22 results

capacity - the maximum amount that something can contain

17 people over the maximum capacity

17 people over the maximum capacity
Let the maximum capacity be c. We have:
[B]c + 17[/B]

450 people attended a concert at the center. the center was 3/4 full. what is the capacity of the mu

450 people attended a concert at the center. the center was 3/4 full. what is the capacity of the music center.
Let the capacity be c. We're given:
3c/4 = 450
To solve this equation, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=450&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]600[/B]

A bus holds 45 students. How many buses were taken on a field trip if 13 students travels by car and

A bus holds 45 students. How many buses were taken on a field trip if 13 students travels by car and total of 320 students went on a trip?
[U]Find the number of students who went on the bus:[/U]
Number of students who went on the bus = Total students on field trip - students who traveled by car
Number of students who went on the bus = 320 - 13
Number of students who went on the bus = 307
Calculate the number of buses needed:
Number of buses needed = Number of students who went on the bus / Bus Capacity
Number of buses needed = 307 / 45
Number of buses needed = 6.822
We round up for a full bus to get [B]7 buses[/B]

A bus is carrying 135 passengers, which is 3/4 of the capacity of the bus. What is the capacity of t

A bus is carrying 135 passengers, which is 3/4 of the capacity of the bus. What is the capacity of the bus
Let the capacity of the bus be c. We're given:
3c/4 = 135
To solve for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=135&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this equation into our search engine [/URL]and we get:
c = [B]180[/B]

A cube has an edge that is x cm long. What is the capacity of C(x)?

A cube has an edge that is x cm long. What is the capacity of C(x)?
Capacity is another word for volume, or the amount an object will hold. Given a side x, the capacity (volume) of a cube is:
C(x) = [B]x^3[/B]

A gas tank contains 5.3 gallons. The capacity of the tank is 12.5 gallons. How much will it cost to

A gas tank contains 5.3 gallons. The capacity of the tank is 12.5 gallons. How much will it cost to fill the tank at $1.30 per gallon.
[U]Calculate the empty portion of the gas tank:[/U]
Empty portion = Capacity - Gas gallons remaining
Empty portion = 12.5 - 5.3
Empty portion (in gallons) = 7.2
[U]Calculate the cost to fill the tank:[/U]
Cost to fill the tank = Empty portion (in gallons) * cost per gallon
Cost to fill the tank = 7.2 * $1.30
Cost to fill the tank = [B]$9.36[/B]

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for stu

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1030, How many children, students, and adults attended?
Let c be the number of children's tickets, s be the number of student's tickets, and a be the number of adult's tickets. We have 3 equations:
[LIST=1]
[*]a + c + s = 143
[*]a = 0.5c
[*]12a + 5c + 7s =1030
[/LIST]
Substitute (2) into (1)
0.5c + c + s = 143
1.5c + s = 143
Subtract 1.5c from each side
4. s = 143 - 1.5c
Now, take (4) and (2), and plug it into (3)
12(0.5c) + 5c + 7(143 - 1.5c) = 1030
6c + 5c + 1001 - 10.5c = 1030
Combine like terms:
0.5c + 1001 = 1030
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.5c%2B1001%3D1030&pl=Solve']equation calculator[/URL] to get [B]c = 58[/B].
Plug this back into (2)
a = 0.5(58)
[B]a = 29
[/B]
Now take the a and c values, and plug it into (1)
29 + 58 + s = 143
s + 87 = 143
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B87%3D143&pl=Solve']equation calculator[/URL] again, we get [B]s = 56[/B].
To summarize, we have:
[LIST]
[*]29 adults
[*]58 children
[*]56 students
[/LIST]

A school bus can safely carry as many as 76 students. If 19 students are already on the bus, how man

A school bus can safely carry as many as 76 students. If 19 students are already on the bus, how many more can board the bus?
Remaining boarders = total capacity - students on the bus
Remaining boarders = 76 - 19
Remaining boarders = [B]57[/B]

A theater is 3/4 full. When 96 people leave, the theater is only 35% full. How many seat are there

A theater is 3/4 full. When 96 people leave, the theater is only 35% full. How many seats are there?
Let the full capacity of seats in the theater be s. We're given:
3/4s - 96 = 0.35s (Since 35% is 0.35)
We also know that 3/4 = 0.75, so let's use this to have decimals:
0.75s - 96 = 0.35s
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75s-96%3D0.35s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]240[/B]

Combined Gas Law

Free Combined Gas Law Calculator - This will solve for any of the 6 items in the Combined Gas Law using pressure, volume (Capacity), and temperature.

(P_{1} x V_{1})/T1 = (P_{2} x V_{2})/T2

(P

Cones

Free Cones Calculator - Calculates and solves for Radius, height, Volume (Capacity), Lateral Area, and Surface Area of a Cone.

Cube

Free Cube Calculator - Solves for Volume (Capacity), Lateral Area,Surface Area, and the value of a side for a cube.

Cylinders

Free Cylinders Calculator - Calculates and solves for Radius, Diameter, Volume (Capacity), Lateral Area, and Surface Area of a Cylinder.

Density

Free Density Calculator - Solves for any of the 3 items in the Density Formula, Density (D), Mass (M), and Volume (V) (Capacity), with 2 given items.

Find Requested Value

Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters.
5.2 4.9 2.9 5.3 3.0
4.0 5.2 5.2 3.2 4.7
3.2 3.5 4.8 4.0 5.1
Use the data to obtain a point estimate of the mean forced vital capacity for all asthmatics

Find the confidence interval specified.

Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters.
5.1 4.9 4.7 3.1 4.3
3.7 3.7 4.3 3.5 5.2
3.2 3.5 4.8 4.0 5.1
Use the data to obtain a 95.44% confidence interval for the mean forced vital capacity for all asthmatics. Assume that ? = 0.7.

In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pres

In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pressure is a measure of a hurricane's destruction capacity, what happens to this destructive power when the wind speed doubles?
Let P = pressure and v = velocity (wind speed)
We are given p = v^2
Double velocity, so we have a new pressure P2:
P2 = (2v)^2
P2 = 4v^2
Compare the 2:
p = v^2
p = 4v^2
Doubling the wind speed [B]quadruples, or 4 times[/B] the pressure.

It is estimated that weekly demand for gasoline at new station is normally distributed, with an aver

It is estimated that weekly demand for gasoline at new station is normally distributed, with an average of 1,000 and standard deviation of 50 gallons. The station will be supplied with gasoline once a week. What must the capacity of its tank be if the probability that its supply will be exhausted in a week is to be no more than 0.01?
0.01 is the 99th percentile
Using our [URL='http://www.mathcelebrity.com/percentile_normal.php?mean=+1000&stdev=50&p=99&pl=Calculate+Percentile']percentile calculator[/URL], we get [B]x = 1116.3[/B]

Pool Volume

Free Pool Volume Calculator - Given a round shaped pool, this calculates the volume (Capacity) in gallons of the pool when filled with water

Pyramids

Free Pyramids Calculator - Solves for Volume (Capacity), Surface Area, height, or radius of a Pyramid.

Rectangular Solid

Free Rectangular Solid Calculator - Solves for Volume (Capacity) of rectangular solid

Lateral Area of rectangular Solid

Surface Area of rectangular solid.

Lateral Area of rectangular Solid

Surface Area of rectangular solid.

Spheres

Free Spheres Calculator - Calculates and solves for Volume (Capacity), Surface Area, and Radius of a Sphere.