You read online that the probability of being dealt four‑of‑a‑kind in a five‑card poker hand is 1 / 4165 . Explain carefully what this means. In particular, explain why it does not mean that if you are dealt 4165 five‑card poker hands, one will be four‑of‑a‑kind. Select the best explanation from the choices. It does mean that if you are dealt 4165 five‑card poker hands, one will be four‑of‑a‑kind. It does not mean that all will be four‑of‑a‑kind. The probability is actually saying that only on the 4165 th poker hand will you get a four‑of‑a‑kind, not just on any of the 4165 poker hands. The probability is actually saying that in the long run, with a large number of five‑card poker hands, the fraction in which you will be dealt a four‑of‑a‑kind is 1 / 4165 . The chance you will be dealt four‑of‑a‑kind is 1 / 4165 only on the first hand. This chance will then increase with each new hand you are dealt until you eventually win.

answer: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest

the answer is a.

135 and 80

step-by-step explanation:

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.