Prealgebra (6th Edition)
6th Edition
ISBN: 9780134179018
Author: Jamie Blair, John Tobey Jr., Jeffrey Slater, Jenny Crawford
Publisher: PEARSON
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Chapter 7, Problem 17T
To determine
To calculate: The solution of the equation
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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.
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):
Statistics
Chapter 7 Solutions
Prealgebra (6th Edition)
Ch. 7.1 - Fill in the blanks. To solve the equation y+8=17,...Ch. 7.1 - Fill in the blanks. To solve the equation a1=7, we...Ch. 7.1 - Fill in the blanks. To solve the equation x15=82,...Ch. 7.1 - Fill in the blanks. To solve the equation x+15=22,...Ch. 7.1 - Fill in the blanks. Before we solve the equation...Ch. 7.1 - Fill in the blanks. Before we solve the equation...Ch. 7.1 - Fill in each blank with the missing phrase. To...Ch. 7.1 - Fill in each blank with the missing phrase. To...Ch. 7.1 - Fill in each blank with the missing phrase. To...Ch. 7.1 - Fill in each blank with the missing phrase. To...
Ch. 7.1 - Fill in each blank with the missing phrase. We...Ch. 7.1 - Fill in each blank with the missing phrase. We...Ch. 7.1 - Solve and check your answer. a6=19Ch. 7.1 - Solve and check your answer. y4=11Ch. 7.1 - Solve and check your answer. a+9=1Ch. 7.1 - Solve and check your answer. x+13=1Ch. 7.1 - Solve and check your answer. 5=x+5Ch. 7.1 - Solve and check your answer. 7=y+6Ch. 7.1 - Solve and check your answer. 79=y4Ch. 7.1 - Solve and check your answer. 811=x4Ch. 7.1 - Solve and check your answer. 712=x6+32Ch. 7.1 - Solve and check your answer. 813=x2+32Ch. 7.1 - Solve and check your answer. 8+42=a+64Ch. 7.1 - Solve and check your answer. 5+32=a+57Ch. 7.1 - Solve and check your answer. 12x111x1=5Ch. 7.1 - Solve and check your answer. 8x+77x+2=3Ch. 7.1 - Solve and check your answer. 1216=4y+83yCh. 7.1 - Solve and check your answer. 89=3x42xCh. 7.1 - Solve and check your answer. 6x65x+1=2+4Ch. 7.1 - Solve and check your answer. 11x+1210x1=4+11Ch. 7.1 - Solve and check your solution. 16=x3Ch. 7.1 - Solve and check your solution. 3=x2Ch. 7.1 - Solve and check your solution. 14=y2Ch. 7.1 - Solve and check your solution. 4=a6Ch. 7.1 - Solve and check your solution. a4=6+9Ch. 7.1 - Solve and check your solution. y3=911Ch. 7.1 - Solve and check your solution. x4=8+6Ch. 7.1 - Solve and check your solution. x5=6+2Ch. 7.1 - Solve and check your solution. y2=4+22Ch. 7.1 - Solve and check your solution. x1=5+42Ch. 7.1 - Solve and check your solution. 3x5=9Ch. 7.1 - Solve and check your solution. 57x=15Ch. 7.1 - Solve and check your solution. 23a=18Ch. 7.1 - Solve and check your solution. 58a=15Ch. 7.1 - Solve and check your solution. 76y=42+5Ch. 7.1 - Solve and check your solution. 37y=524Ch. 7.1 - Solve and check your solution. 3(2x)=24Ch. 7.1 - Solve and check your solution. 4(6x)=48Ch. 7.1 - Solve and check your solution. 6=2(5x)Ch. 7.1 - Solve and check your solution. 2=6(4x)Ch. 7.1 - Solve and check your solution. 8x+4(4x)=48Ch. 7.1 - Solve and check your solution. 6x+3(3x)=45Ch. 7.1 - Solve and check your solution. 6(2x)3x=30Ch. 7.1 - Solve and check your solution. 5(5x)4x=29Ch. 7.1 - Solve and check your solution. 102=3(4x)+2xCh. 7.1 - Solve and check your solution. 63=2(3x)+3xCh. 7.1 - Solve and check your solution. 213=5x+3(4x)Ch. 7.1 - Solve and check your solution. 328=8x+2(2x)Ch. 7.1 - Solve and check your solution. x=9Ch. 7.1 - Solve and check your solution. x=16Ch. 7.1 - Solve and check your solution. x=4Ch. 7.1 - Solve and check your solution. x=6Ch. 7.1 - Solve. a. 2x=12 b. x2=12 c. x2=12 d. x+2=12Ch. 7.1 - Solve. a. 5y=20 b. y5=20 c. x5=20 d. x+5=20Ch. 7.1 - Solve. a. y10=9 b. y+10=9 c. y10=9 d. 10y=9Ch. 7.1 - Solve. a. x6=11 b. x+6=11 c. x6=11 d. 6x=11Ch. 7.1 - Solve. 15=a+5Ch. 7.1 - Solve. 2=y+7Ch. 7.1 - Solve. 5x+24x=4Ch. 7.1 - Solve. 7x+36x=4Ch. 7.1 - Solve. x7=2+32Ch. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Prob. 76ECh. 7.1 - Prob. 77ECh. 7.1 - Prob. 78ECh. 7.1 - Prob. 79ECh. 7.1 - Prob. 80ECh. 7.1 - The sum of each row, each column, and each...Ch. 7.1 - Prob. 82ECh. 7.1 - Prob. 83ECh. 7.1 - Prob. 84ECh. 7.1 - Prob. 85ECh. 7.1 - Prob. 86ECh. 7.1 - Prob. 87ECh. 7.1 - Prob. 88ECh. 7.1 - Prob. 89ECh. 7.1 - Prob. 1QQCh. 7.1 - Prob. 2QQCh. 7.1 - Prob. 3QQCh. 7.1 - Prob. 4QQCh. 7.2 - Write in words the question asked by each...Ch. 7.2 - Write in words the question asked by each...Ch. 7.2 - Prob. 3ECh. 7.2 - Fill in the boxes in each step with the values...Ch. 7.2 - Prob. 5ECh. 7.2 - Fill in the boxes in each step with the values...Ch. 7.2 - Prob. 7ECh. 7.2 - Fill in the boxes in each step with the values...Ch. 7.2 - Prob. 9ECh. 7.2 - Solve and check your solution. 3y9=12Ch. 7.2 - Prob. 11ECh. 7.2 - Solve and check your solution. 7x10=18Ch. 7.2 - Prob. 13ECh. 7.2 - Solve and check your solution. 15=6y3Ch. 7.2 - Prob. 15ECh. 7.2 - Solve and check your solution. 3x2=12Ch. 7.2 - Prob. 17ECh. 7.2 - Solve and check your solution. 6w+7=67Ch. 7.2 - Prob. 19ECh. 7.2 - Solve and check your solution. 5y9=74Ch. 7.2 - Prob. 21ECh. 7.2 - Solve and check your solution. 36=4x8Ch. 7.2 - Solve and check your solution. 1=75yCh. 7.2 - Solve and check your solution. 2=94xCh. 7.2 - Prob. 25ECh. 7.2 - Solve and check your solution. 10=46xCh. 7.2 - Prob. 27ECh. 7.2 - Solve and check your solution. 3=92yCh. 7.2 - Prob. 29ECh. 7.2 - Simplify the left side of the equation by...Ch. 7.2 - Prob. 31ECh. 7.2 - Simplify the left side of the equation by...Ch. 7.2 - Prob. 33ECh. 7.2 - Simplify the left side of the equation by...Ch. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Solve and check your solution. 2y+6=12Ch. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - Solve and check your solution. 13x=8x+20Ch. 7.2 - Prob. 56ECh. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - Prob. 60ECh. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - Prob. 63ECh. 7.2 - Prob. 64ECh. 7.2 - Prob. 1QQCh. 7.2 - Prob. 2QQCh. 7.2 - Prob. 3QQCh. 7.2 - Prob. 4QQCh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - Solve and check your solution. 4(2x+1)=53xCh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Solve and check your solution. 4(x2)=2(x+6)+31Ch. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Solve and check your solution. 3(5x+1)4x=16Ch. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Solve and check your solution. (x2+3x1)(2x+1)=x25Ch. 7.3 - Prob. 38ECh. 7.3 - Is x=19 a solution to (2x+9)+(3x2)(5x+1)=2(x6)(x1)...Ch. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Prob. 1QQCh. 7.3 - Prob. 2QQCh. 7.3 - Prob. 3QQCh. 7.3 - Prob. 4QQCh. 7.4 - Fill in the blanks. To solve x3+x5=10 we multiply...Ch. 7.4 - Prob. 2ECh. 7.4 - Fill in each box with the correct number to...Ch. 7.4 - Prob. 4ECh. 7.4 - Solve and check your solution. x8+x4=3Ch. 7.4 - Prob. 6ECh. 7.4 - Solve and check your solution. x6+x4=5Ch. 7.4 - Prob. 8ECh. 7.4 - Solve and check your solution. x2x5=6Ch. 7.4 - Prob. 10ECh. 7.4 - Solve and check your solution. 3x+23=92Ch. 7.4 - Prob. 12ECh. 7.4 - Solve and check your solution. 5x+18=34Ch. 7.4 - Prob. 14ECh. 7.4 - Solve and check your solution. 5x12=18Ch. 7.4 - Prob. 16ECh. 7.4 - Solve and check your solution. 2x+12=37Ch. 7.4 - Prob. 18ECh. 7.4 - Solve and check your solution. 4x+23=16Ch. 7.4 - Prob. 20ECh. 7.4 - Solve and check your solution. x3+x=8Ch. 7.4 - Prob. 22ECh. 7.4 - Solve and check your solution. x3+x=6Ch. 7.4 - Prob. 24ECh. 7.4 - Solve and check your solution. x2+x=6Ch. 7.4 - Prob. 26ECh. 7.4 - Solve and check your solution. x42x=3Ch. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Solve and check your solution. 59+x6=23Ch. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Translate using symbols. [1.3.2] Twelve less than...Ch. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 1QQCh. 7.4 - Prob. 2QQCh. 7.4 - Prob. 3QQCh. 7.4 - Prob. 4QQCh. 7.5 - Prob. 1ECh. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Salary Comparison Mark is a teaching assistant at...Ch. 7.5 - Prob. 18ECh. 7.5 - Prob. 19ECh. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - Prob. 23ECh. 7.5 - Geometry A triangle has a perimeter of 24 inches....Ch. 7.5 - Prob. 25ECh. 7.5 - Geometry The perimeter of a rectangle is 74 feet....Ch. 7.5 - Price of College Books Jacob bought 2 books for...Ch. 7.5 - Number of Skiers On Monday the total number of...Ch. 7.5 - Prob. 29ECh. 7.5 - Prob. 30ECh. 7.5 - Prob. 31ECh. 7.5 - Geometry A triangle with all sides of equal length...Ch. 7.5 - a. Find the missing numbers for sequence x, then...Ch. 7.5 - Prob. 34ECh. 7.5 - Prob. 35ECh. 7.5 - a. Find the missing numbers for sequence x, then...Ch. 7.5 - [5.6.1]Checker Board The dimensions of an opened...Ch. 7.5 - Use the following information for problems 13. The...Ch. 7.5 - Prob. 2QQCh. 7.5 - Use the following information for problems 13. The...Ch. 7.5 - Concept Check The high school marching band...Ch. 7 - Prob. 1RPCh. 7 - Prob. 2RPCh. 7 - Prob. 3RPCh. 7 - Prob. 4RPCh. 7 - Solve and check your solution. 5+22=x5Ch. 7 - Solve and check your solution. 67a=221Ch. 7 - Solve and check your solution. 3x+2(4x)=182Ch. 7 - Solve and check your solution. x=18Ch. 7 - Prob. 9RPCh. 7 - Solve and check your solution. 6x8=34Ch. 7 - Solve and check your solution. 2y+16=58Ch. 7 - Solve and check your solution. 20=87yCh. 7 - Prob. 13RPCh. 7 - Solve and check your solution. 14y=19Ch. 7 - Solve and check your solution. 8x75x=15Ch. 7 - Solve and check your solution. 6x=9x+36Ch. 7 - Solve and check your solution. 5x=2x+30Ch. 7 - Solve and check your solution. 3x85x=6Ch. 7 - Prob. 19RPCh. 7 - Prob. 20RPCh. 7 - Solve and check your solution. 8x95x+18=3x2+2xCh. 7 - Prob. 22RPCh. 7 - Prob. 23RPCh. 7 - Solve and check your solution. 4(2x+9)+5x=3Ch. 7 - Prob. 25RPCh. 7 - Prob. 26RPCh. 7 - Prob. 27RPCh. 7 - Solve and check your solution. (5x2+x2)(5x25)=6x+9Ch. 7 - Prob. 29RPCh. 7 - Solve and check your solution. x5x2=6Ch. 7 - Solve and check your solution. y+y5=12Ch. 7 - Prob. 32RPCh. 7 - Solve and check your solution. 2x34=13Ch. 7 - Prob. 34RPCh. 7 - Solve and check your solution. 13=3y+12Ch. 7 - Prob. 36RPCh. 7 - For exercises 36 and 37: Write an equation. Solve...Ch. 7 - Prob. 38RPCh. 7 - For each of the following problems: a. Define the...Ch. 7 - For each of the following problems: a. Define the...Ch. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Prob. 3TCh. 7 - Prob. 4TCh. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Solve and check. 3=74yCh. 7 - Solve and check. 6x+49x=15Ch. 7 - Solve and check. 14x=2x+16Ch. 7 - Solve and check. 2x+4(3x6)=4(6x+2)Ch. 7 - Solve and check. 3(2x+6)+3x=27Ch. 7 - Solve and check. 4(x1)=6(x+2)+48Ch. 7 - Solve and check. (3x22x+1)+(3x210)=5x+5Ch. 7 - Prob. 16TCh. 7 - Prob. 17TCh. 7 - Prob. 18TCh. 7 - Write the answers. Use the following information...Ch. 7 - Prob. 20TCh. 7 - Write the answers. Use the following information...Ch. 7 - Write the answers. Use the following information...Ch. 7 - Write the answers. Use the following information...Ch. 7 - Write the answers. Use the following information...
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- Page < 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_forwardPlease draw a graph that represents the system of equations f(x) = x2 + 2x + 2 and g(x) = –x2 + 2x + 4?arrow_forward
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Publisher:Cengage Learning
Interpreting Graphs of Quadratic Equations (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=BHgewRcuoRM;License: Standard YouTube License, CC-BY
Solve a Trig Equation in Quadratic Form Using the Quadratic Formula (Cosine, 4 Solutions); Author: Mathispower4u;https://www.youtube.com/watch?v=N6jw_i74AVQ;License: Standard YouTube License, CC-BY