move in y.
Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=42000&slope=+2%2F5&xtwo=2&ytwo=39000&bvalue=+&pl=You+entered+2+points']use our slope calculator[/URL] to get:
Slope = -[B]3,000[/B]

A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, r

A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, running at a rate of 5 feet per second. The cop is running at a rate of 6.5 feet per second. How many seconds will it take for the police officer to catch the criminal?
Distance = Rate * Time
[U]Criminal:[/U]
5t + 20
[U]Cop[/U]:
6.5t
We want to know when their distances are the same (cop catches criminal). So we set the equations equal to each other:
5t + 20 = 6.5t
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=5t%2B20%3D6.5t&pl=Solve']we type it in our search engine[/URL] and we get:
t = 13.333 seconds

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 fe

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 feet longer than the width, then how wide is the field?
We're given:
[LIST=1]
[*]l = w + 40
[/LIST]
And we know the perimeter of a rectangle is:
P = 2l + 2w
Substitute (1) into this formula as well as the given perimeter of 1120:
2(w + 40) + 2w = 1120
Multiply through and simplify:
2w + 80 + 2w = 1120
Group like terms:
4w + 80 = 1120
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B80%3D1120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 260[/B]

A rectangular prism has a width of x feet, a length of y feet, and a height of h feet. Express its v

A rectangular prism has a width of [I]x[/I] feet, a length of [I]y[/I] feet, and a height of [I]h[/I] feet. Express its volume in square inches.
V = width * length * height
V = xyh
12 inches to a foot, so:
In cubic feet, we have 12 * 12 * 12 = 1728 cubic inches
V [B]= 1728xyh[/B]

A right triangle has legs of 9 feet and 12 feet. How long is the hypotenuse?

A right triangle has legs of 9 feet and 12 feet. How long is the hypotenuse?
A common right triangle ratio is 3:4:5
9 = 3 * 3
12 = 3 * 4
3 * 5 = 15, so we have [B]15 feet[/B]

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will excee

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will exceed flood stage. How long can the river rise at this rate without exceeding flood stage?
Let the number of inches be i. Remember 12 inches to a foot, so we have 2 feet = 12*2 = 24 inches.
[LIST]
[*]Inequality: 3i <= 24. (since more than means the river can go [U]up to[/U] 2 feet or 24 inches
[/LIST]
To solve the inequality for I, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3i%3C%3D24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]I <= 8
This means after 8 hours, the river will flood[/B]

A robot runs 6 feet in a second. How many feet can it run in a minute?

A robot runs 6 feet in a second. How many feet can it run in a minute?
6 feet / second * 60 seconds / minute =[B] 360 feet / minute[/B]

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the coaster after the first descent.
90 feet above and then we descend 105 feet, meaning we subtract:
90 - 105 = -15.
We read this [B]15 feet below ground level[/B]

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the roller coaster after the first descent.
90 feet above ground level is written as +90
Descending 105 feet means we subtract 105 feet to get:
+90 - 105 = [B]-15 or 15 feet below ground level[/B]

A roof drops 4 feet for every 12 feet forward. Determine the slope of the roof.

A roof drops 4 feet for every 12 feet forward. Determine the slope of the roof.
Slope = Rise or Drop / Run
Slope = 4/12
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F12&frac2=3%2F8&pl=Simplify']type 4/12 into our search engine[/URL] and get:
Slope. = [B]1/3[/B]

A room is 15 ft long and 12 feet wide. What are the length and width of the room in yards?

A room is 15 ft long and 12 feet wide. What are the length and width of the room in yards?
Since 3 feet = 1 yard, we have:
Length in yards = Length in feet / 3
Length in yards = 15/3
Length in yards = 5
Width in yards = Width in feet / 3
Width in yards = 12/3
Width in yards = 4

A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 10

A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds later. At what rate is the scuba diver going deeper down in the water
If we take these as coordinates on a graph, where y is the depth and x is the time, we calculate our slope or rate of change where (x1, y1) = (10, 30) and (x2, y2) = (40, 100)
Rate of change = (y2 - y1)/(x2 - x1)
Rate of change = (100 - 30)/(40 - 10)
Rate of change = 70/30
Rate of change =[B] 2.333 feet per second[/B]

A skydiver falls 144 feet in three seconds. How far does the skydiver fall per second?

A skydiver falls 144 feet in three seconds. How far does the skydiver fall per second?
144 feet/3 seconds
Divide top and bottom by 3 to get feet per second
[B]48 feet per second[/B]

A spacecraft with a volume of 800 cubic feet is leaking air at a rate of .4 cubic feet every n minut

A spacecraft with a volume of 800 cubic feet is leaking air at a rate of .4 cubic feet every [I]n[/I] minutes. How many minutes until the spacecraft has no air?
800 cubic feet / .4 cubic feet every n minutes = 2000 (n minute parts)
Total time = [B]2000n[/B]

A stack of lumber is 8 feet wide, 5 feet high, and 2 feet long. Give the volume of the stack

A stack of lumber is 8 feet wide, 5 feet high, and 2 feet long. Give the volume of the stack
The lumber stack is a rectangular solid. The Volume V is found from the length (l), width (w), and height (h) by:
V = lwh
Plugging in our given values, we get:
V = 2 * 8 * 5
V = [B]80 cubic feet[/B]

A stick that is ten feet tall casts a shadow of 12 feet. If a tree has a 96 foot shadow, how tall is

A stick that is ten feet tall casts a shadow of 12 feet. If a tree has a 96 foot shadow, how tall is the tree?
Set up a proportion of wood height to shadow length where h is the height of the tree:
10/12 = h/96
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=10&num2=h&den1=12&den2=96&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = [B]80 feet[/B]

A straight road to the top of a hill is 2500 feet long and makes an angle of 12 degrees with the hor

A straight road to the top of a hill is 2500 feet long and makes an angle of 12 degrees with the horizontal. Find the height of the hill.
Height = Distance * Sin(Horizon Angle)
Height = 2500 * [URL='http://www.mathcelebrity.com/anglebasic.php?entry=12&coff=&pl=sin']Sin(12)[/URL]
Height = 2500 * 0.207911691
Height = [B]519.78 feet[/B]

A street sign is 85 inches tall. How tall is it in feet and inches?

