Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus
11th Edition
ISBN: 9780134434636
Author: Allyn J. Washington, Richard Evans
Publisher: PEARSON
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Chapter 27.2, Problem 45E
To determine
The slope of a line tangent to the curve
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For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical)
Date IBM9/7/2010 $125.959/8/2010 $126.089/9/2010 $126.369/10/2010 $127.999/13/2010 $129.619/14/2010 $128.859/15/2010 $129.439/16/2010 $129.679/17/2010 $130.199/20/2010 $131.79
5) State any theorems that you use in determining your solution.
a) Suppose you are given a model with two explanatory variables such that:
Yi = a +ẞ1x1 + ẞ2x2i + Ui, i = 1, 2, ... n
Using partial differentiation derive expressions for the intercept and slope
coefficients for the model above.
[25 marks]
b)
A production function is specified as:
Yi = α + B₁x1i + ẞ2x2i + Ui,
i = 1, 2, ... n,
u₁~N(0,σ²)
where:
y = log(output), x₁ = log(labor input), x2 = log(capital input)
The results are as follows:
x₁ = 10, x2 = 5, ỹ = 12, S11 = 12, S12= 8, S22 = 12, S₁y = 10,
= 8, Syy = 10,
S2y
n = 23 (individual firms)
i) Compute values for the intercept, the slope coefficients and σ².
[20 marks]
ii)
Show that SE (B₁) = 0.102.
[15 marks]
iii)
Test the hypotheses: ẞ1
=
1 and B2 = 0, separately at the 5%
significance level. You may take without calculation that SE (a) = 0.78
and SE (B2) = 0.102
[20 marks]
iv)
Find a 95% confidence interval for the estimate ẞ2.
[20 marks]
Page < 2
of 2
- ZOOM +
The set of all 3 x 3 upper triangular matrices
6) Determine whether each of the following sets, together with the standard
operations, is a vector space. If it is, then simply write 'Vector space'. You do not
have to prove all ten vector space axioms. If it is not, then identify one of the ten
vector space axioms with its number in the attached sheet that fails and also show
that how it fails.
a) The set of all polynomials of degree four or less.
b) The set of all 2 x 2 singular matrices.
c) The set {(x, y) : x ≥ 0, y is a real number}.
d) C[0,1], the set of all continuous functions defined on the interval [0,1].
7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and
show that it is orthogonal to both u and v.
8) a) Find the equation of the least squares regression line for the data points
below.
(-2,0), (0,2), (2,2)
b) Graph the points and the line that you found from a) on the same Cartesian
coordinate plane.
Chapter 27 Solutions
Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus
Ch. 27.1 - Prob. 1PECh. 27.1 - Prob. 2PECh. 27.1 - Prob. 1ECh. 27.1 - Prob. 2ECh. 27.1 - Prob. 3ECh. 27.1 - Prob. 4ECh. 27.1 - Prob. 5ECh. 27.1 - Prob. 6ECh. 27.1 - Prob. 7ECh. 27.1 - Prob. 8E
