inverse - opposite or contrary in position

A group of students at a school takes a history test. The distribution is normal with a mean of 25,

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4.
(a) Everyone who scores in the top 30% of the distribution gets a certificate.
(b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?
(a) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.70&pl=Calculate+Critical+Z+Value']Top 30% is 70% percentile[/URL]
Inverse of normal distribution(0.7) = -0.5244005
Plug into z-score formula, -0.5244005 = (x - 25)/4
[B]x = 22.9024[/B]
(b) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.95&pl=Calculate+Critical+Z+Value']Top 5% is 95% percentile[/URL]
Inverse of normal distribution(0.95) = 1.644853627
Plug into z-score formula, 1.644853627 = (x - 25)/4
[B]x = 31.57941451[/B]

A varies directly as B and inversely as C.

A varies directly as B and inversely as C.
There exists a constant k such that:
[B]a = kb/c
[/B]
Inversely means we divide by and directly means we multiply by

a varies directly with b and inversely with c

a varies directly with b and inversely with c
Direct variation means we multiply.
Inverse variation means we divide.
There exists a constant k such that:
[B]a = kb/c[/B]

a varies inversely with b, c and d

a varies inversely with b, c and d
Varies inversely means we divide. Given a constant, k, we have:
[B]a = k/bcd[/B]

Additive Inverse Property

Free Additive Inverse Property Calculator - Demonstrates the Additive Inverse property using a number. A + (-A) = 0
Numerical Properties

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
b. What proportion of the vehicles would be going less than 50 mph?
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?
d. In what way do you think the actual distribution of speeds differs from a normal distribution?
a. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=65&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<65) = [B]22.66%[/B]
b. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+50&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<50) = [B]0.4269%[/B]
c. [URL='http://www.mathcelebrity.com/zcritical.php?a=0.9&pl=Calculate+Critical+Z+Value']Inverse of normal for 90% percentile[/URL] = 1.281551566
Plug into z-score formula: (x - 71)/8 = 1.281551566
[B]x = 81.25241252[/B]
d. [B]The shape/ trail differ because the normal distribution is symmetric with relatively more values at the center. Where the actual has a flatter trail and could be expected to occur.[/B]

C varies directly as the cube of a and inversely as the 4th power of B

C varies directly as the cube of a and inversely as the 4th power of B
The cube of a means we raise a to the 3rd power:
a^3
The 4th power of B means we raise b to the 4th power:
b^4
Varies directly means there exists a constant k such that:
C = ka^3
Also, varies inversely means we divide by the 4th power of B
C = [B]ka^3/b^4[/B]
Varies [I]directly [/I]as means we multiply by the constant k.
Varies [I]inversely [/I]means we divide k by the term which has inverse variation.
[MEDIA=youtube]fSsG1OB3qdk[/MEDIA]

F varies directly as g and inversely as r^2

F varies directly as g and inversely as r^2
[U]Givens and assumptions[/U]
[LIST]
[*]We take a constant of variation called k.
[*][I]Varies directly means we multiply our variable term by k[/I]
[*][I]Varies inversely means we divide k by our variable term[/I]
[/LIST]
The phrase varies directly or varies inversely means we have a constant k such that:
[B]F = kg/r^2[/B]

f varies jointly with u and h and inversely with the square of y.

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]

Facebook provides a variety of statistics on its Web site that detail the growth and popularity of t

Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site.
On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent.
a. Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30.
b. Find the 95th percentile, and express it in a sentence.
a. P(X >=0.30), calculate the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+0.30&mean=+0.28&stdev=+0.05&n=+1&pl=P%28X+%3E+Z%29']z-score[/URL] which is:
Z = 0.4
P(x>0.4) = [B]0.344578 or 34.46%[/B]
b. Inverse Normal (0.95) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.95&pl=Calculate+Critical+Z+Value']calculator[/URL] = 1.644853627
Use NORMSINV(0.95) on Excel
0.28 + 0.05(1.644853627) = [B]0.362242681 or 36.22%[/B]

Fisher Transformation and Fisher Inverse

Free Fisher Transformation and Fisher Inverse Calculator - Given a correlation coefficient (r), this calculates the Fisher Transformation (z).

Given a Fisher Transformation (r), this calculates the Fisher Inverse (r)

Given a Fisher Transformation (r), this calculates the Fisher Inverse (r)

Hyperbolic Inverse

Free Hyperbolic Inverse Calculator - Calculates hyperbolic function values:
arcsinh, arccosh, arctanh, arccsch, arcsech, arccoth

If p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equ

If p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equal to 2.
We set up the variation equation with a constant k such that:
p = k/q^2 [I](inversely proportional means we divide)
[/I]
When q is 4 and p is 2, we have:
2 = k/4^2
2 = k/16
Cross multiply:
k = 2 * 16
k = 32
Now, the problem asks for p when q = 2:
p = 32/2^2
p = 32/4
p = [B]8[/B]

If y varies directly as x and inversely as z, then which equation describes the relation?