A street sign is 85 inches tall. How tall is it in feet and inches?
Since 12 inches is a foot, we have:
12 goes into 85 7 times remainder 1
So we have [B]7 feet, 1 inch[/B]

A student was trying to determine a formula for changing speeds that are written in feet per second

A student was trying to determine a formula for changing speeds that are written in feet per second into miles per hour. If a sprinter runs at a speed of n feet per second, what is her speed in miles per hour?
3600 seconds per hour = 3600n feet per hour
5280 feet per mile so we have:
3600n feet per hour / 5280 feet per mile = [B]0.6818n feet per second[/B]

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 met

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 meters, what is its new position?
240 meters below sea level means a negative number, so we start with:
-240
Descending 160 meters means our depth decreases, so we subtract:
-240 - 160 = -400
Ascends means our depth increases, so we add:
-400 + 390 = [B]-10 or 10 feet below sea level
[MEDIA=youtube]ngToCpLBgH4[/MEDIA][/B]

a submarine is 450 feet below sea level. It descends 300 feet. What is its new position?

a submarine is 450 feet below sea level. It descends 300 feet. What is its new position?
We start at 450 feet below sea level. We descend another 300 feet, so we're now at:
-450 - 300 = -750
Negative depth means below sea level, so the submarine is at [B]750 feet below sea level[/B]

A submarine is 75 feet below sea level. It descends another 25 feet every 10 seconds for 3 minutes.

A submarine is 75 feet below sea level. It descends another 25 feet every 10 seconds for 3 minutes. What integer represents the submarines current location?
Assumptions and givens:
[LIST]
[*]Let m be the number of minutes
[*]10 seconds is 1/6 of a minute, 6 (10) seconds blocks per minute * 3 minutes = 18 (10 second blocks)
[*]Below sea level is a negative number
[/LIST]
[U]Current depth:[/U]
-25(18) - 75
-450 - 75
[B]-525[/B]

A tree is 23.1 feet tall. What is its height in meters ? Use the following conversion: 1 meter is 3.

A tree is 23.1 feet tall. What is its height in meters ? Use the following conversion: 1 meter is 3.3 feet
23.1 feet * 1 meter / 3.3 feet = [B]7 meters[/B]

A trench is 40 feet long and the trencher goes 2 feet per minute. How long does it take to dig the

A trench is 40 feet long and the trencher goes 2 feet per minute. How long does it take to dig the trench?
2 feet per minute * x minutes = 40 feet
Divide each side by 2
[B]x = 20 minutes[/B]

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continuous at a constant speed of 40 feet per minute for the last 50 feet.
(i) Determine which animal won the race.
(ii). By how much time the animal won the race.
(iii) Explain one life lesson from the race.
We know the distance formula is:
d = rt
For the turtle, he has a rate (r) of 20 feet / minute and distance (d) of 100. We want to solve for time:
[URL='https://www.mathcelebrity.com/drt.php?d=+100&r=+20&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 5
The rabbit has 3 parts of the race:
Rabbit Part 1: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Rabbit Part 2: The rabbit stops for 3 minutes (t = 3)
Rabbit Part 3: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Total time for the rabbit from the 3 parts is (t) = 1.25 + 3 + 1.25
Total time for the rabbit from the 3 parts is (t) = 5.5
[LIST]
[*](i) The [B]turtle won[/B] the race because he took more time to finish and they both started at the same time
[*](ii) We subtract the turtles time from the rabbit's time: 5.5 - 5 = [B]0.5 minutes which is also 30 seconds[/B]
[*](iii) [B]Slow and Steady wins the race[/B]
[/LIST]

a well driller charges $9.00 per foot for the first 10 feet, 9.10 per foot for the next 10 feet, $9.

a well driller charges $9.00 per foot for the first 10 feet, 9.10 per foot for the next 10 feet, $9.20 per foot for the next 10 feet, and so on, at a price increase of $0.10 per foot for succeeding intervals of 10 feet. How much does it cost to drill a well to a depth of 150 feet?
Set up the cost function C(f) where f is the number of feet:
Cost = 9(10) + 9.1(10) + 9.2(10) + 9.3(10) + 9.4(10) + 9.5(10) + 9.6(10) + 9.7(10) + 9.8(10) + 9.9(10) + 10(10) + 10.1(10) + 10.2(10) + 10.3(10) + 10.4(10)
Cost = [B]1,455[/B]

A wide receiver sprints at a speed of 8.6 feet per second. How many feet would he expect the wide re

A wide receiver sprints at a speed of 8.6 feet per second. How many feet would he expect the wide receiver to run in 25 seconds?
8.6 feet per second * 25 seconds = [B]212.5 feet[/B]

A yardstick casts a shadow of 8 inches. At the same time, a tree casts a shadow of 52 feet. How tall

A yardstick casts a shadow of 8 inches. At the same time, a tree casts a shadow of 52 feet. How tall is the tree?
Setup a proportion of height to shadow distance where h is the height of the tree:
36/8 = h/52
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=36&num2=h&den1=8&den2=52&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = [B]234 feet[/B]

A young dad, who was a star football player in college, set up a miniature football field for his fi

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true?
The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway.
Imagine a third post midway between the two goal posts. It has the same height as the two goalposts.
From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

Allan built an additional room onto his house. The length of the room is 3 times the width. The peri

Allan built an additional room onto his house. The length of the room is 3 times the width. The perimeter of the room is 60 feet. What is the length of the room
A room is a rectangle. We know the perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]l = 3w
[*]P = 60
[/LIST]
Plug (1) and (2) into our rectangle perimeter formula:
2(3w) + w = 60
6w + w = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2Bw%3D60&pl=Solve']Type this equation into our search engine[/URL] to solve for w:
w = 8.5714
Now plug w = 8.5714 into equation 1 to solve for l:
l = 3(8.5714)
l = [B]25.7142[/B]

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 18

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 1800 feet per minute. Let m be the number of minutes. Which of the following expressions describe the height of the airplane after any given number of minutes?
Let m be the number of minutes. Since a descent equals a [U]drop[/U] in altitude, we subtract this in our Altitude function A(m):
[B]A(m) = 38,800 - 1800m[/B]

An alligators tail length, T, varies directly as its body length, B. An alligator with a body length

An alligators tail length, T, varies directly as its body length, B. An alligator with a body length of 5.6 feet has a tail length of 4.9 feet. What is the tail length of an alligator whos body length is 4.8 feet
Set up a proportion of T/B
5.6/4.9 = t/4.8
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=5.6&num2=t&den1=4.9&den2=4.8&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]t = 5.49[/B].

An electrician starts off the day with 600 feet of copper wiring on his truck. During the course of

An electrician starts off the day with 600 feet of copper wiring on his truck. During the course of the day he uses pieces 100, 82, 25, and 40 feet long. The next day, he purchases another 400 feet and puts it on his truck and later in the day uses pieces of 41, 39, and 44 feet long. How many feet of wiring are still on the truck at the end of the second day?
If the electrician uses pieces, we subtract. If he purchases pieces, we add. So we have:
600 - 100 - 82 - 25 - 40 + 400 - 41 - 39 - 44 = [B]629 feet[/B]

Anna painted 1/6 of a wall, Eric painted 1/5 of the wall, and Meadow painted 1/4 of the wall. There

Anna painted 1/6 of a wall, Eric painted 1/5 of the wall, and Meadow painted 1/4 of the wall. There are now 3910 square feet left to paint. How many square feet did Anna paint?
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=5&num3=6&pl=LCM']Using 60 as a common denominator through least common multiple[/URL], we get:
1/6 = 10/60
1/5 = 12/60
1/4 = 15/60
10/60 + 12/60 + 15/60 = 37/60
Remaining part of the wall is 60/60 - 37[B]/[/B]60 = 23/60
3910/23 = 170 for each 1/60 of a wall
Anna painted 1/6 or 10/60 of the wall. So we multiply 170 * 10 = [B]1,700 square feet[/B]

anne is building bookcases that are 3.4 feet long. How many complete shelves can be cut from a 12-fo

anne is building bookcases that are 3.4 feet long. How many complete shelves can be cut from a 12-foot board?
We divide 12 feet of board by 3.4 per bookcase and we get:
12/3.4 = 3.52
So complete boards = [B]3[/B]

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure 6 inches wide by 2 feet long, how many boards will she need to complete the job?
Area of platform which is a rectangle:
A = lw
A = 10 * 7
A = 70
Area of boards which are rectangles:
A = lw
A = 2 * 6
A = 12
We divide our platform area by our board area to get the number of boards needed:
Boards needed = Platform Area / Board Area
Boards needed = 70/12
Boards needed = 5.83333
We round up if we want full boards to be [B]6[/B]

At 2:18 Pm, a parachutist is 4900 feet above the ground. At 2:32 pm, the parachutist is 2100 above t

At 2:18 Pm, a parachutist is 4900 feet above the ground. At 2:32 pm, the parachutist is 2100 above the ground. Find the average rate of change in feet per minute
Average Rate of Change = Change in Distance / Change in time
Average Rate of Change = (4900 - 2100) / (2:32 - 2:18)
Average Rate of Change = 2800 / 14
Average Rate of Change = [B]200 feet per minute[/B]

Bill raises the flag 15 feet above the ground. Then he lowers it 8 feet and raises it another 2 feet

Bill raises the flag 15 feet above the ground. Then he lowers it 8 feet and raises it another 2 feet. how far above the ground is the flag now?
We tally up the positives and negatives:
Raise = +15
Lower = -8
Raise = +2
Total = +15 - 8 + 2
Total = [B]9 feet above the ground[/B]

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 fe

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W.
Plugging our numbers in for P = 22 and L = 5, we get:
22 = 2(5) + 2W
22 = 10 + 2w
Rewritten, we have:
10 + 2w = 22
[URL='https://www.mathcelebrity.com/1unk.php?num=10%2B2w%3D22&pl=Solve']Plug this equation into the search engine[/URL], we get:
[B]w = 6[/B]

Building A is 150 feet shorter than Building B. The height of both building is 1530 feet. Find the h

Building A is 150 feet shorter than Building B. The height of both building is 1530 feet. Find the height of both building A and B.
Let a be the height of building A
Let b be the height of building B
We're given two equations:
[LIST=1]
[*]a = b - 150
[*]a + b = 1530
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for a:
(b - 150) + b = 1530
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b-150%2Bb%3D1530&pl=Solve']type it in our search engine[/URL] and we get:
b = [B]840[/B]
To solve for a, we substitute b = 840 into equation (1):
a = 840 - 150
a = [B]690[/B]

DeAndre is a spelunker (someone who explores caves). One day DeAndre is exploring a cave that has a

DeAndre is a spelunker (someone who explores caves). One day DeAndre is exploring a cave that has a series of ladders going down into the depths. Every ladder is exactly 10 feet tall, and there is no other way to descend or ascend (the other paths in the cave are flat). DeAndre starts at 186 feet in altitude, and reaches a maximum depth of 86 feet in altitude.Write an equation for DeAndre's altitude, using x to represent the number of ladders DeAndre used (hint: a ladder takes DeAndre down in altitude, so the coefficient should be negative).
Set up a function A(x) for altitude, where x is the number of ladders used. Each ladder takes DeAndre down 10 feet, so this would be -10x. And DeAndre starts at 186 feet, so we'd have:
[B]A(x) = 186 - 10x[/B]

Death Valley in California is 282 feet below sea level. Grant Hill Park, which is right across from

Death Valley in California is 282 feet below sea level. Grant Hill Park, which is right across from our school is 167 feet above sea level. How many feet higher is Grant Hill compared to Death Valley?
Below sea level is written as a negative, so we have:
Difference in feet = 282 - (-167)
Difference in feet = [B]449 feet[/B]

Determine a conversion ratio that could be used to convert miles to inches

Determine a conversion ratio that could be used to convert miles to inches.
We know that 1 mile equals 5,280 feet.
We know that 1 foot equals 12 inches.
So 1 miles = 5,280 feet * 12 inches per foot= [B]63,360 inches[/B]

During a performance, a juggler tosses one ball straight upward while continuing to juggle three oth

