Correct Answer: C. 2

Explanation

\(log_{10}(3x+1) + log_{10}4 = log_{10}(9x+2)\)

\(log_{10}4(3x+1) = log_{10}(9x+2)\)

4(3x+1) = 9x + 2

12x -4 = 9x + 2

12x - 9x = 2 + 4

3x = 6

x = 2

Correct Answer: C. -1

Explanation

\(\frac{3^{(1-n)}}{9^{-2n}}=\frac{1}{9}\\

3^{1-n}\times 3^{-2(-2n)} = 3^{-2}\\

1-n-2(-2n)= -2\\

1-n+4n=-2\\

n=-1\)

Correct Answer: D. 91.4, 89

Explanation

The mean is just the average of all the test scores, which is found by adding up the scores and dividing by the number of scores (15). This gives 91.4 as the mean. The mode is the score which occurs most frequently. In this case, the mode is 89. The median, the middle score of the sequence, is 91.

Correct Answer: A. \(\frac{\sqrt{5}}{2}\)

Correct Answer: B. x = 1 and y = 1

Explanation

x + y = 2........... (i)

3x - 2y = 1......(ii)

From (i): x = 2 - y ..........(iii)

subt. (2 - y) for x in (ii)

3(2 - y) 2y = 1

6 - 3y - 2y = 1

-5y = 1 - 6 = -5

y = \(\frac{-5}{-5}\) = 1

subst. (i) for y in (iii)

x = 2 - 1 = 1

x = 1, y = 1

Correct Answer: b. 47.67

Correct Answer: C. 70

Correct Answer: B. 32

Explanation

2 + 3 + 4 + 5 + 6 + 3 +3 + 0 + 2 + 2 + 2 = 32

Correct Answer: C. 0

Explanation

log 6 + log 2 - log 12

= \(\log (\frac{6 \times 2}{12})\)

= \(\log 1\)

= 0

Correct Answer: D. 34_five, 21_six, 22_three

Explanation

22_three, 34_five, 21_six = (2 x 3)(2 x 3^o), (3 x 5¹) = (4 x 5⁰), (2 x 6¹) + (1 x 6⁰)

= (6 + 2), (15 + 4), (12 + 1) = 8_ten, 29_ten, 13_ten in descending order

29_ten, 13_ten, 8_ten = 34_five, 21_six, 22_three