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Fombitz answered: 13805 problems
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test/326469: Suppose that you are drawing cards from a set of 6 cards, the colors of which are red, blue, orange, yellow, pink, and green. What is the probability of drawing a red card followed by a blue card without replacement?
1 solutions

Answer 233732 by Fombitz(13828) About Me  on 2010-07-28 14:57:01 (Show Source):
You can put this solution on YOUR website!
P(R)=1%2F6
P(B)=1%2F5
P(R then B)=%281%2F6%29%281%2F5%29=1%2F30


Trigonometry-basics/326467: Three forces with magnitudes of 250 ibs 60degrees N of E, 100 ibs 30degrees N of W, and 200 ibs S act on an object. Find the direction and magnitude of the resultant force.
I have no clue how to even begin a problem like this, thank you for taking the time to look at this.
1 solutions

Answer 233731 by Fombitz(13828) About Me  on 2010-07-28 14:55:12 (Show Source):
You can put this solution on YOUR website!
First pick a coordinate system.
Let North be positiive y.
Let East be positive x.
Then find the x,y components of each force.
"250 lbs 60 degrees N of E"=250(cos(60),sin(60))=(125,216.5)
"100 lbs 30 degrees N of W"=100(cos(150),sin(150))= (-86.6,50)
"200 lbs S"=200(0,-1)=(0,-200)
Then sum the x and y components to get the resultant.
(Fx,Fy)=(125,216.5)+(-86.6,50)+(0,-200)
(Fx,Fy)=(38.4,66.5)
You can find the resultant magnitude and direction,
r=sqrt%2838.4%5E2%2B66.5%5E2%29=76.8
tan%28theta%29=66.5%2F38.4
theta=60
.
.
.
76.8 lbs 60 degrees North of East.
act on an object. Find the direction and magnitude of the resultant force.


Trigonometry-basics/326461: Convert the following polar coordinates into rectangular coordinates.
(-2, pi/4)
Thanks for looking at this.
1 solutions

Answer 233730 by Fombitz(13828) About Me  on 2010-07-28 14:48:04 (Show Source):
You can put this solution on YOUR website!
Are these polar coordinates in magnitude, angle format?
Negative magnitudes are not allowed.
They are the square root of a sum of squares.
Please re-post.


Polynomials-and-rational-expressions/326462: 4a^2-196=0
1 solutions

Answer 233729 by Fombitz(13828) About Me  on 2010-07-28 14:45:55 (Show Source):
You can put this solution on YOUR website!
+4a%5E2-196=0+
4%28a%5E2-49%29=0
a%5E2-49=0
%28a-7%29%28a%2B7%29=0
Two solutions" a=7, a=-7


Expressions-with-variables/326299: Use completing the square to solve the following equation. (Enter solutions from smallest to largest. If the solutions are complex, enter them from smallest to largest value of the imaginary part.)
-6=2x^2-13x
1 solutions

Answer 233728 by Fombitz(13828) About Me  on 2010-07-28 14:42:12 (Show Source):


Travel_Word_Problems/326459: If a train leaves Salt Lake City going 70 Miles per hour, and another leaves NY going 80 miles per hour, where do they pass each other?
1 solutions

Answer 233727 by Fombitz(13828) About Me  on 2010-07-28 14:39:03 (Show Source):
You can put this solution on YOUR website!
What distance are you using for the distance between Salt Lake City and NY?


Radicals/326301: 9x^-6xy +y^-81 factored--how to simplify
1 solutions

Answer 233725 by Fombitz(13828) About Me  on 2010-07-28 14:37:53 (Show Source):
You can put this solution on YOUR website!
9x%5E%28-6xy%29+%2By%5E%28-81%29
Any hints as to what you're looking for in terms of simplification??


test/326326: graph the inequality on a plane
x+y<2
1 solutions

Answer 233723 by Fombitz(13828) About Me  on 2010-07-28 14:35:40 (Show Source):
You can put this solution on YOUR website!
x%2By%3C2
y%3C-x%2B2
Graph the line y=-x%2B2
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-x%2B2%29
Pick a point not on the line.
(0,0) looks good.
Check the inequality.
0%3C2
True
(0,0) is in the solution region.
Shade the region containing (0,0).
Solved by pluggable solver: Plot Any Inequality
Graphing function y%3C-x%2B2:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C-x%2B2+%29


test/326323: A bank offer two bank plan. The anywhere plan charge 30 cent per check. the Accucheck plan cost $1.36 a month plus 22 cent per check. for what number of checks would the Accucheck plan cost less than the Anywhere plan?
IS IT
a 17 or more
b less than 17 check
c more than 17 checks
d 17 check
1 solutions

Answer 233720 by Fombitz(13828) About Me  on 2010-07-28 14:33:06 (Show Source):
You can put this solution on YOUR website!
Find the point when,
Anywhere>Accucheck
30%2AC%3E136%2B22%2AC
8%2AC%3E136
C%3E17
.
.
.
c) is the correct answer.


test/326325: solve the system of the equations by graphing than classify the system
2x-y=8
2x+3y=0
what is the solution of the system
is the system consistent or inconsistent
is the system dependent or independent
1 solutions

Answer 233718 by Fombitz(13828) About Me  on 2010-07-28 14:30:51 (Show Source):
You can put this solution on YOUR website!
2x-y=8
y=2x-8
.
.
.

.
.
.
2x%2B3y=0
3y=-2x
y=-%282%2F3%29x
.
.
.

.
.
.
Looks like (3,-2) is a solution.
Verify by using both equations.
2x-y=8
2%283%29-%28-2%29=8
6%2B2=8
8=8
TRUE
.
.
.
2x%2B3y=0
2%283%29%2B3%28-2%29=0
6-6=0
TRUE
.
.
There is one solution so the system is consistent and independent.


Volume/326458: find the polymomial that represents the volume of a cube is each side measures x+6
1 solutions

Answer 233717 by Fombitz(13828) About Me  on 2010-07-28 14:26:07 (Show Source):
You can put this solution on YOUR website!
The volume of a cube given the measure of side s is,
V=s%5E3
highlight%28V%28x%29=%28x%2B6%29%5E3%29


Miscellaneous_Word_Problems/326430: A farmer raises wheat and corn on 430 acres of land. He wants to plant 62 more acres of wheat than corn. How many acres of each should he plant?



Thanks for your help. jkng07@ca.rr.com
1 solutions

Answer 233716 by Fombitz(13828) About Me  on 2010-07-28 14:25:10 (Show Source):
You can put this solution on YOUR website!

W%2BC=430
W=C%2B62
Substitute eq. 2 into eq.1,
C%2B62%2BC=430
2C%2B62=430
2C=368
C=184
SO then,
W=184%2B62
W=246
.
.
.
246 acres of wheat, 184 acres of corn


Linear-equations/326437: what is the slope of the line 5x-3y=15?
F) 5/3
G) -5/3
H) 5
I) -5
1 solutions

Answer 233715 by Fombitz(13828) About Me  on 2010-07-28 14:22:26 (Show Source):
You can put this solution on YOUR website!
5x-3y=15
Convert to slope-intercept form, y=mx%2Bb
-3y=-5x%2B15
y=%285%2F3%29x-5
.
.
.
m=5%2F3


Number-Line/326450: I have a number line with 13 tick(tallies [places for numbers) I have to make up an appropriate scale to graph the following numbers.
{-7 , -2.5 , -1.5 , 0 , 6 , 9 }
THANKS SOOO MUCH!
Bella.
1 solutions

Answer 233714 by Fombitz(13828) About Me  on 2010-07-28 14:21:10 (Show Source):
You can put this solution on YOUR website!
Your values range from -7 to 9, that's 16 spots.
You have 13 ticks so you can't have a spacing of 1.
Why don't you start at -12 and have a spacing of 2.
(-12,-10,-8,-6,-4,-2,0,2,4,6,8,10,12)
Then you'll be able to fit all of your data.


test/326455: solve each system by substitution
x+3y=2
-x+y=1
1 solutions

Answer 233713 by Fombitz(13828) About Me  on 2010-07-28 14:18:24 (Show Source):
You can put this solution on YOUR website!
1.x%2B3y=2
2.-x%2By=1
From eq. 2,
y=1%2Bx
Substitute in eq. 1,
x%2B3%281%2Bx%29=2
x%2B3%2B3x=2
4x=-1
highlight%28x=-1%2F4%29
Then from above,
y=1%2Bx
y=1-1%2F4
highlight%28y=3%2F4%29


Equations/326432: L*(1+p)^(12*z)=R*(1+r)^(z-1)*D*((C^z-1)/(C-1)). how do I solve this for z??
1 solutions

Answer 233711 by Fombitz(13828) About Me  on 2010-07-28 14:02:28 (Show Source):
You can put this solution on YOUR website!

Take the log of both sides.
Then simplify
Remember
log%28%28AB%29%29=log%28%28A%29%29%2Blog%28%28B%29%29
log%28%28A%5En%29%29=nlog%28%28A%29%29
I'll do the left hand side to get you started.

log%28%28L%2A%281%2Bp%29%5E%2812z%29%29%29=log%28%28L%29%29%2B12z%2Alog%28%281%2Bp%29%29
Gather all the z terms on one side, all the constant terms on the other side.
You'll end up with a fraction with many log terms in the numerator and denominator.


Quadratic_Equations/326433: r^2-9=0
how would you slove this?
1 solutions

Answer 233710 by Fombitz(13828) About Me  on 2010-07-28 13:54:54 (Show Source):
You can put this solution on YOUR website!
+r%5E2-9=0
Factoring,
+%28r%2B3%29%28r-3%29=0
Two solutions:
+r%2B3=0
+r=-3
.
.
+r-3=0
+r=3
.
.
Directly,
+r%5E2=9
+r=0+%2B-+3


Probability-and-statistics/326435: PROBLEM 1


The 2003 Zagat Restaurant Survey provides food, décor, and service ratings for some of the top restaurants
across the United States. For 15 top-ranked restaurants located in Boston, the average price of a dinner
including, one drink and tip, was $48.60. You are leaving for a business trip to Boston and will eat dinner at
three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business
associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants
will exceed $50. Suppose that you randomly select three restaurants for dinner.




a. What is the probability that none of the meals will exceed the cost covered by your company?
b. What is the probability that one of the meals will exceed the cost covered by your company?
c. What is the probability that two of the meals will exceed the cost covered by your company?

d. What is the probability that all three of the meals will exceed the cost covered by your company?
PROBLEM 2


Military radar and missile detection system are designed to warn a country of an enemy attack. A
reliability question is whether a detection system will be able to identify an attack and issue a warning.
Assume that a particular detection system has a .90 probability of detecting a missile attack.

a. What is the probability that single detection system will detect the attack?
b. If two detection systems are installed in the same area and operating independently, what is the
probability that at least one of the systems will detect the attack?
c. If three systems are installed, what is the probability that at least one of the systems will detect
the attack?
d. Would you recommend the multiple detection systems be used? Explain.
I would recommed 3 detection systems be installed. Like a wise man says there is saftey in numbers




PROBLEM 3




Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.

a. Compute the probability of receiving three calls in a 5-minute interval of time.
b. Compute the probability of receiving exactly 10 calls in 15 minutes.
c. Suppose, no calls are currently on hold. If the agent takes 5 minutes to complete the current
call, how many callers do you expect to be waiting by that time? What is the probability that
none will be waiting?
d. If no calls are currently being processed, what is the probability that the agent can take 3 minutes
for personal time without being interrupted by a call?
PROBLEM 4

Trading volume on the New York Stock Exchange is heaviest during the first half hour (early morning)
and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of
shares) for 13 days in January and February are shown here (Barron's, January 23, 2006;
February 13, 2006; and February 27, 2006)

Trading Volume (millions of shares)
163

171

174

180

194

198

201

202

211

211

212

214

265



The probability distribution of trading volume is approximately normal.
a. Compute the mean and standard deviation to use as estimates of the population mean and
standard deviation.

b. What is the probability that, on a randomly selected day, the early morning trading volume will be
less than 180 million shares?

c. What is the probability that, on a randomly selected day, the early morning trading volume will
exceed 230 million shares?
d. How many shares would have to be traded for the early morning trading volume on a particular
day to be among the busiest 5% of days?

