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Recent problems solved by 'stanbon'
stanbon answered: 57288 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299, >>NextTravel_Word_Problems/403978: Stan and Hilda can mow the lawn in 40 minutes if they work together. If Hilda works twice as fast as Stan, how long would it take Stan to mow the lawn alone?
1 solutions
Answer 285557 by stanbon(57361)   on 2011-02-03 17:56:44 (Show Source):
You can put this solution on YOUR website!Stan and Hilda can mow the lawn in 40 minutes if they work together. If Hilda works twice as fast as Stan, how long would it take Stan to mow the lawn alone?
------
Stan time = 2x hr/job ; rate = 1/(2x) job /hr
---
Hilda time = x hr/job ; rate = 1/x job/hr
---
Together time = (2/3) hr/job ; rate = (3/2)job/hr
===
Equation:
rate + rate = together rate
1/x + 1/(2x) = 3/2
---
Multiply thru by 2x:
2 + 1 = 3x
---
x = 1 hr
Stan's time = 2 hr to do the job alone
=====
Cheers,
Stan H.
|
Equations/403934: Given y is two times x, z is three times x, and x + y + 3z = 12. What are the values of x, y, and z ?
1 solutions
Answer 285528 by stanbon(57361) on 2011-02-03 16:26:02 (Show Source):
You can put this solution on YOUR website! Given y is two times x, z is three times x, and x + y + 3z = 12. What are the values of x, y, and z ?
----
Equations:
y = 2x
z = 3x
x + y + 3z = 12
----
Substitutue and solve for "x":
x + 2x + 9x = 12
12x = 12
x = 1
---
y = 2x = 2
z = 3x = 3
============================
Cheers,
Stan H.
=============
|
Probability-and-statistics/403928: I need some help with these questions.
Mary and jim are taking the same math class and have a quiz coming up next tuesday. The probability that mary studies is 0.8 and the probability that jim studies is 0.7.
1. If Mary and Jim studying are independent events then waht is the probability that mary and jim both study?
2. What is the probability that mary studies if we know that jim studies?
3. What is the probability that mary studies OR jim does not?
Thanks for your help.
1 solutions
Answer 285526 by stanbon(57361) on 2011-02-03 16:22:13 (Show Source):
You can put this solution on YOUR website!Mary and jim are taking the same math class and have a quiz coming up next tuesday. The probability that mary studies is 0.8 and the probability that jim studies is 0.7.
1. If Mary and Jim studying are independent events then what is the probability that mary and jim both study?:::0.8*0.7
---------------------------------------------------
2. What is the probability that mary studies if we know that jim studies?
P(Mary studies|jim studies) = 0.8 because they are independent
---------------------------------------------------)
3. What is the probability that mary studies OR jim does not?
P(mary does OR jim does not) = P(mary) + p(jim not) -P(mary and Jim does not)
= 0.8 + 0.3 - (0.8*0.3)
---
= 1.1-0.24
---
= 0.86
===========
Cheers,
Stan H.
|
Equations/403923: HELLO HOW WOULD YOU SOLVE:
(-22)(2) + 5 (-3 - 5)?
shOW WORK PLEASE
1 solutions
Answer 285521 by stanbon(57361) on 2011-02-03 16:08:19 (Show Source):
You can put this solution on YOUR website! The apartments in Vincent's apartment house are numbered consecutively on each floor. The sum of his next door neighbor's number is 2409. What are the numbers?
----
Equation:
x + x+1 = 2409
2x = 2408
x = 1204
x+1 = 1205
==========
Cheers,
Stan H.
|
Graphs/403910: What is the vertex of the function x2 − 14x − 95 = 0?
and
What is the vertex of the function 2x2 + 16x + 21 = 0?
1 solutions
Answer 285519 by stanbon(57361) on 2011-02-03 16:00:15 (Show Source):
You can put this solution on YOUR website!What is the vertex of the function x^2 − 14x − 95 = 0?
Complete the square:
x^2+ 14x + 7^2 = 95+7^2
(x+7)^2 = 144
Vertex: (-7,-144)
-------------------
and
What is the vertex of the function 2x2 + 16x + 21 = 0?
x = -b/2a = -16*(4) = -4,
f(-4) = 2(-4)^2+16(-4)+21 = -11
======
Vertex: (-4,-11)
=====================
Cheers,
Stan H.
|
Evaluation_Word_Problems/403769: Evaluate 2r/s for r=15 and 5=3, simplify your answer 2r/s
Can someone please help me solve this math problem, I would greatly appreciate it.
