Tecart
three drivers competed in the same fifteen drag races. the mean and standard
deviation for the race times of each of the drivers are given.
driver a had a mean race time of 4.01 seconds and a standard deviation of 0.05
seconds
driver b had a mean race time of 3.96 seconds and a standard deviation of 0.12
seconds
driver c had a mean race time of 3.99 seconds and a standard deviation of 0.19
seconds.
a.
which driver had the fastest typical race time?
b.
which driver's race times were the most variable?
c.
which driver do you predict will win the next drag race? support your
prediction using the inean and standard deviation.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x

answer: b f g .

step-by-step explanation: