Rafael is training for a triathlon, which includes swimming, biking, and running. The graph shows the total hours he spent swimming over the first 4 weeks of his training.
• Is the relationship between the time spent
swimming and the number of weeks proportional?
Complete the statements.
Swim Training
30
27
• The points ?
a straight line that
24
?
21
through the origin.
Time (h)
18
15
12
6
0 1 2 3 4 5 6 7 8 9 10
Weeks

Consider the table below. x y -1 -5 0 5 1 11 2 13 3 11 complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

The graph of the the function f(x) is given below. find [tex]\lim_{x \to 0\zero} f(x)[/tex] [tex]\lim_{x \to 1+\oneplus} f(x)[/tex] [tex]\lim_{x \to 0-\zeroneg} f(x)[/tex]