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Recent problems solved by 'stanbon'
stanbon answered: 57279 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, >>NextExponential-and-logarithmic-functions/110978: A radioactive element sodium-24 has a half-life of 14 hours and is used to help locate obstructions in blood flow. A procedure requires 1.5 grams and is scheduled to take place in 37 hours.
At what rate is the sodium-24 decaying?
What is the minimum amount of sodium-24 that must be on hand now?
1 solutions
Answer 80999 by stanbon(57352)   on 2007-11-18 19:51:15 (Show Source):
You can put this solution on YOUR website!A radioactive element sodium-24 has a half-life of 14 hours and is used to help locate obstructions in blood flow. A procedure requires 1.5 grams and is scheduled to take place in 37 hours.
---------
EQUATION:
A(t) = Ao(1/2)^(t/14)
1.5 = Ao(1/2)^(37/14)
Ao = 1.5 / [(1/2)^(37/14)]
Ao = 1.5 / 0.16011...
Ao = 9.369 grams
--------------------
At what rate is the sodium-24 decaying?
[9.369-1.5]/37 = 0.21266 grams per hour
-----------------------------
What is the minimum amount of sodium-24 that must be on hand now?
9.369 grams
==============
Cheers,
Stan H.
|
Proportions/111010: on some days, a bakery packages cupcakes 4 to a box. On other days, they package cupcakes 6 or 8 to a box. On a given day, all of the cupcakes baked were packaged and there was one cupcake left over. Which of the following could not be the number of cupcakes baked on that day?
1 solutions
Answer 80998 by stanbon(57352) on 2007-11-18 19:41:11 (Show Source):
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Quadratic-relations-and-conic-sections/111009: ok. i have gotten to x=3(-9 +/-(square root of 71) /all over 10) +3
i need to figure out what x can be. thank you
1 solutions
Answer 80982 by stanbon(57352) on 2007-11-18 18:54:26 (Show Source):
You can put this solution on YOUR website!i have gotten to x=3(-9 +/-(square root of 71) /all over 10) +3
i need to figure out what x can be
----------
I can't imagine how you came up with this but.......
x = 3[-9 +- sqrt(71)/10] + 3
x = 3[-9+(1/10)sqrt(71)] +3
Or
x = 3[-9-(1/10)sqrt(71)] +3
==================================================
Cheers,
Stan H.
|
Equations/110992: 1.) 3x/(x+1) + 6/2x = 7/x
2.) 6x/(x+4) + 4 = 2x+2/(x-1)
3.) 7x+1/2x+5 + 1 =10x-3/3x
4.) 10/x^2-2x + 4/x = 5/x-2
1 solutions
Answer 80976 by stanbon(57352) on 2007-11-18 18:34:45 (Show Source):
You can put this solution on YOUR website!1.) 3x/(x+1) + 6/2x = 7/x
x(x+1) is the LCM
Multiply thru by the LCM:
3x^2 + 3(x+1) = 7(x+1)
3x^2 + 3x+3 = 7x+7
3x^2-4x-3=0
x = [4 +- sqrt(16-4*3*-3)]/6
x = [4 +- sqrt(52)]/6
x = [4 +- 2sqrt(13)]/6
x = [2 +- sqrt(13)]/3
x = (2 + sqrt(13))/3 or x = (2 - sqrt(13))/3
==========================
2.) 6x/(x+4) + 4 = (2x+2)/(x-1)
Multiply thru by (x+4)(x-1) to get:
6x(x-1) + 4(x+4)(x-1) = 2(x+1)(x+4)
6x^2-6x + 4x^2+12x-16 = 2x^2+10x+8
8x^2 -4x -24 = 0
4(2x^2 -x -12) = 0
2x^2 - x -12 = 0
x = [1 +- sqrt(1 -4*2*-12)]/4
x = [1 +- sqrt(97)]/4
x = (1+ sqrt(97))/4 or x = (1-sqrt(97))/4
===============
Cheers,
Stan H.
3.) 7x+1/2x+5 + 1 =10x-3/3x
4.) 10/x^2-2x + 4/x = 5/x-2
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Miscellaneous_Word_Problems/110988: Biologists collected a sample of 600 fish form Lake Marie on May 1st and tagged each of them. When they returned on June 1st, a new sample of 800 fish was collected and 10 of these had been previosuly tagged. Use this experiment to approximate fish popultion of Lake Linda.
1 solutions
Answer 80969 by stanbon(57352) on 2007-11-18 18:00:31 (Show Source):
You can put this solution on YOUR website!Biologists collected a sample of 600 fish form Lake Marie on May 1st and tagged each of them. When they returned on June 1st, a new sample of 800 fish was collected and 10 of these had been previosuly tagged. Use this experiment to approximate fish population of Lake Linda.
--------------
Let Real population be "x" fish.
-------
Proportion:
Real pop/sample = tagged pop/tagged sample
x/600 = 800/10
x = 600*800/10
x = 48,000 fish
====================
Cheers,
Stan H.
|
Travel_Word_Problems/110986: This question is from textbook algebra stucture and method
An ultralight plane had been flying for 40 min when a change in wind direction doubled its ground speed. The entire trip of 160 mi took 2 h. How far did the plane travel during the first 40 min?
