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Recent problems solved by 'stanbon'
stanbon answered: 57327 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 , 57300..57329, >>Next
Travel_Word_Problems/513157: Meg rowed her boat upstream a distance of 39 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 5 mph, find the average speed of the boat relative to the water.
***I need it worked out in detail please and thank you
1 solutions
Answer 342889 by stanbon(57400)   on 2011-10-11 16:23:13 (Show Source):
You can put this solution on YOUR website!Meg rowed her boat upstream a distance of 39 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 5 mph, find the average speed of the boat relative to the water.
----
Upstream DATA:
distance = 39 miles ; rate = b-5 mph ; time = d/r = 39/(b-5) hrs
------------------
Downstream DATA:
distance = 39 miles ; rate = b+5 mph ; time = d/r = 39/(b+5) hrs
----------------
Equation:
time + time = 16 hrs
---
39/(b-5) + 39/(b+5) = 16
---
1/(b-5) + 1/(b+5) = 16/39
[b+5+b-5]/b^2-25 = 16/39
----
39*2b = 16b^2-400
39b = 8b^2-200
8b^2-39b-200 = 0
---
Positive solution:
b = 8 mph (speed of the boat relative to the water)
================
Cheers,
Stan H.
============
|
Rate-of-work-word-problems/513152: A tank can be filled by a hose in 15 hours. It can be emptied by a drainpipe in 25 hours. If the drainpipe is open while the tank is being filled, how long does it take to fill the tank?
1 solutions
Answer 342888 by stanbon(57400) on 2011-10-11 16:13:22 (Show Source):
You can put this solution on YOUR website!A tank can be filled by a hose in 15 hours. It can be emptied by a drainpipe in 25 hours. If the drainpipe is open while the tank is being filled, how long does it take to fill the tank?
----------
Fill rate: 1/15 job/hr
-----
Drain rate: 1/25 job/hr
--------------------------
Together rate: 1/x job/hr
----------------------------
Equation:
rate - rate = rate
1/15 - 1/25 = 1/x
---
Multiply thru by 75x to get:
5x - 3x = 75
2x = 75
x = 37.5 hrs (time to fill the tank together)
==============================================
Cheers,
stan H.
==============
|
Linear-systems/512971: Part A. For the given system, determine the best method (Graphing, Substitution, Addition) for solving.
3x - 2y = 8
x = -2y
Part B. Explain why you chose that method.
Part C. Solve the system. Give the final solution expressed as (x,y) point. (Showing your steps
1 solutions
Answer 342822 by stanbon(57400) on 2011-10-11 10:39:40 (Show Source):
You can put this solution on YOUR website!For the given system, determine the best method (Graphing, Substitution, Addition) for solving.
3x - 2y = 8
x = -2y
Part B. Explain why you chose that method.
Substitution because the 2nd equation is all set up for substitution.
------
Part C. Solve the system. Give the final solution expressed as (x,y) point. (Showing your steps
---
Substitute for "x" and solve for "y":
3(-2y) - (2y) = 8
----
-6y-2y = 8
-8y = 8
y = -1
---
Solve for "x":
x = -2y
x = -2*-1 = 2
=====================
solution: (2,-1)
=======================
cheers,
Stan H.
===============
|
Probability-and-statistics/512965: When water flows across farm land, some of the soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow on the amount of soil washed away. Flow is measured in liters per second and the eroded soil is measured in kilograms. The data are given in the following table.
Flow rate .31 .85 1.26 2.47 3.75
Eroded soil .82 1.95 2.18 3.01 6.07
The association between flow rate and amount of eroded soil is positive or negative? how so?
1 solutions
Answer 342819 by stanbon(57400) on 2011-10-11 10:31:38 (Show Source):
You can put this solution on YOUR website!The data are given in the following table.
Flow rate .31 .85 1.26 2.47 3.75
Eroded soil .82 1.95 2.18 3.01 6.07
The association between flow rate and amount of eroded soil is positive or negative? how so?
---
Ans: Amt. of eroded soil increases as flow rate increases.
So the association (slope) is positive.
================
Cheers,
stan H.
|
Travel_Word_Problems/512933: An airplane travels 150km/h for 2 hours at 138 degrees from Omaha. How far south is the plane from Omaha after those two hours?
1 solutions
Answer 342818 by stanbon(57400) on 2011-10-11 10:27:44 (Show Source):
You can put this solution on YOUR website!An airplane travels 150km/h for 2 hours at 138 degrees from Omaha. How far south is the plane from Omaha after those two hours?
------
Note: I'm assuming zero degrees is due North from Omaha so the
trig angle followed by the plane is really -48 degrees (4th Quadrant).
