plane - a flat, two-dimensional surface that extends indefinitely

41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The rema

41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The remaining 30 passengers are girls. How many passengers are on the plane?
Add up the percents:
41% + 36% + 11% = 88%
This means that (100% - 88% = 12%) are girls.
So if the total amount of passengers on the plane is p, we write 12% s 0.12, and we have:
0.12p = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=0.12p%3D30&pl=Solve']Type this equation into our search engine[/URL], and we get:
p = [B]250[/B]

A jet left Nairobi and flew east at an average speed of 231 mph. A passenger plane left four hours l

A jet left Nairobi and flew east at an average speed of 231 mph. A passenger plane left four hours later and flew in the same direction but with an average speed of 385 mph. How long did the jet fly before the passenger plane caught up?
Jet distance = 231t
Passenger plane distance = 385(t - 4)
385(t - 4) = 231t
385t - 1540 = 231t
Subtract 231t from each side
154t = 1540
[URL='https://www.mathcelebrity.com/1unk.php?num=154t%3D1540&pl=Solve']Type 154t = 1540[/URL] into the search engine, we get [B]t = 10.
[/B]
Check our work:
Jet distance = 231(10) = 2,310
Passenger plane distance = 385(10 - 4) = 385 * 6 = 2,310

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hour

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hours head start. How far from the starting point are the planes?
Use the formula D = rt where
[LIST]
[*]D = distance
[*]r = rate
[*]t = time
[/LIST]
The plan traveling 150 mph for 3 hours:
Time 1 = 150
Time 2 = 300
Time 3 = 450
Now at Time 3, the other plane starts
Time 4 = 600
Time 5 = 750
Time 6 =
450 + 150t = 550t
Subtract 150t
400t = 450
Divide each side by 400
t = 1.125
Plug this into either distance equation, and we get:
550(1.125) = [B]618.75 miles[/B]

A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that lin

A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that line.
Our line equation is:
y = mx + b
We're given:
m = 4/5
(x, y) = (0, 0)
So we have:
0 = 4/5(0) + b
0 = 0 + b
b = 0
Therefore, our line equation is:
y = 4/5x
[URL='https://www.mathcelebrity.com/function-calculator.php?num=y%3D4%2F5x&pl=Calculate']Start plugging in values here to get a list of points[/URL]

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 plane takes off at 11:53 and lands at 9 minutes to 2. How long is the flight?

A plane takes off at 11:53 and lands at 9 minutes to 2. How long is the flight?
9 minutes to 2 is 1:51
11:53 to 1:53 is exactly 2 hours.
1:51 is 2 minutes less than 1:53.
So we have [B]1 hour and 58 minutes[/B]

An airplane carries 500 passengers 45% are men, 20% are children. The number of women in the airplan

An airplane carries 500 passengers 45% are men, 20% are children. The number of women in the airplane is
If we assume the sample space is either men, women, or children to get 100% of the passengers, we have:
PercentWomen = 100% - Men - Children
PercentWomen = 100% - 45% - 20%
PercentWomen = 35%
Calculate Women passengers
Women passengers = Total passengers * Percent Women
Women passengers = 500 * 35%
Women passengers = [B]175[/B]

An airplane flies at 250 mph. How far will it travel in 5 h at that rate of speed?

An airplane flies at 250 mph. How far will it travel in 5 h at that rate of speed?
Distance = Rate x Time
Distance = 250mph x 5h
Distance = [B]1,250 miles[/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 airport has 13 scheduled arrivals every day. This week, 28 private planes also landed there. How

An airport has 13 scheduled arrivals every day. This week, 28 private planes also landed there. How many planes flew into the airport this week?
A week has 7 days.
13 scheduled arrivals per day times 7 days = 91 scheduled planes
Next, we add 28 private planes:
91 + 28 = [B]119 planes[/B]

At night, the average temperature on the surface of Saturn is -150 C. During the day, the temperatur

At night, the average temperature on the surface of Saturn is -150 C. During the day, the temperature rises 27 C. What is the average temperature on the planet's surface during the day?
Rising temperature means we add, so we have:
-150+ 27 = [B]-123C[/B]

Equation of a Plane

Free Equation of a Plane Calculator - Given three 3-dimensional points, this calculates the equation of a plane that contains those points.

