A number is chosen at random from the whole numbers 1, 2, 3, ..., 50. Work out the probability that the number is:

- an odd number or a factor of 10.

- a square number or a factor of 8.

- a multiple of 4 or a multiple of 5.

3/5.

6/25

2/5.

Step-by-step explanation:

1. Prob(An odd number is drawn) = 25/50 = 1/2  (as a half of the numbers 1 - 50 are odd).

Prob (factor of 10 is drawn) = 5/50 = 1/10.     (10,20,30,40,50 are the factors).)

So Prob(odd or factor of 10 is drawn) = 1/2 + 1/10 = 6/10

= 3/5.

2. Square numbers are 1, 4, 9, 16, 25, 36 and 49. Probability = 7/50.

Factors of 8 are, 8, 16, 24, 32, 40, 48 .

we do not count 16 in our calculations because it is a square number and has been counted already so probability = 5/50

So the required probability = 7/50 + 5/50 = 12/50 = 6/25.

3. Multiples of 4 are 4, 8, 12, 16 , 20, 24, 28, 32, 36, 40, 44, 48. (12 numbers).

Probability of a multiple of 4 =  12/50.

Multiples of 5 are 5, 10, 15 , 20, 25, 30, 35, 40 , 45 , 50.

We don't count 20 or 40 as they are multiples of 4 so

Prob(multiple of 5) = 8/50

Required probability =  8/50 + 12/50 = 20/50

= 2/5.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2