Taking an Uber ride in NYC has an initial fee of $2.55 with an additional charge of $1.75 per mile (we will ignore the small per minute waiting fee). In equation form, cost = 2.55 + 1.75(miles). a local NYC resident records the number of miles for his first 25 rides with Uber. The mean distance of his rides is 5.6 miles with a standard deviation of 1.2 miles. a) Find the mean cost of the 25 trips. b) Calculate the standard deviation of the cost of the 25 trips.

a) The mean cost of the 25 trips is:

$12.35.

b) The standard deviation of the cost of the 25 trips is:

$52.50

Step-by-step explanation:

a) Data and Calculations:

Initial fee (fixed) = $2.55

Variable (additional) charge = $1.75 per mile

Equation = 2.55 + 1.75(miles)

Trips = 25

Mean distance for first 25 rides = 5.6 miles

Standard deviation = 1.2 miles

Mean cost of the 25 trips = 2.55 + 1.75 (5.6) = $12.35

Total cost = $308.75 (25 * 12.35) based on mean cost

Standard deviation of the cost of the 25 trips:

Total standard deviation for the 25 trips = 30 miles (1.2 * 25)

= $52.50 (1.2 * 25 * $1.75)

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.