If y varies directly as x and inversely as z, then which equation describes the relation?
Directly means we multiply, inversely means we divide, so we have a constant k such that:
[B]y = kx/z[/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

K varies inversely with square root of m and directly with the cube of n.

K varies inversely with square root of m and directly with the cube of n.
[LIST]
[*]We take a constant c as our constant of proportionality.
[*]The word inversely means we divide
[*]The word directly means we multiply
[/LIST]
[B]k = cn^3/sqrt(m)[/B]

m is inversely proportional to the square of p-1 when p=4 m=5 find m when p=6

m is inversely proportional to the square of p-1 when p=4 and m=5. find m when p=6
Inversely proportional means there is a constant k such that:
m = k/(p - 1)^2
When p = 4 and m = 5, we have:
5 = k/(4 - 1)^2
5 = k/3^2
5 = k/9
[U]Cross multiply:[/U]
k = 45
[U]The problems asks for m when p = 6. And we also now know that k = 45. So plug in the numbers:[/U]
m = k/(p - 1)^2
m = 45/(6 - 1)^2
m = 45/5^2
m = 45/25
m = [B]1.8[/B]

Matrix Properties

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

* Determinant = det(A)

* Inverse = A

* Transpose = A

* 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

Multiplicative Inverse Property

Free Multiplicative Inverse Property Calculator - Demonstrates the Multiplicative Inverse property using a number.
Numerical Properties

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 varies directly as the square of r and inversely as q and s and p = 40 when q = 5, r = 4 and s = 6

p varies directly as the square of r and inversely as q and s and p = 40 when q = 5, r = 4 and s = 6, what is the equation of variation?
Two rules of variation:
[LIST=1]
[*]Varies directly means we multiply
[*]Varies inversely means we divide
[/LIST]
There exists a constant k such that our initial equation of variation is:
p = kr^2/qs
[B][/B]
With p = 40 when q = 5, r = 4 and s = 6, we have:
4^2k / 5 * 6 = 40
16k/30 = 40
Cross multiply:
16k = 40 * 30
16k = 1200
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=16k%3D1200&pl=Solve']equation calculator[/URL], we get:
k = [B]75[/B]
So our final equation of variation is:
[B]p = 75r^2/qs[/B]

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

r varies directly with s and inversely with the square root of t

r varies directly with s and inversely with the square root of t
Varies directly means we multiply
Varies inversely means we divide
There exists a constant k such that:
[B]r = ks/sqrt(t)[/B]

Rational Number Subtraction

Free Rational Number Subtraction Calculator - Subtracting 2 numbers, this shows an equivalent operations is adding the additive inverse. p - q = p + (-q)

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.
a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80^{th} percentile of the distribution of the average of 49 fly balls
a. N(250, 50/sqrt(49)) = [B]0.42074[/B]
b. Calculate Z-score and probability = 0.08 shown [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+240&mean=+250&stdev=+7.14&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Using the Z-score formula, we have
0.8416 = (x - 250)/50
x = [B]292.08[/B]

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and
a standard deviation of 50 feet.
a. If X = distance in feet for a fly ball, then X ~
b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.
a. [B]N(250, 50/sqrt(1))[/B]
b. Calculate [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+220&mean=250&stdev=50&n=+1&pl=P%28X+%3C+Z%29']z-score[/URL]
Z = -0.6 and P(Z < -0.6) = [B]0.274253[/B]
c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Z-score formula: 0.8416 = (x - 250)/50

x = [B]292.08[/B]

x = [B]292.08[/B]

t varies directly with the square of r and inversely with w

t varies directly with the square of r and inversely with w
There exists a constant k such that:
[B]t = kr^2/w[/B]
[I]Directly means multiply and inversely means divide[/I]

Variation Equations

Free Variation Equations Calculator - 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 is the inverse of dividing by 3

What is the inverse of dividing by 3
[B]Multiplying by 3[/B]
Suppose we have 2 divided by 3:
2/3
To undo this operation to get to 2 again, we'd multiply by 3:
2/3 * 3 = 2

Write an equation that relates the quantities. G varies jointly with t and q and inversely with the

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]

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]

z varies directly with x and inversely with y

z varies directly with x and inversely with y
[LIST]
[*]The phrase directly means we multiply.
[*]The phrase inversely means we divide
[*]Variation means there exists a constant k such that:
[/LIST]
[B]z = kx/y[/B]

z varies inversely as the square of t. if z=4 when t=2, find z when t is 10

z varies inversely as the square of t. if z=4 when t=2, find z when t is 10
Varies inversely means there exists a constant k such that:
z = k/t^2
If z = 4 when t = 2, we have:
4 = k/2^2
4 = k/4
Cross multiply and we get:
k = 4 * 4
k = 16
Now the problem asks to find z when t is 10:
z = k/t^2
z = 16/10^2
z = 16/100
z = [B]0.16[/B]

z varies inversely with w, x, and y

z varies inversely with w, x, and y
Inversely means their exists a constant k such that:
[B]z = k/wxy[/B]