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Recent problems solved by 'stanbon'
stanbon answered: 57151 problems
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53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>NextPolynomials-and-rational-expressions/86713: I have a question that states: use descartes' rule of signs to determine the possible number of positive and negative zeros of the function f(x)=x^6+4x^5-4x^4+5x^3-5x^2+x-5
1 solutions
Answer 62725 by stanbon(57219)   on 2007-06-27 21:22:26 (Show Source):
You can put this solution on YOUR website!use descartes' rule of signs to determine the possible number of positive and negative zeros of the function f(x)=x^6+4x^5-4x^4+5x^3-5x^2+x-5
------
# of positive roots = 5,3, or 1
---------
f(-x)=x^6-4^5-4x^4-5x^3-5x^2-x-5
# of negative roots = 1
===========
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/86710: I have a question that I cannot understand due tomorrow and have absolutely no clue how to do it. It states: use descartes' Rule of Signs to determine the possible number of positive real zeros of the function f(x)=-5x^3+x^2-2x+5
1 solutions
Answer 62724 by stanbon(57219) on 2007-06-27 21:17:53 (Show Source):
You can put this solution on YOUR website!use descartes' Rule of Signs to determine the possible number of positive real zeros of the function f(x)=-5x^3+x^2-2x+5
--------
# of positive zeroes = # of sign changes or some multiple of 2 less
# of changes = 2
f(x) has 2 or 0 positive zeroes
-----------------------
f(-x)=5x^3+x^2+2x+5
# of changes = 0
f(x) has 0 negative zeroes
-----------------
Cheers,
Stan H.
|
Surface-area/86707: Find the Area i am needing a little assistance with these problems, i have been tryint to figure them out but i can't seem to get the right answer. can someone please help me
1) A rectangle with perimeter 56 and width 13
2) A regular polygon with 12 sides of legnth s and apothem 2
(Give your answer in terms of s)
3) Two similar cones have scale factor 5:2, If the total area of the larger cone is 375, find the total of the smaller cone
1 solutions
Answer 62723 by stanbon(57219) on 2007-06-27 21:09:56 (Show Source):
You can put this solution on YOUR website!Find the Area i am needing a little assistance with these problems,
1) A rectangle with perimeter 56 and width 13
Perimeter = 2(length+width)
56 = 2(length+13)
28 = length + 13
length = 15
Area = width*length
Area = 13*15 = 195 sq. units
------------------------------------------
2) A regular polygon with 12 sides of length s and apothem 2
(Give your answer in terms of s)
Area = (1/2)*apothem*side*number of sides
Area = (1/2)*2*s*12
Area = 12s square units
--------------
3) Two similar cones have scale factor 5:2, If the total area of the larger cone is 375, find the total of the smaller cone.
-------
5:2 means 5x/2x
If 5x=375
x= 75
Then 2x = 150 sq. units (smaller cone area)
----------
Cheers,
Stan H.
|
Circles/86709: 1)Write an equation of the circle with center (1,-1) if (-1/2,-1) lies on the circle
I know this is not suppose to be in this catagory but i really need help with this problem.
2) The slope of any line perpendicular to the line y=-1/3x-4
1 solutions
Answer 62721 by stanbon(57219) on 2007-06-27 20:58:11 (Show Source):
You can put this solution on YOUR website!1)Write an equation of the circle with center (1,-1) if (-1/2,-1) lies on the circle
-------
EQUATION:
(x-1)^2 + (y+1)^2 = r^2
If it passes thru ((-1/2),-1), solve for r as follows
(-1/2 - 1)^2 + (-1+1)^2 = r^2
(-3/2)^2 + 0^2 = r^2
r = (3/2)
EQUATION:
(x-1)^2 + (y+1)^2 = (9/4)
-----------------------------
2) The slope of any line perpendicular to the line y=-1/3x-4
The given line has a slope of -1/3
Any line perpendicular to it must have a slope of 3/1
-----------------------------
Cheers,
Stan H.
|
Circles/86708: May i get some help on this problem
Two circles have areas of 49*pi and 36 *pi. find the ratio of their radii
1 solutions
Answer 62719 by stanbon(57219) on 2007-06-27 20:51:59 (Show Source):
You can put this solution on YOUR website!Formula:
Area = pi*r^2
---------
Two circles have areas of 49*pi and 36 *pi. find the ratio of their radii
1st circle: pi*r^2 = 49pi
r^2=49
r=7
-----------
2nd circle: pi*r^2 = 36pi
r^2=36
r=6
-----------
Ratio of the two radii = 7:6
==================
Cheers,
Stan H.
|
Permutations/86701: Can you please assist me with this?
