"Some debit and credit card companies require their customers to choose personal identification numbers (PINs). Customers choose 4 digits from 10 possible digits, and does not repeat digits. How many different possible PINs are there?"

5040 ways

Step-by-step explanation:

In solving this problem we will use the method of permutations.

The formula for permutation is

nPr = n!/(n-r)!

Back to our question, we are required to choose 4 digits out of 10 digits. Now in solving this:

The number of ways of selecting 4 digits from 10 digits

= 10P4

= 10!/(10-4)!

= 10!/6!

= 10x9x8x7x6!/6!

= 5040 ways

Note that 6! on the numerator cancels out 6! On the denominator.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).