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Recent problems solved by 'stanbon'
stanbon answered: 57194 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209, >>Nextexpressions/723192: solve the following equation for x: 3x^3+9x^2-18x=0
1 solutions
Answer 443061 by stanbon(57262)   on 2013-03-07 13:06:21 (Show Source):
You can put this solution on YOUR website!solve the following equation for x:
----
3x^3+9x^2-18x=0
------
3x(x^2+3x-6) = 0
----
solve x^2+3x-6 = 0
---
x = [-3 +- sqrt(9-4*-6)]/2
---
x = [-3 +- sqrt(33)]/2
----
Ans: x = 3 or x = [-3 +- sqrt(33)]/2
=======================================
Cheers,
Stan H.
================
|
Radicals/723140: Solve: ^4(x^2)*^5(x^3)
Answer will be one of the following:
^20(x^5)
^10(x)
^x^10(x)
^x^20(x)
Any help would be very much appreciated!
Thank you
1 solutions
Answer 443042 by stanbon(57262) on 2013-03-07 10:47:47 (Show Source):
You can put this solution on YOUR website!4 is the index number and under the radical is x^2 which is to be multiplied by 5 as the index number and under the radical is x^3.
--------------------------
^4(x^2)*^5(x^3)
------
(4th root of x^2) * (5th root of x^3)
------
Least common multiple for 4th and 5th is 20th
-----
= (20th root of x^10) * (20th root of x^12)
----
= 20th root of x^22
---
= x*(20th root of x^2)
-------------------
Cheers,
Stan H.
===================
|
Polynomials-and-rational-expressions/723137: (1/5x^3+2x^2-3/10)-(-2/5x^3+2x^2+7/1000) Subtract.. Please help I keep getting lost and having to start over again. Thank you in advance.
1 solutions
Answer 443040 by stanbon(57262) on 2013-03-07 10:37:38 (Show Source):
You can put this solution on YOUR website!(1/5x^3+2x^2-3/10)-(-2/5x^3+2x^2+7/1000)
--------------
Gather the "like" terms:
-----
((1/5)+(2/5)x^3 + (2-2)x^2 + ((-3/10)-(7/1000))
------
= (3/5)x^3 + 0*x^2 + ((-300/1000)-(7/1000))
------
= (3/5)x^3 - (307/1000)
==========================
Cheers,
Stan H.
|
Money_Word_Problems/723131: A piano is marked up 45% from its wholesale price of $950. What is the retail price of the piano after a 10% coupon and 6% sales tax is applied?
1 solutions
Answer 443038 by stanbon(57262) on 2013-03-07 10:32:15 (Show Source):
You can put this solution on YOUR website!A piano is marked up 45% from its wholesale price of $950. What is the retail price of the piano after a 10% coupon and 6% sales tax is applied?
-----
Start: 950
Then: 1.45*950 = 1377.5
Then: 0.90*1377.5 = 1239.75
Finally: 1.06*1239.75 = $1314.14
====================================
Cheers,
Stan H.
============
|
Geometry_Word_Problems/723132: The length of a rectangle is 1 less than three times it's width. The perimeter is 30 feet. Find the length of this rectangle
1 solutions
Answer 443037 by stanbon(57262) on 2013-03-07 10:27:57 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is 1 less than three times it's width. The perimeter is 30 feet. Find the length of this rectangle
====
Let width be "x".
Then length = "3x-1".
----
Equation:
Perimeter = 2(length + width)
---
30 = 2(3x-1+x)
---
15 = 4x-1
4x = 16
x = 4
----
length = 3x-1 = 3*4-1 = 11 feet
====================================
Cheers,
Stan H.
============
|
Linear-systems/723130: Is the ordered pair (-4,-9) a solution to the linear equation: y=3/4x-6?
1 solutions
Answer 443036 by stanbon(57262) on 2013-03-07 10:24:21 (Show Source):
You can put this solution on YOUR website! Is the ordered pair (-4,-9) a solution to the linear equation:
y=3/4x-6?