In how many different orders can you arrange 4 vases on a bookcase self?
1 solutions
Answer 62718 by stanbon(57219) on 2007-06-27 20:48:11 (Show Source):
You can put this solution on YOUR website!In how many different orders can you arrange 4 vases on a bookcase self?
# of ways to choose the 1st vase = 4
# of ways to choose the 2nd vase = 3
# of ways to choose the 3rd vase = 2
# of ways to choose the last vase = 1
---------------
# of ways to arrange 4 vases = 4*3*2*1= 4! = 24
=================
Cheers,
Stan H.
|
Numbers_Word_Problems/86694: Solve Algebraically using only one variable. Find three consecutive even integers such that the product of the first integer and the third integer is equal to four less than ten times the second integer.
1 solutions
Answer 62714 by stanbon(57219) on 2007-06-27 19:37:52 (Show Source):
You can put this solution on YOUR website!Find three consecutive even integers such that the product of the first integer and the third integer is equal to four less than ten times the second integer.
---------
Comment: Even numbers are always multiples of 2
----------
1st number: 2x
2nd number: 2x+2
3rd number: 2x+4
EQUATION:
(2x)(2x+4)=10(2x+2)-4
Divide thru by 4 to get:
x(x+2) = 5(x+1)-1
x^2+2x = 5x+4
x^2-3x-4=0
(x-4)(x+1)=0
Positive answer:
x=4
--------
1st number : 2x = 8
2nd number : 10
3rd number : 12
=========================
Cheers,
Stan H.
|
Radicals/86684: I need help with the following problem: ^3 squareroot of-8/27....I do not not know if I have written this correctly. Can someone please help me with this? Thanks
1 solutions
Answer 62713 by stanbon(57219) on 2007-06-27 19:31:07 (Show Source):
|
Miscellaneous_Word_Problems/86695: Solve algebraically using only one variable. The length of a rectangle is two more than twice its width. If the area of the rectangle is 84, find the length and width.
1 solutions
Answer 62711 by stanbon(57219) on 2007-06-27 19:28:30 (Show Source):
You can put this solution on YOUR website!Solve algebraically using only one variable. The length of a rectangle is two more than twice its width. If the area of the rectangle is 84, find the length and width.
------------
Let the width be x; then the length is 2x+2
EQUATION:
Area = width*length
84 = x(2x+2)
42 = x(x+1)
x^2+x-42=0
(x+7)(x-6)=0
Positive answer:
x=6 (width)
2x+2 = 14 (length)
==============
Cheers,
Stan H.
|
Graphs/86693: Ok stuck on this one.
Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?
1 solutions
Answer 62708 by stanbon(57219) on 2007-06-27 19:12:42 (Show Source):
You can put this solution on YOUR website!Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?
----------
Let # of nickels be "x" ; Value of these is 5x cents.
# of dimes is "50-x" ; Value of these is 10*(50-x) = 500-10x cents
----------------
EQUATION:
value + value = 350 cents
5x + 500-10x = 350
-5x = -150
x=30 (number of nickels)
50-x = 20 (number of dimes)
============
Cheers,
Stan H.
|
Probability-and-statistics/86682: I need help if someone can help me with just these three problems and please explain them to me step by step because i am having difficulty with them....I would greatly appreciated it...
Problem #1
Draw a vendiagram and use the given information to fill in the number of elements for each region.
n (A ' ) = 28 , n(B) = 25, n (A' U B ' ) = 45, n(A (upside down U ) B )=12
Problem #2
Let A and B independent events with P (A) = (1)/(4) and P(B) = (1)/(5).