During a performance, a juggler tosses one ball straight upward while continuing to juggle three others. The height f(t), in feet, of the ball is given by the polynomial function f(t) = ?16t^2 + 26t + 3, where t is the time in seconds since the ball was thrown. Find the height of the ball 1 second after it is tossed upward.
We want f(1):
f(1) = ?16(1)^2 + 26(1) + 3
f(1) = -16(1) + 26 + 3
f(1) = -16 + 26 + 3
f(1) = [B]13[/B]

Erica is 5 feet tall and has a shadow of 2 feet. A nearby tree has a shadow of 18 feet. How tall is

Erica is 5 feet tall and has a shadow of 2 feet. A nearby tree has a shadow of 18 feet. How tall is the tree?
Set up a proportion of feet tall to shadow height where n is the height of the tree
5/2 = n/18
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5&num2=n&den1=2&den2=18&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
n =[B]45 feet[/B]

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in the center and when she had painted a circle with a 5-foot diameter, she used one quart of paint. How many more quarts of paint must Fantasia buy to finish her room?
The area formula for a circle is:
Area = pir^2
Area of full room
Radius = D/2
Radius = 25/2
Radius = 12.5
Area = 3.1415 * 12.5 * 12.5
Area = 490.625
Area of 5-foot diameter circle
Radius = D/2
Radius = 5/2
Radius = 2.5
Area = 3.1415 * 2.5 * 2.5
Area = 19.625
So 1 quart of paint covers 19.625 square feet
Area of unpainted room = Area of Room - Area of 5-foot diameter circle
Area of unpainted room = 490.625 - 19.625
Area of unpainted room = 471
Calculate quarts of paint needed:
Quarts of paint needed = Area of unpainted Room / square feet per quart of paint
Quarts of paint needed = 471/19.625
Quarts of paint needed = [B]24 quarts[/B]

fifty feet less than 2n feet

fifty feet less means we subtract 50 from 2n.
2n - 50

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley 216 feet below sea level.
Below sea level is the same as being on the opposite side of zero on the number line. To get the difference, we do the following:
1,684 - (-216)
Since subtracting a negative is a positive, we have:
1,684 + 216
[B]1,900 feet[/B]

Find the volume of the box. The box shows the length is 6 feet, the width is 4 feet, and the height

Find the volume of the box. The box shows the length is 6 feet, the width is 4 feet, and the height is 3 feet.
The shape is a rectangular solid. The Volume (V) is shown below:
V = lwh
V = 6 * 4 * 3
V = [B]72 cubic feet[/B]

Five one -foot rulers laid end to end reach how many inches?

Five one -foot rulers laid end to end reach how many inches?
Since [URL='https://www.mathcelebrity.com/linearcon.php?quant=5&pl=Calculate&type=foot']1 foot = 12 inches from our conversion calculator[/URL], we have:
5 feet = [B]60 inches[/B]

For the first 10 seconds of the ride, the height of the coaster can be determined by h(t) = 0.3t^3 -

For the first 10 seconds of the ride, the height of the coaster can be determined by h(t) = 0.3t^3 - 5t^2 + 21t, where t is the time in seconds and h is the height in feet. classify this polynomial by degree and by number of terms.
[URL='http://www.mathcelebrity.com/polynomial.php?num=0.3t%5E3-5t%5E2%2B21t&pl=Evaluate']Using our polynomial calculator, we determine[/URL]:
[LIST]
[*]The degree of the polynomial is 3
[*]There are 3 terms
[/LIST]

Frequency and Wavelength and Photon Energy

Free Frequency and Wavelength and Photon Energy Calculator - Provides the following 3 items using the speed of light and Plancks constant (h):

- Given a frequency of centimeters, feet, meters, or miles the calculator will determine wavelength in Hz, KHz, MHz, GHz

- Given a wavelength of Hz, KHz, MHz, GHz, the calculator will determine frequency in centimeters, feet, meters, or miles

- Calculates photon energy

- Given a frequency of centimeters, feet, meters, or miles the calculator will determine wavelength in Hz, KHz, MHz, GHz

- Given a wavelength of Hz, KHz, MHz, GHz, the calculator will determine frequency in centimeters, feet, meters, or miles

- Calculates photon energy

From 187 feet below sea level, Paul took off in his helicopter and ascended 613 feet. What is Pauls

From 187 feet below sea level, Paul took off in his helicopter and ascended 613 feet. What is Pauls elevation now?
Sea Level is 0 feet. 187 feet below sea level = -187 feet.
So we have 613 - 187 = [B]426 feet above sea level[/B].

George and William both ran a one mile race. William won the race with a time of 4 minutes and 30 se

George and William both ran a one mile race. William won the race with a time of 4 minutes and 30 seconds. If George was 480 feet behind William when the race finished, how long did it take George to run the entire mile? (George continued to run at the same pace.)
When the race was done, George completed:
5280 feet in a mile - 480 feet = 4800 feet
set up a proportion of distance traveled to time where n is the time needed to run the mile
4800/4.5 = 5280/n
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=4800&num2=5280&den1=4.5&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = 4.95
5280/4800 = 1.1
Setup another proportion with the 1.1 factor of distance to time:
4800 * 1.1/4.5 * 1.1 = 5280/4.95
4.95 = 4 minutes and .95*60 seconds
4.95 = [B]4 minutes and 57 seconds[/B]

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking a

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take until they're at the same altitude?
Set up the Altitude function A(m) where m is the number of minutes that went by since now.
Set up Graham's altitude function A(m):
A(m) = 14040 - 50m <-- we subtract for descending
Set up Max's altitude function A(m):
A(m) = 12500 + 20m <-- we add for ascending
Set the altitudes equal to each other to solve for m:
14040 - 50m = 12500 + 20m
[URL='https://www.mathcelebrity.com/1unk.php?num=14040-50m%3D12500%2B20m&pl=Solve']We type this equation into our search engine to solve for m[/URL] and we get:
m = [B]22[/B]

heat loss of a glass window varies jointly as the window's area and the difference between the outsi

heat loss of a glass window varies jointly as the window's area and the difference between the outside and the inside temperature. a window 6 feet wide by 3 feet long loses 1,320 btu per hour when the temperature outside is 22 degree colder than the temperature inside.
Find the heat loss through a glass window that is 3 feet wide by 5 feet long when the temperature outside is 9 degree cooler than the temperature inside.
Find k of the equation:
6*3*22*k = 1320
396k = 1,320
k = 3.33333 [URL='https://www.mathcelebrity.com/1unk.php?num=396k%3D1320&pl=Solve']per our equation solver[/URL]
Now, find the heat loss for a 3x5 window when the temperature is 9 degrees cooler than the temperature inside:
3*5*9*3.333333 = [B]450 btu per hour[/B]

How many feet are in y yards?

