Two spies have to communicate using a secret code. They need to create exactly 30 possible
precoded messages, using a single number and letter. Which structure should the code have?

C. Select a number from {1, 2, 3, 4, 5, 6} and a vowel.

Step-by-step explanation:

Let's start this with a simple example: how many messages are possible using one number from {7, 9} and one letter from {a, b}. It will be 4 as 7a, 7b, 9a and  9b. This result can also come by multiplying the number of digits used and number of alphabets used - here number of digits are 2 (they are 7 and 9) and number of alphabets used are 2 (they are 'a' and 'b'). So 2 × 2 = 4.

[NOTE : In this question 7a and a7 are same]

Maximum number of options consists of vowels as letters so we will first find the number of digits needed if vowels are used as letters.

The number of vowels are 5 (they are 'a', 'e', 'i', 'o', 'u').

The number of possible precodes needed = 30

Let the number of digits needed be 'n'.

Then n × 5 = 30

∴ n = 6

Therefore the number of digits needed is 6 which is there in option C. The digits are {1, 2, 3, 4, 5, 6}

Therefore option C is the answer.

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Step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.