Find P(A (Upside down U) B) and P(A U B)
Problem #3
In the previous section, we described an experiment in which the numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. Find each probability
The probability that the first number is 3, given the following.
a. The sum is 7.
b. The sum is 8.
1 solutions
Answer 62706 by stanbon(57219) on 2007-06-27 19:08:02 (Show Source):
You can put this solution on YOUR website!Draw a vendiagram and use the given information to fill in the number of elements for each region.
n (A ' ) = 28 , n(B) = 25, n (A' U B ' ) = 45, n(A (upside down U ) B )=12
-----
Draw two intersecting circles inside a rectangle.
Label them A and B.
Put a 12 in the intersection of A and B.
Since B has 25 put 25-12 = 13 in the remaining section of B.
Since A' is 28 put a 28-13 = 15 in the rectangle but in neither circle.
Since (A' OR B') = (A and B)' put 45-(13+15)=17 in the unnumbered region
of A.
---------------
Problem #2
Let A and B independent events with P (A) = (1)/(4) and P(B) = (1)/(5).
Find P(A (Upside down U) B)
since A and B are independent the answer is (1/4)(1/5) = 1/20
-----------------
P(A U B) = P(A)+P(B)-P(A intersect B) = 1/4 + 1/5 - 1/20 = 8/20 = 2/5
-------------------
Problem #3
In the previous section, we described an experiment in which the numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. Find each probability
The probability that the first number is 3, given the following.
a. The sum is 7.
b. The sum is 8.
-------
Answered Previously.
=====================
Cheers,
Stan H.
|
Probability-and-statistics/84441: This question is from textbook Elementary Statistics
It is known that steroids give users an advantage in athletic contests, but it is also known that steriod use is banned in athletes. As a result, a steroid testing program has been instituted and athletes are randomly tested. The test procedures are believed to be equally effective on both users and nonusers and claim to be 98% accurate. If 90% of the athletes affected by this testing program are clean, what is the probability that the next athlete tested will be a user and fail the test?
I'm not sure, but can you use the equation P(A and B) = P(A) * P(B knowing A)
1 solutions
Answer 62701 by stanbon(57219) on 2007-06-27 18:47:20 (Show Source):
You can put this solution on YOUR website!It is known that steroids give users an advantage in athletic contests, but it is also known that steriod use is banned in athletes. As a result, a steroid testing program has been instituted and athletes are randomly tested.
The test procedures are believed to be equally effective on both users and nonusers and claim to be 98% accurate.
If 90% of the athletes affected by this testing program are clean, what is the probability that the next athlete tested will be a user and fail the test?
------------------------
P(fail|user)=0.98
P(pass|nonuser)=0.98
P(nonuser)=0.90
P(user)=0.10
------------------
Your Problem:
P(user and fail)= P(fail | user)*P(user)
= 0.98*0.90
= 0.882
==========================
Cheers,
Stan H.
|
Probability-and-statistics/84170: You can be selected for the Varsity Baskeball Team if your shooting score is at 70% probability of sucess. Your trial scores over 4 sessions were a mean of 65.2, a mode of 68.4, a median of 72, and a range of 6 . You should be, on active reserve, the second string team,admitted to team or not be considered
1 solutions
Answer 62696 by stanbon(57219) on 2007-06-27 18:28:27 (Show Source):
You can put this solution on YOUR website!You can be selected for the Varsity Baskeball Team if your shooting score is at 70% probability of sucess. Your trial scores over 4 sessions were a mean of 65.2, a mode of 68.4, a median of 72, and a range of 6 . You should be, on active reserve, the second string team,admitted to team or not be considered
------------
Not be considered as your average is 65.2% and you would need an average of
70% to be selected.
==============
Cheers,
Stan H.
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Probability-and-statistics/86612: can someone help me with these problems when you have a few min. thanks.
Problem #1
Suppose you have three jars with the following contents: 2 black balls and 1 white ball in the first, 1 black ball and 2 white balls in the second, and 1 black ball and 1 white ball in the third. One jar is to be selected, and then 1 ball is to be drawn from the selected jar. If
the probabilities of selecting the first, second, or third jar are 1/ 2, 1/ 3, and 1 /6, respectively,find the probabilities that if a white ball is drawn, it came from the following jars.