1 solutions
Answer 80966 by stanbon(57352) on 2007-11-18 17:51:06 (Show Source):
You can put this solution on YOUR website!An ultralight plane had been flying for 40 min when a change in wind direction doubled its ground speed. The entire trip of 160 mi took 2 h. How far did the plane travel during the first 40 min?
--------------
Against the wind DATA:
Time = 2/3 hr. ; distance = x miles ; rate = x/(2/3) = 3x/2 mph
----------------------------
With the wind DATA:
Time = (4/3) hr ; distance = 160-x ; rate = d/t = (160-x)/(4/3) mph
------------------------------
rate with the wind = 2*rate against the wind
(160-x)/(4/3) = 2(3x/2)
3(160-x)/4 = 3x
480-3x = 12x
480 = 15x
x = 32 miles
--------------------
Cheers,
Stan H.
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Radicals/110981: I am working a problem and need to know tif either x-3x-16 or x^2-x-12 can be factored?? Thank you for your help!
1 solutions
Answer 80965 by stanbon(57352) on 2007-11-18 17:38:05 (Show Source):
You can put this solution on YOUR website!need to know if either x-3x-16 or x^2-x-12 can be factored??
------------
x-3x-16
= -2x-16
= -2(x++8)
==============
x^2-x-12
= (x-4)(x+3)
=============
Cheers,
Stan H.
|
Linear-equations/110982: these are suppose to be fractions but i did not know how to put them in.
1/3x + 3/4x = 13 the one third and the three fourths are fractions. thanks for the help.
1 solutions
Answer 80962 by stanbon(57352) on 2007-11-18 17:31:19 (Show Source):
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Linear-equations/110983: A. 5x + 6y =18 for y
When graphed this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line?
1 solutions
Answer 80961 by stanbon(57352) on 2007-11-18 17:28:45 (Show Source):
You can put this solution on YOUR website!5x + 6y =18 for y
When graphed this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line?
---------------
slope-Intercept form:
y (-5/6)x+3
-------------------
Graph:
---------------------
slope = -5/6
==================
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/110933: HOW MANY YEARS WILL IT TAKE $3000 TO GROW TO $4667 IF IT IS INVESTED AT AN ANNUAL RATE OF 13%, COMPOUNDED CONTINUOUSLY? ROUND YOUR ANSWER TO ONE DECIMAL PLACE.
1 solutions
Answer 80954 by stanbon(57352) on 2007-11-18 16:21:08 (Show Source):
You can put this solution on YOUR website!HOW MANY YEARS WILL IT TAKE $3000 TO GROW TO $4667 IF IT IS INVESTED AT AN ANNUAL RATE OF 13%, COMPOUNDED CONTINUOUSLY? ROUND YOUR ANSWER TO ONE DECIMAL PLACE.
-------------
A(t) = Ao*e^rt
4667 = 3000*e^(0.13t)
e^(0.13t) = 1.555666666
Take the natural log to get:
0.13t = 0.441904...
t = 3.4 years
===============
Cheers,
Stan H.
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Proportions/110969: A building is casting a 100 ft. shadow at the same time that a 5 ft. post is casting a 1 ft. shadow.
Write a proportion that involves the height of the building, the height of the post, and legnths of the shadows.
How high is the building?
1 solutions
Answer 80948 by stanbon(57352) on 2007-11-18 16:11:59 (Show Source):
You can put this solution on YOUR website!A building is casting a 100 ft. shadow at the same time that a 5 ft. post is casting a 1 ft. shadow.
Write a proportion that involves the height of the building, the height of the post, and length of the shadows.
---------
Let height of the building be "x":
Proportion:
x/100 = 5/1
x = 500 ft
------------------------
How high is the building?
The building is 500 ft. high
======================
Cheers,
Stan H.
|
Proportions/110968: On Sunday, 845 people went to the zoo. On Tuesday, 169 people went. What is the percent of decrease from Sunday to Tuesday?
1 solutions
Answer 80943 by stanbon(57352) on 2007-11-18 16:05:35 (Show Source):
You can put this solution on YOUR website!On Sunday, 845 people went to the zoo. On Tuesday, 169 people went. What is the percent of decrease from Sunday to Tuesday?
---------------
Decrease quantity: 845-169 = 676
Percent Decrease: 676/845 = 0.80 = 80%
----------------
Cheers,
Stan H.
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Functions/110840: Could someone please help me?
Given f(x)=x^2 and g(x)=3x-1, find (f*g)(2) and (g*f)(x)
Any help will be greatly appreciated.
1 solutions
Answer 80858 by stanbon(57352) on 2007-11-17 22:27:20 (Show Source):
You can put this solution on YOUR website!Given f(x)=x^2 and g(x)=3x-1, find (fog)(2) and (gof)(x)
-------------
(fog)(2) = f[g(2)] = f[3*2-1] = f[5] = 25
---------------
(gof)(x) = g[f(x)] = g[x^2] = 3x^2-1
==================
Cheers,
Stan H.
