Zara has forgotten her 4-digit PIN code. She knows the first digit is a prime number and the 4 digits make a number divisible by 2. How many different sets of 4 digits could it be?

2,500 different sets

Step-by-step explanation:

According to the scenario, calculation of the given data are as follows,

Let 4-digit PIN code be WXYZ

As first digit is a prime number

So, W = 1, 2, 3, 5, 7

n(W) = 5

X and Y are number from 0 - 9

So, n(X) = 10 & n(Y) = 10

Z makes the whole number divisible by 2.

So, Z must even number

So, Z = 0,2,4,6,8 or n(Z) = 5

We can calculate the number of different sets by using following formula,

n(W) × n(X) × n(Y) × n(Z)

By putting the value, we get

5 × 10 × 10 × 5 = 2,500

b

step-by-step explanation:

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116