A factory produces ball bearings whose diameters are meant to have a mean of 3\text{ mm}3 mm3, start text, space, m, m, end text. Suppose that the actual sizes are normally distributed with a mean of 3\text{ mm}3 mm3, start text, space, m, m, end text and a standard deviation of 0.2\text{ mm}0.2 mm0, point, 2, start text, space, m, m, end text. The overseers took a random sample of n=100n=100n, equals, 100 ball bearings to see if their mean diameter was significantly different than the target. The mean diameter of the ball bearings in the sample was \bar x=2.96\text{ mm} x ˉ =2.96 mmx, with, \bar, on top, equals, 2, point, 96, start text, space, m, m, end text. To see how likely a sample like theirs was to occur by random chance alone, the factory overseers performed a simulation. They simulated 757575 samples of n=100n=100n, equals, 100 diameters from a normal population with a mean of 3\text{ mm}3 mm3, start text, space, m, m, end text and standard deviation of 0.2\text{ mm}0.2 mm0, point, 2, start text, space, m, m, end text. They recorded the mean of the diameters in each sample. Here are the sample means from their 757575 samples:

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)