3/6 cups of flower. Or 1/2 cups of flower more than the sugar.
((10,5 + 513) - 14,2) - 7 =502.3
A direct variation equation is one that requires y varies directly as x and looks like this in equation form:
![\frac{y}{x} =k](https://tex.z-dn.net/?f=%20%5Cfrac%7By%7D%7Bx%7D%20%3Dk%20)
where k is the constant of variation. If we solve this for y, we have y = kx, which happens to be a linear function... a line. k here, then, serves as the slope. So what we are given as points on a direct variation function are actually points on a line. The equation for this requires that we find the slope and then rewrite the formula accordingly. First the slope:
![m(k)=\frac{-4-(-3)}{-12-(-9)}=\frac{-4+3}{-12+9}=\frac{1}{3}](https://tex.z-dn.net/?f=%20m%28k%29%3D%5Cfrac%7B-4-%28-3%29%7D%7B-12-%28-9%29%7D%3D%5Cfrac%7B-4%2B3%7D%7B-12%2B9%7D%3D%5Cfrac%7B1%7D%7B3%7D%20%20%20%20)
Now we need to write the equation by using one of the points' coordinates. I picked the first point that has an x coordinate of -9 and a y coordinate of -3. Fitting those into the slope-intercept form of a line,
![-3=\frac{1}{3}(-9)+b](https://tex.z-dn.net/?f=%20-3%3D%5Cfrac%7B1%7D%7B3%7D%28-9%29%2Bb%20%20)
which simplifies to
-3 = -3 + b and b = 0. That means that the equation of direct variation is
or just
![y=\frac{1}{3}x](https://tex.z-dn.net/?f=%20y%3D%5Cfrac%7B1%7D%7B3%7Dx%20%20)
Roper is not using a simple random sample. The samples are calculated to get 500 males and 500 females. This would be very unlikely or improbable to take place in a simple random sample. The design that they are using is a stratified sampling (dividing the population into groups) with 2 strata and these are the males and females.