Let \(U = \{ \text { all sode pops} \} ; A = \{ \text { all diet sode pops} \} ; B = \{ \text { all cola soda pops} \} ; C = \{ \text { all sode pops in cans} \} ; \text { and } D = \{ \text { all caffeine- free soda pops} \} .\) Describe the given set in words. A' \(\cap \) C Select one: a. All non-diet soda pops and all soda pops in cans b. All non-diet soda pops in cans c. All diet soda pops in cans d. All diet soda pops and all soda pops in cans Let \(U = \{ \) all soda pops \(\} ; A = \{ \) all diet soda pops \(\} ; B = \{ \) all cola soda pops \(\} ; C = \{ \) all soda pops in cans \(\} \) ; and \(D = \{ \) all caffeine-free soda pops \(\} \) . Describe the given set in words. 

 

\(A ^ { \prime } \cap C\) 

 

Select one:

 a. All non-diet soda pops and all soda pops in cans 

b. All non-diet soda pops in cans 

c. All diet soda pops in cans 

d. All diet soda pops and all soda pops in cans 

Tickets to a basketball game can be ordered online for a set price per ticket plus a \(\$ 5.50\) service fee. The total cost in dollars for ordering \(5\) tickets is \(\$ 108.00\) . Which linear function represents \(c\) , the total cost, when \(x\) tickets are ordered? 

\(c ( x ) = 5.50 + 20.50 x\) 

\(c ( x ) = 5.50 x + 20.50\) 

\(c ( x ) = 5.50 + 21.60 x\) 

\(c ( x ) = 5.50 x + 21.60\) 

The third \(( 3^ { rd} ) \) and seventh \(( 7^ { th} ) \) terms of an arithmetic sequence are seven \(( 7 ) \) and fifteen \(( 15 ) \) respectively. i. Write two linear equations showing the relationships between the terms and the first term \(a\) and the common difference \(d\) . [ \(2\) marks ] ii. Solve the equations ( part i) for the first term \(a\) and the common difference \(d\) . iii. Using the values derived for \(a a d\) determine the sum of the first one hundred \(( 100 ) \) terms of the sequence. 

Explain why the function is discontinuous at the given number a. (Select all that apply.) 

\(f ( x ) = \{ \begin{array} { l l } { \frac { x ^ { 2 } - 2 x } { x ^ { 2 } - 4 } } & { \text { if } x \neq 2 } \\ { 1 } & { \text { if } x = 2 } \end{array} a = 2\) 

\(\square \lim _ { x \rightarrow 2 ^ { + } } f ( x ) \) and \(\lim _ { x \rightarrow 2 ^ { - } } f ( x ) \) are finite, but are not equal. 

\(\square \lim _ { x \rightarrow 2 } f ( x ) \) does not exist. 

\(\square f ( 2 ) \) is undefined. 

\(\square f ( 2 ) \) is defined and \(\lim _ { x \rightarrow 2 } f ( x ) \) is finite, but they are not equal. 

\(\square \) none of the above 

Solve the system. Use any method you wish. 

\(x + y + 2 = 0     \)       (1)

\(x^ 2 + y^ 2 + 4y - 3x = - 4\)        (2)

Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 

A. The solution set is \(\{ \} \) .

    (Simplify your answer. Type an ordered pair. Type exact answers, using radicals as needed. Use a comma to separate answer as needed.)

B. There is no solution. 

9.5 Solve Applications of Quadratic Equations 

Question \(13\) 

An rock is thrown downward from a platform that is \(158\) feet above ground at \(75\) feet per second. Use the projectile formula \(h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \) to determine when the rock hit the ground. [Recall that \(v _ { 0 } \) is the initial velocity of the object and \(h _ { 0 } \) is the inital height of the object.]

Answer: The rock will hit the ground after \(\square \)

Note: Round any numerical responses to two decimal places. If there are multiple answers, separate them with commas.