---
Substitute: -9 = (3/4)(-4)-6
---
-9 = -3 -6
---
-9 = -9
----
Answer: Yes
================
Cheers,
Stan H.
================
|
logarithm/722999: Help please!
Express y as a function of x in 2 = 1/3  - x^1/2 - C where C>0 constant.
1 solutions
Answer 442977 by stanbon(57262) on 2013-03-06 22:12:35 (Show Source):
You can put this solution on YOUR website!Express y as a function of x in 2 = 1/3 - x^1/2 - C where C>0 constant.
-----------------------
2log52(y) = (1/3)log52(x^2+1) - sqrt(x) - C
---------
2log52(y)-(1/3)log52(x^2+1) = -sqrt(x)-C
----
log62[y^2/(x^2+1)^(1/3)] = -sqrt(x)-C
-----
y^2/(x^2+1)^(1/3) = 52^(-sqrt(x)-C)
----
y^2 = (x^2+1)^(1/3)*52^(-sqrt(x)-C)
----
y = +-sqrt[(x^2+1)^(1/3)*52^(-sqrt(x)-C)
===========================================
Cheers,
Stan H.
|
logarithm/722987: how long will it take for the populations of a certain country to double if its annual growth rate is 6.2%?
1 solutions
Answer 442973 by stanbon(57262) on 2013-03-06 21:59:38 (Show Source):
You can put this solution on YOUR website!how long will it take for the populations of a certain country to double if its annual growth rate is 6.2%?
----
The yearly multiplier is 1.0625
----
Solve (1.0625)^k = 2
----
k = log(2)/log(1.0625) = 11.43 years
=============
Cheers,
Stan H.
|
Trigonometry-basics/722988: Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of θ, where −π/2 < θ < π/2.
(4 = sqrt (64 − x^2)) , x = 8 sin θ
4=?
Find sin θ and cos θ.
sin θ= ?
cos θ=?
1 solutions
Answer 442971 by stanbon(57262) on 2013-03-06 21:55:49 (Show Source):
You can put this solution on YOUR website!Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of θ, where −π/2 < θ < π/2.
(4 = sqrt (64 − x^2)) , x = 8 sin θ
16 = 64-x^2
x^2 = 32
x = 4sqrt(2) or x = -4sqrt(2)
-----
Substitute for "x":
8sin(theta) = 4sqrt(2) or 8sin(theta) = -4sqrt(2)
---------------------
sin(theta) = sqrt(2)/2; and cos(theta) = sqrt(2/2) in QI
or sin(theta) = -sqrt(2)/2 and cos(theta) = sqrt(2)/2) in QIV
======================
Find sin θ and cos θ.
sin θ= ?
cos θ=?
======
Cheers,
Stan H.
|
test/722990: Johnny says that if a family has two children, then. the only possibilities are two boys, two girls, or one boy and one girl. Because there are only three possibilities, Johnny claims the probability of having two boys is 1/3. Is Johnny correct? Why or why not?
1 solutions
Answer 442970 by stanbon(57262) on 2013-03-06 21:47:47 (Show Source):
You can put this solution on YOUR website!Johnny says that if a family has two children, then. the only possibilities are two boys, two girls, or one boy and one girl. Because there are only three possibilities, Johnny claims the probability of having two boys is 1/3. Is Johnny correct? Why or why not?
----
No.
The possible arrangements are:
bb ; bg ; gb ; gg
---
Each has probability 1/4
=============================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/722989: A small business buys a computer for $4900. After 4 years the value of the computer is expected to be $200. For accounting purposes the business uses straight-line depreciation (this means that if V is the value of the computer at time t, then a linear equation is used to relate V and t) to assess the value of the computer at a given time.
(a) Find a linear equation that models the value V of the computer t years since its purchase.
1 solutions
Answer 442969 by stanbon(57262) on 2013-03-06 21:45:46 (Show Source):
You can put this solution on YOUR website!A small business buys a computer for $4900. After 4 years the value of the computer is expected to be $200. For accounting purposes the business uses straight-line depreciation (this means that if V is the value of the computer at time t, then a linear equation is used to relate V and t) to assess the value of the computer at a given time.