Ch. 27.1 - Prob. 9ECh. 27.1 - Prob. 10ECh. 27.1 - Prob. 11ECh. 27.1 - Prob. 12ECh. 27.1 - Prob. 13ECh. 27.1 - Prob. 14ECh. 27.1 - Prob. 15ECh. 27.1 - Prob. 16ECh. 27.1 - Prob. 17ECh. 27.1 - Prob. 18ECh. 27.1 - Prob. 19ECh. 27.1 - Prob. 20ECh. 27.1 - Prob. 21ECh. 27.1 - Prob. 22ECh. 27.1 - Prob. 23ECh. 27.1 - Prob. 24ECh. 27.1 - Prob. 25ECh. 27.1 - In Exercises 3–34, find the derivatives of the...Ch. 27.1 - Prob. 27ECh. 27.1 - Prob. 28ECh. 27.1 - Prob. 29ECh. 27.1 - Prob. 30ECh. 27.1 - Prob. 31ECh. 27.1 - Prob. 32ECh. 27.1 - Prob. 33ECh. 27.1 - Prob. 34ECh. 27.1 - Prob. 35ECh. 27.1 - Prob. 36ECh. 27.1 - Prob. 37ECh. 27.1 - Prob. 38ECh. 27.1 - Prob. 39ECh. 27.1 - Prob. 40ECh. 27.1 - Prob. 41ECh. 27.1 - Prob. 42ECh. 27.1 - Prob. 43ECh. 27.1 - Prob. 44ECh. 27.1 - Prob. 45ECh. 27.1 - Prob. 46ECh. 27.1 - Prob. 47ECh. 27.1 - Prob. 48ECh. 27.1 - Prob. 49ECh. 27.1 - Prob. 50ECh. 27.1 - Prob. 51ECh. 27.1 - Prob. 52ECh. 27.1 - Prob. 53ECh. 27.1 - Prob. 54ECh. 27.1 - The blade of a saber saw moves vertically up and...Ch. 27.1 - Prob. 56ECh. 27.1 - Prob. 57ECh. 27.1 - Prob. 58ECh. 27.1 - Prob. 59ECh. 27.1 - Prob. 60ECh. 27.2 - Prob. 1PECh. 27.2 - Prob. 2PECh. 27.2 - Prob. 1ECh. 27.2 - Prob. 2ECh. 27.2 - Prob. 3ECh. 27.2 - Prob. 4ECh. 27.2 - Prob. 5ECh. 27.2 - Prob. 6ECh. 27.2 - Prob. 7ECh. 27.2 - Prob. 8ECh. 27.2 - Prob. 9ECh. 27.2 - Prob. 10ECh. 27.2 - Prob. 11ECh. 27.2 - Prob. 12ECh. 27.2 - Prob. 13ECh. 27.2 - Prob. 14ECh. 27.2 - Prob. 15ECh. 27.2 - Prob. 16ECh. 27.2 - Prob. 17ECh. 27.2 - Prob. 18ECh. 27.2 - Prob. 19ECh. 27.2 - Prob. 20ECh. 27.2 - Prob. 21ECh. 27.2 - Prob. 22ECh. 27.2 - Prob. 23ECh. 27.2 - Prob. 24ECh. 27.2 - Prob. 25ECh. 27.2 - Prob. 26ECh. 27.2 - Prob. 27ECh. 27.2 - Prob. 28ECh. 27.2 - Prob. 29ECh. 27.2 - Prob. 30ECh. 27.2 - Prob. 31ECh. 27.2 - Prob. 32ECh. 27.2 - Prob. 33ECh. 27.2 - In Exercises 3–34, find the derivatives of the...Ch. 27.2 - Prob. 35ECh. 27.2 - Prob. 36ECh. 27.2 - Prob. 37ECh. 27.2 - Prob. 38ECh. 27.2 - Prob. 39ECh. 27.2 - Prob. 40ECh. 27.2 - Prob. 41ECh. 27.2 - Prob. 42ECh. 27.2 - Prob. 43ECh. 27.2 - Prob. 44ECh. 27.2 - Prob. 45ECh. 27.2 - Prob. 46ECh. 27.2 - Prob. 47ECh. 27.2 - Prob. 48ECh. 27.2 - Prob. 49ECh. 27.2 - Prob. 50ECh. 27.2 - Prob. 51ECh. 27.2 - Prob. 52ECh. 27.2 - Prob. 53ECh. 27.2 - Prob. 54ECh. 27.3 - Prob. 1PECh. 27.3 - Prob. 2PECh. 27.3 - Prob. 1ECh. 27.3 - Prob. 2ECh. 27.3 - Prob. 3ECh. 27.3 - Prob. 4ECh. 27.3 - Prob. 5ECh. 27.3 - Prob. 6ECh. 27.3 - Prob. 7ECh. 27.3 - Prob. 8ECh. 27.3 - Prob. 9ECh. 27.3 - Prob. 10ECh. 27.3 - Prob. 11ECh. 27.3 - Prob. 12ECh. 27.3 - Prob. 13ECh. 27.3 - Prob. 14ECh. 27.3 - Prob. 15ECh. 