Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. when carrying 10 gallons of fuel, the airplane weighs 2165 pounds. when carrying 44 gallons of fuel, it weighs 2386 pounds. how much does the airplane weigh if it is carrying 48 gallons of fuel?

You have two points relating fuel and weight.

(15,2187) and (35,2303)

slope = (2303-2187)/(35-15) = 5.8

intercept = ?

2187 = 5.8*15 + b

b = 2100

Equation:

f(x) = 5.8x + 2100

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f(50) = 2390 lbs.

the expected value of the random variable : 0, 1 and 2

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4