(a) Find a linear equation that models the value V of the computer t years since its purchase.
---
You have two points relating time and value: (0,4000) and (4,200)
---
slope = (200-4000)/4 = -3800/4 = -950
intercept = f(0) = 4000
-----
Equation:
value(x) = -950x + 4000 where x is the number of years.
----------
Cheers,
Stan H.
=================
|
test/722980: log[10](x)+log[10](3x+55)=2
How do you solve this?
1 solutions
Answer 442966 by stanbon(57262) on 2013-03-06 21:40:40 (Show Source):
You can put this solution on YOUR website!log[10](x)+log[10](3x+55)=2
-----
log[x(3x+55)] = 2
----
3x^2+55x = 10^2
---
3x^2 + 55x -100 = 0
----
x = [-55 +- sqrt(55^2-4*3*-100)]/6
----
x = 5/3 or x = -20
---
Usable solution:
x = 5/3
==================
Cheers,
Stan H.
==================
|
Average/722981: gerald had scores of 80,92,89,and 95 on four exams in his algebra class. what score will he need on his fifth exam to have an overall average of 90
1 solutions
Answer 442965 by stanbon(57262) on 2013-03-06 21:33:37 (Show Source):
You can put this solution on YOUR website!gerald had scores of 80,92,89,and 95 on four exams in his algebra class. what score will he need on his fifth exam to have an overall average of 90
----
Let the 5th exam score be "x":
(80+92+89+95+x)/5 = 90
---
356+x = 450
x = 94
===========
Cheers,
Stan H.
=============
|
Probability-and-statistics/722361: Swift Auto Service has taken advantage of some of the results
you provided (HW #4) and has improved their process. Their oil &
lube “service time per car” still follows a normal distribution, but
now with a mean of 30 minutes per car, and a standard deviation
of 4.0 minutes.
b) if you select a random sample of 16 oil & lube jobs, what is
the probability the sample mean “service time” from that group
will be shorter than 28 minutes ?
1 solutions
Answer 442806 by stanbon(57262) on 2013-03-06 07:31:51 (Show Source):
You can put this solution on YOUR website!follows a normal distribution, but
now with a mean of 30 minutes per car, and a standard deviation
of 4.0 minutes.
b) if you select a random sample of 16 oil & lube jobs, what is
the probability the sample mean “service time” from that group
will be shorter than 28 minutes ?
-----
x-bar = 28 min
--------------------
z(28) = (28-30)/[4/sqrt(16)) = -2
----
P(x-bar < 28) = P(z < -2) = 0.0228
==============
Cheers,
Stan H.
==============
|
Probability-and-statistics/722362: Swift Auto Service has taken advantage of some of the results
you provided (HW #4) and has improved their process. Their oil &
lube “service time per car” still follows a normal distribution, but
now with a mean of 30 minutes per car, and a standard deviation
of 4.0 minutes.
c) how large would your random sample need to be, so that your
sample mean “service time” would be 99% likely to be within
1 minute of the true population mean service time ?
1 solutions
Answer 442805 by stanbon(57262) on 2013-03-06 07:27:29 (Show Source):
You can put this solution on YOUR website!Swift Auto Service has taken advantage of some of the results
you provided (HW #4) and has improved their process. Their oil &
lube “service time per car” still follows a normal distribution, but
now with a mean of 30 minutes per car, and a standard deviation
of 4.0 minutes.
c) how large would your random sample need to be, so that your
sample mean “service time” would be 99% likely to be within
1 minute of the true population mean service time ?
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Since E = z*s/sqrt(n),
n = [z*s/E]^2 = [2.5758*4/1]^2 = 106 when rounded down
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Cheers,
Stan H.
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Probability-and-statistics/722435: 1. Joe has been given a 10 multiple-choice question in his Geography class. Each question has 5 answers, of which only one is correct. Since Joe has not studied for the quiz, he plans in guessing all of the answers. What is the probability that he answers at least one question correctly?