How many feet are in y yards?
1 yard = 3 feet
y yards = 3 feet * y
y yards = [B]3y[/B]

How many square feet are in a square yard?

How many square feet are in a square yard?
A square yard = 1 yard * 1 yard
Since 1 yard = 3 feet, we have:
A square yard = 3 feet * 3 feet = [B]9 feet[/B]

If 800 feet of fencing is available, find the maximum area that can be enclosed.

If 800 feet of fencing is available, find the maximum area that can be enclosed.
Perimeter of a rectangle is:
2l + 2w = P
However, we're given one side (length) is bordered by the river and the fence length is 800, so we have:
So we have l + 2w = 800
Rearranging in terms of l, we have:
l = 800 - 2w
The Area of a rectangle is:
A = lw
Plug in the value for l in the perimeter into this:
A = (800 - 2w)w
A = 800w - 2w^2
Take the [URL='https://www.mathcelebrity.com/dfii.php?term1=800w+-+2w%5E2&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']first derivative[/URL]:
A' = 800 - 4w
Now set this equal to 0 for maximum points:
4w = 800
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%3D800&pl=Solve']Typing this equation into the search engine[/URL], we get:
w = 200
Now plug this into our perimeter equation:
l = 800 - 2(200)
l = 800 - 400
l = 400
The maximum area to be enclosed is;
A = lw
A = 400(200)
A = [B]80,000 square feet[/B]

If cement cost $4 per cubic foot, how much does a cubic yard of cement cost?

If cement cost $4 per cubic foot, how much does a cubic yard of cement cost?
There are 3 feet in a yard
3 x 3 x 3 = 27 cubic feet in a yard
Total cost = 27 cubic feet * $4 per cubic foot = [B]$108[/B]

If Enika walked n yards, how many feet did she walk?

If Enika walked n yards, how many feet did she walk?
1 yard = 3 feet, so we have:
n yards = [B]3n feet[/B]

If the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of pi

If the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of pi
C = 2pir, so we have:
C = 16?
16? = 2?r
Divide each side by 2?:
r = 16?/2?
r = 8
Now, the area of a circle A is denoted below:
A = ?r^2
Given r = 8 from above, we have:
A = ?(8)^2
A = [B]64?[/B]

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide must the field be?
The perimeter of a rectangle P, is denoted as:
P = 2l + 2w
We're given l = 25, and P = 120, so we have
2(25) + 2w = 120
Simplify:
2w + 50 = 120
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B50%3D120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 35[/B]

In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs

In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 16 feet of fence for the shortest side and 20 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
Using our [URL='https://www.mathcelebrity.com/righttriangle.php?angle_a=&a=&angle_b=&b=16&c=20&pl=Calculate+Right+Triangle']right triangle calculator[/URL]:
Remaining side = 12
Total fencing needed is 16 + 20 + 12 = [B]48 feet of fencing[/B]

It is recommended that a ladder be placed 2 feet away from the Wall for every 5 feet of height. How

It is recommended that a ladder be placed 2 feet away from the Wall for every 5 feet of height. How far from the Wall should a 20 foot ladder be placed?
Set up a proportion:
2ft away from the wall / 5ft = (x)ft away from the wall / 20ft
[URL='http://www.mathcelebrity.com/prop.php?num1=2&num2=x&den1=5&den2=20&propsign=%3D&pl=Calculate+missing+proportion+value']Run this proportion through our calculator by typing[/URL]: 2/5=x/20
x = [B]8 ft[/B]

It took 3.5 gallons of paint to cover a wall that is 985 square feet. How many gallons will it take

It took 3.5 gallons of paint to cover a wall that is 985 square feet. How many gallons will it take to cover a wall that is 6501 square feet?
Set up a proportion of gallons of paint to square feet where n is the number of gallons of paint to cover 6501 square feet
3.5/985 = n/6501
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3.5&num2=n&den1=985&den2=6501&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
n = [B]23.1[/B]

Janet would like to put up a straight 100 foot fence. If she places a post every 10 feet, how many p

Janet would like to put up a straight 100 foot fence. If she places a post every 10 feet, how many posts will she need?
[LIST=1]
[*]0 feet
[*]10 feet
[*]20 feet
[*]30 feet
[*]40 feet
[*]50 feet
[*]60 feet
[*]70 feet
[*]80 feet
[*]90 feet
[*]100 feet
[/LIST]
[B]11 posts[/B]

Janey is n feet tall. How many inches tall is she?

Janey is n feet tall. How many inches tall is she?
1 foot = 12 inches
n feet = [B]12n[/B] inches

Jethro wants a swimming pool in his backyard, so he digs a rectangular hole with dimensions 40 feet

Jethro wants a swimming pool in his backyard, so he digs a rectangular hole with dimensions 40 feet long, 20 feet wide, and 5 feet deep. How many cubic feet of water will the pool hold?
This is a rectangular solid. The volume is l x w x h:
V = 40 x 20 x 5
V = [B]4,000 cubic feet[/B]

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft squared. What are the dimensions of the kennel? How many feet of fencing did she use? Explain.
Area of a square with side length (s) is:
A = s^2
Given A = 64, we have:
s^2 = 64
[URL='https://www.mathcelebrity.com/radex.php?num=sqrt(64%2F1)&pl=Simplify+Radical+Expression']Typing this equation into our math engine[/URL], we get:
s = 8
Which means the dimensions of the kennel are [B]8 x 8[/B].
How much fencing she used means perimeter. The perimeter P of a square with side length s is:
P = 4s
[URL='https://www.mathcelebrity.com/square.php?num=8&pl=Side&type=side&show_All=1']Given s = 8, we have[/URL]:
P = 4 * 8
P = [B]32[/B]

Katie bought a ribbon that was 4 feet long. How many inches long was Katie’s ribbon?

