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Recent problems solved by 'stanbon'
stanbon answered: 57178 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, >>NextTravel_Word_Problems/249530: the speed of train A is 12 mph slower than the speed of train B. Train A travles 220 miles in the same time it takes train B to travel 280 miles. Find the speed of each train.
1 solutions
Answer 181727 by stanbon(57246)   on 2009-12-13 23:21:19 (Show Source):
You can put this solution on YOUR website!the speed of train A is 12 mph slower than the speed of train B. Train A travles 220 miles in the same time it takes train B to travel 280 miles. Find the speed of each train.
-------------
Train A DATA:
distance = 220 miles ; rate = x-12 mph ; time = d/r = 220/(x-12) hrs
----------------
Train B DATA:
distance = 280 miles ; rate = x mph ; time d/r = 280/x hrs
----------------------
Equation:
time A = time B
220/x-12 = 280/x
220x = 280(x-12)
220x = 280x - 3360
-60x = -3360
x = 56 mph (train B rate)
---
x-12 = 44 mph (train A rate)
=================================
Cheers,
Stan H.
|
Probability-and-statistics/249531: Suppose 105 newly created pairs of jeans are placed in a large bin to be checked for quality. Of these, 7 will not be of high enough quality to sell. Suppose that two pairs of jeans are randonly selected, without replacement, from the bin. What is the chance that both pairs of jeans selected will be substandard? Give solution as a reduced fraction in lowest terms and approximated to the nearest ten thousandth.
1 solutions
Answer 181726 by stanbon(57246) on 2009-12-13 23:16:34 (Show Source):
You can put this solution on YOUR website!Suppose 105 newly created pairs of jeans are placed in a large bin to be checked for quality. Of these, 7 will not be of high enough quality to sell. Suppose that two pairs of jeans are randonly selected, without replacement, from the bin. What is the chance that both pairs of jeans selected will be substandard? Give solution as a reduced fraction in lowest terms and approximated to the nearest ten thousandth.
------------
Pick two pairs are sub: 7C2
Pick two pairs without restriction: 105C2
--------------
P(2 sub) = 7C2/105C2 = 21/5460 =0.0038
----------------------------------------------
Cheers,
Stan H.
|
Probability-and-statistics/249541: Find the probability of selecting two consecutive threes when two cards are drawn without replacement from a standard deck of 52 playing cards. Round your answer to four decimal places.
1 solutions
Answer 181725 by stanbon(57246) on 2009-12-13 23:12:10 (Show Source):
You can put this solution on YOUR website!Find the probability of selecting two consecutive threes when two cards are drawn without replacement from a standard deck of 52 playing cards. Round your answer to four decimal places.
-----------------------------------------
Pick 2 threes: 4C2 = 6 ways
----------------------------------
Pick 2 cards without restriction: 52C2
----------------------------------------
P(2 threes) = 6/22100 = 3/11050 = 0.00027149...
Cheers,
Stan H.
|
logarithm/249542: Maria is twice as old as Jasmine. Six years ago, Maria was three times as old as Jasmine was then. Find the age of each girl.
1 solutions
Answer 181724 by stanbon(57246) on 2009-12-13 23:08:22 (Show Source):
You can put this solution on YOUR website!Maria is twice as old as Jasmine. Six years ago, Maria was three times as old as Jasmine was then. Find the age of each girl.
---------------
NOW DATA:
Let Maria by "m"
Let Jasmine b "j"
--------------------------
Equations:
m = 2j
(m-6) = 3(j-6)
-----------------
Substitute for "m" and solve for "j":
(2j-6) = 3(j-6)
2j-6 = 3j-18
j = 12 (Jasmine's age now)
Since m = 2j, m = 24 (Maria's age now)
=======================================
Cheers,
Stan H.
------
|
Permutations/249532: a group of 6 men and 4 women.... three people are selected to attend a conference.
in how man ways can group of 3 women be selected from the 4
if all groups are equally likely to be selected whats the probability that the group will conisist of all women
1 solutions
Answer 181723 by stanbon(57246) on 2009-12-13 23:03:36 (Show Source):
You can put this solution on YOUR website!a group of 6 men and 4 women.... three people are selected to attend a conference.
