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Recent problems solved by 'stanbon'
stanbon answered: 57911 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 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899 , 57900..57929, >>Next
Equations/119427: This question is from textbook Student Math Journal
John's weekly allowance is x dollars. If John spends 5/6 of his weekly allowance on a movie, he has ? dollars of his allowance left. How do I write this equation? Thanks.
1 solutions
Answer 87488 by stanbon(57984)   on 2008-01-09 20:39:34 (Show Source):
You can put this solution on YOUR website!John's weekly allowance is x dollars. If John spends 5/6 of his weekly allowance on a movie, he has ? dollars of his allowance left. How do I write this equation?
----------------------------
EQUATION:
x - (5/6)x = ?
Cheers,
Stan H.
|
Equations/119429: This question is from textbook mathematics concepts and skills
In 1996, the salary of the governor of New York was about $10,000 more than two times the salary of the governor of Arkansas. The total of the two salaries was $190,000. Find the 1996 salaries of each state's governor.
_________
I tried doing this:
190,000=2a+10,000
180,000=2a
90,000=a
So saying that $90,000 is Arkansas's salary, that means that New York's is 190,000! But when I add that up, it doesn't make any sense anymore. I don't get this. Can you help me please?
1 solutions
Answer 87487 by stanbon(57984) on 2008-01-09 20:33:33 (Show Source):
You can put this solution on YOUR website!In 1996, the salary of the governor of New York was about $10,000 more than two times the salary of the governor of Arkansas. The total of the two salaries was $190,000. Find the 1996 salaries of each state's governor.
-----------------
Let Arkansas gov. salary be "x" : NY gov salary will be 2x+10,000
--------------
EQUATION:
Ark sal + NY sal = 190000
x + 2x+10,000 = 190,000
3x = 180000
x = 60,000 (Ark gov. salary)
2x+10,000 = 120000+ 10000= 130,000 (NY gov salary)
==================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/119418: hello, i need help w. this certain word problem
maria bought seven boxes. a week later half of all her boxes were destroyed in a fire. there are now only 22 boxes left. with how many did she start?
thank you in advance.
1 solutions
Answer 87486 by stanbon(57984) on 2008-01-09 20:26:22 (Show Source):
You can put this solution on YOUR website!maria bought seven boxes. a week later half of all her boxes were destroyed in a fire. there are now only 22 boxes left. with how many did she start?
-----------
Let number at the start be "x".
EQUATIOn:
x+7 -(x+7)/2 =22
2x+14-x-7= 44
x+7 = 44
x = 37
============
Cheers,
Stan H.
|
Travel_Word_Problems/119410: How do I put this word problem into an equation?
May rides her bike the same distance that leah walks. May rides her bike 10 km/h faster than leah walks. If it takes May 1 hour and Leah 3 hours to travel that distance, how fast does each travel?
I can figure the equation out, i just need help puting the word problem into a equation
1 solutions
Answer 87481 by stanbon(57984) on 2008-01-09 19:36:51 (Show Source):
You can put this solution on YOUR website!May rides her bike the same distance that leah walks. May rides her bike 10 km/h faster than leah walks. If it takes May 1 hour and Leah 3 hours to travel that distance, how fast does each travel?
------------
May DATA:
Time = 1 hr ; rate = x km/hr ; distance = 1x = x km
---------
Leah DATA:
Time = 3 hrs; rate = (x-10)km/hr ; distance = 3(x-10) = 3x-30 km
------------------------
EQUATION:
distance = distance
x = 3x-30
2x = 30
x = 15 km/hr (May's rate)
x-10 = 5 km/hr (Leah's rate)
==============================
Cheers,
Stan H.
|
Inequalities/119409: The cost for a long distance telephone call is $0.36 for the first minute and $0.21 for each additional minute or portion thereof. Write an inequality representing the number of minutes a person could talk without exceeding $3.
1 solutions
Answer 87478 by stanbon(57984) on 2008-01-09 19:04:55 (Show Source):
You can put this solution on YOUR website!The cost for a long distance telephone call is $0.36 for the first minute and $0.21 for each additional minute or portion thereof. Write an inequality representing the number of minutes a person could talk without exceeding $3.
----------
Let "x" be the number of minutes of talk.
EQUATION:
0.36 + 0.21x < 3
----------
Cheers,
Stan H.
|
Equations/119407: Write the number in the form a + bi.
(square root of 4) + 10
Solve the quadratic equation by completing the square.
x^2+10x+14=0
1 solutions
Answer 87476 by stanbon(57984) on 2008-01-09 19:00:44 (Show Source):
You can put this solution on YOUR website!Write the number in the form a + bi.
