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#10. A student finishes the first half of an exam in 2/3 the time it takes to finish the second half . If the entire exam takes an hour, how many minutes does she spend on the first half of the exam?
The back of the book sets up the problem like this... 5/3S = 60, then
3/5 * 5/3S = 3/5*60, then S=36....
I do not understand how they came up with the 5/3, then I figured 2/3 + 2/3 + 1hr = 5/3, but why did they multiply the recipricols and then place 3/5 on the other side *60? 1 solutions
Answer 153739 by solver91311(16868) on 2009-07-21 13:59:28 (Show Source):
You can put this solution on YOUR website!
Let represent the time, in minutes, it took to finish the second half of the exam. Then we are given that is the time, in minutes, it took to finish the first half of the exam. Add these two quantities for the total time, again in minutes, to finish the exam which is 60 because there are 60 minutes in 1 hour. So:
But , so:
So far, so good.
There are two ways to go about solving from here. You can either multiply both sides by 3:
And then multiply both sides by :
Or, you can combine those two steps into one, as your book shows, but multiplying by the reciprocal of the fractional coefficient on the variable. (That is because we know that )
Achieving the same result, as one would expect.
John

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Finance/203764: Geometry A square pool has side length p. The border of the pool is 1 ft wide. The combined area of the border and the pool is 400 ft^2. Find the length and the area of the pool. 1 solutions
Answer 153734 by solver91311(16868) on 2009-07-21 13:16:29 (Show Source):
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Travel_Word_Problems/203758: Please help me solve, Iam unsure how to set up the problem... it shows in the book but I cannot understand the explanation
#6. If a car travels 1/100 kilometer each second, how many kilometers does it travel in an hour?
I tried this 1/100*120 seconds... this is not right, I dont understand why. 1 solutions
Answer 153732 by solver91311(16868) on 2009-07-21 12:54:28 (Show Source):
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Graphs/203285: Question 7 (Multiple Choice Worth 1 points)
Choose the best directions for graphing the equation y= (1/2)x + 1.
a.Graph the point (0,1) and count up 1 and to the right 2 to find another point on the line.
b.Graph the point (1,0) and count up 1 and to the right 2 to find another point on the line.
c.Graph the point (0,1) and count to the right 1 and up 2 to find another point on the line.
d.Graph the point (1,0) and count to the right 1 and up 2 to find another point on the line.
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Question 8 (Multiple Choice Worth 1 points)
What kind of line is created when you graph the equation x=2?
a.Horizontal line
b.Oblique line
c.Vertical line
d.No line is created.
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Question 9 (Multiple Choice Worth 1 points)
What is the slope of the line x=2?
a.Zero
b.Undefined
c.2
d.Not enough information.
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Question 10 (Multiple Choice Worth 1 points)
What is the slope of the line y= -3?
a.Zero
b.Undefined
c.-3
d.Not enough information.
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Question 11 (Multiple Choice Worth 1 points)
Choose the equation that is written in standard form.
a.y= -3x +4
b.2y = x+8
c.x = 3y-6
d.4x -2y = 10
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Question 12 (Multiple Choice Worth 1 points)
Find the x intercept of the graph represented by the equation 3x + 4y = 12.
a.(0,3)
b.(3,0)
c.(4,0)
d.(0,4)
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Question 13 (Multiple Choice Worth 1 points)
Find the y intercept of the graph represented by the equation 3x + 4y = 12.
a.(0,3)
b.(3,0)
c.(4,0)
d.(0,4)
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Question 14 (Multiple Choice Worth 1 points)
Choose ALL the points that are solutions to the equation y= 2x -5.
a.(0,-5)
b.(1,3)
c.(-1,-7)
d.(1/2, -4)
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Question 15 (Multiple Choice Worth 1 points)
Choose the equation of the line with a slope of 2/3 and y passing through the point (6,-2).
a.y= (2/3)x -6
b.y= (2/3)x -2
c.y= (2/3) x -4
d.y = (3/2) x -6
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Question 16 (Multiple Choice Worth 1 points)
Choose the equation of the line passing through the points (-2,3) and (-4,1).
a.y = x -1
b.y = (-1/3)x + 7/3
c.y= x-4
d.y = x + 5
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Question 17 (Multiple Choice Worth 1 points)
Choose the equation of the vertical line passing through the point (-2,1).