Katie bought a ribbon that was 4 feet long. How many inches long was Katie’s ribbon?
1 foot = 12 inches so we have:
4 feet * 12 inches / foot = [B]48 inches[/B]

Keith is cutting two circular table tops out of a piece of plywood. the plywood is 4 feet by 8 feet

Keith is cutting two circular table tops out of a piece of plywood. the plywood is 4 feet by 8 feet and each table top has a diameter of 4 feet. If the price of a piece of plywood is $40, what is the value of the plywood that is wasted after the table tops are cut?
Area of the plywood = 4 * 8 = 32 square feet
[U]Calculate area of 1 round top[/U]
Diameter = 2
Radius = Diameter/2 = 4/2 = 2
Area of each round top = pir^2
Area of each round top = 3.14 * 2 * 2
Area of each round top = 12.56 square feet
[U]Calculate area of 2 round tops[/U]
Area of 2 round tops = 12.56 + 12.56
Area of 2 round tops = 25.12 sq feet
[U]Calculate wasted area:[/U]
Wasted area = area of the plywood - area of 2 round tops
Wasted area = 32 - 25.12
Wasted area = 6.88 sq feet
[U]Calculate cost per square foot of plywood:[/U]
Cost per sq foot of plywood = Price per plywood / area of the plywood
Cost per sq foot of plywood = 40/32
Cost per sq foot of plywood = $1.25
[U]Calculate the value of the plywood:[/U]
Value of the plywood = Wasted Area sq foot * Cost per sq foot of plywood
Value of the plywood = 6.88 * 1.25
Value of the plywood = [B]$8.60[/B]

Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10

Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10 feet, how many posts will she need?
Perimeter (P) of a square with side s:
P = 4s
Given s = 40, we have:
P = 4(40)
P = 160 feet
160 feet / 10 foot spaces = [B]16 posts[/B]

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden or a round garden with the fencing.
Laura did some calculations and found that a circular garden would give her 1380 more square feet than a square garden. How many feet of fencing were in the roll that Laura found? (Round to the nearest foot.)
Feet of fencing = n
Perimeter of square garden = n
Each side of square = n/4
Square garden's area = (n/4)^2 = n^2/16
Area of circle garden with circumference = n is:
Circumference = pi * d
n = pi * d
Divide body tissues by pi:
d = n/pi
Radius = n/2pi
Area = pi * n/2pi * n/2pi
Area = pin^2/4pi^2
Reduce by canceling pi:
n^2/4pi
n^2/4 * 3.14
n^2/12.56
The problem says that the difference between the square's area and the circle's area is equal to 1380 square feet.
Area of Circle - Area of Square = 1380
n^2/12.56 - n^2/16 = 1380
Common denominator = 200.96
(16n^2 - 12.56n^2)/200.96 = 1380
3.44n^2/200.96 = 1380
Cross multiply:
3.44n^2 = 277,324.8
n^2 = 80,617.7
n = 283.9
Nearest foot = [B]284[/B]

Linear Conversions

Free Linear Conversions Calculator - Converts to and from the following linear measurements for a given quantity:

Inches

Feet

Yards

Miles

Micrometer

Millimeters

Centimeters

Meters

Kilometers

Furlongs

Inches

Feet

Yards

Miles

Micrometer

Millimeters

Centimeters

Meters

Kilometers

Furlongs

Marita's nose is 2 inches long and her head is 9 inches tall. Assume Mount Rushmore was carved using

Marita's nose is 2 inches long and her head is 9 inches tall. Assume Mount Rushmore was carved using the same ratio. If Teddy Roosevelt's head is 60 feet tall, how long should his nose be? Round to the nearest foot, if necessary.
Set up a proportion/ratio of head height to nose height where n is the nose height for 60 feet head height:
9/2 = 60/n
[U]Using our [URL='https://www.mathcelebrity.com/prop.php?num1=9&num2=60&den1=2&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we see that:[/U]
n = [B]13.33 rounded to the nearest foot is 13 feet[/B]

Math Problem Solving (Help Please)

A box in the shape of a rectangular prism is used in a movie scene. The base of the box measures 6 feet by 5 feet. The box has a volume of 195 cubic feet. The director hires an actor who is 6 feet 4 inches tall. Can the actor stand up straight in the box?
Also I do need to show my work so please write down the work to solve this. Thanks!

Math Problem Solving (Help Please)

Volume of rectangular prism is:
V = lwh
Plugging in the numbers you gave:
195 = (6)(5)h
195 = 30h
Divide each side by 30
h = 6.5
6.5 feet is 6 feet, 6 inches. This is 2 inches more than your actor, so [B]yes[/B], he will fit in the box standing up.

Mount McKinley in Alaska, the highest mountain in North America, is 20,320 feet above sea level. Dea

Mount McKinley in Alaska, the highest mountain in North America, is 20,320 feet above sea level. Death Valley, the lowest point, is 280 feet below sea level. What is the difference in height between Mount McKinley and Death Valley?
Regarding height with respect to sea level...
[LIST]
[*]Above sea level is written as positive height
[*]Below sea level is written as negative height
[/LIST]
So we have:
+20,320 - -280
+20,320 + 280
[B]20,600[/B]

Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest

Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?
Above sea level is listed as positive (+)
Below sea level is listed as negative (-)
We have:
Difference = +29,028 - (-1312)
Difference = 29028 + 1312
[URL='https://www.mathcelebrity.com/longdiv.php?num1=29028&num2=1312&pl=Add']Difference[/URL] = [B]30,340[/B]

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in s

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in size. What is the total area of the field?
Area of each plot is 5x5 = 25 square feet.
Total area = Area per plot * number of plots
Total area = 25 sq ft * 9
Total area = [B]225 sq ft[/B]

Represent the number of inches in 7 feet

Represent the number of inches in 7 feet
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']type in 7 feet to our search engine and we get[/URL]:
7 feet = [B]84 inches[/B]

Rick is taller than Luke, who is taller than Bruce. Steve is taller t Han Bruce, but not as tall as

Rick is taller than Luke, who is taller than Bruce. Steve is taller than Bruce, but not as tall as Rick. If Luke is 6 feet tall, do we know if Steve is taller than 6 feet?
Luke and Steve are between Rick and Bruce, but that is all we know. We don't know if Luke is taller or Steve is taller.
Answer is [B] NO[/B]

Sean is helping his dad build a tiled walkway in their backyard. The walkway will be 606060 feet lon

Sean is helping his dad build a tiled walkway in their backyard. The walkway will be 60 feet long and 2 feet wide. The local hardware store sells tiles which are 2 by 2 feet and come in boxes of 6.
There isn't a calculator for Rational Word Problems.

