Combinatorial Enumeration. That whole class was a rollercoaster ride of mind-blowing generating functions to prove crazy things. The exam had ridiculous questions like 'count the number of cactus trees with n vertices such that etc etc etc' and you'd do three pages of terrible terrible sums and algebra. Then your final answer would be something beautiful like n/2 and you'd breath a sigh of relief and thank the math gods.
1. 2/3. Flip 2/3 into 3/2 and then multiply and simplify.
2. 30/91. Flip 7/6 to 6/7 and then multiply. You cannot simplify the fraction.
3. 26/27. Flip 9/10 to 10/9 and then multiply. You cannot simplify the fraction.
4. 44.2. Multiply it as if there was no decimal. Then count the number of digits after the decimal in each factor. Then put the same number of digits behind the decimal in the product.
5. 98.75. Multiply it as if there was no decimal. Then count the number of digits after the decimal in each factor. Then put the same number of digits behind the decimal in the product.
6. 3.36. Multiply it as if there was no decimal. Then count the number of digits after the decimal in each factor. Then put the same number of digits behind the decimal in the product.
7. 2. Multiply the divisor by as many 10’s as necessary until you get a whole number. Remember to multiply the dividend by the same number of 10’s. Then divide it normally.
8. 10.93 (rounded). Multiply the divisor by as many 10’s as necessary until you get a whole number. Remember to multiply the dividend by the same number of 10’s. Then divide it normally. I rounded it to the hundredth.
Hope this helps!
Answer:
(x - 2)² - 30
Step-by-step explanation:
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 4x
f(x) = x² + 2(- 2)x + 4 - 4 - 26 = (x - 2)² - 30
Answer:
- True for Co-Prime Numbers
- False for Non Co-Prime Numbers
Step-by-step explanation:
<u>STATEMENT:</u> The LCM of two numbers is the product of the two numbers.
This statement is not true except if the two numbers are co-prime numbers.
Two integers a and b are said to be co-prime if the only positive integer that divides both of them is 1.
<u>Example: </u>
- Given the numbers 4 and 7, the only integer that divides them is 1, therefore they are co-prime numbers and their LCM is their product 28.
- However, consider the number 4 and 8. 1,2 and 4 divides both numbers, they are not co-prime, Their LCM is 8 which is not the product of the numbers.
