Simplify each expression. Thanks 4n 6 n-3 2n 7) a+4_6 2a +6 2 8) 9) x+5...
1. Simplify each expression, for n = 5 a) 8n + 2 b) n2 - 2n+n d) 19 - 3n + e) (3n - 3) + 15-n-18
Use the definition of 0 to show that 5n^5 +4n^4 + 3n^3 + 2n^2 + n 0(n^5).Use the definition of 0 to show that 2n^2 - n+ 3 0(n^2).Let f,g,h : N 1R*. Use the definition of big-Oh to prove that if/(n) 6 0(g{n)) and g(n) 0(h{n)) then/(n) 0(/i(n)). You should use different letters for the constants (i.e. don't use c to denote the constant for each big-Oh).
8 and 9 plz Multiply or divide. Simplify. (4 points each) 5x x+x-6 3x 5x+5 6) 0 Add or subtract. Simplify. (3 points) -? 9 120S 21-7 2-7 x-1 x-1
3 л л 4 2 6 5 5 6 1 2n n 7 12 8 and/or 11 10 + 8 The figure above shows a generalized life cycle for land plants. Each number within a circle or square represents a specific plant structure (a plant type or part), and each number over an arrow represents a process such as meiosis, mitosis, or fertilization. Which number corresponds to a zygote? O 1 O 3 O 5 09 O 11
2. Simplify: (n + 2)! (1) n! (2n-1)! (2) (2n + 1)! (2n + 2)! (3) (2n)!
Assume that algorithm A1's running time roughly equals to T1(n) = 4n^2 + 2n + 6 and algorithm A2's running time roughly equals to T2(n) = 2n lg(n) + 10 . Suppose that Computer A's cpu runs 10^8 instructions/sec. When the input size equals to 10^4, 10^6, and 10^12 respectively, how long will algorithm A1 take to finish for each input size in the WORST case? How long will algorithm A2 take to finish for each input size in the...
10. Simplify each expression and write it without using factorial notation. (3 marks each) (n+4)! (n+2)! a. b. (n-r+1)! (n-y-2)!
Number 3 +4n + 8 is O(n). 3. Give a formal proof that f(n) 5m3 +3n2 4. Give a formal proof that f(n)-7*2n+ 9m3 is O(2n). 5. Give a formal proof that log (n + 1) is O(log n).
1. Evaluate the expression when x=-5 - 3x² + 2x - 7 2. Simplify: 4+ 2(x + 3) – 7(2x - 5) 3. Subtract: (5y² + 4y + 3) - (y? – 7y + 10)
A tetraploid cell (4n = 8): a. could be an autotetraploid from two parents, each 2n = 4 b. could be an allotetraploid from two parents, each 2n = 2 c. could be an allotetraploid from two parents, 1n = 2, 3n = 6 d. A or B e. A or C