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Numbers_Word_Problems/110858: One positive number is 5 times another number. The difference between the two numbers is 124, find the numbers.
1 solutions
Answer 80853 by stanbon(57352) on 2007-11-17 22:14:52 (Show Source):
You can put this solution on YOUR website!One positive number is 5 times another number. The difference between the two numbers is 124, find the numbers.
------------------------------------------
EQUATIONS:
x = 5y
x-y =124
---------------------
Substitute into x-y=124 to solver for y:
5y-y=124
4y = 124
y = 31
-------------
Substite into x=5y to solve for "x":
x = 5*31 = 155
====================
Cheers,
Stan H.
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Rate-of-work-word-problems/110856: If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?
1 solutions
Answer 80844 by stanbon(57352) on 2007-11-17 21:59:13 (Show Source):
You can put this solution on YOUR website!If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?
---------------------
x dollars buys 300 jellybeans
Convert to "cents"
(100 cents)x buys 300 jellybeans
---------------
Divide both sides by 100x to get:
1 cent buys 300/100x jellybeans = 3/x jellybeans
-----------------
Multiply both sides by 50 to get:
50 cents buys 50(3/x) = 150/x jellybeans
=====================
Cheers,
Stan H.
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Rate-of-work-word-problems/110811: This question is from textbook
John can complete a paper route in 20 minutes. Steve can complete the same route in 30 minutes. How long will it take to complete the route if they worked together?
1 solutions
Answer 80804 by stanbon(57352) on 2007-11-17 16:31:36 (Show Source):
You can put this solution on YOUR website!John can complete a paper route in 20 minutes. Steve can complete the same route in 30 minutes. How long will it take to complete the route if they worked together?
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John DATA:
Time = 20 min/job ; Rate = 1/20 job/min
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Steve DATA:
Time = 30 min/job ; Rate = 1/30 job/min
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Together DATA:
Time = x min/job ; Rate = 1/x job/min
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EQUATION:
rate + rate = together rate
1/20 + 1/30 = 1/x
(30+20)/600 = 1/x
50/600
5/60 = 1/x
x = 60/5 = 12 minutes (time for this to do the job together)
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Cheers,
Stan H.
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Linear-equations/110814: This question is from textbook Algebra and Trigonometry
How do I solve this problem
Determine if the function is one-to-one.
If the function is one-to-one, find a formula for the inverse.
f(x)=(x+5)to the 3rd.
1 solutions
Answer 80803 by stanbon(57352) on 2007-11-17 16:20:05 (Show Source):
You can put this solution on YOUR website!Determine if the function is one-to-one.
If the function is one-to-one, find a formula for the inverse.
f(x)=(x+5)to the 3rd.
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one-to-one:
y = (x+5)^3
for each value of x there is one value of y:
x = (y^(1/3))-5
for each value of y there is one value of x:
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Inverse:
Interchange x and y and solve for y:
x = (y+5)^3
y = (x^(1/3))-5
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Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/110817: Please help my teacher is not explaining this to me right and im terrible at linear Equations and word problems please help.
1. You have 94 coins in a bottle. If the coins are only nickels and quarters and they total $17.50, how many of each do you have??
2.Max collects coins. he has a combination of dimes and quarters totaling 33 coins dating circa 1970 the total value is $6.15 how many dimes and quarters does he have??
3.There were 160 concert tickets sold. The Adults cost $22 and Students cost $8.50, the ticket sales totaled $2899. How many of each ticket were sold??
1 solutions
Answer 80802 by stanbon(57352) on 2007-11-17 16:12:30 (Show Source):
You can put this solution on YOUR website!1. You have 94 coins in a bottle. If the coins are only nickels and quarters and they total $17.50, how many of each do you have??
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Let # of nickels be "x" ; Value of these is 5x cents
# of quarters is "94-x" ; Value of these is 25(94-x)= 2350-25x cents
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EQUATION:
value + value = 1750 cents
5x + 2350-25x 1750
-20x = -600
x = 30 (# of nickels)
94-x = 64 (# of quarters)
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2.Max collects coins. he has a combination of dimes and quarters totaling 33 coins dating circa 1970 the total value is $6.15 how many dimes and quarters does he have??
Let # of quarters be x ; value is 25x cents
# of dimes is 33-x ; value is 10(33-x) = 330-10x cents
EQUATION:
value + value = 615 cents
25x + 330-10x = 615 cents
15x = 285
x = 19 (# of quarters)
33-x = 14 (# of dimes)
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3.There were 160 concert tickets sold. The Adults cost $22 and Students cost $8.50, the ticket sales totaled $2899. How many of each ticket were sold??
Let number of adult tickets be "x" ; value is 22x dollars
# of student tickets is "160-x" ; value is 8.5(160-x)= 1360-8.5x dollars
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EQUATION:
value + value = 2899 dollars
22x + 1360-8.5x = 2899
13.5x = 1539
x = 114 (# of adult tickets)
160-x = 46 (# of student tickets)
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Cheers,
Stan H.
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