a.x = -2
b.x = 1
c.y = -2
d.y = 1
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Question 18 (Multiple Choice Worth 1 points)
Choose the equation of the line passing through the points (3,4) and (1,-6).
a.y = 5x - 19
b.y = (1/5)x + 15/5
c.y = (1/5)x - 2
d.y = 5x - 11
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Question 19 (Multiple Choice Worth 1 points)
Choose the ordered pair that is the solution to the following system of equations: y= 2x + 1 and y = x -5.
a.(-6, -1)
b.(-6,-11)
c.(4,9)
d.(4,-1)
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Question 20 (Multiple Choice Worth 1 points)
Choose the orderred pair that is the solution to the following system of equations: -3x + y = 4 and -7x + y = 12.
a.(-2,-2)
b.(-2,2)
c.(2,-2)
d.(2,2)
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Question 21 (Multiple Choice Worth 1 points)
Choose the ordered pair that is the solution to the following system of equations: 5x - 2y = 3 and 3x + 4y = 7.
a.(1,-1)
b.(-1,1)
c.(-1,-1)
d.(1,1)
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Question 22 (Essay Worth 1 points)
Give an ordered pair that is the solution to the equation y = 5x + 2.
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Question 23 (Multiple Choice Worth 1 points)
Choose the equation of the line that is perpendicular to the line shown in the graph and passes through the point shown in the graph.
a.y = x - ll
b.y= 3x – 11
c.y = -3x - 11
d.y = -x + 11
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Question 24 (Multiple Choice Worth 1 points)
Choose the equation of the line that is perpendicular to the line shown in the graph and passes through the point shown in the graph.
a.y = 2x + 7
b.y = -2x + 10
c.y = 2x - 10
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Question 25 (Multiple Choice Worth 1 points)
The figure shown below looks like a trapezoid. By definition, a trapezoid is a four-sided figure with at least two parallel sides. Choose the best description below of how to determine whether the figure shown is or is not a trapezoid.
a.Find the slope of the line between point (-9,5) and point (-3,8). Then find the slope of the line between point (4,-1) and point (3,5). If the slopes are opposite reciprocals, then the figure is a trapezoid.
b.Find the slope of the line between point (-3,8) and point (3,5). Then find the slope of the line between point (-9,5) and point (4,-1). If the slopes are the same, then the figure is a trapezoid.
c.Find the slope of the line between point (-9,5) and point (3,5). Then find the slope of the line between point (-3,8) and point (4,-1). If the slopes are the same, then the figure is a trapezoid.
d.Find the slope of the line between point (-3,8) and point (3,5). Then find the slope of the line between point (-9,5) and point (4,-1). If the slopes are opposite reciprocals, then the figure is a trapezoid.
: Question 7 (Multiple Choice Worth 1 points)
Choose the best directions for graphing the equation y= (1/2)x + 1.
a.Graph the point (0,1) and count up 1 and to the right 2 to find another point on the line.
b.Graph the point (1,0) and count up 1 and to the right 2 to find another point on the line.
c.Graph the point (0,1) and count to the right 1 and up 2 to find another point on the line.
d.Graph the point (1,0) and count to the right 1 and up 2 to find another point on the line. 1 solutions
Answer 153393 by solver91311(16868) on 2009-07-17 00:20:31 (Show Source):
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Graphs/203289: Question 1 (Multiple Choice Worth 3 points)
Given y = 2x – 4, choose the statement that accurately describes this line.
a.The slope is 2 and the y intercept is 4.
b.The slope is 2 and the y intercept is -4.
c.The slope is 4 and the y intercept is 2.
d.The slope is -4 and they y intercept is 2.
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Question 2 (Multiple Choice Worth 3 points)
The slope of the line that passes through (2, -4) and (-6, 2) is:
a.-4/3
b.3/2
c.1/4
d.-3/4
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Question 3 (Multiple Choice Worth 3 points)
Complete this sentence with the correct choice: y = 4 is a horizontal line with ________.
a.undefined slope.
b.a slope of 4.
c.a slope of 0.
d.None of the above will make a true statement.