In how many ways can a group of 3 women be selected from the 4
4C3 = 4C1 = 4
-----------------------
If all groups are equally likely to be selected?
Whats the probability that the group will consist of all women
---
P(all women) = 4/10C3 = 4/120
================================
Cheers,
Stan H.
|
Probability-and-statistics/249533: FM radio stations with high signal strength in New Orleans break down into the followong categories:
Hip hop-2
Religious-6
Country-2
Rock-3
Talk radio-2
Other-5
If someone driving in NO tuned in to am FM radio station with high signal strength what would be the chances he would not get a country or hip hop station? Give anser as a fraction in lowest terms.
1 solutions
Answer 181719 by stanbon(57246) on 2009-12-13 22:42:44 (Show Source):
You can put this solution on YOUR website!FM radio stations with high signal strength in New Orleans break down into the followong categories:
Hip hop-2
Religious-6
Country-2
Rock-3
Talk radio-2
Other-5
If someone driving in NO tuned in to am FM radio station with high signal strength what would be the chances he would not get a country or hip hop station? Give anser as a fraction in lowest terms.
---------------------
Ways to succeed: 4
Total stations: 20
---
P(country or hip hop) = 4/20 = 1/5
====================================
Cheers,
Stan H.
|
Linear-equations/249474: Rationalize the denominator and simplify.
(49√14)/(21√3)
1 solutions
Answer 181690 by stanbon(57246) on 2009-12-13 20:31:13 (Show Source):
You can put this solution on YOUR website!Rationalize the denominator and simplify.
(49√14)/(21√3)
---
Multiply numerator and denominator by sqrt(3) to get:
---------------
(49sqrt(42))/(21*3)
------
= (49sqrt(42))/63
---
Cancle the common factor of 7:
= 7sqrt(42)/9
========================
Cheers,
Stan H.
|
Numbers_Word_Problems/249471: if the sum of three consecutive even numbers is equal to two times the largest number what is the largest number?
1 solutions
Answer 181683 by stanbon(57246) on 2009-12-13 20:21:02 (Show Source):
You can put this solution on YOUR website!if the sum of three consecutive even numbers is equal to two times the largest number what is the largest number?
---------------------
1st: 2x-2
2nd: 2x
3rd: 2x+2
---------
Equations;
6x = 2(2x+2)
2x = 4
x = 2
-----------
largest: 2x+2 = 6
======================
Cheers,
Stan H.
|
Probability-and-statistics/249415: Container A has 3 blue marbles and 2 purple marbles, and Container B has 1 purple marble and 3 green marbles. An experiment consists of randomly selecting a marble from container A then selecting a marble from container B. What is the sample space? What is the probability of choosing a combination that includes a purple marble?
1 solutions
Answer 181681 by stanbon(57246) on 2009-12-13 20:17:04 (Show Source):
You can put this solution on YOUR website!Container A has 3 blue marbles and 2 purple marbles, and Container B has 1 purple marble and 3 green marbles. An experiment consists of randomly selecting a marble from container A then selecting a marble from container B. What is the sample space? What is the probability of choosing a combination that includes a purple marble?
---------------------
1st choice: purple is chosen 2 Ways
2nd choice: Anything is chosen 4 ways
-------------------------
8 combinations have a purple marble.
---------------------------------
1st choice is anything:: 5 ways
2nd choice is purple: 1 way
5 combinations have a purple marble.
--------------------------------------
Total of 13 ways to have a combination that includes a purple marble
------------------
# of unrestricted combinations: 5*4 = 20
---------------
P(comb. includes a purple) = (13)/20
========================================
Cheers,
Stan H.
|
Linear-equations/249461: Find the length of the third side of the right triangle. Assume that c represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places.
a = 1, b = 6
1 solutions
Answer 181675 by stanbon(57246) on 2009-12-13 20:00:39 (Show Source):
You can put this solution on YOUR website!Find the length of the third side of the right triangle. Assume that c represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places.
a = 1, b = 6
------------------------
c = sqrt(1^2 + 6^2)
---
c = sqrt(37)
===================
Cheers,
Stan H.
|
Money_Word_Problems/249436: Hello!