Thank you,
Sincerely
Sharon
1 solutions
Answer 285477 by stanbon(57361) on 2011-02-03 10:24:34 (Show Source):
You can put this solution on YOUR website!Evaluate 2r/s for r=15 and s=3, simplify your answer 2r/s
-----
(2r)/s)
---
(2*15)/3
---
(30)/3
= 10
=========================
Cheers,
Stan H.
|
Geometry_Word_Problems/403760: a nut store normally sells cashews $9 per pound and almonds for $3.50 per pound. But at the end of the month and the almonds had not sold well, so in order to sell 60 pounds of almonds, the manager decided to mix the 60 pounds of almonds with some cashews and sell the mixture for $7.50 per pound. How many pounds of cashews should be mixed with the almonds to ensure no change in the profit?
1 solutions
Answer 285473 by stanbon(57361) on 2011-02-03 10:11:22 (Show Source):
You can put this solution on YOUR website! a nut store normally sells cashews $9 per pound and almonds for $3.50 per pound. But at the end of the month and the almonds had not sold well, so in order to sell 60 pounds of almonds, the manager decided to mix the 60 pounds of almonds with some cashews and sell the mixture for $7.50 per pound. How many pounds of cashews should be mixed with the almonds to ensure no change in the profit?
----------------
Equations:
Quantity Eq: a + c = 60
Value Eq:::3.5a + 9c = 7.5*60
-----
Multiply thru 1st by 35
Multiply thru 2nd by 10
-------------------
35a + 35c = 35*60
35a + 90c = 75*60
-----
Subtract and solve for "c":
55c = 40*60
c = 43.64 lbs (amt of cashews needed in the mixture)
================
Cheers,
Stan H.
==============
|
Linear_Equations_And_Systems_Word_Problems/403761: The highest waterfall in the world is Angel Falls in Venezuela at 1000 meters. Write an inequality that describes the height h (in meters) of every other waterfall. Graph the inequality.
1 solutions
Answer 285470 by stanbon(57361) on 2011-02-03 10:03:15 (Show Source):
You can put this solution on YOUR website!The highest waterfall in the world is Angel Falls in Venezuela at 1000 meters. Write an inequality that describes the height h (in meters) of every other waterfall.
-------
h(x) < 1000m where x is any of the other waterfalls.
===========
Cheers,
Stan H.
|
Probability-and-statistics/403748: Alice and Bob work on a math problem independently. The probability that Alice solves the
problem is 0.8 and the probability that Bob solves it is 0.6.
(a) What is the probability that both solve the problem?
(b) What is the probability that neither solves it?
(c) What is the probability that exactly one of them solves it?
(d) Given that exactly one of them solves the problem, what is the probability that it is
Bob?
A string of Christmas lights has 20 bulbs and if any bulb fails then the whole string goes out.
Suppose that each bulb has a 5% chance of failure during the Christmas holidays and that
the 20 bulbs are independent of each other.
What is the probability that the string of lights will go out during the holidays?
1 solutions
Answer 285465 by stanbon(57361) on 2011-02-03 09:51:59 (Show Source):
You can put this solution on YOUR website!Alice and Bob work on a math problem independently. The probability that Alice solves the problem is 0.8 and the probability that Bob solves it is 0.6.
(a) What is the probability that both solve the problem?:0.6*0.8
------------------------------
(b) What is the probability that neither solves it?:0.4*0.2
------------------------------
(c) What is the probability that exactly one of them solves it?
Ans: 1 - [0.48+0.08] = 0.44
---------------------------------
(d) Given that exactly one of them solves the problem, what is the probability that it is Bob?
Ans: P(Bob|one solves) = P(Bob AND one solves)/P(one solves)
= (0.6*0.2)/0.44 = 0.27
-----------------------------------
A string of Christmas lights has 20 bulbs and if any bulb fails then the whole string goes out.
Suppose that each bulb has a 5% chance of failure during the Christmas holidays and that the 20 bulbs are independent of each other.
What is the probability that the string of lights will go out during the holidays?
P(failure) = 0.05
P(not fail) = 0.95
Ans: P(string out) = 1 - P(none fail) = 1-0.95^20 = 0.6415
===========================
Cheers,
Stan H.
