Explanation Procedure used: Synthetic Division: “1. Write the coefficients of f ( x ) . Be certain that the powers are in descending order and that zeros are inserted for missing powers. 2. Carry down the left coefficient, then multiply it by r , and place this product under the second coefficient of the top line. 3. Add the two numbers in the second column and place the result below. Multiply this sum by r and place the product under the third coefficient of the top line. 4. Continue this process until the bottom row has as many numbers as the top row”. The Factor Theorem: “If f ( r ) = 0 , then x = r is a zero of f ( x ) , x − r is a factor of f ( x ) and x = r is a root of the equation f ( x ) = 0 ”. Calculation: Divide the polynomial t 5 − 3 t 4 − t 2 − 6 by t − 3 as follows. The remainder is zero, t − 3 is a factor of t 5 − 3 t 4 − t 2 − 6 . The powers of t are in descending order, write down the coefficient of f ( t ) and zeros are inserted for missing powers, write 3 for the divisor t − 3 and place 3 to the right. 1 − 3 0 − 1 0 − 6 3 Carry the left coefficient 1 to the bottom line and multiply it by 3 , and place the product 3 under the second coefficient − 3 of the top line and proceed in this similar manner to find the remainder. 1 − 3 0 − 1 0 − 6 3 Ȁ

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 15.1, Problem 34E

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Whether t−3 is factor of t5−3t4−t2−6 or not by using factor theorem and synthetic division.

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Chapter 15.1, Problem 33E

Chapter 15.1, Problem 35E

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(a) Test the hypothesis. Consider the hypothesis test Ho = : against H₁o < 02. Suppose that the sample sizes aren₁ = 7 and n₂ = 13 and that $² = 22.4 and $22 = 28.2. Use α = 0.05. Ho is not ✓ rejected. 9-9 IV (b) Find a 95% confidence interval on of 102. Round your answer to two decimal places (e.g. 98.76).

Let us suppose we have some article reported on a study of potential sources of injury to equine veterinarians conducted at a university veterinary hospital. Forces on the hand were measured for several common activities that veterinarians engage in when examining or treating horses. We will consider the forces on the hands for two tasks, lifting and using ultrasound. Assume that both sample sizes are 6, the sample mean force for lifting was 6.2 pounds with standard deviation 1.5 pounds, and the sample mean force for using ultrasound was 6.4 pounds with standard deviation 0.3 pounds. Assume that the standard deviations are known. Suppose that you wanted to detect a true difference in mean force of 0.25 pounds on the hands for these two activities. Under the null hypothesis, 40 = 0. What level of type II error would you recommend here? Round your answer to four decimal places (e.g. 98.7654). Use a = 0.05. β = i What sample size would be required? Assume the sample sizes are to be equal.…

= Consider the hypothesis test Ho: μ₁ = μ₂ against H₁ μ₁ μ2. Suppose that sample sizes are n₁ = 15 and n₂ = 15, that x1 = 4.7 and X2 = 7.8 and that s² = 4 and s² = 6.26. Assume that o and that the data are drawn from normal distributions. Use απ 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) for a true difference in means of 3? (c) Assuming equal sample sizes, what sample size should be used to obtain ẞ = 0.05 if the true difference in means is - 2? Assume that α = 0.05. (a) The null hypothesis is 98.7654). rejected. The P-value is 0.0008 (b) The power is 0.94 . Round your answer to four decimal places (e.g. Round your answer to two decimal places (e.g. 98.76). (c) n₁ = n2 = 1 . Round your answer to the nearest integer.

Chapter 15 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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Whether t − 3 is factor of t 5 − 3 t 4 − t 2 − 6 or not by using factor theorem and synthetic division.

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Whether t−3 is factor of t5−3t4−t2−6 or not by using factor theorem and synthetic division.

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Chapter 15 Solutions