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants i

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants it to be 5 times as long as it is wide. What dimensions should the play area be?
Sheila wants:
[LIST=1]
[*]l =5w
[*]2l + 2w = 100 <-- Perimeter
[/LIST]
Substitute (1) into (2)
2(5w) + 2w = 100
10w + 2w = 100
12w = 100
Divide each side by 12
[B]w = 8.3333[/B]
Which means l = 5(8.3333) -->[B] l = 41.6667[/B]

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large redwood tree was, the ranger said that he wouldn't tell its height, but would give Sonia a clue. How tall is the redwood tree Sonia asked about?
Sonia said the tree is 64 times my height. The tree is also 112 feet taller than the tree next to it. The two trees plus my height total 597.5 feet.
[LIST]
[*]Rangers's height = n
[*]Tree height = 64n
[*]Smaller tree height = 64n - 112
[*]Total height = 64n - 112 + 64n = 597.5
[/LIST]
Solve for [I]n[/I] in the equation 64n - 112 + 64n = 597.5
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(64 + 64)n = 128n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
128n - 112 = + 597.5
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -112 and 597.5. To do that, we add 112 to both sides
128n - 112 + 112 = 597.5 + 112
[SIZE=5][B]Step 4: Cancel 112 on the left side:[/B][/SIZE]
128n = 709.5
[SIZE=5][B]Step 5: Divide each side of the equation by 128[/B][/SIZE]
128n/128 = 709.5/128
n = 5.54296875
Tree height = 64 * ranger height
Tree height = 64 * 5.54296875
Tree height = [B]354.75 feet[/B]

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is runn

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second.
i. After how many seconds will Sophie catch Claire?
ii. If the race is 500 feet, who wins?
i.
Sophie's distance formula is given as D = 5s
Claire's distance formula is given as D = 3s + 100
Set them equal to each other
5s = 3s + 100
Subtract 3s from both sides:
2s = 100
Divide each side by 2
[B]s = 50[/B]
ii. [B]Sophie since after 50 seconds, she takes the lead and never gives it back.[/B]

Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis

Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis rope. Stacys rope is 23 feet long. Write and solve an equation to find the length t of Travis rope.
Let Stacy's rope be s. Travis's rope be t. We have:
s = 3t - 4
s = 23
So [B]3t - 4 = 23
[/B]
[URL='http://www.mathcelebrity.com/1unk.php?num=3t-4%3D23&pl=Solve']Paste this equation into our search engine[/URL] to get [B]t = 9[/B].

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.
a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80^{th} percentile of the distribution of the average of 49 fly balls
a. N(250, 50/sqrt(49)) = [B]0.42074[/B]
b. Calculate Z-score and probability = 0.08 shown [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+240&mean=+250&stdev=+7.14&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Using the Z-score formula, we have
0.8416 = (x - 250)/50
x = [B]292.08[/B]

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and
a standard deviation of 50 feet.
a. If X = distance in feet for a fly ball, then X ~
b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.
a. [B]N(250, 50/sqrt(1))[/B]
b. Calculate [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+220&mean=250&stdev=50&n=+1&pl=P%28X+%3C+Z%29']z-score[/URL]
Z = -0.6 and P(Z < -0.6) = [B]0.274253[/B]
c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Z-score formula: 0.8416 = (x - 250)/50

x = [B]292.08[/B]

x = [B]292.08[/B]

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height re

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother?
[LIST]
[*]Let the height of the family without the mom be f. Let the height of the mother be m.
[*]Averages mean we add the heights and divide by the number of people who were measured.
[/LIST]
We're given two equations:
[LIST=1]
[*](f + m)/6 = 6
[*]f/5 = 6
[/LIST]
Cross multiplying equation (2), we get:
f = 5 * 6
f = 30
Plug f = 30 into equation (1), we get:
(30 + m)/6 = 6
Cross multiplying, we get:
m + 30 = 6 * 6
m + 30 = 36
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]6[/B]
[SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base line about 40 feet behind third base. How far would the outfielder have to throw the ball to first base?
We have a right triangle. From home base to third base is 90 feet. We add another 40 feet to the outfielder behind third base to get: 90 + 40 = 130
The distance from home to first is 90 feet.
Our hypotenuse is the distance from the outfielder to first base.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=130&side2input=90&hypinput=&pl=Solve+Missing+Side']Using our Pythagorean theorem calculator[/URL], we get:
d = [B]158.11 feet[/B]

The distance to the nearest exit door is less than 100 feet. Use d to represent the distance (in fee

The distance to the nearest exit door is less than 100 feet. Use d to represent the distance (in feet) to the nearest exit door.
Less than means we use the < sign:
[B]d < 100[/B]

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find th

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find the width of the flag.
for a rectangle, the Perimeter P is given by:
P = 2l + 2w
P[URL='https://www.mathcelebrity.com/rectangle.php?l=505&w=&a=&p=1520&pl=Calculate+Rectangle']lugging in our numbers for Perimeter and width into our rectangle calculator[/URL], we get:
l =[B] 255[/B]

The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensi

The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensions?
We're given 2 equations:
[LIST=1]
[*]l = 3w
[*]P = 80 = 2l + 2w = 80
[/LIST]
Substitute (1) into (2) for l:
2(3w) + 2w = 80
6w + 2w = 80
8w = 80
Divide each side by 8:
8w/8 = 80/8
w = [B]10
[/B]
Substitute w = 10 into (1)
l = 3(10)
l = [B]30[/B]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
P = 2l + 2w
Since P = 120, we have:
(1) 2l + 2w = 120
We are also given:
(2) l = 3w - 6
Substitute equation (2) into equation (1)
2(3w - 6) + 2w = 120
Multiply through:
6w - 12 + 2w = 120
Combine like terms:
8w - 12 = 120
Add 12 to each side:
8w = 132
Divide each side by 8 to isolate w:
w =16.5
Now substitute w into equation (2)
l = 3(16.5) - 6
l = 49.5 - 6
l = 43.5
So (l, w) = (43.5, 16.5)

