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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 σ_{1}, a population standard deviation 2 of σ_{2} 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

* 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]