Decide whether a discrete or continuous random variable is the best model for each of the following variables: (a) the time until a projectile returns to earth. (b) the number of times a transistor in a computer memory changes state in one operation. (c) the volume of gasoline that is lost to evaporation during the filling of a gas tank. (d) the outside diameter of a machined shaft.

a) continuous random variable; b) discrete random variable; c)  continuous random variable; d)  continuous random variable

Step-by-step explanation:

In the case of a), b), and d), the variables are continuous random variables, because all of them are measured in a continuous scale. It means that between any two values of the scale, you can find infinite values. Height of something, time, length, are all continuous variables. For example, the outside diameters of a machined shaft could be 30 mm or 31mm, but also it could be 30.1, 30.2, 30.3 and so on. You could measure any value in the scale. The volume of gasoline also can take any value in a continuous scale. The time until a projectile returns to Earth probably needs to be measured very accurately, so again you can expect any value in the scale. When you’ re studying continuous variables the tool that you’ re using to measure it would be your limit to define how many values you can find between other two values.

The number of times a transistor in a computer memory changes state in one operation is a discrete random variable. It can only take finite values (0, 1, 2 and so on), so you can’ t find infinite values between two values. Discrete values always represent exact quantities that can be counted.

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

if x = 1, then the answer is 3.5