If a manufacturer sells x units of a product, his R=20x and C=2000 + 8x +.0025X^2 determine how many units he should sell to have maximum profit...
So far I know that P= R-C
So P = -.0025x^2 + 12x -2000
and
-b/2a=x soo... x=2400
how do i do the next step? I feel so dumb...
THanks so much
1 solutions
Answer 181670 by stanbon(57246) on 2009-12-13 19:35:33 (Show Source):
You can put this solution on YOUR website!Hello!
If a manufacturer sells x units of a product, his R=20x and C=2000 + 8x +.0025X^2 determine how many units he should sell to have maximum profit...
So far I know that P= R-C
So P = -.0025x^2 + 12x -2000
and
-b/2a=x soo... x=2400
----------------
Good job. And 2400 is the number of units
to sell to maximimize profit.
------------------
Cheers,
Stan H.
|
Probability-and-statistics/249423: If casino Keno were fair, how much should it pay to a player who bets $10 to bet 6 numbers and matches 5 numbers? The odds against matching 5 numbers when you bet 6 numbers in casino Keno are about 322 to 1.
(Points :3)
1 solutions
Answer 181668 by stanbon(57246) on 2009-12-13 19:27:35 (Show Source):
You can put this solution on YOUR website!If casino Keno were fair, how much should it pay to a player who bets $10 to bet 6 numbers and matches 5 numbers?
The odds against matching 5 numbers when you bet 6 numbers in casino Keno are about 322 to 1.
----
P(for) = 1/323
P(against) = 322/323
-----------------------
Random Number values: -10, x-10
---
For a fair game, expected value is zero.
------
Let "x" be the payoff.
-10(322/323) + (x-10)(1/323) = 0
Multiply thru by 323 to get:
-3230 + x-10 = 0
x = $3240
==================
Cheers,
Stan H.
|
Finance/249163: a person invests $20000 partly at 5%, partly at 6% and partly at 6.5%. the total interest is $1170. three times of the amount invested at 6% equals the amount invested at 5% and 6.5% combined. how much is invested in each?
1 solutions
Answer 181565 by stanbon(57246) on 2009-12-13 13:44:48 (Show Source):
You can put this solution on YOUR website!a person invests $20000 partly at 5%, partly at 6% and partly at 6.5%. the total interest is $1170. three times of the amount invested at 6% equals the amount invested at 5% and 6.5% combined. how much is invested in each?
-------------------------------
Equations:
x + y + z = 20000
0.05x + 0.06y + 0.065z = 1170
3y = x + z
---------------------------
Modify and Rearrange:
x + y + z = 20000
50x+60y+65z=1170000
x - 3y + z = 0
---------------------------
Using a matrix method I got the following.
x = 7000
y = 5000
z = 8000
----
That answer does make sense. In my earlier post
I had dropped a zero on the 1170*1000
===============================================================
Cheers,
Stan H.
-------------------
|
Finance/249164: a car makes u turn in 6 seconds. what is the average angular velocity in the turn?
1 solutions
Answer 181531 by stanbon(57246) on 2009-12-13 08:22:20 (Show Source):
You can put this solution on YOUR website!a car makes u turn in 6 seconds. what is the average angular velocity in the turn?
---------------
ang velocity = pi/6 radians/sec or 180/6 = 30 degrees/second
================
Cheers,
Stan H.
|
Probability-and-statistics/248584: What is the best point estimate for the population proportion? Explain why that point estimate is best.
1 solutions
Answer 181522 by stanbon(57246) on 2009-12-13 07:16:08 (Show Source):
You can put this solution on YOUR website!What is the best point estimate for the population proportion? Explain why that point estimate is best.
----------
p = 1/2 because it is not biased toward success or failure.
================
Cheers,
Stan H.
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Probability-and-statistics/249154: In a math class, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. What is the probability that in a randomly selected group of five students from the class, there will be two freshmen girls and three freshmen boys? Express your answer as a decimal to the nearest thousandth.