PROBLEM 5




The average score for male golfers is 95 and the average score for female golfers is 106 (Golf Digest,
April 2006). Use these values as the population means for men and women and assume that the
population standard deviation σ = 14 strokes for both. A simple random sample of 30 male golfers
and another simple random sample of 45 female golfers will be taken.

a. Show the sampling distribution of x for male and female golfers.




b. What is the probability that the sample mean is within 3 strokes of the populations mean for the
sample of male golfers?

c. What is the probability that the sample mean is within 3 strokes of the populations mean for the
sample of female golfers?
d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 3 strokes of
the population mean higher? Why?

PROBLEM 6



Playbill magazine reported that the mean annual household income of its readers is $119,155.
(Playbill, January 2006). Assume this estimate of the mean annual household income is based on
a sample of 80 households, and based on past studies, the population standard deviation is known
to be σ = $30,000.
a. Develop a 90% confidence interval estimate of the population mean.


b. Develop a 95% confidence interval estimate of the population mean.



c. Develop a 99% confidence interval estimate of the population mean.
1 solutions

Answer 233709 by Fombitz(13828) About Me  on 2010-07-28 13:52:17 (Show Source):
You can put this solution on YOUR website!
One problem at a time.
Break them up and re-post.


Quadratic_Equations/326438: Complete the square x^2-20x=50. Not that brilliant when it comes to completing the square problems, None of the steps to do it makes any sense. Asking for it in a (x+y)^2 form i think.
1 solutions

Answer 233708 by Fombitz(13828) About Me  on 2010-07-28 13:51:03 (Show Source):
You can put this solution on YOUR website!
x%5E2-20x=50
Take (1/2) of the x-coefficient, square it, add it to both sides.
%28-20%2F2%29%5E2=100
x%5E2-20x%2B100=50%2B100
%28x-10%29%5E2=150
Take the square root of both sides.
x-10=0+%2B-+sqrt%28150%29
highlight%28x=10+%2B-+5sqrt%286%29%29


Linear-equations/326439: What is the y-intercept of the line -3x+4y=12?
A) 3/4
B) -3/4
C) 3
D) -3
1 solutions

Answer 233707 by Fombitz(13828) About Me  on 2010-07-28 13:47:37 (Show Source):
You can put this solution on YOUR website!
To find the y-intercept, set x=0 and solve for y.
-3x%2B4y=12
4y=12
y=3
.
.
.
C) is the correct answer.


Trigonometry-basics/326441: Convert the given complex number in rectangular form to polar form.
- square root 3 +i
Appreciate you looking at this.
1 solutions

Answer 233706 by Fombitz(13828) About Me  on 2010-07-28 13:44:44 (Show Source):
You can put this solution on YOUR website!

r=sqrt%284%29
r=2
.
.
.
tan%28theta%29=y%2Fx=1%2F%28-sqrt%283%29%29
theta=150 degrees
.
.
.
(-sqrt%283%29,1%29)--->(2,150)


Mixture_Word_Problems/326419: How many mg of a metal containing 45% nickel must be combined with 6 mg of pure nickel to form an alloy 78% nickel?
1 solutions

Answer 233704 by Fombitz(13828) About Me  on 2010-07-28 13:33:38 (Show Source):
You can put this solution on YOUR website!
Let X be the number of mg of 45% nickel.
45X%2B100%286%29=78%28X%2B6%29
45X%2B600=78X%2B468
-33X=-132
highlight%28X=4%29
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4 mg of 45% nickel needs to be added.