1 solutions
Answer 442803 by stanbon(57262) on 2013-03-06 07:21:16 (Show Source):
You can put this solution on YOUR website!1. Joe has been given a 10 multiple-choice question in his Geography class. Each question has 5 answers, of which only one is correct. Since Joe has not studied for the quiz, he plans in guessing all of the answers. What is the probability that he answers at least one question correctly?
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Binomial Problem with n = 10 ; p(correct) = 1/5 ; p(wrong) = 4/5
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P(at least one correct) = 1 - P(none correct) = 1 - (4/5)^10 = 0.8926
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Cheers,
Stan H.
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Probability-and-statistics/722567: This question is on normal distribution, I need some help understanding how to solve these problems. I am taking a NCPace course through the military and do not have an actual instructor to ask for help.
Determine the answers to the following questions which relate to a sample of students who took a physics test. Their scores were normally distributed with a mean of 70 and a standard deviation of 10. What percentage of students made 90 on the test?
Using the rules of normal distribution my answer would be 1.18%. I just don't know if I am going about solving this the correct way. Thank you in advance.
Respectfully,
STG2(SW/EXW)Purvis, Sarah M. , USN
1 solutions
Answer 442802 by stanbon(57262) on 2013-03-06 07:18:22 (Show Source):
You can put this solution on YOUR website!scores were normally distributed with a mean of 70 and a standard deviation of 10. What percentage of students made 90 on the test?
Using the rules of normal distribution my answer would be 1.18%. I just don't know if I am going about solving this the correct way.
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Find the z-score of 90.
z(90) = (90-70)/10 = 2
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Then P(x > 90) = P(z > 2)
Using a TI-84 calculator I get:
P(z > 2) = normalcdf(2,100) = 0.0228 or 2.28%
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Let me know if you need further help.
Cheers,
Stan H.
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Travel_Word_Problems/722374: A passenger train leaves the train depot four hours after the cargo train traveling in the same direction leaves the same depot the cargo train is traveling 10 mph slower than the passenger train given that the passenger train the freight train passes the freight train in two hours find the speed of each train
1 solutions
Answer 442735 by stanbon(57262) on 2013-03-05 20:25:50 (Show Source):
You can put this solution on YOUR website!A passenger train leaves the train depot four hours after the cargo train traveling in the same direction leaves the same depot
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the cargo train is traveling 10 mph slower than the passenger train
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given that the passenger train the freight train passes the freight train in two hours find the speed of each train
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Passenger train DATA
time = 2 hrs ; rate = r + 10 mph ; distance = 2r + 20 miles
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Cargo train DATA:
time = 6 hrs ; rate = r mph ; distance = 6r miles
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Equation:
distance = distance
6r = 2r+20
4r = 20
r = 5 mph (cargo train rate)
r+10 = 15 mph (passenger train rate)
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Cheers,
Stan H.
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Linear-equations/722376: I can't figure out how to do this problem.
The sum of three times a number and 7 more than the number is the same as the difference between-11 and twice the number. What is the number?
1 solutions
Answer 442729 by stanbon(57262) on 2013-03-05 19:31:03 (Show Source):
You can put this solution on YOUR website!The sum of three times a number and 7 more than the number is the same as the difference between-11 and twice the number. What is the number?
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3x + (3x+7) = -11-2x
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10x+7 = -11-2x
12x = -18
x = -3/2
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/722363: Payrolls for the 3 highest paid baseball teams (the Yankees, Red Sox, and Angels) for 2006 totaled 418 million. If the team payroll for the Yankees is 75 million dollars higher than the Red Sox and the Red sox is 17 million dollars higher than the Angels, then what was the 2006 payroll for each team?
My work:
Yankees= 75+R (R stands for Red Sox)
Red Sox= 17+A (A stands for Angels)
Angels= X
X+17+X+75+X=418
X=108.666666667 or 108.67
Angels= 108.67
Red Sox= 125.67
Yankees= 200.67
When added together it comes out to: 435.01
I am close to the 418, I just can't figure out where i messed up. I assume in my equation.
