Which of the following variables for data about a track team is a discrete variable? a) the height of a team memberb) the weight of a team memberc) the number of times that a team member finished first in a raced) the time recorded for the last race that was run by a team membere) the time recorded for a one-mile race by a team member

C

Step-by-step explanation:

Discrete data includes numbers that are exclusively integers, i.e, ... -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 7 and so on. It do not include the other real numbers that are not integers. You can recognize discrete data, for example, in a grah, as there will be only isolated points and not a continuous line.

The height of a member is continuous as we can have every number between 0 and the top height. There can be 1.50 m, 1.51m, 1.5000001m, 1.65m, 1,644444449, and so on with every number (obviously, we will not have heights of 5.78 m because of simply nature). So, we discard option a.

Exactly the same as heights happens with weight. We can ahve any weight you may imagine from the less weight to the top. 100.45555555 pounds is a posible weight, for example. With this, we discard option b.

The time is also continuous. Lets think in minutes. A runner can register 7 minutes, 7.2 minutes, 7.098686 minutes, and so on for every number. We can use every fraction you imagine. So we can discard options d and e.

However the number of times is discrete, because the number of races are discrete. There are 1, 2, 3, 4,... races. We can not have 5.5 races, it is impossible. So, the number of times a runner finished ahead is discrete. There is no member that finished 7.2 times first, we can find either 7 times or 8 times, but not 7.2. So, option c is the correct.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.