A) The third jar
Problem #2
Laura Johnson, a game show contestant, could win one of two prizes: a shiny new
Porsche or a shiny new penny. Laura is given two boxes of marbles. The first box has
50 pink marbles in it and the second box has 50 blue marbles in it. The game show
host will pick someone from the audience to be blindfolded and then draw a marble
from one of the two boxes. If a pink marble is drawn, she wins the Porsche. Otherwise,
Laura wins the penny.* Can Laura increase her chances of winning by redistributing
some of the marbles from one box to the other? Explain.
1 solutions
Answer 62678 by stanbon(57219) on 2007-06-27 14:11:41 (Show Source):
You can put this solution on YOUR website!1st Problem:
p(3rd jar|white)
=[P(3rd jar and white)/P(w)
=[(1/6)*(1/2)]/]P(white and 1st)+P(white and 2nd)+P(white and 3rd)]
=[1/12]/[(1/2)(1/4)+(1/3)(2/3)+(1/6)(1/2)]
= [1/12]/[31/72]
= 6/31
================
2nd Problem:
As it stands her chances of winning are 1/2
If she changes the mixture to Jar1 with x pink and 50-x white and Jar2 with 50-x pink and and x white, the probability of pink is still
(1/2)(x/50) + 1/2(50-x)/50
= (1/2)[x/50 + (50-x)/50]
= 1/2 [ (50x+2500-50x)/2500] = (1/2)(1) = 1/2
=========
Cheers,
Stan H.
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Probability-and-statistics/86614: I need help with this math please explain it to me...Once someone has a few minutes i appreciate it.
Problem #1
Suppose two dice are rolled. Let A be the event that the sum of the two dice is 7. Find an event B related to numbers on the dice such that A and B are
a. independent;
b. dependent.
Problem #2
Body Types A study on body types gave the following
results: 45% were short; 25% were short and overweight;
and 24% were tall and not overweight. Find the probabilities
that a person is the following.
a. Overweight
b. Short, but not overweight
c. Tall and overweight
1 solutions
Answer 62675 by stanbon(57219) on 2007-06-27 13:39:33 (Show Source):
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Probability-and-statistics/86633: can someone help me understand how to solve this type of problems thanks...
Problem #1
Using the union rule to answer the following questions.
suppose n(A (A LETTER "u" UPSIDE DOWN) b) = 5
n(A U B) = 35
n (A) = 13
what is n(B)?
Problem #2
Show that the stamtements is true by drawing venn diagrams and shading the regions representing the sets on each side of the equals sign.
(A (UPSIDE DOWN U) B)' = A' U B'
1 solutions
Answer 62674 by stanbon(57219) on 2007-06-27 13:38:12 (Show Source):
You can put this solution on YOUR website!Problem #1
Using the union rule to answer the following questions.
suppose n(A (A LETTER "u" UPSIDE DOWN) b) = 5
n(A U B) = 35
n (A) = 13
what is n(B)?
Ans:
n(A union B) = n(A)+n(B)-n(A intersect B)
35 = 13 + n(B) - 5
n(B) = 35-8
n(B) = 27
======================
Problem #2
Show that the statements is true by drawing venn diagrams and shading the regions representing the sets on each side of the equals sign.
(A (UPSIDE DOWN U) B)' = A' U B'
Draw two intersecting circles in a rectangle.
Draw it again.
Shade (A intersect B)' in the 1st
Shade (A' union B') in the 2nd
------
Do the two shaded areas look the same?
They should. This is one piece of DeMoivre's Rule.
============
Cheers,
Stan H.