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Question 4 (Multiple Choice Worth 3 points)
What would be the missing piece of information given the following information:
Find the slope of the line that passes through the points (2, 6) and (4, 10).
m = ?
a.2
b.6
c.1
d.9
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Question 5 (Multiple Choice Worth 3 points)
What would be the missing piece of information given the following information:
Find the equation of the line that passes through the points (2, 6) and (4, 10).
y = 2x + ?
a.4
b.2
c.7
d.5
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Question 6 (Multiple Choice Worth 3 points)
What would be the missing piece of information given the following information:
Find the equation of the line that passes through the points (3, -1) and (2, 5).
y = -6x + ?
a.17
b.15
c,20
d.11
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Question 7 (Multiple Choice Worth 2 points)
How would you would graph the linear equation y = -2x + 6?
a.First plot the point (6,0) and then count up two and to the right 1.
b.First plot the point (6,0) and then count down two and to the right 1
c.First plot the point (0,6) and then count up two and to the right 1
d.First plot the point (0,6) and then count down two and to the right 1 1 solutions
Answer 153392 by solver91311(16868) on 2009-07-17 00:18:30 (Show Source):
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Permutations/203313: Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What is the probability of drawing an ace and a king?
I have: 4/52 x 4/51 = 4/663 is this permutation correct? 1 solutions
Answer 153391 by solver91311(16868) on 2009-07-17 00:16:35 (Show Source):
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Probability-and-statistics/203178: Given:
A= {1,3, 5, 7}
B= {c, d}
S= {x e I 0 < x <10 } u {x x is a letter of the word dice}
Find each of the following stes.
a) A'
b) B'
c) A u B'
d) (A u B)
I am sorry I don't have all the write keys for the union and the funky looking E/ = and I don't know the correct term for it either.
All I really need to know is what A' means.
Thank you! 1 solutions
Answer 153320 by solver91311(16868) on 2009-07-15 20:21:59 (Show Source):
You can put this solution on YOUR website!
You didn't specify, but I suspect that is your universe set. It has to be, otherwise expressions like don't make any sense. Given that S is the Universe set, , read 'the complement of A', means "everything that is in S that is NOT in A". The union of two sets is everything that is in one set and everything in the other set as well.
It will be helpful to first enumerate . First we have a set of integers, larger than zero but less than ten, so:
and then we have the letters of the word 'dice':
Put them all together:
From that set, cross out each element of and you are left with the complement of , or
You should be able to figure out the rest.
Notation: means "such that", means "is an element of", is the set of integers.
John

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Rectangles/203193: the diagonals of the following rectangle have which coordinates for their point of intersection?
-2,7 1,9 5,3 2,1
a. 1,5
b.1.5,5
c.1.5,3
d.0.5,4 1 solutions
Answer 153316 by solver91311(16868) on 2009-07-15 19:18:31 (Show Source):
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test/203167: Hi,
Need some help on this question. It's a practice test question and I'm a bit confused.
Graph the following system and solve the linear programming problem:
Maximize: P=7x+10y
subject to: {2x+5y<=80
{4x+3y<=104
x>=0; y>=0
Thank you! 1 solutions
Answer 153284 by solver91311(16868) on 2009-07-15 14:43:48 (Show Source):
You can put this solution on YOUR website!
Graph the two lines. Note that (0,0) is in the solution set for both of them, hence the solution set for each of the inequalities is the half-plane region below and to the left of the graphed line. The two non-negative constraints further bound the area of feasibility to above and to the right of the coordinate axes. See graph:
Considering the two non-negative constraints, the area of feasibility is the quadrilateral region bounded by the two coordinate axes, the green graph line on the top and the red graph line on the right.
The proof is beyond the scope of this discussion, so take it on faith that the optimum point will be one of the vertices of the feasibility area, namely: (0,0), (0,16), (26,0), or (20, 8).
Substitute the coordinate values for the 4 possible optimum points into your objective function and see which one has the maximum result.
You can calculate the other two and decide which is maximum.
John

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real-numbers/203104: This question is from textbook Intermediate Algebra
-25, -28/7, -18/5, -Pi, -0.763, -0.333..., 0, 1/10, 2/7, Pi/4, sqrt3, 9, 52.8, 283/5
From the above list, list all the irrational numbers.
I think that -Pi is one of them? 1 solutions
Answer 153251 by solver91311(16868) on 2009-07-15 00:18:48 (Show Source):
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Linear_Equations_And_Systems_Word_Problems/203111: find two consecutive integers whose sum is 89. to solve this problem, let x be the smaller of these integers. what's the larger of these two consecutive integers?
write an equation that says that this sum is equal to 89.
sole this equation
What are the two numbers? 1 solutions
Answer 153245 by solver91311(16868) on 2009-07-14 23:03:05 (Show Source):
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Geometry_Word_Problems/203070: A rectangular track was being built so that the length of one of the short sides was half the length of one of the long sides. The track was supposed to be 300 yards around. At the last minute, the plans for the track were changed and a semicircle was added at each of the short ends. What is the distance around the track after the plans were modified?
