Math Challenge No. 1

Explanation
The function is defined by the pattern where the y-value is obtained by multiplying the x-value by 2 raised to the power of (x-1). For example, when x=1, y=2^(1-1) = 2^0 = 1. When x=2, y=2^(2-1) = 2^1 = 2. Following this pattern, when x=5, y=2^(5-1) = 2^4 = 16. Therefore, the value of y is 16, not 32.

Explanation
The arithmetic sequence has a common difference of 3, meaning each term is obtained by adding 3 to the previous term. To find the 30th term, we start with the first term (2) and add the common difference (3) a total of 29 times. This gives us 2 + 29 * 3 = 2 + 87 = 89. Therefore, the 30th term of the sequence is 89.

Explanation
To find the number of pounds of cashews needed, we can set up an equation based on the given information. Let x represent the number of pounds of cashews. The total cost of the peanuts and cashews mixture is (20 * 35) + (x * 50) pesos. The total weight of the mixture is 20 + x pounds. The average price per pound is 40 pesos. Setting up the equation (20 * 35) + (x * 50) = (20 + x) * 40, we can solve for x. Simplifying the equation gives 700 + 50x = 800 + 40x. By subtracting 40x from both sides and simplifying, we get 10x = 100. Dividing both sides by 10 gives x = 10. Therefore, 10 pounds of cashews must be used.

Explanation
A 12-sided polygon is called a dodecagon. This term is derived from the Greek words "dodeka" meaning twelve and "gonia" meaning angle. A dodecagon has twelve sides and twelve angles. It is a regular polygon, meaning that all of its sides and angles are equal in length and measure. The term "dodecagon" can be written in lowercase or uppercase letters, but it always refers to the same shape.

Explanation
The number 27,720 is the smallest number that is divisible by each natural number less than or equal to 12. This can be determined by finding the least common multiple (LCM) of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, which is 27,720.