--------------------------------------------------------------
Draw the picture.
The plane has gone 2*150 = 300 km
---
The south component of its flight = 150cos(-48) = 150*0.6691 = 100.37 km
========================
Cheers,
Stan H.
|
Geometry_Word_Problems/512959: if the sum of the lengths of two sides of a triangle is 18, what is the largest possible integral value for the 3rd side?
1 solutions
Answer 342816 by stanbon(57400) on 2011-10-11 10:18:24 (Show Source):
You can put this solution on YOUR website!if the sum of the lengths of two sides of a triangle is 18, what is the largest possible integral value for the 3rd .
---
Ans: 17
If the 3rd side is 18 the two other sides combined would
only connect the endpoints of the 18-line to form a line:
and would not form a triangle.
If the 3rd side is more than 18 the two "other" sides would
not even connect the endpoints of the 18-line: thus no
triangle would be formed.
================
Cheers,
Stan H.
|
Graphs/512936: please help me solve this inequality and set it on a number line -7<9x+2<11
1 solutions
Answer 342812 by stanbon(57400) on 2011-10-11 10:07:02 (Show Source):
You can put this solution on YOUR website!solve this inequality and set it on a number line
-7<9x+2<11
-----
Subtract 2 along the line to get:
-9 < 9x < 9
---
Divide thru by 9 to get:
-1 < x < 1
===================
Draw a number line.
Plot x = -1 and x = 1 with an open circle on each point.
Connect those open circles with a line segment.
---
That is your graph of the solution.
Cheers,
Stan H.
|
test/512953: The of three integers is 22 the second integer is 3 more than the first integer and the third integer is one less than twice the first integer find the integers
1 solutions
Answer 342808 by stanbon(57400) on 2011-10-11 09:59:58 (Show Source):
You can put this solution on YOUR website!The ?? of three integers is 22 the second integer is 3 more than the first integer and the third integer is one less than twice the first integer find the integers
----
Word missing in your post.
|
test/512954: Find three consecutive even integers suck that the sum of twice the third integer and the integer is 12 less than 4 times the first integer
1 solutions
Answer 342806 by stanbon(57400) on 2011-10-11 09:58:28 (Show Source):
You can put this solution on YOUR website!Find three consecutive even integers such that the sum of twice the third integer and the ?? integer is 12 less than 4 times the first integer
----
1st: 2x-2
2nd: 2x
3rd: 2x+2
-------------------------
Note: A word is missing from your post.
|
test/512950: Four number are in the ratio 2:4:5:7 the sum of the first two numbers is 12 more than the difference between the fourth and third numbers find the numbers
1 solutions
Answer 342805 by stanbon(57400) on 2011-10-11 09:56:27 (Show Source):
You can put this solution on YOUR website!Four number are in the ratio 2:4:5:7 the sum of the first two numbers is 12 more than the difference between the fourth and third numbers find the numbers
-----
2x; 4x ; 5x ; 7x
------------------
2x+4x = (7x-5x)+12
6x = 2x+12
4x = 12
x = 3
----
2x = 6
4x = 12
5x = 15
7x = 21
=============
Cheers,
Stan H.
===============
|
Rate-of-work-word-problems/512923: It takes Sara 2 hours to paint a fence and Daniel 4 hours to paint the same fence. How long will it take to paint the fence if they work together?
1 solutions
Answer 342795 by stanbon(57400) on 2011-10-11 09:23:50 (Show Source):
You can put this solution on YOUR website!It takes Sara 2 hours to paint a fence and Daniel 4 hours to paint the same fence. How long will it take to paint the fence if they work together?
----
Sara rate: 1/2 job/hr
Dan rate:: 1/4 job/hr
---
Together rate: 1/x job/hr
------
Equation:
rate + rate = together rate
1/2 + 1/4 = 1/x
Multiply thru by 4x to get:
2x + x = 4
3x = 4
x = 3/4 hr. (time to do the job together)
==============
Cheers,
Stan H.
================
|
Probability-and-statistics/512815: Studies have shown a particular television commercial is understood by 25% of first grade students and 80% of fourth grade students. If a television advertising agency randomly selects one first grader and one fourth grader, what is the probability neither child would understand the commercial, assuming the children's reactions are independent?
1 solutions
Answer 342793 by stanbon(57400) on 2011-10-11 08:39:25 (Show Source):
You can put this solution on YOUR website!Studies have shown a particular television commercial is understood by 25% of first grade students and 80% of fourth grade students. If a television advertising agency randomly selects one first grader and one fourth grader, what is the probability neither child would understand the commercial, assuming the children's reactions are independent?
