Margery plans a vacation with costs for airfare, hotel (5 nights), sightseeing, and meals. If she receives a 10% discount on additional hotel nights, what will she spend?

Correct Answer: A

Rationale: To calculate Margery's total cost, we first need to find the cost without the discount. Let's say the original cost is x. With a 10% discount, she saves 10% of the cost of additional hotel nights. Since she is staying for 5 nights, the discount applies to 4 additional nights (5 - 1 night already included). Therefore, she saves 10% of 4 nights' cost. If x is the cost of 1 night, the total cost without discount is 5x. With the 10% discount, she saves 0.1 * 4x = 0.4x. So, the cost after discount is 5x - 0.4x = 4.6x. Given that the total cost is 5x for 5 nights, we can equate 5x to 4.6x to find x. Solving for x, we get x = Total cost / 5 = 5x / 5 = 4.6x / 5. Therefore, x = 4.6x / 5, which simplifies to x = 0.92 * 5x. This means 1 night's cost is 0.92 times the total cost for 5 nights. Given the total cost is $1328.35, we find the cost for 1 night is $1328.35 / 5 = $265.67. So, Margery will spend $1328.35 for her vacation.

Correct Answer: B

Rationale: The correct answer is B (0.23). To find the percentage of funds donated for construction costs, we need to consider the given percentage, which is 23%. In decimal form, 23% is represented as 0.23. Choices A, C, and D are incorrect because they do not match the correct decimal equivalent of 23%, which is 0.23. It's essential to convert percentages to decimal form accurately to calculate the correct percentage of funds allocated for a specific purpose.

Correct Answer: C

Rationale: To compare the fractions, it is beneficial to convert them to decimals or find a common denominator. When converted to decimals: 1/2 = 0.50, 5/8 = 0.625, 2/3 ≈ 0.666, and 7/9 ≈ 0.778. Therefore, the correct order from least to greatest is 1/2, 5/8, 2/3, 7/9. Choice A is incorrect because it places 7/9 first, which is the greatest fraction. Choice B is incorrect as it incorrectly lists the fractions. Choice D is incorrect as it starts with 7/9, which is the largest fraction instead of the smallest.

Correct Answer: B

Rationale: In this math expression, the correct answer is B) -20. To simplify the expression, we follow the order of operations (PEMDAS/BODMAS). First, we perform the multiplication and division operations from left to right. So, 7 * 3 = 21 and 4 * 2 = 8. Then, we perform the addition and subtraction operations from left to right. Thus, 6 + 21 - 8 = 19 - 8 = 11. However, there is a negative sign in front of the expression, so the final result is -11, making option B correct. Option A) -42 is incorrect because the calculation was not done correctly, leading to the wrong answer. Option C) 23 is incorrect as it seems to be a result of adding all the numbers together without following the correct order of operations. Option D) 20 is incorrect as it does not account for the negative sign in front of the expression. Educationally, this question reinforces the importance of following the order of operations to simplify mathematical expressions accurately. It highlights the significance of performing multiplication and division before addition and subtraction to obtain the correct solution. Understanding and applying PEMDAS/BODMAS rules are fundamental skills in mathematics that students need to master to solve problems correctly.

Correct Answer: B

Rationale: The correct answer is 'B: Low positive correlation.' In a low positive correlation, the variables tend to increase together, but the relationship is not strong. This description fits the data set provided. Choice A, 'High positive correlation,' is incorrect because the correlation is not strong. Choice C, 'Low negative correlation,' is incorrect as the variables are not decreasing together. Choice D, 'No correlation,' is incorrect because there is a relationship between the variables, albeit weak.