Final answer:
The variances v(x) and v(x - 42) will be the same because variance measures the spread of the values around the mean, and this spread is unaffected by subtracting a constant from all values of the random variable.
Step-by-step explanation:
When calculating the variance of a random variable x, denoted as v(x), and the variance of a transformed random variable x - 42, denoted as v(x - 42), the variances will be the same. This does not change because variance is a measure of dispersion that is not affected by changes in location or shifts in the random variable; it only takes into account the spread of values around the mean. Subtracting 42 from each value of the random variable shifts the distribution by 42 units but does not affect how spread out the distribution is, therefore the variance remains unchanged.