Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
2nd Edition
ISBN: 9780618912407
Author: MCDOUGAL LITTEL
Publisher: Mcdougal Littel
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Expert Solution & Answer
Chapter 2.2, Problem 22E
Solution
To evaluate the given polynomial function for the given value of x by using the synthetic substitution.
The value of the given polynomial function is 248 .
Given:
f(x)=x4+3x−20 ; x=4
Calculation:
Consider,
f(x)=x4+3x−20f(x)=x4+0x3+0x2+3x−20
Write the coefficients of f(x) in order of descending exponents and write the value at which f(x) is being evaluated to the left. That is,
4|1 0 0 3 −20¯
Now bring down the leading coefficient, then multiply the leading coefficient by x -value, then write the product under the second coefficient, and then add. Repeat this process for all the remaining coefficients. That is,
4| 1 0 0 3 −20 ↓ 4 16 64 268 ↓ ↓ ↓ ↓¯ 1↗ 4↗ 16↗ 67 ↗ 248
Hence f(4)=248 .
Chapter 2 Solutions
Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
Ch. 2.1 - Prob. 1GPCh. 2.1 - Prob. 2GPCh. 2.1 - Prob. 3GPCh. 2.1 - Prob. 4GPCh. 2.1 - Prob. 5GPCh. 2.1 - Prob. 6GPCh. 2.1 - Prob. 7GPCh. 2.1 - Prob. 8GPCh. 2.1 - Prob. 1ECh. 2.1 - Prob. 2E
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- Problem #1 You apply to two different graduate programs at a specific university: one in geology and one in environmental sciences. Let P(G) = 0.8, where P(G) represents the probability that you get accepted into the geology program. Let P(E) = 0.72, where P(E) represents the probability that you get accepted into the environmental sciences program. Let P(GE) = 0.65. a). Create a Venn diagram that represents this information. b). First, calculate P(GUE). Then, using complete sentence, interpret what P(GUE) represents in the context of this problem.arrow_forwardProblem #3 Let P(G|Q) = 0.03, P(G) = 0.2, and P(Q) = 0.5. a). Find P(GnQ). b). Find P(G UQ). c). Are events G and Q independent or dependent? Explain your reasoning.arrow_forwardProblem #4 Suppose a random variable, X, has the following probability distribution table. X 1 2 3 4 5 60 P(X=x) 0.29 0.11 0.32 0.18 a). Find P(X = 5). b). Find P(2≤ X ≤4). c). Find P(2arrow_forward
- Problem #5 You play a game where you have a 35% chance of winning and a 65% chance of losing (no ties are permitted). If you play the game multiple times in a row, the probability of winning and losing remains the same for each attempt. a). If you play the game 40 times, what is the probability that you lose all of the 40 games? b). If you play the game 40 times, what is the probability that you win exactly 25 times?arrow_forward4. (18 pts) Suppose that A is a 3×3 matrix with eigenvalues 2₁ = 0, λ₂ = −1 and 23 = 1, and corresponding eigenvectors V₁ = 0 [] ΓΟΤ (1₁ = 0), V2 = (₁₁ = -1), V3 = (λ3 = 1). 12. (1) Find the matrix A. (2) Find A20 d Y(t) (3) Find the unique solution of the differential equation =AY(t), t≥ 0 dt with the initial condition Y(0) =arrow_forward[1 3 1] 2. (16 pts) Consider a matrix A = 273, determine [26 2 (1) The basis set for the column space of A. (2) The basis set for the row space of A. (3) The range space of A. (4) The basis set for the null space of A.arrow_forward
- Brandon is an amateur marksman. When he takes aim at a particular target on the shooting range, there is a .1 probability that he will hit it. One day, Brandon decides to attempt to hit 10 such targets in a row. Assuming that Brandon is equally likely to hit each of the 10 targets, what is the probability that he will hit at least one of them?Round your answer to the nearest hundredth.arrow_forwardWhen Hugo is serving at a restaurant, there is a .03 probability that each party will request a high chair for a young child. During one hour, Hugo served 10 parties. Assuming that each party is equally likely to request a high chair, what is the probability that at least one party will request a high chair?Round your answer to the nearest hundredth.arrow_forwardWhen Hiroto is writing, there is \[0.92\]probability that there will be no spelling mistakes on a page. One day, Hiroto writes an essay that is \[11\] pages long. Assuming that Hiroto is equally likely to have a spelling mistake on each of the \[11\] pages, what is the probability that he will have a spelling mistake on at least one of the pages?Round your answer to the nearest tenth.arrow_forward
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