Question

In: Advanced Math

Answer the following using Binomial theorem and Pascal's Triangle: a. Find the middle term in the...

Answer the following using Binomial theorem and Pascal's Triangle:

a. Find the middle term in the expansion of (4xx3)14

b. Use Pascal’s triangle to expand (3x + 2y)6.

Solutions

Expert Solution


Related Solutions

(x+5y)^21 expand using Pascal's triangle
(x+5y)^21 expand using Pascal's triangle
Compute the following binomial probabilities using the table of Cumulative Binomial Probabilities. Give your answer to...
Compute the following binomial probabilities using the table of Cumulative Binomial Probabilities. Give your answer to 3 places past the decimal. c) Binomial pmf value: b(10; 15, 0.3)   d) Binomial pmf value: b(11; 20, 0.4) e) P(2 ≤ X ≤ 7) when X ~ Bin(15, 0.2)   f) P(X ≥ 9) when X ~ Bin(15, 0.2) g) P(6 < X ≤ 9) when X ~ Bin(15, 0.2)  
1. Find all solutions to the following linear congruences using Fermat’s Little Theorem or Euler’s Theorem...
1. Find all solutions to the following linear congruences using Fermat’s Little Theorem or Euler’s Theorem to help you. Show all your steps. (a) 3462x ≡ 6 173 (mod 59) (b) 27145x ≡ 1 (mod 42)
Use Stokes' Theorem to find the circulation of F⃗ =2yi⃗ +2zj⃗ +4xk⃗  around the triangle obtained by...
Use Stokes' Theorem to find the circulation of F⃗ =2yi⃗ +2zj⃗ +4xk⃗  around the triangle obtained by tracing out the path (3,0,0) to (3,0,4), to (3,4,4) back to (3,0,0). Circulation = ∫CF⃗ ⋅dr⃗  = Second time I've asked this question because chegg cant solve this problem correct. 24sqrt(2) is the wrong answer
Use Stoke's Theorem to find the circulation of F⃗ =7yi⃗ +3zj⃗ +2xk⃗ around the triangle obtained...
Use Stoke's Theorem to find the circulation of F⃗ =7yi⃗ +3zj⃗ +2xk⃗ around the triangle obtained by tracing out the path (5,0,0) to (5,0,3) to (5,5,3) back to (5,0,0)
Small triangle. Answer the following. a. State a definition for small triangle that would eliminate a...
Small triangle. Answer the following. a. State a definition for small triangle that would eliminate a counterexample to ASA. b. Explain why using this definition eliminates the possibility of a counterexample to ASA.
Suppose 16 coins are tossed. Find the probability of getting the following result using the binomial...
Suppose 16 coins are tossed. Find the probability of getting the following result using the binomial probability formula and the normal curve approximation. Exactly 6 heads. Binomial probability = ​(Round to 4 decimal​ places.) Normal curve approximation almost = ​(Round to 4 decimal​ places.)
Find to 4 decimal places the following binomial probabilities using the normal approximation. a. n =...
Find to 4 decimal places the following binomial probabilities using the normal approximation. a. n = 140, p = 0.42, P(x = 64) P(x = 64) = b. n = 100, p = 0.58, P(51 ≤ x ≤ 60) P(51 ≤ x ≤ 60) = c. n = 90, p = 0.42, P(x ≥ 41) P(x ≥ 41) = d. n = 102, p = 0.74, P(x ≤ 75) P(x ≤ 75) =
Find to 4 decimal places the following binomial probabilities using the normal approximation. a. n =...
Find to 4 decimal places the following binomial probabilities using the normal approximation. a. n = 130, p = 0.42, P(x = 77) P(x = 77) = b. n = 100, p = 0.57, P(52 ≤ x ≤ 61) P(52 ≤ x ≤ 61) = c. n = 90, p = 0.41, P(x ≥ 38) P(x ≥ 38) = d. n = 103, p = 0.75, P(x ≤ 75) P(x ≤ 75) =
Using Fermat't Little Theorem for primality test. Answer the following. Show work for credit. (a) Test...
Using Fermat't Little Theorem for primality test. Answer the following. Show work for credit. (a) Test whether each of the following numbers is primes: 101, 341, and 1105. Try at least two bases if needed, and state if the number is pseudoprime to any base you try. You may use a claculator to compute large powers. (MS Excel can be used) (b) Find a composit number that is pseudoprime to base 3 and 7 but not pseudoprime to base 2...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT