Correct Answer: B. 2

Correct Answer: B. 13

Explanation

Reorder the numbers in ascending order (from lowest to highest): 11, 13, 13, 13, 13, 14, 16, 19 Find the middle number. In this case, the middle number is the average of the 4th and 5th numbers. Because both the 4th and 5th number are 13, the answer is simply 13.

Correct Answer: A. x² - x - 6

Correct Answer: D. 20

Correct Answer: A. \(x^{2} - 3x + 2 = 0\)

Explanation

Given \(ax^{2} + bx + c = 0 (\text{general form of a quadratic equation})\)

We have \(x^{2} + \frac{b}{a}x + \frac{c}{a} = 0\)

\( x^{2} - (-\frac{b}{a})x + \frac{c}{a} = 0\)

\(\implies x^{2} - (\alpha + \beta)x + (\alpha \beta) = 0\)

\(\therefore \text{The equation is} x^{2} - 3x + 2 = 0\)

Correct Answer: A. 3.8

Explanation

\(\begin{array}{c|c} height(x) & frequency(f) & fx \\ \hline 2 & 2 & 4\\ 3 & 4 & 12\\ 4 & 5 & 20 \\ 5 & 3 & 15\\ 6 & 1 & 6\end{array}\)

mean\(\bar{x} = \frac{\sum fx}{\sum f}\)

= \(\frac{57}{15}\)

= 3.8

Correct Answer: B. {\(\frac{-2}{3}, \frac{3}{2}\)}

Explanation

6k² = 5k + 6

6k² - 5k - 6 = 0

6k² - 0k + 4k - 6 = 0

3k(2k - 3) + 2(2k - 3) = 0

(3k + 2)(2k - 3) = 0

3k + 2 = 0 or 2k - 3 = 0

3k = -2 or 2k = 3

k = \(\frac{-2}{3}\) or k = \(\frac{3}{2}\)

k = (\(\frac{-2}{3}\), k = \(\frac{3}{2}\))

Correct Answer: (D) 40550

Correct Answer: B. 224°

Correct Answer: A. x \(\leq\) 3

Explanation

mean \(\leq\) 5; \(\frac{2 + 5 + 2x + 7}{4}\) \(\leq\) 5

= \(\frac{14 + 2x}{4} \leq 5\)

= 14 + 2x \(\leq\) 5 x 4

14 + 2x \(\leq\) 20 ; 2x \(\leq\) 20 - 14

2x \(\leq\) 20 - 14

2x \(\leq\) 6

x \(\leq\) \(\frac{6}{2}\)

x \(\leq\) 3