27.3 - Prob. 16ECh. 27.3 - Prob. 17ECh. 27.3 - Prob. 18ECh. 27.3 - Prob. 19ECh. 27.3 - Prob. 20ECh. 27.3 - Prob. 21ECh. 27.3 - Prob. 22ECh. 27.3 - Prob. 23ECh. 27.3 - Prob. 24ECh. 27.3 - Prob. 25ECh. 27.3 - Prob. 26ECh. 27.3 - Prob. 27ECh. 27.3 - Prob. 28ECh. 27.3 - Prob. 29ECh. 27.3 - Prob. 30ECh. 27.3 - Prob. 31ECh. 27.3 - Prob. 32ECh. 27.3 - Prob. 33ECh. 27.3 - Prob. 34ECh. 27.3 - Prob. 35ECh. 27.3 - Prob. 36ECh. 27.3 - Prob. 37ECh. 27.3 - Prob. 38ECh. 27.3 - Prob. 39ECh. 27.3 - Prob. 40ECh. 27.3 - Prob. 41ECh. 27.3 - Prob. 42ECh. 27.3 - Prob. 43ECh. 27.3 - Prob. 44ECh. 27.3 - Prob. 45ECh. 27.3 - Prob. 46ECh. 27.3 - Prob. 47ECh. 27.3 - Prob. 48ECh. 27.3 - Prob. 49ECh. 27.3 - Prob. 50ECh. 27.3 - Prob. 51ECh. 27.3 - Prob. 52ECh. 27.3 - Prob. 53ECh. 27.3 - Prob. 54ECh. 27.4 - Prob. 1PECh. 27.4 - Prob. 1ECh. 27.4 - Prob. 2ECh. 27.4 - Prob. 3ECh. 27.4 - Prob. 4ECh. 27.4 - Prob. 5ECh. 27.4 - Prob. 6ECh. 27.4 - Prob. 7ECh. 27.4 - Prob. 8ECh. 27.4 - Prob. 9ECh. 27.4 - Prob. 10ECh. 27.4 - Prob. 11ECh. 27.4 - Prob. 12ECh. 27.4 - In Exercises 3–40, solve the given...Ch. 27.4 - Prob. 14ECh. 27.4 - Prob. 15ECh. 27.4 - Prob. 16ECh. 27.4 - Prob. 17ECh. 27.4 - In Exercises 3–40, solve the given...Ch. 27.4 - Prob. 19ECh. 27.4 - Prob. 20ECh. 27.4 - Prob. 21ECh. 27.4 - Prob. 22ECh. 27.4 - Prob. 23ECh. 27.4 - Prob. 24ECh. 27.4 - Prob. 25ECh. 27.4 - Prob. 26ECh. 27.4 - Prob. 27ECh. 27.4 - Prob. 28ECh. 27.4 - Prob. 29ECh. 27.4 - Prob. 30ECh. 27.4 - Prob. 31ECh. 27.4 - Prob. 32ECh. 27.4 - Prob. 33ECh. 27.4 - Prob. 34ECh. 27.4 - Prob. 35ECh. 27.4 - Prob. 37ECh. 27.4 - Prob. 39ECh. 27.4 - Prob. 40ECh. 27.5 - Prob. 1PECh. 27.5 - Prob. 2PECh. 27.5 - Prob. 1ECh. 27.5 - Prob. 2ECh. 27.5 - Prob. 3ECh. 27.5 - Prob. 4ECh. 27.5 - Prob. 5ECh. 27.5 - Prob. 6ECh. 27.5 - Prob. 7ECh. 27.5 - Prob. 8ECh. 27.5 -
In Exercises 3–34, find the derivatives of the...Ch. 27.5 - Prob. 10ECh. 27.5 - Prob. 11ECh. 27.5 - Prob. 12ECh. 27.5 - Prob. 13ECh. 27.5 - Prob. 14ECh. 27.5 - Prob. 15ECh. 27.5 - Prob. 16ECh. 27.5 - Prob. 17ECh. 27.5 - Prob. 18ECh. 27.5 - Prob. 19ECh. 27.5 - Prob. 20ECh. 27.5 - Prob. 21ECh. 27.5 - Prob. 22ECh. 27.5 - Prob. 23ECh. 27.5 - Prob. 24ECh. 27.5 - Prob. 25ECh. 27.5 - Prob. 26ECh. 27.5 - Prob. 27ECh. 27.5 - Prob. 28ECh. 27.5 - Prob. 29ECh. 27.5 - Prob. 30ECh. 27.5 - Prob. 31ECh. 27.5 - Prob. 32ECh. 27.5 - Prob. 33ECh. 27.5 - Prob. 34ECh. 27.5 - Prob. 35ECh. 27.5 - Prob. 36ECh. 27.5 - Prob. 37ECh. 27.5 - Prob. 38ECh. 27.5 - Prob. 39ECh. 27.5 - Prob. 40ECh. 27.5 - Prob. 41ECh. 27.5 - Prob. 42ECh. 27.5 - Prob. 43ECh. 27.5 - Prob. 44ECh. 27.5 - Prob. 45ECh. 27.5 - Prob. 46ECh. 27.5 - Prob. 47ECh. 27.5 - Prob. 48ECh. 27.5 - Prob. 49ECh. 27.5 - Prob. 50ECh. 27.5 - Prob. 51ECh. 27.5 - Prob. 52ECh. 27.5 - Prob. 53ECh. 27.5 - Prob. 54ECh. 27.5 - Prob. 55ECh. 27.5 - Prob. 56ECh. 27.6 - Prob. 1PECh. 27.6 - Prob. 2PECh. 27.6 - Prob. 1ECh. 27.6 - Prob. 2ECh. 27.6 - Prob. 3ECh. 27.6 - Prob. 4ECh. 27.6 - Prob. 5ECh. 27.6 - Prob. 6ECh. 27.6 - Prob. 7ECh. 27.6 - Prob. 8ECh. 27.6 - Prob. 9ECh. 27.6 - Prob. 10ECh. 27.6 - Prob. 11ECh. 27.6 - Prob. 12ECh. 27.6 - Prob. 13ECh. 27.6 - Prob. 14ECh. 27.6 - Prob. 15ECh. 27.6 - Prob. 16ECh. 27.6 - Prob. 17ECh. 27.6 - Prob. 18ECh. 27.6 - Prob. 19ECh. 27.6 - Prob. 20ECh. 27.6 - Prob. 21ECh. 27.6 - Prob. 22ECh. 27.6 - Prob. 23ECh. 27.6 - Prob. 24ECh. 27.6 - Prob. 25ECh. 27.6 - Prob. 26ECh. 27.6 - Prob. 27ECh. 27.6 - Prob. 28ECh. 27.6 - Prob. 29ECh. 27.6 - Prob. 30ECh. 27.6 - Prob. 31ECh. 27.6 - Prob. 32ECh. 27.6 - Prob. 33ECh. 27.6 - Prob. 34ECh. 27.6 - Prob. 35ECh. 27.6 - Prob. 36ECh. 27.6 - Prob. 37ECh. 27.6 - Prob. 38ECh. 27.6 - Prob. 39ECh. 27.6 - Prob. 40ECh. 27.6 - Prob. 41ECh. 27.6 - Prob. 42ECh. 27.6 - Prob. 43ECh. 27.6 - Prob. 44ECh. 27.6 - Prob. 45ECh. 27.6 - In Exercises 33–54, solve the given...Ch. 27.6 - Prob. 47ECh. 27.6 - Prob. 48ECh. 27.6 - Prob. 49ECh. 27.6 - Prob. 50ECh. 27.6 - Prob. 51ECh. 27.6 - Prob. 52ECh. 27.6 - Prob. 53ECh. 27.6 - Prob. 54ECh. 27.6 - Prob. 55ECh. 27.6 - Prob. 56ECh. 27.7 - Prob. 1PECh. 27.7 - Prob. 2PECh. 27.7 - Prob. 1ECh. 27.7 - Prob. 2ECh. 27.7 - Prob. 3ECh. 27.7 - Prob. 4ECh. 27.7 - In Exercises 3–36, evaluate each limit (if it...Ch. 27.7 - Prob. 6ECh. 27.7 - Prob. 7ECh. 27.7 - Prob. 8ECh. 27.7 - Prob. 9ECh. 27.7 - Prob. 10ECh. 27.7 - Prob. 11ECh. 27.7 - Prob. 12ECh. 27.7 - Prob. 13ECh. 27.7 - Prob. 14ECh. 27.7 - Prob. 15ECh. 27.7 - Prob. 16ECh. 27.7 - Prob. 17ECh. 27.7 - Prob. 18ECh. 27.7 - Prob. 19ECh. 27.7 - Prob. 20ECh. 27.7 - Prob. 21ECh. 27.7 - Prob. 22ECh. 27.7 - Prob. 23ECh. 27.7 - Prob. 24ECh. 27.7 - Prob. 25ECh. 27.7 - Prob. 26ECh. 27.7 - Prob. 27ECh. 27.7 - Prob. 28ECh. 27.7 - Prob. 29ECh. 27.7 - In Exercises 3–36, evaluate each limit (if it...Ch. 27.7 - Prob. 31ECh. 27.7 - Prob. 32ECh. 27.7 - Prob. 33ECh. 27.7 - Prob. 34ECh. 27.7 - Prob. 35ECh. 27.7 - Prob. 36ECh. 27.7 - Prob. 37ECh. 27.7 - Prob. 38ECh. 27.7 - Prob. 39ECh. 27.7 - Prob. 40ECh. 27.7 - Prob. 41ECh. 27.7 - Prob. 42ECh. 27.7 - Prob. 43ECh. 27.7 - Prob. 44ECh. 27.7 - Prob. 45ECh. 27.7 - Prob. 46ECh. 27.7 - Prob. 47ECh. 27.7 - Prob. 48ECh. 27.8 - Prob. 1PECh. 27.8 - In Exercises 1 and 2, make the given changes in...Ch. 27.8 - Prob. 2ECh. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 4ECh. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 6ECh. 27.8 - Prob. 7ECh. 27.8 - Prob. 8ECh. 27.8 - Prob. 9ECh. 27.8 - Prob. 10ECh. 27.8 - Prob. 11ECh. