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MaTh PrObLeMs FoR aLl!!!!!!!

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Find the next number and GENERAL TERM for each of the following sequence. Justify each answer.

1) 3,8,15,24,35,48...

2) 6,14,18,28,30,42...

3) 1/6, 1/3, 1/2, 2/3, 5/6, 1,...

4) 4,1,0,1,4,9...

5) 2,8,26,80,242,728...

6) 15,210,63,220,243,230...

7) 2,7,4,14,6,21...

8) -1,4,1,6,3,8

9) 1,5,13,29,61,125...

10) 10,21,33,46,60,75...
 
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9 Answer the whole of this question on a sheet of graph paper.
A taxi company has “SUPER” taxis and “MINI” taxis.
One morning a group of 45 people needs taxis.
For this group the taxi company uses x “SUPER” taxis and y “MINI” taxis.
A “SUPER” taxi can carry 5 passengers and a “MINI” taxi can carry 3 passengers.
So 5x + 3y 45.
(a) The taxi company has 12 taxis.
Write down another inequality in x and y to show this information. [1]
(b) The taxi company always uses at least 4 “MINI” taxis.
Write down an inequality in y to show this information. [1]
(c) Draw x and y axes from 0 to 15 using 1 cm to represent 1 unit on each axis. [1]
(d) Draw three lines on your graph to show the inequality 5x + 3y 45 and the inequalities from parts
(a) and (b).
Shade the unwanted regions. [6]
(e) The cost to the taxi company of using a “SUPER” taxi is $20 and the cost of using a “MINI” taxi is
$10.
The taxi company wants to find the cheapest way of providing “SUPER” and “MINI” taxis for this
group of people.
Find the two ways in which this can be done. [3]
(f) The taxi company decides to use 11 taxis for this group.
(i) The taxi company charges $30 for the use of each “SUPER” taxi and $16 for the use of each
“MINI” taxi.
Find the two possible total charges. [3]
(ii) Find the largest possible profit the company can make, using 11 taxis. [1] PLease help me Ill appreciate it
 
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