Trigonometry-basics/326427: cos^2 5x-sin^2 5x=cos10x
1 solutions

Answer 233703 by Fombitz(13828) About Me  on 2010-07-28 13:31:22 (Show Source):


Equations/326286: write the equation and find the number of: seven times the difference of 7 and a number fives 70. would it be as follows 7(X)-7=70 or 7-x-(7)=70
1 solutions

Answer 233701 by Fombitz(13828) About Me  on 2010-07-28 13:18:53 (Show Source):
You can put this solution on YOUR website!
What does "fives 70" mean?


Linear-systems/326411: how would I solve this system of equations:
7x+3y=12
3x+7y=6
I have the solution but could you write out the solution in full with details please?
1 solutions

Answer 233700 by Fombitz(13828) About Me  on 2010-07-28 13:17:29 (Show Source):
You can put this solution on YOUR website!
1.7x%2B3y=12
2.3x%2B7y=6
From eq. 1,
3y=-7x%2B12
y=-%287%2F3%29x%2B4
Substitute into eq. 2,
3x%2B7%28-%287%2F3%29x%2B4%29=6
3x-%2849%2F3%29x%2B28=6
9x-49x%2B84=18
-40x=-66
highlight%28x=33%2F20%29
Then using eq.1,
231%2F20%2B3y=240%2F20
3y=9%2F20
highlight%28y=3%2F20%29


Sequences-and-series/326423: An=3n-1
1 solutions

Answer 233699 by Fombitz(13828) About Me  on 2010-07-28 13:11:27 (Show Source):
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What's the question?


Graphs/326331: Hi i have 2 graphs y=8+2cos((pix)/6) and y= 3.5+e^(0.07x) and i need to find the values of x when y1=y2 aka 8+2cos((pix)/6)= 3.5+e^(0.07x but don't know how to do it any help would be great.
1 solutions

Answer 233698 by Fombitz(13828) About Me  on 2010-07-28 13:10:35 (Show Source):
You can put this solution on YOUR website!

Three solutions from www.wolframalpha.com, just type in the equation
8+2cos((pi*x)/6)=(3.5+e^(0.07x))
x1=16.40988
x2=20.79707
x3=25.46053
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http://www.wolframalpha.com/input/?i=8%2B2cos%28%28pi*x%29%2F6%29%3D%283.5%2Be%5E%280.07x%29%29


Quadratic-relations-and-conic-sections/326333: Can you show me how to get the equation of a parabola with a focus(0,8) and the directrix y=0?
1 solutions

Answer 233697 by Fombitz(13828) About Me  on 2010-07-28 12:57:55 (Show Source):
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The vertex lies halfway between the focus and the directrix.
The vertex is then (0,4).
Use the focus-vertex form of a parabola,
4p%28y-k%29=%28x-h%29%5E2
p is the distance from the focus to the vertex
p=4
4%284%29%28y-4%29=%28x-0%29%5E2
y-4=%281%2F16%29x%5E2
highlight%28y=%281%2F16%29x%5E2%2B4%29
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Systems-of-equations/326395: 3x-4y=6
-x+y=-1
1 solutions

Answer 233695 by Fombitz(13828) About Me  on 2010-07-28 12:52:12 (Show Source):
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1.3x-4y=6
2.-x%2By=-1
Multiply eq.2 by 3 and add the equations,
3x-4y-3x%2B3y=6-3
-y=3
highlight%28y=-3%29
Then use either equaiton to solve for x.
-x-3=-1
-x=2
highlight%28x=-2%29


Quadratic_Equations/326409: Determine the number of solutions of x2 - 5x + 40 = 0.
1 solutions

Answer 233694 by Fombitz(13828) About Me  on 2010-07-28 12:48:38 (Show Source):
You can put this solution on YOUR website!
Every quadratic eqaution has two solutions, no exceptions.


Number-Line/326413: name the point 2/5 of the distance from -5 to 6
1 solutions

Answer 233693 by Fombitz(13828) About Me  on 2010-07-28 12:46:03 (Show Source):
You can put this solution on YOUR website!
The distance from -5 to 6 is 6-%28-5%29=11.
DELTA=%282%2F5%2911=22%2F5
P=-5%2BDELTA=-5%2B22%2F5=-25%2F5%2B22%2F5=-3%2F5