8. a) Two cards are drawn without replacement from a standard deck of \( 52 \) cards. Determine the probability that neither card is a diamond. (1 mark)
b) Two cards are drawn with replacement from a standard deck of \( 52 \) cards. Determine the probability that one card is a ten and the other is a queen. (1 mark)
a) \(\frac{248}{663}\)
b)\(\frac{8}{663}\)
Find the inverse for each of the following functions.
\(f ( x ) = 3 x + 1\)
\(g ( x ) = 1 x ^ { 3 } - 5\)
\(h ( x ) = \frac { 3 } { x + 5 }\)
\(j ( x ) = \sqrt[ 3 ] { x + 1 }\)
The total revenue from the sale of a popular book is approximated by the rational function \( R ( x ) = \frac { 1700 x ^ { 2 } } { x ^ { 2 } + 4 } \) , where \( x \) is the number of years since publication and \( R ( x ) \)
is the total revenue in millions of dollars.
(a) Find the total revenue at the end of the first year.
(b) Find the total revenue at the end of the second year.
