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Total marbles =6+5+9=20= 6 + 5 + 9 = 20. “Not green” means red or blue: 6+5=116 + 5 = 11 favorable outcomes. Probability =1120= \dfrac{11}{20}. Option C is correct. On PERT, “not” events are often quicker by subtraction: 1−P(green)=1−920=11201 - P(\text{green}) = 1 - \frac{9}{20} = \frac{11}{20}. Reduce fractions when possible; here 1120\frac{11}{20} is already simplest. Always check totals and categories to avoid overlooking a color or miscounting. Recognizing complementary probabilities speeds problem solving, especially when the direct count is cumbersome.

✅ Batch 17 (Questions 161–170) complete.

Want me to continue with Batch 18 (Questions 171–180) in the same format?

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• Mathematics

• Reading

• Writing

Batch 18: Questions 171–180

The word rejoiced means to feel joy or celebration. Context clues show farmers had endured drought; when rain arrived, they would celebrate. Option B fits perfectly. Options A, C, and D contradict the emotional tone. On the PERT, vocabulary-in-context questions require students to use surrounding information to infer meaning. Recognizing emotional cues like “long-awaited rain” signals relief and happiness. This strengthens reading comprehension across literature and informational passages.

The sentence links cause (hospital invested in prevention) to effect (declined chronic admissions). Option B summarizes it accurately. The other options contradict or add false details. On PERT, cause-and-effect reading items require condensing one action and its outcome into a single clear statement.

Solve x2−9=0x^2 - 9 = 0 by factoring as a difference of squares: (x−3)(x+3)=0(x - 3)(x + 3) = 0. By the zero-product property, either x−3=0x - 3 = 0 (so x=3x = 3) or x+3=0x + 3 = 0 (so x=−3x = -3). Thus, the solution set is {−3,3}\{-3, 3\}, option B. An alternative approach is to isolate x2=9x^2 = 9 and take square roots, remembering both the positive and negative roots: x=±3x = \pm 3. A common error is to report only the principal (positive) root. On the PERT, recognizing special patterns like difference of squares streamlines problem solving. Verifying solutions takes seconds: substitute x=3x=3 and x=−3x=-3 into the original equation; both yield 9−9=09 - 9 = 0. Comfort with factoring and simple radicals lays the groundwork for quadratics that don’t factor nicely, where completing the square or the quadratic formula may be required.

Subtract 7 from both sides: −3x≥−6-3x \ge -6. Divide by −3-3, reversing the inequality: x≤2x \le 2. Option A is correct. Inequality items test sign management: multiplying or dividing by a negative flips the direction. Verify with test points: pick x=2x=2 → 7−3(2)=17-3(2)=1 satisfies “≥1\ge 1.” Pick x=3x=3 → 7−9=−27-9=-2 fails. Graphically, the solution is all real numbers left of (and including) 2. Remember to keep steps parallel to equation solving but add the “flip rule” for negative factors to avoid a common trap.