Exercise 1.3. a telephone number consists of ten digits, of which the first digit is one of 1; 2; : : : ; 9 and the others can be 0; 1; 2; : : : ; 9. what is the probability that 0/ appears at most once in a telephone number, if all the digits are chosen completely at random

The probability that "0" appears at most once in a telephone number is 0.82

Step-by-step explanation:

Telephone number = 10 digits

First digit = (1,2......9)------> there are 9 possible digits

digit 2 - digit 10 = (0,1,2......9) -----> there are 10 possible digits

Let's find the total amount of telefone numbers with those characteristics:

possible first digit X possible second digit X...............X possible tenth digit

9X10X10X10X10X10X10X10X10X10 =

Let's find the amount of telephone numbers that "0" appears at most once (it means 0 will occur either once or will not occur):

If "0" appears once, the rest of the numbers should be 1.2.....9 (9 possible digits)

9X10X9X9X9X9X9X9X9X9 =

If "0" doesn't appear, the ten digits should be 1,2....9

9X9X9X9X9X9X9X9X9X9 =

Finally, find the probability

P=(favorable outcomes/total outcomes)

P= = 0.82

22 and 22

step-by-step explanation:

10 plus 12 equals 22.

12 plus 10 also equals 22 because regardless of what order they're in, they're gonna equal the same thing.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.