(square root of 4) + 10
--------
There is no "i" term in the problem you have posted:
Ans: 2+10 = 12+0i
====================
Solve the quadratic equation by completing the square.
x^2+10x+14=0
x^2+10x+(10/2)^2 = (10/2)^2
(x+5)^2 = 25
x+5 = 5 or x+5 = -5
x = 0 or x = -10
==============
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/119408: In a chemistry lab, a student measured 1.0 cubic centimeters of acid to use in an experiment. The actual amount of acid that the student used was .95 cubic centimeters. What was the percent of error in the student's measurement? Give your answer to the nearest tenth of a percent.
1 solutions
Answer 87475 by stanbon(57984) on 2008-01-09 18:52:28 (Show Source):
You can put this solution on YOUR website!In a chemistry lab, a student measured 1.0 cubic centimeters of acid to use in an experiment. The actual amount of acid that the student used was .95 cubic centimeters. What was the percent of error in the student's measurement? Give your answer to the nearest tenth of a percent.
---------
Quantity of error: 1-0.95 = 0.05 cu cm
---------------------------------
Percent of error 0.05/1.0 = 5% error
=============================
Cheers,
Stan H.
|
Equations/119381:
How much pure alcohol must be added to 40 oz of a 25%
solution to produce a mixture that is 40% alcohol?
1 solutions
Answer 87455 by stanbon(57984) on 2008-01-09 17:45:27 (Show Source):
You can put this solution on YOUR website!How much pure alcohol must be added to 40 oz of a 25%
solution to produce a mixture that is 40% alcohol?
-----------------
25% solution DATA:
Amt = 40 oz ; amt of active ingredient = 0.25*40 = 10 oz
-------------------
Pure solution DATA:
Amt = x oz ; amt of active ingredient = 100%*x = x oz
-----------------
40% Mixture DATA:
amt. = 40+x oz ; amt of active ingredient = 0.40(40+x)=16+0.4x oz
===================
EQUATION:
active + active = active
10 + x = 16 + 0.4x
0.6x = 6
x = 10 oz (amt. of 100% alcohol needed for the mixture)
===========
Cheers,
Stan H.
|
Equations/119376: i didnt have enough time to ask the teacher.
a line passes throughthe given points. write an equation for the live in point-slope form. then rewrite the equation in slope-intercept form.
(6,-4) (-3,5)
y1-y2/x1-x2
i got
5-(-4)/-3-6
is that right?
so you add 5-(-4). but i thought you were supposed to subtract everytime though. can u clear this up for me? thanks
1 solutions
Answer 87453 by stanbon(57984) on 2008-01-09 17:32:51 (Show Source):
You can put this solution on YOUR website!a line passes throughthe given points. write an equation for the live in point-slope form. then rewrite the equation in slope-intercept form.
(6,-4) (-3,5)
y1-y2/x1-x2
i got
[5-(-4)]/[-3-6] = 9/-8 = -1
is that right?
Yes, that is right.
so you add 5-(-4). but i thought you were supposed to subtract everytime though.
You DID subtract; but when you subtract -4 from 5 you add +4 and +5 to get +9.
can u clear this up for me? thanks
===========================
Cheers,
Stan H.
|
Probability-and-statistics/119319: Each of the letters D E T E R M I N E D is written on a card. YOu mix the cards thoroughly. What is the probability of selecting an E, then an M? The first card is replaced before selecting the second card.
1 solutions
Answer 87405 by stanbon(57984) on 2008-01-09 14:00:30 (Show Source):
You can put this solution on YOUR website!Each of the letters D E T E R M I N E D is written on a card. YOu mix the cards thoroughly. What is the probability of selecting an E, then an M? The first card is replaced before selecting the second card.
----------
Prob (E) = 3/10
Prob (M) = 1/10
---------------
The draw results are independent because you replaced the 1st card drawn.
Therefore P(E then M) = (3/10)(1/10)= 3/100
=================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/119320: a water tank can be filled in 20 hours by an inlet pipe and emptied in 25 hours by an outlet pipe. how long will it take to fill the tank if both pipes are left open?
1 solutions
Answer 87402 by stanbon(57984) on 2008-01-09 13:56:44 (Show Source):
You can put this solution on YOUR website!a water tank can be filled in 20 hours by an inlet pipe and emptied in 25 hours by an outlet pipe. how long will it take to fill the tank if both pipes are left open?
----------------
Inlet pipe DATA:
Time = 20 hrs/job ; Rate = 1/20 job/hr
--------------
Outlet pipe DATA:
Time = 25 hrs/job ; Rate = 1/25 job/hr
---------------
Together DATA:
Time = x hr/job ; Rate = 1/x job/hr
-----------------
EQUATION:
In rate - out rate = together rate
1/20 + 1/25 = 1/x
Multiply thru by 100x to get:
5x + 4x = 100
9x = 100
x = 100/9 = 11 1/9 hrs
================
Cheers,
Stan H.
|
Quadratic_Equations/119294: What is the simplified form of cos30degrees + (sin210degrees)(cos^2 150degrees)?
