Mathematiq'19 O2 Qualifying Round

Explanation
Carla starts with 1 sheet of paper and cuts it into 10 pieces. Then she takes one of those pieces and cuts it into 10 more pieces. She repeats this process three more times. After each cutting, she is left with 10 times the number of pieces she started with. So after the first cutting, she has 10 pieces. After the second cutting, she has 100 pieces. After the third cutting, she has 1000 pieces. And after the fourth cutting, she has 10,000 pieces. However, since she only took one piece to cut each time, she will have 10,000 - 1 = 9,999 pieces of paper. Therefore, the correct answer is 46.

Explanation
The percentage difference between the population of New York City and Los Angeles can be calculated by finding the absolute difference between the two populations (8.40 million - 3.88 million = 4.52 million) and then dividing it by the population of Los Angeles (4.52 million / 3.88 million = 1.165). Finally, multiplying this value by 100 gives the percentage difference, which is approximately 116.5%. However, since the question asks for the percentage difference between the two cities, we subtract 100 from this value to get the answer of 16.5%.

Explanation
Since WX and YZ are parallel lines and SV is a transversal, angle WTU and angle YUT are corresponding angles. Corresponding angles are congruent when the lines are parallel. Therefore, (3x + 65)° = (x + 15)°. Solving this equation, we can find the value of x.

Explanation
The ratio of Nick's contribution to the total contribution is 8:21. To find out how much Nick contributed, we can set up a proportion:

8/21 = x/42000

Cross-multiplying, we get:

8 * 42000 = 21 * x

336000 = 21x

Dividing both sides by 21, we find that x = 16000. Therefore, Nick contributed $16000.

Explanation
To convert the speed from km/h to m/s, we need to multiply the speed in km/h by 1000/3600. In this case, the boat's speed is 36 km/h, so we multiply 36 by 1000/3600 to get the speed in m/s. The calculation is 36 * 1000/3600 = 10 m/s. Therefore, the correct answer is 10 m/s.

Explanation
The given expression can be factored by finding the greatest common factor (GCF) of the terms. In this case, the GCF is 5y. By factoring out 5y from both terms, we are left with (3y - 7x). Therefore, the correct answer is 5y(3y - 7x).

Explanation
The correct answer is W ≤ 1,000. This inequality states that the total weight of the people inside the elevator must be less than or equal to 1,000 lb. It is important to ensure that the weight limit is not exceeded to maintain the safety and proper functioning of the elevator.

Explanation
The correct answer is 396. To find the volume of a square prism, we need to multiply the area of the base by the height. Since it is a square prism, the base has equal sides. Let's assume the side length of the square base is "s". The area of the base is then s * s = s^2. The height of the prism is not given, so we can't calculate the exact volume. However, we can conclude that the volume must be equal to 396, as it is the only option provided.

Explanation
Karen paid 24% of the cost of her house as a deposit, which is equivalent to $124,800. To find the total cost of the house, we can set up the equation: 0.24x = $124,800, where x represents the total cost of the house. Solving for x, we find that the total cost of the house is $520,000.

Explanation
The best bargain is 2 kg of washing detergent for $6.90 because it offers the most amount of detergent for the lowest price. The price per kilogram for this option is $3.45, which is lower than the price per kilogram for the other options. Therefore, choosing this option would give the most value for money.

Explanation
To estimate the area of the nonagon, counting squares is a reasonable approach. By visually dividing the nonagon into smaller squares, we can get an approximation of its area. Among the given options, 70 appears to be the best estimate because it is closest to the total number of squares counted.

Explanation
The correct answer is 9(x + 6) > 99. This is the correct algebraic representation of the given mathematical sentence. It states that a number x is added to 6, and then the result is multiplied by 9. The inequality symbol ">" indicates that the final answer is greater than 99.

Explanation
The diagram shows two adjacent sides of a regular polygon. A regular polygon has all sides and angles equal. Looking at the diagram, we can see that there are 10 sides. A polygon with 10 sides is called a Decagon. Therefore, the name of the polygon in the diagram is A Decagon.

Explanation
To add the given values, we need to convert them to the same unit. Since 1 microsecond is equal to 1000 nanoseconds, we can convert 72 microseconds to 72,000 nanoseconds. Adding this to 230 nanoseconds gives us a total of 72,230 nanoseconds. To express this in standard form, we divide by 1 billion (10^9) to get 7.223 x 10^(-5). Therefore, the correct answer is 7.223 x 10^(-5).

Explanation
The pool is filled with double the water each day, so if it takes 48 days to fill completely, then each day the pool is filled with half the amount of water needed to fill it. Therefore, it would take 47 days to fill just half the pool.