Thanks
1 solutions
Answer 442728 by stanbon(57262) on 2013-03-05 19:24:37 (Show Source):
You can put this solution on YOUR website! Payrolls for the 3 highest paid baseball teams (the Yankees, Red Sox, and Angels) for 2006 totaled 418 million. If the team payroll for
the Yankees is 75 million dollars higher than the Red Sox and the
Red sox is 17 million dollars higher than the Angels, then what was the 2006 payroll for each team?
My work:
Yankees= 75+R = 75+17+A = 92+A (R stands for Red Sox)
Red Sox= 17+A (A stands for Angels)
Angels= X
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Equation:
A + 17+A + 92+A = 418
3A + 109 = 418
3A = 309
A = 103
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etc.
Cheers,
Stan H.
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Triangles/722346: The segment connecting point A(1,2) to point B(4,2) is one side of a 30º-60º-90º triangle, , but you do not know which side. It could be the shorter leg, the longer leg or the hypotenuse.
How many 30º-60º-90º triangles can be drawn under these conditions?
For each triangle, state:
• the coordinates of point C.
• the lengths of the 3 sides.
I have all the lengths of all sides of every triangle and the coordinate C for every triangle except four.
I have all 12 possible triangles, but when AB is the hypotenuse, I cannot find the coordinate of C.
Please help me find a way or a formula to solve for coordinate C when I have all side lengths and two other points? Thank you very much!
1 solutions
Answer 442725 by stanbon(57262) on 2013-03-05 19:08:42 (Show Source):
You can put this solution on YOUR website!The length from A to B is 3
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If AB is the hypoteuse, the side opposite the 30 degree
angle is (1/2)(3 = 3/2
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The side opposite the 60 degree angle is [sqrt(3)/2]*3 = (3/2)sqrt(3)
====================================================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/722349: Please factor this polynomial so that it is in the FOIL solution:
15c+35
1 solutions
Answer 442724 by stanbon(57262) on 2013-03-05 18:57:30 (Show Source):
You can put this solution on YOUR website!Please factor this polynomial so that it is in the FOIL solution:
15c+35
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Note: FOIL relates to the multiplying of two binomial
of the factoring of a quadratic. It does not apply
to your problem.
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15c+35 = 5(3c+7)
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Cheers,
Stan H.
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Average/722351: if john makes a 77% on his test and ansewered 34 questions correct, how many questions were on the test
1 solutions
Answer 442723 by stanbon(57262) on 2013-03-05 18:54:03 (Show Source):
You can put this solution on YOUR website!if john makes a 77% on his test and ansewered 34 questions correct, how many questions were on the test
----
Let "x" be the number of questions.
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Equation:
0.77x = 34
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x = 34/0.77
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x = 44 when rounded down
===========================
Cheers,
Stan H.
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Percentage-and-ratio-word-problems/722345: I have some small candies i want to sell in packages of 15 candies for $0.25 per package. how much would I charge for 60 candies?
1 solutions
Answer 442722 by stanbon(57262) on 2013-03-05 18:50:53 (Show Source):
You can put this solution on YOUR website!I have some small candies i want to sell in packages of 15 candies for $0.25 per package. how much would I charge for 60 candies?
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Use a proportion:
cost/number = cost/number
c/60 = 25/15
----
c = 60(25/15) = 100
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Cost for 15 is $1.00
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Cheers,
Stan H.
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Mixture_Word_Problems/722341: How many liters of 70% acid solution must be mixed with 10% acid solution to get 480 L of a 60% acid solution
1 solutions
Answer 442721 by stanbon(57262) on 2013-03-05 18:40:41 (Show Source):
You can put this solution on YOUR website! How many liters of 70% acid solution must be mixed with 10% acid solution to get 480 L of a 60% acid solution
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Using 2 variables:
Quantity Eq::: x + y = 480 L
Acid Eq::::: 70x+10y = 60*480
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Modify for elimination:
70x + 70y = 70*480
70x + 10y = 60*480
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Subtract and solve for "y":
60y = 10*480
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y = 80 L (amt. of 10% solution needed)
----
x = 400 L (amt. of 70% solution needed)
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Cheers,
Stan H.
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