-------------------
1st grade don't understand: 0.75
4th grade don't understand: 0.20
----
P(both 1st and 4th don't understand): 0.75*0.20 = 15%
================
Cheers,
Stan H.
================
|
Mixture_Word_Problems/512903: How many kg of dies apricots worth 8.30 per kilogram should be mixed with dried apples worth 6.50 per kilgram to produce 12 kg of a mixture worth 6.95 per kilogram?
1 solutions
Answer 342791 by stanbon(57400) on 2011-10-11 08:29:11 (Show Source):
You can put this solution on YOUR website!How many kg of dried apricots worth 8.30 per kilogram should be mixed with dried apples worth 6.50 per kilgram to produce 12 kg of a mixture worth 6.95 per kilogram?
---------------
Equations:
Quantity Eq: p + a = 12 kg
Value Eq:: 8.3p+6.5a = 6.95*12
----------------------------------------
Multiply thru Quantity by 830
Multiply thru Value by 100
----------------------------------
830p + 830a = 830*12
830p + 650a = 695*12
--------------------------
180a = 135*12
a = 9 (# of kg of apples)
---
p = 12-9 = 3 kg (# of kg of apricots)
===========================================
Cheers,
Stan H.
==============
|
Linear-equations/512916: please help me with this.I do not have any idea how to begin solving this.
f(x)=x^2-2x+3, g(x)=-2x+2 and h(x)=|x-3| What is the correct evaluation of f(2)?
thank you
1 solutions
Answer 342789 by stanbon(57400) on 2011-10-11 08:17:40 (Show Source):
You can put this solution on YOUR website!f(x)=x^2-2x+3, g(x)=-2x+2 and h(x)=|x-3|
What is the correct evaluation of f(2)?
----------
f(x) = x^2-2x+3
f(2) = 2^2-2*2+3
f(2) = 4-4+3
f(2) = 3
===============
Cheers,
Stan H.
===============
|
Miscellaneous_Word_Problems/512914: Luke paints a car in 6 hours while Daniel paints the same car in 3 hours. If they work together how long will it take them to paint the car?
1 solutions
Answer 342788 by stanbon(57400) on 2011-10-11 08:15:20 (Show Source):
You can put this solution on YOUR website!Luke paints a car in 6 hours while Daniel paints the same car in 3 hours. If they work together how long will it take them to paint the car?
--------------
Luke rate: 1/6 job/hr
Dan rate: 1/3 job/hr
---
Together rate: 1/x job/hr
================================
Equation:
rate + rate = together rate
1/6 + 1/3 = 1/x
Multiply thru by 18x
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3x + 6x = 18
9x = 18
x = 2 hrs (time to do the job together)
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Cheers,
Stan H.
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Probability-and-statistics/512855: If there are 5 questions and each question has two possible answers, how many different combinations of answers are there? and what are they?
Example:
1. Cheese or Knife
2. Truth or Lie
3. Water or Friend
4. Intervene or Ignore
5. Stand or Sit
I started with trying to write out all the possible combinations but that just got me more confused. the answers aren't just simple true/false either and I think that really confused me, also.
thank you! :D
1 solutions
Answer 342787 by stanbon(57400) on 2011-10-11 08:10:49 (Show Source):
You can put this solution on YOUR website!If there are 5 questions and each question has two possible answers, how many different combinations of answers are there? and what are they?
Example:
1. Cheese or Knife
2. Truth or Lie
3. Water or Friend
4. Intervene or Ignore
5. Stand or Sit
-------------------
Ans: 2^5 = 32 possible answers
===================================
Cheers,
Stan H.
==========
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Probability-and-statistics/512911: From a large number of actuarial exam scores, a random sample of 250 scores is selected, and it is found that 177 of these 250 are passing scores. Based on this sample, find a 90% confidence interval for the proportion of all scores that are passing. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.
What is the lower limit of the 90% confidence interval?
What is the upper limit of the 90% confidence interval?
1 solutions
Answer 342785 by stanbon(57400) on 2011-10-11 08:06:06 (Show Source):
You can put this solution on YOUR website!From a large number of actuarial exam scores, a random sample of 250 scores is selected, and it is found that 177 of these 250 are passing scores.
--------------------------
Based on this sample, find a 90% confidence interval for the proportion of all scores that are passing. Then complete the table below.
--------------------------
p-hat = 177/250 = 0.708
ME = 1.645*sqrt[0.708*0.292/250] = 0.047
------------------
Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.
What is the lower limit of the 90% confidence interval?::0.71-0.05 = 0.66
What is the upper limit of the 90% confidence interval?::0.71+0.05 = 0.76
============================
Cheers,
Stan H.