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Probability-and-statistics/86635: Can someone correct this for me please....thanks
Problem #1
A marble is drawn from a box containing 3 yellow, 4 white, and 8 blue marbles. Find the odds in favor of drawing the following.
a. A yellow marble
My answer 3/15
b. A blue marble
my answer 4/15
c. A white marble
My answer 8/15
Problem #2
. Body Types A study on body types gave the following
results: 45% were short; 25% were short and overweight;
and 24% were tall and not overweight. Find the probabilities
that a person is the following.
a. Overweight
b. Short, but not overweight
c. Tall and overweight
1 solutions
Answer 62673 by stanbon(57219) on 2007-06-27 13:27:34 (Show Source):
You can put this solution on YOUR website!Problem #1
A marble is drawn from a box containing 3 yellow, 4 white, and 8 blue marbles. Find the odds in favor of drawing the following.
a. A yellow marble
P(yellow) = 3/15; P(not yellow)= 12/15;
Odds in favor of yellow = [3/15]/[12/15] = 3:12
----------------
b. A blue marble
P(blue) = 8/15; P(not blue)=7/15;
Odds in favor of blue = [8/15]/[7/15]= 8:7
-------------------
c. A white marble
Odds in favor of white = 4:11
------------------------
Problem #2
. Body Types A study on body types gave the following
results: 45% were short; 25% were short and overweight;
and 24% were tall and not overweight. Find the probabilities
that a person is the following.
Draw a contingency table with rows "short" and "tall"
and with columns "over weight" and "not over weight".
Enter the given data in the proper boxes or at the sum of row or column.
Fill in the empty boxes so the row and column sums are proper.
Then:
a. P(Overweight) = P(short and over) + P(tall and over) = 0.25+0.31= 0.56
b. P(Short, but not overweight) = 0.20
c. P(Tall and overweight) = 0.31
================
Cheers,
Stan H.
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Probability-and-statistics/86637: I need help understanding how to solve these problems...
Problem #1
Let A and B be independent events with P(A) = (1)/(4) and P(B) = (1)/(5)
Find P (A (An upside down letter U) B) and P (A U B).
Problem #2
In the previous section, we described an experiment in which the numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. Find each probability
The probability that the first number is 3, given the following.
a. The sum is 7.
b. The sum is 8.
1 solutions
Answer 62671 by stanbon(57219) on 2007-06-27 13:00:17 (Show Source):
You can put this solution on YOUR website!Problem #1
Let A and B be independent events with P(A) = (1)/(4) and P(B) = (1)/(5)
Find P (A (An upside down letter U) B)= (1/4)(1/5) = 1/20
---------------
and P (A U B) = P(A) + P(B) - P(A and B)
= (1/4) + 1/5) -1/20
= 9/20-1/20
= 8/20
----------------------------
Problem #2
In the previous section, we described an experiment in which the numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. Find each probability
Sample space:
1+2=3; 1+3=4; 1+4=5 ;1+5=6
2+1=3; 2+3=5; 2+4=6 ; 2+5=7
3+1=4; 3+2=5; 3+4=7; 3+5= 8
4+1=5; 4+2=6; 4+3=7; 4+5=9
5+1=6; 5+2=7; 5+3=8; 5+4=9
The probability that the first number is 3, given the following.
a. P(The sum is 7) = 1/20
b. P(The sum is 8) = 2/20
===============================
Cheers,
Stan H..
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Probability-and-statistics/86638: Can someone help me with these problems how to solve them..thanks
Problem #1
If two cards are drawn without replacement from an ordinary deck, find the probabilities of the following results.
The second is black, given that the first is a spade.
Problem #2
Pam Snow invites 10 relatives to a party: her mother, 2 aunts, 3 uncles, 2 brothers, 1 male cousin, and 1 female cousin. If the chances of any one guest arriving first are equally likely, find the probabilities that the first guest to arrive is as follows.
a. An uncle or a cousin
b. A male or a cousin
c. A female or a cousin
1 solutions
Answer 62670 by stanbon(57219) on 2007-06-27 12:36:38 (Show Source):
You can put this solution on YOUR website!Problem #1
If two cards are drawn without replacement from an ordinary deck, find the probabilities of the following results.
The second is black, given that the first is a spade.
Since a spade was drawn and not replace there are 25 black cards in the deck
after the 1st draw.
