A coded message from a CIA operative to his Russian KGB counterpart is to be sent in the form Q4ET, where the first and last entries must be consonants; the second, an integer 1 through 9; and the third, one of the six vowels. How many different ciphers can be transmitted?

21,600

Step-by-step explanation:

If in the coding system being used there are 6 vowels (A, E, I , O, U and Y)

Number of Consonants =26-6 =20

First entry must be a consonant, therefore the first entry can be chosen in 20 ways.The second entry must be an integer 1 through 9, therefore the second entry can be chosen in 9 ways.The third entry must be one of the six vowels, therefore the third entry can be chosen in 6 ways.The last entry must be a consonant, therefore the last entry can be chosen in 20 ways.

Therefore:

Number of different possible ciphers =20*9*6*20

=21600

The point (5, 10) will work for the rule y=x+5.y= 10 x= 510=5+510=10therefore the ordered pair (5, 10) works for the rule