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Number-Line/512909: on a number line, where would 3/10 be located?
1 solutions
Answer 342784 by stanbon(57400) on 2011-10-11 07:55:53 (Show Source):
You can put this solution on YOUR website!on a number line, where would 3/10 be located?
--------------
Draw a number line.
Plot x = 0 and x = 1 on the line
---
Mark off 9 equal sections between 0 and 1.
---
Starting at 0, count 3 segments to the right.
The right-most mark for that segment is 3/10.
===================
Cheers,
Stan H.
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Linear-equations/512905: I need help graphing this - A line passes through the point P (-2,3) and has the slope of -1/2.
1 solutions
Answer 342782 by stanbon(57400) on 2011-10-11 07:51:31 (Show Source):
You can put this solution on YOUR website!A line passes through the point P (-2,3) and has the slope of -1/2.
----
Form y = mx + b
----
You have y = 3 when x = -2 and you have m = (-1/2).
Solve for "b":
---
3 = (-1/2)(-2) + b
-----
3 = 1 + b
b = 2
==============
Equation:
y = (-1/2)x + 2
===========================
Cheers,
Stan H.
=================
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Linear-systems/512754: solve the system of equations:
8x-y+z=-23
4x+2y-3z=-16
x-3y+2z=-2
1 solutions
Answer 342732 by stanbon(57400) on 2011-10-10 22:05:47 (Show Source):
You can put this solution on YOUR website!solve the system of equations:
8x-y+z=-23
4x+2y-3z=-16
x-3y+2z=-2
--------
I used a matrix method on a TI-84 to get:
x = -3
y = 1
z = 2
============================
Cheers,
Stan H.
============
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Numbers_Word_Problems/512749: What is the sum of three consecutive odd numbers that add up to 63?
1 solutions
Answer 342730 by stanbon(57400) on 2011-10-10 22:01:58 (Show Source):
You can put this solution on YOUR website!What is the sum of three consecutive odd numbers that add up to 63?
----
1st 2x-1
2nd 2x+1
3rd 2x+3
-----------------
Equation:
sum = 63
6x+3 = 63
6x = 70
x = 10
----
1st: 2x-1 = 19
2nd: 21
3rd: 23
=================
Cheers,
Stan H.
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Mixture_Word_Problems/512742: Critical Thinking:
Without solving, explain what is wrong with the following mixture problem: How many liters of 25% ethanol should be added to 20 liters of 48% ethanol to obtain a solution of 58% ethanol? Now go through an algebraic solution. What happens?
1 solutions
Answer 342727 by stanbon(57400) on 2011-10-10 21:58:14 (Show Source):
You can put this solution on YOUR website!Without solving, explain what is wrong with the following mixture problem: How many liters of 25% ethanol should be added to 20 liters of 48% ethanol to obtain a solution of 58% ethanol? Now go through an algebraic solution. What happens?
---
No amounts of 25% and 48% solutions will give you a 58% solution.
-------------
Attempt:
0.25x + 0.48*20 = 0.58(x+20)
---
25x + 48*20 = 58x +58*20
-23x = 10*20
x = -200/23 (amt of 25% solution: MEANINGLESS)
================
Cheers,
Stan H.
================
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Permutations/512737: The calibration of a filling machine broke, causing it to underfill 5 jars of jam. The jars were accidentally mixed in with 13 properly filled jars. All the jars look the same. 3 jars are chosen from the batch and weighed. What is the probability that exactly 2 jars are underweight?
Round your answer to 3 decimal places.
1 solutions
Answer 342722 by stanbon(57400) on 2011-10-10 21:50:34 (Show Source):
You can put this solution on YOUR website!The calibration of a filling machine broke, causing it to underfill 5 jars of jam. The jars were accidentally mixed in with 13 properly filled jars. All the jars look the same. 3 jars are chosen from the batch and weighed. What is the probability that exactly 2 jars are underweight?
Round your answer to 3 decimal places.
---
Binomial Problem with n = 3 and p(under) = 5/18
---------------
P(x = 2) = 3C2(5/18)^2(13/18) = binompdf(3,5/18,2) = 0.1672
===============
Cheers,
Stan H.
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Permutations/512722: How many permutations of two letters are possible from the four letters a,b,c,d?
1 solutions
Answer 342714 by stanbon(57400) on 2011-10-10 21:37:49 (Show Source):
You can put this solution on YOUR website!How many permutations of two letters are possible from the four letters a,b,c,d?
---
4P2 = 4!/(4-2)! = 4*3 = 12 permutations
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Cheers,
Stan H.
==============
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