============
|
Probability-and-statistics/403750: a sample has a mean of m=82, you obtain a score of x=56. would you perfer a standard deviation of s=2 or s=10
1 solutions
Answer 285459 by stanbon(57361) on 2011-02-03 09:34:47 (Show Source):
You can put this solution on YOUR website!a sample has a mean of m=82, you obtain a score of x=56. would you prefer a standard deviation of s=2 or s=10
---
If s = 2 the z-score of 56 would be (56-82)/2 = -13
If s = 10 the z-score of 56 would be (56-82)/10 = -1.3
-----
I would prefer that s = 10 so my score of 56 would be fewer standard deviations below the mean.
====
Cheers,
Stan H.
|
Linear-systems/403753: graph the equation 0.3x-2.6y=8.1
1 solutions
Answer 285457 by stanbon(57361) on 2011-02-03 09:32:26 (Show Source):
You can put this solution on YOUR website! graph the equation 0.3x-2.6y=8.1
--- graph the equation 0.3x-2.6y=8.1
Multiply thru by 10 to rid of those decimals:
3x - 26y = 81
---
Solve for "y":
y = (3/26)x - (81/26)
-----------------------------
Plot a couple of points and draw a line thru them to get:
(0,(81/26)) and (26,3-(81/26))
----
--------------
Cheers,
Stan H.
|
Money_Word_Problems/403664: A child's ticked costs $15 and adult tickets cost $20. The station wants to spend no more than $800 on tickets. They also want the number of child tickets to be greater than twice the number of adult tickets.
How do I graph the system of four inequalities to show possible numbers of tickets that the station can buy?
Thanks!
1 solutions
Answer 285386 by stanbon(57361) on 2011-02-02 21:40:40 (Show Source):
You can put this solution on YOUR website! A child's ticket costs $15 and adult tickets cost $20. The station wants to spend no more than $800 on tickets. They also want the number of child tickets to be greater than twice the number of adult tickets.
How do I graph the system of four inequalities to show possible numbers of tickets that the station can buy?
------
Let y be number of child tickets.
Let x be the number of adult tickets.
------
Value: 15y + 20x <= 800
y <= (-4/3)x + (160/3)
------------------------
Quantity: y > 2x
x >= 0
y >= 0
-----
Cheers,
Stan H.
=======
|
Linear_Equations_And_Systems_Word_Problems/403662: The sum of two numbers is 42. One number plus 2 times the other number is 57. What are the numbers?
1 solutions
Answer 285382 by stanbon(57361) on 2011-02-02 21:22:55 (Show Source):
You can put this solution on YOUR website!The sum of two numbers is 42. One number plus 2 times the other number is 57. What are the numbers?
-------
Equations:
x + y = 42
x + 2y = 57
-----------------
Subtract the top from the bottom and solve for "y":
y = 15
---
Solve for "x":
x + y = 42
x + 15 = 42
x = 27
========
Cheers,
Stan H.
========
|
Probability-and-statistics/403626: A box contains 28 transitors, 5 of which are defective. If 5 are sold at random, find the probability that at least 1 is defective. Express your answer as a fraction.
1 solutions
Answer 285367 by stanbon(57361) on 2011-02-02 20:30:30 (Show Source):
You can put this solution on YOUR website!A box contains 28 transitors, 5 of which are defective. If 5 are sold at random, find the probability that at least 1 is defective. Express your answer as a fraction.
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P(>=1 defective) = 1 - P(none defective)
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= 1 - 28C5/33C5
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= 1 - 0.4141
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= 0.5859
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Cheers,
Stan H.
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Probability-and-statistics/403485: Suppose that 30 randomly selected subjects are randomly assigned to three different treatment groups, 10 subjects in each. Each group is given one of three different drugs (A, B, or C) and the subjects’ responses are measured on a ratio scale.
We want to know test the hypothesis that the mean group responses are not all equal with a 5% significance level:
Sum ofSquares df MeanSquare F Sig.(p-value)
Between Groups 3.998 2 1.999 5.312 0.011
Within Groups 10.160 27 0.376
Total 14.158 29
F is 5.312 and p value is 0.011
With that result for the F-test, should we reject the null hypothesis given above?
1 solutions
Answer 285362 by stanbon(57361) on 2011-02-02 20:22:48 (Show Source):
You can put this solution on YOUR website!We want to know test the hypothesis that the mean group responses are not all equal with a 5% significance level:
Sum ofSquares df MeanSquare F Sig.(p-value)
Between Groups 3.998 2 1.999 5.312 0.011
Within Groups 10.160 27 0.376
Total 14.158 29
F is 5.312 and p value is 0.011
=======================================
With that result for the F-test, should we reject the null hypothesis given above?
Ho: means are all equal
Ha: At least one of the means is not equal
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Since the p-value is less than 5%, reject Ho.