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangular word problem calculator[/URL], we have:
[LIST]
[*][B]l = 43.5[/B]
[*][B]w = 16.5[/B]
[/LIST]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangle word problem calculator[/URL], we get:
[LIST]
[*][B]w = 16.5[/B]
[*][B]l = 43.5[/B]
[/LIST]

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the wi

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the width?
5.8 feet less than 6 times the width is an algebraic expression:
6w - 5.8
We set this equal to the length of 50.6
6w - 5.8 = 50.6
Add 5.8 to each side:
6w - 5.8 + 5.8 = 50.6 + 5.8
Cancel the 5.8 on the left side:
6w = 56.4
Divide each side by 6:
6w/6 = 56.4/6
[URL='http://www.mathcelebrity.com/1unk.php?num=6w-5.8%3D50.6&pl=Solve']Typing this problem into the search engine[/URL], we get [B]w = 9.4[/B].
[MEDIA=youtube]gfM-d_Ej728[/MEDIA]

The perimeter of a bedroom door is 28 feet. It is 4 feet wide. How tall is it?

The perimeter of a bedroom door is 28 feet. It is 4 feet wide. How tall is it?
Using our[URL='https://www.mathcelebrity.com/rectangle.php?l=&w=4&a=&p=28&pl=Calculate+Rectangle'] rectangle calculator[/URL], we get:
l = [B]10[/B]

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?
[U]Assumptions and givens:[/U]
[LIST]
[*]The poster has a rectangle shape
[*]l = 6
[*]P = 20
[*]The perimeter of a rectangle (P) is: 2l + 2w = P
[/LIST]
Plugging in our l and P values, we get:
2(6) + 2w = 20
Multiplying through and simplifying, we get:
12 + 2w = 20
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B2w%3D20&pl=Solve']type this equation into our search engine [/URL]and we get:
w = [B]4[/B]

The perimeter of a rectangular backyard is 162 feet. It is 52 feet long. How wide is it?

The perimeter of a rectangular backyard is 162 feet. It is 52 feet long. How wide is it?
We [URL='https://www.mathcelebrity.com/rectangle.php?l=52&w=&a=&p=162&pl=Calculate+Rectangle']use our rectangle solver to solve for w[/URL]. We get:
[B]w = 29[/B]

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?
Set up the perimeter equation:
2l + 2w = P
Given P = 204 and l = 66, we have:
2(66) + 2w = 204
2w + 132 = 204
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B132%3D204&pl=Solve']equation solver,[/URL] we get w = [B]36[/B].

The world record for the mile in the year 1865 was held by Richard Webster of England when he comple

The world record for the mile in the year 1865 was held by Richard Webster of England when he completed a mile in 4 minutes and 36.5 seconds. The world record in 1999 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds.
If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line?
Change times to seconds:
[LIST]
[*]4 minutes and 36.5 seconds = 4*60 + 36.5 = 240 + 36.5 = 276.5 seconds
[*]3 minute and 43.13 seconds = 3*60 + 43.13 = 180 + 43.13 = 223.13 seconds
[/LIST]
Now, find the distance Richard Webster travelled in 3 minutes and 43.13 seconds which is when Hiram El Guerrouj crossed the finish line.
1 mile = 5280 feet:
Set up a proportion of distance in feet to seconds where n is the distance Richard Webster travelled
5280/276.5 = n/223.13
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5280&num2=n&den1=276.5&den2=223.13&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = 4260.85 feet
Distance difference = 5280 - 4260.85 = [B]1019.15 feet[/B]

There are 12 inches per foot. How many inches are there in 14 feet?

There are 12 inches per foot. How many inches are there in 14 feet?
Two ways to solve this. Plug in [URL='http://www.mathcelebrity.com/linearcon.php?quant=14&pl=Calculate&type=foot']14 feet [/URL]into the search engine to get [B]168 inches.[/B]
Or, we do proportions:
12 inches / 1 foot * 14 feet = 12 * 14 = 168 inches per 14 feet.

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is its angle of depression?
The sin of the angle A is the length of the opposite side / hypotenuse.
sin(A) = Opposite / Hypotenuse
sin(A) = 193.4 / 1090/3
sin(A) = 0.1774
[URL='https://www.mathcelebrity.com/anglebasic.php?entry=0.1774&pl=arcsin']We want the arcsin(0.1774)[/URL].
[B]A = 10.1284[/B]

Tristan is building a slide for his kids. The ladder is 6 feet tall and the slide is 10 feet long. W

Tristan is building a slide for his kids. The ladder is 6 feet tall and the slide is 10 feet long. What is the distance between the ladder and the bottom of the slide?
The answer is 8.
We have a 3-4-5 triangle. But it's scaled by 2.
3 * 2 = 6
5 * 2 = 10 (hypotenuse-slide)
4 * 2 = [B]8[/B]

Walking Distance (Pedometer)

Free Walking Distance (Pedometer) Calculator - Given a number of steps and a distance per stride in feet, this calculator will determine how far you walk in other linear measurements.

You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet.

You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet. Company A charges $2.99 per square foot plus a $200 installation charge. Company B charges $19.99 per square yard plus a $500 installation charge. What is the best deal?
Did you notice the word snuck in on this problem? Company B is given in square [I][B]yards[/B][/I], not feet. Let's convert their price to square feet to match company A.
[U]Company B conversion:[/U]
Since we have 1 square yard = 3 feet * 3 feet = 9 square feet, we need to solve the following proportion:
$19.99/square yard * 1 square yard/9 feet = $19.99 square yard / 9 feet = $2.22 / square foot.
Now, let's set up the cost equations C(s) for each Company in square feet (s)
[LIST]
[*]Company A: C(s) = 200 + 2.99s
[*]Company B: C(s) = 500 + 2.22s
[/LIST]
The problem asks for s = 30 feet * 50 feet = 1500 square feet. So we want to calculate C(1500)
[U]Company A:[/U]
C(1500) = 200 + 2.99(1500)
C(1500) = 200 + 4485
C(1500) = 4685
[U]Company B:[/U]
C(1500) = 500 + 2.22(1500)
C(1500) = 500 + 3330
C(1500) = 3830
Since [B]Company B[/B] has the lower cost per square foot, they are the better buy.