A password has to use the following format: , where L can be any of the upper case letters in the alphabet, and D can be any digit including 0. None of the digits or letters can repeat. What is the probability that a random password uses only vowels (A, E,I, O,U) and odd numbers (1,3,5,7,9)? Show work but do not evaluate. What is the probability that the password spells the word “MATH?”

Only vowels and odd numbers:

Spells math:

Step-by-step explanation:

We have four letters, so the probability that one letter is a vowel is 5/26 (we have 5 vowels in a total of 26 letters), then the second letter has a probability of 4/25 of being a vowel (1 vowel used), and so on (third letter being vowel = 3/24 and fourth letter being vowel = 2/23)

Then, for the digits, we do the same, one digits has 5/10 probability of being odd, then the second digit has 4/9, the third has 3/8 and the fourth has 2/7.

So the final probability would be:

To find the probability that the password spells the word “MATH", each letter has to be a specific letter, so the first letter has 1/26 probability, the second has 1/25, and so on:

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

answer is because 4×10=40

and 98×4= is 392

40,392