1 solutions
Answer 181521 by stanbon(57246) on 2009-12-13 07:04:24 (Show Source):
You can put this solution on YOUR website!In a math class, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. What is the probability that in a randomly selected group of five students from the class, there will be two freshmen girls and three freshmen boys? Express your answer as a decimal to the nearest thousandth.
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# of ways to select 2 freshman girls: 12C2
# of ways to select 3 freshman boys: 11C3
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# of ways to pick 5 students without restriction: 30C5
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P(2 frosh girls and 3 frosh boys) = [12C2*11C3]/30C5 = [66*55]/142506=0.0255
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Cheers,
Stan H.
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Functions/249111: I have been trying to figure out how to solve this function. Most of my problem is not knowing the steps to take to get the correct answer they are wanting.
f(x)=8/x, g(x)=9x^2-5
The answers are
A) {x[x is a real number and x not equal to -9
b) {x[x is a real number and x not equal to 5
c) {x[x is a real number
d) {x[x is a real number and x not equal to 0
Please help me!!
1 solutions
Answer 181498 by stanbon(57246) on 2009-12-12 23:13:43 (Show Source):
You can put this solution on YOUR website!f(x)=8/x, g(x)=9x^2-5
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Notice: x cannot be 0 because of 8/x, so g(x) cannot be -5.
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f*g(x) = f(x)*g(x) = (8/x)(9x^2-5) = 72x -(40/x)
The answers are
A) {x[x is a real number and x not equal to -9
b) {x[x is a real number and x not equal to 5
c) {x[x is a real number
d) {x[x is a real number and x not equal to 0
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Answer: d
==============
Cheers,
Stan H.
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expressions/249102: Can you please tell me if I answered this correctly?
t^3+125
t^3+5^3
(t+3)(t^2-5t+5)
Thank you!!!
1 solutions
Answer 181496 by stanbon(57246) on 2009-12-12 23:10:19 (Show Source):
You can put this solution on YOUR website!Can you please tell me if I answered this correctly?
t^3+125
t^3+5^3
(t+3)(t^2-5t+5)
Thank you!!!
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Not quite:
(t+5)(t^2-5t+25)
==============================
Cheers,
Stan H.
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Graphs/249107: I do not understand how to solve for m. I know that this should be y=mx+b
but I cant remember how to do these problems. I have my math final on Monday night and I am really needing help on how to solve these
the question I am showing is "Write an equation of the line that passes through the point (-3,-1) and is perpindicular to the line x + 3y = 9. Can someone help me with this?
1 solutions
Answer 181495 by stanbon(57246) on 2009-12-12 23:04:31 (Show Source):
You can put this solution on YOUR website!Write an equation of the line that passes through the point (-3,-1) and is perpendicular to the line x + 3y = 9.
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Find the slope of the given line:
3y = -x + 9
y = (-1/3)x + 3
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Slope of the given line is -1/3.
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Note: Any line perpendicular to the given line must have slope -3.
----------------
Your Problem:
You want the equation of the line that has slope -3 and passes thru (-3,-1).
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Form of the line is y = mx + b; you need to find "m" and "b":
m = -3
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-1 = -3*-3 + b
-1 = 9 + b
b = -10
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Equation:
y = -3x - 10
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Cheers,
Stan H.
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Linear-equations/249103: directions
find the rate of change for the sitution.
you run 7 miles in one hour and 21 miles in three hours?
1 solutions
Answer 181493 by stanbon(57246) on 2009-12-12 22:46:26 (Show Source):
You can put this solution on YOUR website!find the rate of change for the sitution.
you run 7 miles in one hour and 21 miles in three hours?
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You have 2 points (1,7) and (3,21)
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rate of change = (21-7)/(3-1) = 15/2 = 7 mph
=================================================
Cheers,
Stan H.
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Probability-and-statistics/248949: Human body temperature are normally distributed with a mean of 98.2 F and a standar deviation of 0.62. sally's temperature can be described by Z=1.5. what is her temperature?
1 solutions
Answer 181492 by stanbon(57246) on 2009-12-12 22:40:10 (Show Source):
You can put this solution on YOUR website!Human body temperature are normally distributed with a mean of 98.2 F and a standar deviation of 0.62. sally's temperature can be described by Z=1.5. what is her temperature?
