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b varies directly as a. if b is 78 when a is 13, what is b when a is 23?
b varies directly as a. if b is 78 when a is 13, what is b when a is 23? [URL='https://www.mathcelebrity.com/variation.php?var1=b&cmeth=varies+directly+as&var2=a&init1=b%3D78&init2=a%3D13&g1=a%3D23&pl=Calculate+Variation']Using our direct variation calculator[/URL], we get: b = [B]138[/B]

does the equation y= x/3 represent a direct variation? If so, state the value of k
does the equation y= x/3 represent a direct variation? If so, state the value of k [B]Yes[/B], it's a direct variation equation. We rewrite this as: y = 1/3 * x So k = 1/3, and y varies directly as x.

Given y= 4/3x what is the constant of proportionality
Given y= 4/3x what is the constant of proportionality Direct variation means the constant of proportionality is y/x. Cross multiplying, we get: y/x = [B]4/3[/B]

If 100 runners went with 4 bicyclists and 5 walkers, how many bicyclists would go with 20 runners an
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]

If y varies inversely as X and Y equals 5 when x equals 2 find X when Y is 4
If y varies inversely as X and Y equals 5 when x equals 2 find X when Y is 4. Using our [URL='http://www.mathcelebrity.com/variation.php?var1=y&cmeth=varies+inversely+as&var2=x&init1=y%3D5&init2=x%3D2&g1=y%3D4&pl=Calculate+Variation']inverse variation calculator[/URL], we get x = 2.5

Joint Variation Equations
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.

P varies directly as q and the square of r and inversely as s
P varies directly as q and the square of r and inversely as s There exists a constant k such that: p = kqr^2/s [I]Note: Direct variations multiply and inverse variations divide[/I]

p= 4/q what kind of variation is this?
p= 4/q what kind of variation is this? [B]Inverse Variation [/B]since we divide by q

Sample Size Reliability for μ
Given a population standard deviation σ, a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

Sample Size Requirement for the Difference of Means
Given a population standard deviation 1 of σ1, a population standard deviation 2 of σ2 a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5?
Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5? Direct variation means we set up an equation: h(x) = kx where k is the constant of variation. For h(x) = 44 when x = 2, we have: 2k = 44 [URL='https://www.mathcelebrity.com/1unk.php?num=2k%3D44&pl=Solve']Type this equation into our search engine[/URL], we get: k = 22 The question asks for h(x) when x = 1.5. So we set up our variation equation, knowing that k = 22. kx = h(x) With k = 22 and x = 1.5, we get: 22(1.5) = h(x) h(x) = [B]33[/B]

Variation Equations
This calculator solves the following direct variation equations and inverse variation equations below:
* y varies directly as x
* y varies inversely as x
* y varies directly as the square of x
* y varies directly as the cube of x
* y varies directly as the square root of x
* y varies inversely as the square of x
* y varies inversely as the cube of x
* y varies inversely as the square root of x

What can we conclude if the coefficient of determination is 0.94?
What can we conclude if the coefficient of determination is 0.94? [LIST] [*]Strength of relationship is 0.94 [*]Direction of relationship is positive [*]94% of total variation of one variable(y) is explained by variation in the other variable(x). [*]All of the above are correct [/LIST] [B]94% of total variation of one variable(y) is explained by variation in the other variable(x)[/B]. The coefficient of determination explains ratio of explained variation to the total variation.

X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4
X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4 Varies directly means there is a constant k such that: x = ky^(1/3) When x = 1 and y = 27, we have: 27^1/3(k) = 1 3k = 1 To solve for k, we[URL='https://www.mathcelebrity.com/1unk.php?num=3k%3D1&pl=Solve'] type in our equation into our search engine[/URL] and we get: k = 1/3 Now, the problem asks for y when x = 4. We use our variation equation above with k = 1/3 and x = 4: 4 = y^(1/3)/3 Cross multiply: y^(1/3) = 4 * 3 y^(1/3) =12 Cube each side: y^(1/3)^3 = 12^3 y = [B]1728[/B]

y varies directly as x and inversely as i
y varies directly as x and inversely as I Note: Direct variation means we multiply. Inverse variation means we divide. There exists a constant k such that: [B]y = kx/i[/B]