I know that the width of the rectangular part of the track is 50, and the length is 100. (2x+2x+x+x=300 -> 6x=300 -> x = 50)
Don't know what to do from here. 1 solutions
Answer 153232 by solver91311(16868) on 2009-07-14 19:35:04 (Show Source):
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Polynomials-and-rational-expressions/203020: Find the zeros of all the polynomial functions. Multiply the binomials together. You may use special products, and you may multiply conjugate pairs together first.
1. (x-3i)(x+3i)(x-5)(x+4)
2. (x+3i)(x-3i)(x-2)(x+1)
3. (x+6)(x-7)(x-8)(x+4)(x-1)
4. (x+1)(x+2)(x-3)(x-4)(x+i)(x-i)
5. (x+2+i)(x+2-i)(x-i)(x+i)
6. (x-1+i)(x-1-i)(x+3)(x-5)
7. (x+i)(x-i)(x+1)(x-1)(x+3)
8. (x-i)(x+i)(x-3i)(x+3i)(x+2)(x-2) 1 solutions
Answer 153161 by solver91311(16868) on 2009-07-14 00:24:21 (Show Source):
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Graphs/203015: Write an equation of the line containing the given points and parallel to the given line.
(7, -8); 6x-7y=5
The equation of the line is y= ?????? 1 solutions
Answer 153158 by solver91311(16868) on 2009-07-13 23:50:23 (Show Source):
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Radicals/203016: What does the radical sign tell you to do if, for example you have: 7√2.
Does the sign mean multiply 7 by 2, and you'll get your answer? 1 solutions
Answer 153156 by solver91311(16868) on 2009-07-13 23:29:13 (Show Source):
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test/202891: Let p, q, and r be the following statements:
p: It is raining.
q: The clouds are dark.
r: The temperature is dropping.
Translate the following statements into English
(a) p upside down v r (b) ~p upsidedown v (q v r)
(c) q arrow r (d) (~ rupside down v~ q) arrow ~ p 1 solutions
Answer 153133 by solver91311(16868) on 2009-07-13 17:31:51 (Show Source):
You can put this solution on YOUR website!
The 'upsidedown v', means "and" in English. Replace every instance of with the word "and".
The 'v' symbol, means "or" in English. Replace every instance of with the word "or".
The tilde, (~) means "not" in English. Where ever you see the (~) symbol in front of a statement, insert the word "not" into the statement at a place where it makes sense. For example would be "It is not raining" (rather than "Not it is raining", "It not is raining", or "It is raining not").
An arrow that has an arrowhead only on the right means "if. . .then" Put the statement that precedes the arrow after the 'if' and before the 'then', and put the statement that follows the arrow after the 'then'. A double headed arrow means "if and only if", and the statement to the left of the double headed arrow would come first, then "if and only if" followed by the statement to the right of the arrow.
Otherwise, replace the variables , , and with the statements that define them.
John

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Numbers_Word_Problems/202916: Four girls, Ann, Bobbie, Cathy, and Deb, have $1100; Ann has a certain sum, Bobbie has twice as much as Ann, Cathy has $800, and Deb has $200 more than Cathy; how many dollars has Ann? 1 solutions
Answer 153125 by solver91311(16868) on 2009-07-13 16:59:05 (Show Source):
You can put this solution on YOUR website!
Whoever made up this problem must be a member of Congress. If Cathy has $800 and Deb has $200 more than that, then Deb and Cathy together have $1800, which is $700 more than the 4 girls started with in the first place. No solution to the problem as stated.
John

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Equations/202973: The sum of two numbers is 6 less than twice the first number. Their difference is 10 less than four times the second number. Find each of the numbers. 1 solutions
Answer 153121 by solver91311(16868) on 2009-07-13 16:47:40 (Show Source):
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Probability-and-statistics/202971: X- and y-intercepts of a line given the equation in standard form.
Find both the x-intercept and the y-intercept of the line given by the equation
1.8x-9.4y-6.6 =0
Round your answers to decimal places.
x-intercepts:___
y-intercepts:___ 1 solutions
Answer 153114 by solver91311(16868) on 2009-07-13 16:00:13 (Show Source):
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