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Let the raw score associated with z=1.5 be "x"
x = 1.5*s + u
x = 1.5*0.62 + 98.2
x = 99.13 degrees
====================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/249088: hello
I do not have an exact idea on how to solve this problem below
(x+2)(x-14)(x+1)>0
There will either be a solution set for {x| }
or it will be all real numbers or finally, no solution???
I got as far as multiplying them threw the distributive process. Dont know if this was necessary or not..???
x3rd power -11x2nd power-40x-28 > 0
1 solutions
Answer 181486 by stanbon(57246) on 2009-12-12 22:01:19 (Show Source):
You can put this solution on YOUR website!I do not have an exact idea on how to solve this problem below
(x+2)(x-14)(x+1)>0
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1st: Since the left side cannot be zero
x cannot be -2,14,or -1
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2nd: Draw a number line and mark -2,-1,14 on it.
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3rd: That breaks the line up into 4 intervals.
Choose a check point in each interval to see where
the solutions for the INEQUALITY are.
Test each check point in (x+2)(x-14)(x+1)>0
Note: You only need to check the sign of the answer because you
are comparing the value to zero.
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Checking:
If x = -3, you get -*-*- > 0 ; false, so no solutions in (-inf,-2)
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If x = -3/2, you get +*-*- > 0 ; true, so solutions in (-2,-1)
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If x = 13, you get +*-*+ > 0 ; false, so no solutions in (-1,14)
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If x = 15, you get +*+*+ > 0 ; true, so solutions in (14,+inf)
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Final Answer: (-2,-1)U(14,+inf)
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Cheers,
Stan H.
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Linear-systems/249094: One number is 5 more than another. 5 times the smaller equals 4 times the larger. Find the numbers.
Thank you!! I struggle with these :(
1 solutions
Answer 181485 by stanbon(57246) on 2009-12-12 21:50:03 (Show Source):
You can put this solution on YOUR website!One number is 5 more than another. 5 times the smaller equals 4 times the larger. Find the numbers.
----------------------
Equation:
x = y+5
Note: y is the smaller number.
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5y = 4x
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Substitute for "x" and solve for "y":
5y = 4*(y+5)
5y = 4y+20
y = 20 (smaller number)
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x = y+5 = 25 (larger number)
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Cheers,
Stan H.
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Numbers_Word_Problems/249095: One number is 6 less than another. Three times the smaller is 12 more than twice the larger. Find the numbers.
Thanks
1 solutions
Answer 181483 by stanbon(57246) on 2009-12-12 21:46:14 (Show Source):
You can put this solution on YOUR website!One number is 6 less than another. Three times the smaller is 12 more than twice the larger. Find the numbers.
---------------------------------------
Let the larger number be "x":
Equations:
y = x-6
3y = 2x+12
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Substitute for "y" and solve for "x":
3(x-6) = 2x+12
3x-18 = 2x+12
x = 30 (larger number)
y = x-6 = 24 (smaller number)
=================================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/249093: can you give me atleast 5 problems of "restricted values & reducing rational expression to lowest term" please?? i need it...thanks!:)
1 solutions
Answer 181482 by stanbon(57246) on 2009-12-12 21:39:47 (Show Source):
You can put this solution on YOUR website!can you give me atleast 5 problems of "restricted values & reducing rational expression to lowest term" please?? i need it...thanks!:)
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1) y = x/(x-3)
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2) y = (x-3)/(x^2-6x+9)
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3) y = 1/(5-x)
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4) y = (x-2)/[3(x^2-4)]
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5) y = (x^2+7x)/(x^2 + 14x + 49)
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Cheers,
Stan H.
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Complex_Numbers/249092: what is the answer to -5/8 divided by -15/4?
1 solutions
Answer 181480 by stanbon(57246) on 2009-12-12 21:33:47 (Show Source):
You can put this solution on YOUR website!what is the answer to -5/8 divided by -15/4?
----------------------
Invert the denominator and multiply to get:
(-5/8)*(-4/15)
Cancel common factors: 5 and 4
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= (1/2)(1/3)
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= 1/6
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Cheers,
Stan H.
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