1 solutions
Answer 87384 by stanbon(57984) on 2008-01-09 11:02:27 (Show Source):
You can put this solution on YOUR website!What is the simplified form of cos30degrees + (sin210degrees)(cos^2 150degrees)?
-------------
cos(30) = [sqrt3]/2
sin(210) = -sin(30) = -1/2
cos(150)= -cos(30)= [-sqrt3]/2
---------------------
Your Problem:
{sqrt3]/2 + (-1/2)[[-sqrt3]/2]^2 = [sqrt3]/2 +(-1/2)(3/4)
= [sqrt3]/2 -(3/8)
= 0.8660-0.125
= 0.4910
============
Cheers,
Stan H.
|
Average/119295: In the algebraic slope formula; y=mx+b why is "m" used to identify the slope and "b" the y-intercept?
1 solutions
Answer 87383 by stanbon(57984) on 2008-01-09 10:46:52 (Show Source):
You can put this solution on YOUR website!Sorry; I misread your question.
---------------
The slope tells you how much y changes when x changes one.
Assume you have f(x) = mx +b
When x increases by one you get:
f(x+1) = m(x+1)+b
f(x+1) = mx + m + b
-------
So, how much did y cange when x changed by one?
Subtract to find out, as follows:
f(x+1)-f(x) = mx+m+b - (mx+b) = m
----------
The y value increased by "m" when the x value increased by one,
so "m" is the slope.
=========================
The y-intercept tells you where the graph would cross the y-axis.
The y-axis is the line where x = 0
So, if you have f(x) = mx+b
Then f(0) = m*0 + b = b
Therefore b is the y-intercept.
====================
Cheers,
Stan H.
|
Quadratic_Equations/119296: What value of 'c' would make x^2+2/3x+c a perfect square trinomial ?
1 solutions
Answer 87382 by stanbon(57984) on 2008-01-09 10:45:18 (Show Source):
You can put this solution on YOUR website!What value of 'c' would make x^2+2/3x+c a perfect square trinomial ?
x^2 + (2/3)x + c
Complete the square:
x^2 + (2/3)x + [(2/3)/2]^2
x^2 + (2/3)x + (1/3)^2
x^2 + (2/3)x + (1/9)
c= 1/9
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Cheers,
Stan H.
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Quadratic_Equations/119293: What is the value of k if one exact x-intercept of y=x^2+kx+1 is 3+2sqrt2 ?
1 solutions
Answer 87380 by stanbon(57984) on 2008-01-09 10:41:41 (Show Source):
You can put this solution on YOUR website!What is the value of k if one exact x-intercept of y=x^2+kx+1 is 3+2sqrt2 ?
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If 3+2sqrt2 is a root f(3+2sqrt2)=0
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Therefore: (3+2sqrt2)^2 + k(3+2sqrt2)+1 = 0
k(3+2sqrt2)= -(3+2sqrt2)^2-1
k = -(3+2sqrt2) -1/(3+2sqrt2)
k = -(3+2sqrt2) - (3-2sqrt2)/(9-8)
k = -3-2sqrt2-3+2sqrt2
k = -6
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Cheers,
Stan H.
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Quadratic_Equations/119299: The equation V=12000(0.8)^t describes the value (V) of a car t years after purchase .
a) What was the cars initial value?
b) What was the rate of depreciation expressed as a percentage?
c) What will be the car's value 5 years after it was purchased?
d) Use the graphing calculator to determine the number of years it would take for the car to be worth $824.63 ? Can this part be done without a graphing calculator because I don't have one ?
For (a) I got $12000 , (b) I got 20% (c) I got #3832.16 Please, can someone help me ?
1 solutions
Answer 87379 by stanbon(57984) on 2008-01-09 10:34:18 (Show Source):
You can put this solution on YOUR website!The equation V=12000(0.8)^t describes the value (V) of a car t years after purchase .
a) What was the cars initial value?
Find t(0) to get the initial value:
V(0) = 12000*1 = $12,000
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b) What was the rate of depreciation expressed as a percentage?
Each year you are taking 0.80 of the previous years value.
The depreciation is 0.20 or 20%
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c) What will be the car's value 5 years after it was purchased?
Find V(5)
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d) Use the graphing calculator to determine the number of years it would take for the car to be worth $824.63 ? Can this part be done without a graphing
calculator because I don't have one ?