Prob(black|spade} =25/51
-----------------------------
Problem #2)
Pam Snow invites 10 relatives to a party: her mother, 2 aunts, 3 uncles, 2 brothers, 1 male cousin, and 1 female cousin. If the chances of any one guest arriving first are equally likely, find the probabilities that the first guest to arrive is as follows.
a. An uncle or a cousin)
P(uncle or cousin) = P(uncle) + P(cousin) = 3/10 + 2/10 = 1/2
------------------
b. P(A male or a cousin) = P(male) + P(cousin) - P(male and cousin)
= 6/10 + 2/10 - 1/10 = 7/10
-----------------------
c. P(A female or a cousin ) = P(female)+P(cousin)-P(female cousin)
= 4/10 + 2/10 - 1/10
= 5/10
--------------------
Cheers,
Stan H.
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Probability-and-statistics/86639: Can someone help me with these problems thanks..
Problems #1
Using venn diagram
Let P(Z) = 0.42
P(Y) = 0.35
P (Z U Y) = 0.61
fIND EACH PROBABILITY:
a) P(Z' (UPSIDE DOWN U) Y')
b) P(Z' U Y')
c) P(Z' U Y)
d) P(Z (UPSIDE DOWN U) Y')
1 solutions
Answer 62668 by stanbon(57219) on 2007-06-27 12:24:54 (Show Source):
You can put this solution on YOUR website!Problems #1
Using venn diagram
Let P(Z) = 0.42
P(Y) = 0.35
P (Z U Y) = 0.61
fIND EACH PROBABILITY:
a) P(Z' (UPSIDE DOWN U) Y')
b) P(Z' U Y')
c) P(Z' U Y)
d) P(Z (UPSIDE DOWN U) Y')
------------------------------
Draw two intersecting circles within a rectangle.
Label one circle Z with probability label 0.42
Label the other circle Y with probability label 0.35
Label Y intersect Z with probability 0.07
Label Y intersect Z' with probability 0.35-0.07 = 0.28
Label Z intersect Y' with probability 0.42-0.07 = 0.35
Label (Z union Y)'= 0.30
---------------------------
a) P(Z' intersect Y') = (Z U Y)' = 0.30
b) P(Z' U Y') = (Z intersect Y)' = 0.93
c) P(Z' U Y) = (Z intersect Y') = 0.35
d) P(Z (UPSIDE DOWN U) Y')= 0.35
=====================
Cheers,
Stan H.
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Proportions/86619: This question is from textbook Mathematics for elementary teachers
The problem I need help with is as follows:
A family uses 5 gallons of milk every 3 weeks. At that rate, how many gallons of milk will they need to purchase in a year's time?
This is what I have tried --
5 gallons : 3 weeks = x gallons : 52 weeks
5/3 = x/52 (cross multiply)
3x = 260 (divide by 3)
x = 86.6 or 87 gallons
Thank you for any help.
R. Franke
sylleobear@hotmail.com
1 solutions
Answer 62653 by stanbon(57219) on 2007-06-27 06:22:00 (Show Source):
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Linear_Equations_And_Systems_Word_Problems/86599: Solve the following word problems. Be sure to show the equation you use for the solution
56) Science and medicine. A bus leaves a station at 1 P.M., traveling west at an average rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h. At what time will the two buses by 274 mi apart?
1 solutions
Answer 62644 by stanbon(57219) on 2007-06-26 21:28:03 (Show Source):
You can put this solution on YOUR website!A bus leaves a station at 1 P.M., traveling west at an average rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h. At what time will the two buses by 274 mi apart?
---------------
1st bus DATA;
rate = 44 mph ; time = x hrs ; distance = 44x miles
-------------------
2nd bus DATA:
rate = 48 mph ; time = x-1 hrs ; distance = 48x-48 miles
--------------------
EQUATION:
distance + distance = 274
44x + 48x -48 = 274
92x = 322
x = 3.5 hrs
1 P.M. + 3.5 hrs = 4:30 P.M.
===============
Cheers,
Stan H.
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Expressions-with-variables/86608: This question is from textbook intermediate algebra
It takes Steven 8 hours to clean the yard and mow the yard. Steven and his brother Gregory can do the same job in three hours when they work together. How long does it take Gregory to do the job when he works alone?
