1. the data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.
26 31 40 28 19 23 35 38 43 46 28 30
(a) what is the five-number summary of the data set?
(b) what is the range of the data set? show your work.
highest number 46 minus lowest number 19 equals 27 range
(c) what is the interquartile range (iqr) of the data set? show your work.

Put the numbers in order
19,23,26,28,28,30,31,35,38,40,43,46

minimum = 19
maximum = 46
Q1 =(26 + 28)/2 = 54/2 = 27
Q2 (median) = (30 + 31)/2 = 61/2 = 30.5
Q3 = (38 + 40)/2 = 78/2 = 39

range = max - min = 46 - 19 = 27

Interquartile Range (IQR) = Q3 - Q1 = 39 - 27 = 12

Hence the equation is .

Val has rented the bicycle for 8 days.

Step-by-step explanation:

Given,

The total cost for rent a bicycle = $123

Fixed rental fee = $55

Charge of 1 day = $8.50

Solution,

Let the total number of days Val rented the bicycle be 'x'.

The total cost for rent a bicycle is the sum of fixed rental fee and charge of 1 day multiplied with  total number of days.

Now framing the above sentence in equation form, we get;

The total cost for rent a bicycle = Fixed rental fee + Charge of 1 day × total number of days

On putting the given values, we get;

So the equation can be written as;

Now we solve the expression for calculating total number of days, we get;

Hence the equation is .

Thus Val has rented the bicycle for 8 days.