56)
1, 8,27,64,125, ...
What is the next number in the sequence above?
(I got 216)
75) A company wants to study 6 brands of soap by comparing each brand with every other brand, if each comparison costs $ 2,000, how much will the company spend altogether?
(I got 30,000)
76) what is the smallest number that both 14 and 30 as factors?
(I got 210)
Please help! Thanks!
I agree with your answers, good job
Okay thanks!
Sure! I'd be happy to help you with these questions.
56) The given sequence consists of numbers raised to increasing powers of 3: 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125. So, the pattern is to raise the next number by 3. Therefore, the next number in the sequence is 6^3 = 216. You got it right!
75) To find out how much the company will spend, we need to determine the total number of comparisons to be made. Since there are 6 brands of soap to be compared, we can use the formula for combinations: nC2 = n(n-1)/2.
Plugging in the value of n (6) in the formula, we get: 6(6-1)/2 = 6(5)/2 = 30 comparisons.
Each comparison costs $2,000, so multiplying the number of comparisons (30) by the cost per comparison ($2,000), we find that the company will spend 30 * $2,000 = $60,000 in total. It seems like you made a mistake here. The correct answer is $60,000, not $30,000.
76) To find the smallest number that both 14 and 30 are factors of, we need to find the least common multiple (LCM) of 14 and 30. One way to find the LCM is to factorize the numbers and then take the highest power of each prime factor.
The prime factorization of 14 is 2 * 7, and the prime factorization of 30 is 2 * 3 * 5. Taking the highest power of each prime factor, we get: 2^1 * 3^1 * 5^1 * 7^1 = 210.
Therefore, the smallest number that both 14 and 30 are factors of is 210. You got it right!
I hope this explanation helps! Let me know if you have any more questions.