1 solutions
Answer 62642 by stanbon(57219) on 2007-06-26 21:20:31 (Show Source):
You can put this solution on YOUR website!It takes Steven 8 hours to clean the yard and mow the yard. Steven and his brother Gregory can do the same job in three hours when they work together. How long does it take Gregory to do the job when he works alone?
----------
Steven DATA:
time = 8 hr/job ; rate = 1/8 job/hr
-------------------
Together DATA:
time = 3 hr/job ; rate = 1/3 job/hr
---------------------
Gregory DATA:
time = x hr/job ; rate = 1/x job/hr
-----------------------
EQuATIOn:
rate + rate = together rate
1/8 + 1/x = 1/3
3x + 24 = 8x
5x=24
x = 4.8 hrs = 4 hrs 48 minutes (Gregory time to do the job)
==============
Cheers,
Stan H.
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Expressions-with-variables/86607: This question is from textbook intermediate algebra
The base of a triangle is 5 meters more than its height, and its area is 12 square meters. Find the base and the height of the triangle. [area =1/2*base*height]
1 solutions
Answer 62641 by stanbon(57219) on 2007-06-26 21:15:34 (Show Source):
You can put this solution on YOUR website!The base of a triangle is 5 meters more than its height, and its area is 12 square meters. Find the base and the height of the triangle. [area =1/2*base*height]
--------------
Let the height be "x" meters.
Then the base is "x+5" meters.
EQUATION:
[area =1/2*base*height]
12 = (1/2)*(x+5)*x
24 = x^2+5x
x^2+5x-24=0
(x+8)(x-3)=0
Positive answer: x=3 meters (height)
x+5 = 8 meters (base)
=============
Cheers,
Stan H.
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Money_Word_Problems/86601: 26) Business and finance. Ms. Jordan has been given a loan of $2500 for 1 year. If the interest charged is $275, what is the interest rate on the loan?
1 solutions
Answer 62640 by stanbon(57219) on 2007-06-26 21:04:42 (Show Source):
You can put this solution on YOUR website!Ms. Jordan has been given a loan of $2500 for 1 year. If the interest charged is $275, what is the interest rate on the loan?
---------
Interest = Pricipal*Rate
r= I/P
r = 275/2500
r = 0.11 = 11%
=================
Cheers,
Stan H.
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Graphs/86605: Graph the solution set of each of the following inequalities. Here are some examples of how to use text characters to do the graphing (we’ll be using only the following symbols: less than “<” (for the arrow pointing to the left), greater than “>” (for the arrow pointing to the right), dash (for light lines) “-“, equals (for heavy lines) “=”, plus “+” (for a point of interest), capital “O” (for a point that is not part of the solution), and asterisk “*” for a point that is part of the solution.
x > 1: <-----+---O=====>
0 1
x > 1: <-----+---*=====>
0 1
74) 7(x – 3) > 5x – 14
1 solutions
Answer 62639 by stanbon(57219) on 2007-06-26 21:01:47 (Show Source):
You can put this solution on YOUR website!7(x – 3) > 5x – 14
7x-21>5x-14
2x>7
x > 7/2
--------
Draw a number line.
Label some point as 7/2
Draw a circle around that point.
Draw an arrow to the right starting at that circle.
----------
Cheers,
Stan H.
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Equations/86606: Another very common mistake is in the equation below:
The Equation 6x – (x + 3) = 5 + 2x
First Step Solving 6x – x + 3= 5 + 2x
Write a clear explanation of what error has been made and what could be done to avoid this mistake.
1 solutions
Answer 62638 by stanbon(57219) on 2007-06-26 20:58:06 (Show Source):
You can put this solution on YOUR website!The Equation 6x – (x + 3) = 5 + 2x
First Step Solving 6x – x + 3= 5 + 2x
---------
Applying the negative to (x+3) you should get -x-3
because of the distributive rule.
---------
Cheers,
Stan H.
