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More Questions on This Topic :

Question 1. log2536= ?
  1.    2log256
  2.    12 log536
  3.    log56
  4.    All of these
Answer: Option D
: D

Let y =log2536 =loge36loge25=loge62loge52=2loge62loge5=loge6loge5 = log56 log2536 can be written as, log5262=2log526
or 12log562

Question 2. 3+12x42(4x+1)5 Which of the following best describes the solution to the inequality shown above?
  1.    x≤−137
  2.    x≥−137
  3.    x≤−14
  4.    x≥−14
Answer: Option D
: D

3+12x42(4x+1)5
(3+12x)×52(4x+1)×4
15+60x32x+8
60x32x815
28x7
x728
x14

Question 3. If the system of inequalities y2x+1 and y>12x1 is graphed in the xy-plane above, which quadrant contains no solutions to the system?
  1.    Quadrant II
  2.    Quadrant III
  3.    Quadrant IV
  4.    There are solutions in all four quadrants
Answer: Option C
: C

Given above is the graphical representation of the solution region. It can be seen that the system of linear inequalities have no solution in the fourth quadrant.

Question 4. Maria plans to rent a boat. The boat rental costs $60 per hour, and she will also have to pay for a water safety course that costs $10. Maria wants to spend no more than $280 for the rental and the course. If the boat rental is available only for a whole number of hours, the maximum number of hours for which Maria can rent the boat is ___

: Let n be the number of hours for which Maria rents the boat. Given that rental cost is $60 per hour. Also she has to pay $10 for a water safety course. Hence, the total cost is 60n + 10 . Given that she will spend a maximum of $280. Hence,
60n+10280
60n270
n4.5
Since the boat rental is available only for whole number of hours (n is a whole number), the maximum number of hours for which Maria can rent the boat is 4.