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find th

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find the time taken by aeroplane to cover 1200m initially.
We know from the distance formula (d) using rate (r) and time (t) that:
d = rt
Regular speed:
1200 = rt
Divide each side by t, we get:
r = 1200/t
Reduced speed. 20 minutes = 60/20 = 1/3 of an hour. So we multiply 1,200 by 3
3600 = (r - 40)(t + 1/3)
If we multiply 3 by (t + 1/3), we get:
3t + 1
So we have:
3600 = (r - 40)(3t + 1)
Substitute r = 1200/t into the reduced speed equation:
3600 = (1200/t - 40)(3t + 1)
Multiply through and we get:
3600 = 3600 - 120t + 1200/t - 40
Subtract 3,600 from each side
3600 - 3600 = 3600 - 3600 - 120t + 1200/t - 40
The 3600's cancel, so we get:
- 120t + 1200/t - 40 = 0
Multiply each side by t:
-120t^2 - 40t + 1200 = 0
We've got a quadratic equation. To solve for t, [URL='https://www.mathcelebrity.com/quadratic.php?num=-120t%5E2-40t%2B1200%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this in our search engine[/URL] and we get:
t = -10/3 or t = 3. Since time [I]cannot[/I] be negative, our final answer is:
[B]t = 3[/B]

Men's heights are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. Mimi

Men's heights are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. Mimi is designing a plane with a height that allows 95% of the men to stand straight without bending in the plane. What is the minimum height of the plane?
Using the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=50&mean=69&stdev=2.8&n=1&pl=Empirical+Rule']empirical rule calculator[/URL], we have a [B]63.4[/B] minimum height.

Plane and Parametric Equations in R

Free Plane and Parametric Equations in R^{3} Calculator - Given a vector A and a point (x,y,z), this will calculate the following items:

1) Plane Equation passing through (x,y,z) perpendicular to A

2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

1) Plane Equation passing through (x,y,z) perpendicular to A

2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

Plane Geometry Operations

Free Plane Geometry Operations Calculator - Evaluates and simplifies various plane geometry notation and operations

Sam has x model planes. Anton has 8 more planes than Sam does. How many model planes Does Anton have

Sam has x model planes. Anton has 8 more planes than Sam does. How many model planes Does Anton have? how many planes do they have together?
Sam has x
Anton has [B]x + 8[/B] since the word [I]more[/I] means we add
The word [I]together[/I] means we add, so we have:
Sam + Anton = x + x + 8
Grouping like terms, we have:
Sam + Anton = [B]2x + 8[/B]

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in ga

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel?
Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have:
W(g) = gx + c where c is a constant
We are given:
[LIST]
[*]W(20) = 2012
[*]W(55) = 2208
[/LIST]
We want to know W(65)
Using our givens, we have:
W(20) = 20x + c = 2012
W(55) = 55x + c = 2208
Rearranging both equations, we have:
c = 2012 - 20x
c = 2208 - 55x
Set them both equal to each other:
2012 - 20x = 2208 - 55x
Add 55x to each side:
35x + 2012 = 2208
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=35x%2B2012%3D2208&pl=Solve']equation solver[/URL], we see that x is 5.6
Plugging x = 5.6 back into the first equation, we get:
c = 2012 - 20(5.6)
c = 2012 - 112
c = 2900
Now that we have all our pieces, find W(65)
W(65) = 65(5.6) + 2900
W(65) = 264 + 2900
W(65) = [B]3264[/B]

The planets in the solar system as set G

The planets in the solar system as set G.
Since Pluto was removed as a planet, we have the following set G with 8 elements:
G = [B]{Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}[/B]

Vectors

Free Vectors Calculator - Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

Your brother has $2000 saved for a vacation. His airplane ticket is $637. Write and solve an inequal

Your brother has $2000 saved for a vacation. His airplane ticket is $637. Write and solve an inequality to find how much he can spend for everything else.
Let x be the amount your brother can spend. Subtracting the cost of the plane ticket from savings, we have:
x <= 2000 - 637
[B]x <= 1,363[/B]