Answer:
(b) (a) (d) (a) (c)
Step-by-step explanation:
(i) The probability of an even card is 1/2 because the number of even cards and odd cards are the same so there is a 50% of getting an even card. (b)
(ii) Since the card is replaced, there is still a card for all numbers between 1-20. There are 8 prime numbers and 20 cards so the probability of getting a prime number is 8/20 or 4/10 or 2/5. (a)
(iii) The card was not replaced so there are only 19 cards and there are only 5 numbers that are multiples of 3 and greater than 4. The probability must be 5/19. (d)
(iv) A sure event means that it will happen 100%. So P(A) = 1 since the number one represents 100%. (a)
(v) All cards have replaced and there is only one number that is a multiple of 3 and 5 which is 15. 1 card out of 20 is a desired outcome so 1/20 is the probability. (c)
Answer:
Step-by-step explanation:
Internal dimensions of the box will be smaller considering the thickness of the wood:
- 21 - 1 = 20 cm
- 11 - 1 = 10 cm
- 7 - 0.5 = 6.5 cm (open top)
<u>The volume is now:</u>
Answer:
and 
Step-by-step explanation:
The first system is
and
We substitute x=-3 and y=-3
and 
Both equations are not satisfied
The next system is
and
We substitute x=-3 and y=-3
and 
Both equations are satisfied
The next system is
and 
We substitute x=-3 and y=-3
and
Both equations are not satisfied
The next system is
and
We substitute x=-3 and y=-3
and
Both equations are not satisfied
Part 1:
Step 1:
Find the value of G(16)
Using the equation for g(x) =√x, replace x with 16 and solve:
g(16) = √16 = 4
Step 2:
Now using the answer for g(16) replace x in the equation fir f(x) with 4 and solve:
f(x) = x +2
f(4) = 4+2 = 6
Part 2:
following the same steps as part 1:
f(g(x)) would be replacing x in the equation ofr f(x)with the equation for g(x)
f(g(x)) = √x +2
