B varies jointly as u, v, and w Varies jointly means we have a constant k such that: [B]B = kuvw[/B]

c varies jointly as the square of q and cube of p The square of q means we raise q to the 2nd power: q^2 The cube of p means we raise p to the rdd power: p^3 The phrase [I]varies jointly[/I] means there exists a constant k such that: [B]c = kp^3q^2[/B]

CCP Stat Club is sending a delegate of 2 members to attend the 2015 Joint Statistical Meeting in Seattle. There are 10 qualified candidates. How many different ways can the delegate be selected? 10C2 = [B]45[/B] shown on our [URL='http://www.mathcelebrity.com/permutation.php?num=10&den=2&pl=Combinations']Combinations Calculator[/URL]

f varies jointly with u and h and inversely with the square of y. Variation means we have a constant k. Varies jointly with u and h means we multiply k by hu Varies inversely with the square of y means we divide by y^2 [B]f = khu/y^2[/B]

Five less than a number is at least -7 and at most 7. A number signifies an arbitrary variable, let's call it x. Five less than a number: x - 5 Is at least -7 means greater than or equal to and at most 7 means less than or equal to, so we have a joint inequality: [B]-7 <= x - 5 <= 7[/B]

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]

If 100 runners went with 4 bicyclists and 5 walkers, how many bicyclists would go with 20 runners and 2 walkers? [U]Set up a joint variation equation, for the 100 runners, 4 bicyclists, and 5 walkers:[/U] 100 = 4 * 5 * k 100 = 20k [U]Divide each side by 20[/U] k = 5 <-- Coefficient of Variation [U]Now, take scenario 2 to determine the bicyclists with 20 runners and 2 walkers[/U] 20 = 2 * 5 * b 20 = 10b [U]Divide each side by 10[/U] [B]b = 2[/B]

Free Joint Variation Equations Calculator - Given a joint variation (jointly proportional) of a variable between two other variables with a predefined set of conditions, this will create the joint variation equation and solve based on conditions. Also called combined variation.

k varies jointly with m,n, p The phrase [I]varies jointly[/I] means we have a constant c such that: [B]k= cmnp[/B]

Free Matrix Properties Calculator - Given a matrix |A|, this calculates the following items if they exist:
* Determinant = det(A)
* Inverse = A^-1
* Transpose = A^T
* Adjoint = adj(A)
* Eigen equation (characteristic polynomial) = det|λI - A|
* Trace = tr(A)
* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form
* Dimensions of |A| m x n
* Order of a matrix
* Euclidean Norm ||A||
* Magic Sum if it exists
* Determines if |A| is an Exchange Matrix

S varies jointly with t cubed and v Varied jointly means there exists a constant k such that: [B]s = kt^3v[/B]

Free Static Determinacy and Stability Calculator - Given a number of joints (j) and a number of members (m), this determines if a truss is statically determinate, statically indeterminate, or unstable

Taylor is playing a game using a die and a spinner. The spinner is divided into 4 equal parts with colors green, red, yellow, and purple. Taylor rolls the die and spins the spinner. What is the probability the die shows a 2 and the spinner lands on purple? Probability of rolling a 2 on the die is 1/6 Probability of getting a purple on the spinner is 1/4 Since each event is independent, our joint probability is: P(2 on the die and Purple on the spinner) = P(2 on the die) x P(Purple on the Spinner) P(2 on the die and Purple on the spinner) = 1/6 x 1/4 P(2 on the die and Purple on the spinner) = [B]1/24[/B]

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take? Set up the earnings equation for the volleyball team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 4w + 81 Set up the earnings equation for the wrestling team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 2w + 85 If the raised the same amount in total, set both earnings equations equal to each other: 4w + 81 = 2w + 85 Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides 4w + 81 - 2w = 2w + 85 - 2w [SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE] 2w + 81 = 85 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 81 and 85. To do that, we subtract 81 from both sides 2w + 81 - 81 = 85 - 81 [SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE] 2w = 4 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 4/2 w = [B]2 <-- How many cars it will take [/B] To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2: E = 4(2) + 81 E = 8 + 81 E = [B]89 <-- Total Earnings[/B]

u varies jointly as q and the square of m Varies jointly means we multiply. There exists a constant k such that: [B]u = kqm^2[/B]

Use k as the constant of variation. L varies jointly as u and the square root of v. Since u and v vary jointly, we multiply by the constant of variation k: [B]l = ku * sqrt(v)[/B]

Write an equation that relates the quantities. G varies jointly with t and q and inversely with the cube of w . The constant of proportionality is 8.25 . [LIST] [*]Varies jointly or directly means we multiply [*]Varies inversely means divide [*]The cube of w means we raise w to the 3rd power: w^3 [/LIST] Using k = 8.25 as our constant of proportionality, we have: [B]g = 8.25qt/w^3[/B]

z is jointly proportional to the square of x and the cube of y The square of x means we raise x to the power of 2: x^2 The cube of y means we raise y to the power of 3: y^3 The phrase [I]jointly proportional[/I] means we have a constant k such that: [B]z = kx^2y^3[/B]

Z varies jointly as the 4th power of x and the 5th power of y The 4th power of x means we raise x to the power of 4: x^4 The 5th power of y means we raise y to the power of 5: y^5 The phrase [I]varies jointly[/I] means we have a constant k such that: z = [B]kx^4y^5[/B]

z varies jointly as x and y. If z=3 when x=3 and y=15, find z when x=6 and y=9 Varies jointly means there exists a constant k such that: z = kxy We're given z = 3 when x = 3 and y = 15, so we have: 3 = 15 * 3 * k 3 = 45k Using our [URL='https://www.mathcelebrity.com/1unk.php?num=3%3D45k&pl=Solve']equation solver,[/URL] we see that: k = 1/15 So our joint variation equation is: z = xy/15 Then we're asked to find z when x = 6 and y = 9 z = 6 * 9 / 15 z = 54/15 [URL='https://www.mathcelebrity.com/search.php?q=54%2F15&x=0&y=0']z =[/URL] [B]18/5[/B]