At least one of the means is not equal.
====
Cheers,
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Triangles/403585: How do you determine what type of triangle it is based off of only it's side lengths? For example: Side lengths are 16, 48, and 50. Is this a right triangle?
1 solutions
Answer 285352 by stanbon(57361) on 2011-02-02 19:49:30 (Show Source):
You can put this solution on YOUR website! How do you determine what type of triangle it is based off of only it's side lengths? For example: Side lengths are 16, 48, and 50. Is this a right triangle?
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It's a right triangle if 50^2 = 16^2+48^2
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Cheers,
Stan H.
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Surface-area/403559: how do you solve this triangle 24in by 15in by 19in and get the answer 143in to the second power
1 solutions
Answer 285345 by stanbon(57361) on 2011-02-02 19:26:25 (Show Source):
You can put this solution on YOUR website!how do you solve this triangle 24in by 15in by 19in and get the answer 143in to the second power
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Area = (1/2)base*height
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If 143 is area, base = 15 and height = 19, you get:
Area = (1/2)15*19
Area = (1/2)*285
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Area = 142.5
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Rounded up you get:
Area = 143 in^2
======================
Cheers,
Stan H.
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Travel_Word_Problems/403555: a train travels 150 km in the same time that a plane covers 400 km. if the speed of the plane is 20 km per hr. less than 3 times the speed of the train, find both speeds.
1 solutions
Answer 285342 by stanbon(57361) on 2011-02-02 18:56:26 (Show Source):
You can put this solution on YOUR website!a train travels 150 km in the same time that a plane covers 400 km.
if the speed of the plane is 20 km per hr. less than 3 times the speed of the train, find both speeds.
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Train DATA:
distance = 150 km ; rate = x km/h ; time = 150/x hrs
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Plane DATA:
distance = 400 km ; rate = 3x-20 km/h ; time = 400/(3x-20) hrs
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Equation:
time = time
150/x = 400/(3x-20)
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3/x = 8/(3x-20)
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3(3x-20) = 8x
9x-60 = 8x
x = 60 km/h (train rate)
---
3x-20 = 160 km/h (plane rate)
==================================
Cheers,
Stan H.
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Radicals/403551: If you have a problem like this: 18/ sqrt of 3 + 5 how would you solve?
By multiplying the randicand, you end up with: 18 radical 3/ 3+ 5 radical 3. If you simplify further, you go into an endless randicand distribution
1 solutions
Answer 285339 by stanbon(57361) on 2011-02-02 18:48:20 (Show Source):
You can put this solution on YOUR website!If you have a problem like this: 18/ sqrt of 3 + 5 how would you solve?
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18/(sqrt(3)+5)
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Multiply numerator and denominator by (sqrt(3)-5) to get:
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= [18(sqrt(3)-5)]/[(sqrt(3)+5)(sqrt(3)-5)]
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= [18(sqrt(3)-5)]/(3+25)
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= [18(sqrt(3)-5)]/28
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= [9sqrt(3)-45]/14
==========================
Cheers,
Stan H.
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Permutations/403546: To win the lottery you ,must pick six numbers from 49 balls numbered 1-49. The order in which you pick the balls doesn’t matter. How many different combinations can you pick?
1 solutions
Answer 285335 by stanbon(57361) on 2011-02-02 18:34:20 (Show Source):
You can put this solution on YOUR website!To win the lottery you ,must pick six numbers from 49 balls numbered 1-49. The order in which you pick the balls doesn’t matter. How many different combinations can you pick?
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49C6 = 49!/[(49-6)!*6!] = (49*48*47*46*45*44)/(1*2*3*4*5*6) = 13,983,816
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Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/403479: The maximum load that a horizontal beam can carry is directly proportional to its width. If a beam 1.5 inches wide can support a load of 250 pounds, find the load that a beam of the same type can support if its width is 3.5 inches.
1 solutions
Answer 285303 by stanbon(57361) on 2011-02-02 15:57:17 (Show Source):
You can put this solution on YOUR website!The maximum load that a horizontal beam can carry is directly proportional to its width. If a beam 1.5 inches wide can support a load of 250 pounds, find the load that a beam of the same type can support if its width is 3.5 inches.
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L = kw
--
Solve for "k" using "a beam 1.5 inches wide
can support a load of 250 pounds"
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250 = k*1.5
k = 166.67
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Equation: L = 166.67w
----
Find the load that a beam of the same
type can support if its width is 3.5 inches.
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L = 166.67*3.5
L = 593 1/3 lbs.
================
Cheers,
Stan H.
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