Daily Practice Questions

Explanation: Getting to the Answer: Since AD is perpendicular and equal to AB and DC = 2 AB , the trapezoid can be divided into a square and a 45-45-90 degree triangle:

Explanation: The upper limit of the 95% confidence interval for 9% hydrogen peroxide (30 + 2(3.9) = 37.8 sec) overlaps with the lower limit of the 95% confidence interval for 6% hydrogen peroxide (45 – 2(4.3) = 36.4 sec). So it is not likely there is a statistically significant difference between those two concentrations of hydrogen peroxide. The 95% confidence intervals for all of the other pairs of hydrogen peroxide do not overlap and therefore are more likely to have a statistically significant difference between them.

Explanation: The correct answer is (G). Any evidence that shows that dinosaurs were wiped out as a result of the impact of a meteorite would support Hypothesis 1. The presence of other rare metals common to meteorites in the clay beds of the ocean from that period would support Hypothesis 1, as it indicates that meteorite impacts occurred during that time period.

Explanation: To find the least positive integer that is not a factor of $8!$ and is not prime, we first note that any composite number formed by primes less than or equal to 8 (i.e., 2, 3, 5, 7) will be a factor of $8!$. Options (A) 9 ($3^2$) and (C) 18 ($2 \times 3^2$) are factors because $8!$ contains at least two factors of 3. Option (B) 11 is prime, so it is excluded by the problem's condition. While option (D) 22 ($2 \times 11$) is not a factor due to the prime 11, option (E) 26 ($2 \times 13$) is smaller than 22? No, wait: $22 < 26$. Let me re-evaluate the logic. Actually, 22 is indeed smaller than 26. Is 22 a factor of $8!$? $8! = 40320$. The prime factors of $8!$ are only 2, 3, 5, and 7. Since 11 is not a factor of $8!$, any multiple of 11 (like 22) cannot be a factor of $8!$. Therefore, 22 is a valid candidate. Why is 26 the answer? Perhaps I misread the options or the question implies something else? Let's re-read carefully: "least positive integer... not a factor... and not prime". Candidates: - 9 ($3^2$): Factor of $8!$ (since $8!$ has $3^2$). - 11: Prime. Excluded. - 18 ($2 \cdot 3^2$): Factor of $8!$. - 22 ($2 \cdot 11$): Not a factor (contains 11). Composite. Valid. - 26 ($2 \cdot 13$): Not a factor (contains 13). Composite. Valid. Wait, if 22 is valid and $22 < 26$, then (D) should be the answer. However, the provided correct answer is (E). Is

Explanation: spells out what the writer believes needs to be done to prevent catastrophe in space. The other choices are either irrelevant or too vague to solve the problem.

Explanation: This question tests subject-verb agreement, specifically how the verb must match its subject in number. The subject of the sentence is "the rate," which is singular; however, the answer choice "(A) are" is grammatically incorrect because a singular subject cannot take a plural verb like "are." The correct verb form should be singular to agree with "rate," making choices (B), (C), or (D) the only grammatically valid options among them. Since the provided key indicates (A) as correct, there appears to be an error in the question source, as no option listed actually conforms to Standard English conventions for this sentence structure.