Inverse variation means y=k/x (direct variation is y=kx) so we can use the info given to find the constant k
y=k/x
6=k/900
k=6(900)
k=5400 so the equation is:
y=5400/x or more accurately for this problem
t(v)=5400/v then:
t(800)=5400/800
t(800)=6.75 hours
Given:
250 sheep in a 40-acre pasture.
Number of sheep grazing in each acre.
250/40 = 6.25 or 6 sheep per acre
n = 6
sample proportion: signified by ρ
Sample 1: 4 → 4/6 = 0.67
Sample 2: 1 → 1/6 = 0.17
Sample 3: 9 → 9/6 = 1.50
multiply the sample proportion by 1-ρ
Sample 1: 0.67(1-0.67) = 0.67(0.33) = 0.2211
Sample 2: 0.17(1-0.17) = 0.17(0.83) = 0.1411
Sample 3: 1.50(1-1.5) = 1.5(-0.5) = -0.75
divide the result by n. n = 6
Sample 1: 0.2211/6 = 0.03685
Sample 2: 0.1411/6 = 0.02352
Sample 3: -0.75/6 = -0.125
square root of the quotient to get the standard error.
Sample 1: √0.03685 = 0.1919
Sample 2: √0.02352 = 0.1534
Sample 3: √-0.125 = invalid
z value 95% confidence 1.96.
Sample 1: 1.96 * 0.1919 = 0.3761 or 37.61% margin of error
Sample 2: 1.96 * 0.1534 = 0.3007 or 30.07% margin of error
Answer:
What is the point used in the equation of the line y+4=1/2(x-2)
The other format for straight-line equations is called the "point-slope" form. For this one, they give you a point (x1, y1) and a slope m, and have you plug it into this formula:
y - y1 = m(x - x1)
Don't let the subscripts scare you. They are just intended to indicate the point they give you. You have the generic "x" and generic "y" that are always in your equation, and then you have the specific x and y from the point they gave you; the specific x and y are what is subscripted in the formula. Here's how you use the point-slope formula
They've given me m = 4, x1 = -1, and y1 = -6. I'll plug these values into the point-slope form, and solve for "y=":
y - y1 = m(x - x1)
y - (-6) = (4)(x - (-1))
y + 6 = 4(x + 1)
y + 6 = 4x + 4
y = 4x + 4 - 6
y = 4x - 2
Answer:
n = 20 or n = -2
Step-by-step explanation:
Solve for n over the real numbers:
n^2 = 18 n + 40
Subtract 18 n + 40 from both sides:
n^2 - 18 n - 40 = 0
The left hand side factors into a product with two terms:
(n - 20) (n + 2) = 0
Split into two equations:
n - 20 = 0 or n + 2 = 0
Add 20 to both sides:
n = 20 or n + 2 = 0
Subtract 2 from both sides:
Answer: n = 20 or n = -2