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 13ECh. 27.8 - Prob. 14ECh. 27.8 - Prob. 15ECh. 27.8 - Prob. 16ECh. 27.8 - Prob. 17ECh. 27.8 - Prob. 18ECh. 27.8 - Prob. 19ECh. 27.8 - Prob. 20ECh. 27.8 - Prob. 21ECh. 27.8 - Prob. 22ECh. 27.8 - Prob. 23ECh. 27.8 - Prob. 25ECh. 27.8 - Prob. 26ECh. 27.8 - Prob. 27ECh. 27.8 - Prob. 28ECh. 27.8 - Prob. 29ECh. 27.8 - Prob. 30ECh. 27.8 - Prob. 31ECh. 27.8 - Prob. 32ECh. 27.8 - Prob. 33ECh. 27.8 - Prob. 34ECh. 27.8 - The energy E (in J) dissipated by a certain...Ch. 27.8 - Prob. 36ECh. 27.8 - Prob. 37ECh. 27.8 - Prob. 39ECh. 27.8 - A package of weather instruments is propelled into...Ch. 27.8 - Prob. 41ECh. 27.8 - Prob. 42ECh. 27.8 - Prob. 43ECh. 27.8 - Prob. 45ECh. 27.8 - Prob. 46ECh. 27 - Prob. 1RECh. 27 - Prob. 2RECh. 27 - Prob. 3RECh. 27 - Prob. 4RECh. 27 - Prob. 5RECh. 27 - Prob. 6RECh. 27 - Prob. 7RECh. 27 - Prob. 8RECh. 27 - Prob. 9RECh. 27 - Prob. 10RECh. 27 - Prob. 11RECh. 27 - Prob. 12RECh. 27 - Prob. 13RECh. 27 - Prob. 14RECh. 27 - Prob. 15RECh. 27 - Prob. 16RECh. 27 - Prob. 17RECh. 27 - Prob. 18RECh. 27 - Prob. 19RECh. 27 - Prob. 20RECh. 27 - Prob. 21RECh. 27 - Prob. 22RECh. 27 - Prob. 23RECh. 27 - Prob. 24RECh. 27 - Prob. 25RECh. 27 - Prob. 26RECh. 27 - Prob. 27RECh. 27 - Prob. 28RECh. 27 - Prob. 29RECh. 27 - Prob. 30RECh. 27 - Prob. 31RECh. 27 - Prob. 32RECh. 27 - Prob. 33RECh. 27 - Prob. 34RECh. 27 - Prob. 35RECh. 27 - 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- 1. A consumer group claims that the mean annual consumption of cheddar cheese by a person in the United States is at most 10.3 pounds. A random sample of 100 people in the United States has a mean annual cheddar cheese consumption of 9.9 pounds. Assume the population standard deviation is 2.1 pounds. At a = 0.05, can you reject the claim? (Adapted from U.S. Department of Agriculture) State the hypotheses: Calculate the test statistic: Calculate the P-value: Conclusion (reject or fail to reject Ho): 2. The CEO of a manufacturing facility claims that the mean workday of the company's assembly line employees is less than 8.5 hours. A random sample of 25 of the company's assembly line employees has a mean workday of 8.2 hours. Assume the population standard deviation is 0.5 hour and the population is normally distributed. At a = 0.01, test the CEO's claim. State the hypotheses: Calculate the test statistic: Calculate the P-value: Conclusion (reject or fail to reject Ho): Statisticsarrow_forwardPage < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.arrow_forwardFind the Laplace Transform of the function to express it in frequency domain form.arrow_forward
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