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Let V(t) = 12000(0.8)^t and solve for "t"
I got t = 12
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For (a) I got $12000
Good
(b) I got 20%
Good
(c) I got #3832.16
I got $3,932.20
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Cheers,
Stan H.
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Numeric_Fractions/119302: how do you cancel this algebraic fraction
2a/6b?
I think it could be 1a/3b but am not sure. Thanks x
1 solutions
Answer 87375 by stanbon(57984) on 2008-01-09 10:18:28 (Show Source):
You can put this solution on YOUR website!how do you cancel this algebraic fraction
2a/6b?
I think it could be 1a/3b but am not sure.
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That is correct; you have cancelled the "2" factor
that was in the numerator and in the denominator.
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Comment: You do not need the "1" in your answer;
a/3b would be a good answer.
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Cheers,
Stan H.
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Expressions-with-variables/119255: This question is from textbook
How do i solve y=0.5x+2 and -y=-2x+4 by systems of substitution?
1 solutions
Answer 87353 by stanbon(57984) on 2008-01-08 22:50:09 (Show Source):
You can put this solution on YOUR website!solve y=0.5x+2 and -y=-2x+4 by systems of substitution?
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y = 0.5x+2
-y = -2x+4
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Substitute 0.5x+2 in place of y:
-(0.5x+2) = -2x+4
-0.5x-2 = -2x+4
Add 2x to both sides to get:
1.5x = 6
x = 4
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Substitute to solve for "y":
y = 0.5*4+2
y = 2+2
y = 4
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Cheers,
Stan H.
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Graphs/119252: it is a word problem.....
Brain and three friends bought 3/4 pound of candy.If they slit the candy equally,how much will each person get?(leave ur answer as a fraction)
can u please help me solve this problem??
1 solutions
Answer 87351 by stanbon(57984) on 2008-01-08 22:23:56 (Show Source):
You can put this solution on YOUR website!Each will get (1/4)th of the 3/4 lb.
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Each will get (1/4)(3/4) = 3/16 lb.
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Cheers,
Stan H.
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Equations/119242: The student council is sponsoring a carnival to raise money. Tickets cost $5 for adults and $3 for students. The student council wants to raise $450
a. Write an equation to find the number of each type of ticket they should sell.
b. Graph your equation.
c. Use your graph to find two different combinations of tickets sold.
Please and Thank you!
1 solutions
Answer 87350 by stanbon(57984) on 2008-01-08 22:19:28 (Show Source):
You can put this solution on YOUR website!The student council is sponsoring a carnival to raise money. Tickets cost $5 for adults and $3 for students. The student council wants to raise $450
a. Write an equation to find the number of each type of ticket they should sell.
Let "x" be # of adult tickets; Let "y" be # of student tickets:
Value Equation: 5x+3y=450
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b. Graph your equation.
y = (-5/3)x+150
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c. Use your graph to find two different combinations of tickets sold.
I'll leave that to you.
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Cheers,
Stan H.
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Money_Word_Problems/119243: This question is from textbook California Middle School Mathematics Concepts and Skills Course 2
Your cousin installs weather stripping for x dollars per foot and insulation for (x + 5) dollars per foot. This week he installed 480 feet of weather and stripping and 2200 feet of insulation. His expenses are 7500$. His profit is 11,540$. Find the prices your cousin charges to install insulation and weather stripping.
1 solutions
Answer 87343 by stanbon(57984) on 2008-01-08 21:57:55 (Show Source):
You can put this solution on YOUR website!Your cousin installs weather stripping for x dollars per foot and insulation for (x + 5) dollars per foot. This week he installed 480 feet of weather and stripping and 2200 feet of insulation. His expenses are 7500$. His profit is 11,540$. Find the prices your cousin charges to install insulation and weather stripping.
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Income: 480x + 2200(x+5)
Expenses: 7500
Profit: 11,540
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EQUATION:
Income - Expenses = Profit
480x + 2200(x+5) - 7500 = 11540
480x + 2200x + 11000 - 7500 = 11540
2680x + 3500 = 11540
2680x = 8040
x = $3 (price per foot for weather stripping)
x+5 = $8 (price per foot for insulation)
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Cheers,
Stan H.
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Surface-area/119215: find the ninth term of the sequence 2,6,18,54....using the formula a n=1 x r (n-1)
1 solutions
Answer 87321 by stanbon(57984) on 2008-01-08 20:34:31 (Show Source):
You can put this solution on YOUR website!find the ninth term of the sequence 2,6,18,54....using the formula a(n)=a(1) x r^(n-1)
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The sequence is a geometric sequence with a(1) = 2, and r = 6/2=3
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Formula: a(n) = (a(1))*r^(n-1)
a(9) = 2*3^(8)
a(9) = 13,122
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Cheers,
Stan H.
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