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Money_Word_Problems/86594: Annuity problems have really been giving me a problem lately and we've been moving through this particular chapter rather quickly. A man buys a house for $95,000. He makes a $15,000 down payment and amortizes the rest of the debt with monthly payments over the next 15 years. The interst rate on the debt is 12%, compound monthly. Find the size of each payment.
I'm pretty sure I use the An=R[1-(1+i)^n all divided by i
R=15,000
i= .12 or 12% /(12)
n= 15
This is what I'm guessing but I'm really not sure. Please help me if you can!!!!!!!
1 solutions
Answer 62637 by stanbon(57219) on 2007-06-26 20:55:43 (Show Source):
You can put this solution on YOUR website!I think I answered this for you.
Your interpretation of your formula seems incorrect.
R is not the down payment.
n is not 15
-------------
Cheers,
Stan H.
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Probability-and-statistics/86570: Can someone help me please explain it to me towards these problems. If you can and have a few minutes thanks...for your help
PROBLEM #32
Is it possible for two nonempty sets to have the same intersection and union? If so,
give an example.
pROBLEM #64
Electoral College U.S. presidential elections are decided
by the Electoral College, in which each of the 50 states,
plus the District of Columbia, gives all of its votes to a candidate.†
Ignoring the number of votes each state has in the
Electoral College, but including all possible combinations
of states that could be won by either candidate, how many
outcomes are possible in the Electoral College if there are
two candidates? (Hint: The states that can be won by a candidate
form a subset of all the states.)
1 solutions
Answer 62636 by stanbon(57219) on 2007-06-26 20:34:20 (Show Source):
You can put this solution on YOUR website!PROBLEM #32
Is it possible for two nonempty sets to have the same intersection and union? If so,
give an example.
If the sets are equal they will have the same intersection and union.
Example: A={1,2,3} and B={1,2,3}
-----------------------
pROBLEM #64
Electoral College U.S. presidential elections are decided
by the Electoral College, in which each of the 50 states,
plus the District of Columbia, gives all of its votes to a candidate.†
Ignoring the number of votes each state has in the
Electoral College, but including all possible combinations
of states that could be won by either candidate, how many
outcomes are possible in the Electoral College if there are
two candidates? (Hint: The states that can be won by a candidate
form a subset of all the states.)
-------
There are 2^50 subsets ranging from the set with all the states
to the set with no states. Corresponding to each of these subsets
won by one of the candidates the other candidate wins the complementary
subset.
------------
Cheers,
Stan H.
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Linear_Algebra/86576: ok how do I write an equation or inequality to show the profit a business makes in selling purses at 250 dollars for 80 purses and 45 purses at 400 dollar will I be able to graph the business potential sales. and what are the reasons why we would use a function notation
1 solutions
Answer 62635 by stanbon(57219) on 2007-06-26 20:25:45 (Show Source):
You can put this solution on YOUR website!ok how do I write an equation or inequality to show the profit a business makes in selling purses at 250 dollars for 80 purses and 45 purses at 400 dollar
-----------
How can he make less for selling more purses?
Did you post this correctly?
Cheers,
Stan H.
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Money_Word_Problems/86580: A man buys a house for $95,000. He makes a $15,000 down payment and amortizes the rest of the debt with monthly payment over the next 15 years. The interst rate on the debt is 12%, compound monthly. Find the size of each payment.
Really lost please help!!!!!
1 solutions
Answer 62634 by stanbon(57219) on 2007-06-26 20:22:18 (Show Source):
You can put this solution on YOUR website!A man buys a house for $95,000. He makes a $15,000 down payment and amortizes the rest of the debt with monthly payment over the next 15 years. The interest rate on the debt is 12%, compound monthly. Find the size of each payment.
---------------------
loan balance = original amount(1+i)^n - [P/i][(1+i)^n - 1]
-----------
You want loan balance to be 0
original amount = 95000-15000=80000
i=0.12/12=0.01
n=15*12 = 180 payments
P is the monthly payment
------------
0 = 80000(1.01)^180 - [P/0.01][(1.01)^180 -1]
P/0.01 = 479664.158/4.995801975
P/0.01 = 96013.44496
P =$960.13 (this is the monthly payment)
===========
Cheers,
Stan H.
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