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Recent problems solved by 'stanbon'
stanbon answered: 57351 problems
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2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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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, >>Nexttest/457452: Please help me solve this problem: Two trains are traveling toward eachother from 800 miles apart, each at 80 miles per hour. How long will it be before they meet?
1 solutions
Answer 313854 by stanbon(57424)   on 2011-06-04 18:47:23 (Show Source):
You can put this solution on YOUR website!Two trains are traveling toward eachother from 800 miles apart, each at 80 miles per hour. How long will it be before they meet?
---
Their closing speed is 80+80 = 160 mph
-----
time = distance/rate
--------------
time = 800/160 = 5 hrs.
============================
Cheers,
Stan H.
|
Mixture_Word_Problems/457277: How much of an 8% saline solution should be added to 600ml of a 3% solution to produce a 5% solution?
1 solutions
Answer 313769 by stanbon(57424) on 2011-06-04 08:10:30 (Show Source):
You can put this solution on YOUR website!How much of an 8% saline solution should be added to 600ml of a 3% solution to produce a 5% solution?
---------------
0.08x + 0.03*600 = 0.05(x+600)
-----
Multiply thru by 100 to get:
8x + 3*600 = 5x + 5*600
---
3x = 2*600
---
x = 400ml (amt of 8% solution needed)
===========================================
Cheers,
Stan H.
|
Numbers_Word_Problems/457270: paige is thinking of two numbers that have a product of 180 and difference of 3 what are the two numbers?
1 solutions
Answer 313767 by stanbon(57424) on 2011-06-04 08:01:33 (Show Source):
You can put this solution on YOUR website! Paige is thinking of two numbers that have a product of 180 and difference of 3 what are the two numbers?
----------------
Solve:
x -y = 3
xy = 180
----
Substitute for "x" and solve for "y":
y(y+3) = 180
----
y^2+3y-180 = 0
(y-12)(y+15) = 0
---
If y = 12, x = 15
If y = -15, y = -12
=========================
Cheers,
Stan H.
|
Sequences-and-series/457226: how would i write in a assignment the response to these two questions?
1) consider a general Arithmetic sequence a,a+d,a+2d..., state with reasons, wherher such sequences diverge or converge
2)Consider the general Geometric sequence a,ar,ar^2.. state with reasons, the conditons under which such sequences converge and the limit of the sequence when they do converge/
1 solutions
Answer 313764 by stanbon(57424) on 2011-06-04 07:46:44 (Show Source):
You can put this solution on YOUR website!How would i write in a assignment the response to these two questions?
1) consider a general Arithmetic sequence a,a+d,a+2d..., state with reasons, wherher such sequences diverge or converge
---
Arithmetic sequences always diverge.
=============================================
2)Consider the general Geometric sequence a,ar,ar^2.. state with reasons, the conditons under which such sequences converge and the limit of the sequence when they do converge.
---
The general term is a(n) = a(1)r^(n-1)
The sequence will converge to zero if |r|< 1 and r not equal to 0.
Note: A geometric sequence is not defined for r = 0.
=============
Cheers,
Stan H.
===========
|
Probability-and-statistics/457236: One card is selected from a deck of playing cards. Determine the probability of selecting. A card greater than 9 or a black card.
1 solutions
Answer 313761 by stanbon(57424) on 2011-06-04 07:17:06 (Show Source):
You can put this solution on YOUR website!One card is selected from a deck of playing cards. Determine the probability of selecting. A card greater than 9 or a black card.
-------------
# of cards greater than 9 (if you include the ace) = 4*5 = 20
# of black cards = 26
---
# of cards that satisfy both conditions: 26+20-10 = 36
----
P(card > 9 OR black) = 36/52 = 9/13
================
Cheers,
Stan H.
================
|
Evaluation_Word_Problems/457258: A proposed city ordinance will make it illegal to create sound in a residential area that exceeds 72 decbels during the day and 55 decibels during the night .How many times as intense is the noise level allowed during the day than at night?
1 solutions
Answer 313760 by stanbon(57424) on 2011-06-04 06:58:43 (Show Source):
You can put this solution on YOUR website!A proposed city ordinance will make it illegal to create sound in a residential area that exceeds 72 decibels during the day and 55 decibels during the night .How many times as intense is the noise level allowed during the day than at night?
-------------
M = 10log[I/Io]
-----
72 = 10log[I/Io]
log[I/Io] = 7.2
I/Io = 10^7.2
----
I(72) = 10^7.2*Io
---------------------
Same procedure gives:
I(55) = 10^5.5*Io
----
Dividing I(72)/I(55) you get [10^7.2/10^5.5] = 10^1.7 = 60.12 as intense.
=========================
Cheers,
Stan H.
|
logarithm/457265: Hello I need help solving this exponential equation problem: 9^x+1=15. I took the common log of each side like this, x(log9+1log9)=log15 But now I don't know what to do. I don't know if this is even the right set up in order to solve this. Does anyone know?
1 solutions
Answer 313757 by stanbon(57424) on 2011-06-04 06:46:27 (Show Source):
You can put this solution on YOUR website!9^x+1=15
---
Note: The log of a sum is not the sum of the logs of the terms.
------------
Subtract 1 from both sides to get:
9^x = 14
Not take the log:
x*log(9) = log(14)
---
x = log(14)/log(9)
---
x = 1.2011
============
Cheers,
Stan H.
|
Polygons/457267: how many sides are there in a regular polygon with an exterior angle of 30 degrees
1 solutions
Answer 313756 by stanbon(57424) on 2011-06-04 06:42:20 (Show Source):
You can put this solution on YOUR website!how many sides are there in a regular polygon with an exterior angle of 30 degrees
---
The sum of all the exterior angles is 360 degrees
---
# of exterio = 360/30 = 12
--
Therefore # of sides = 12
=================
Cheers,
Stan H.
|
Evaluation_Word_Problems/457268: Page 548 # 1
Police use blood alcohol content (ABC) to measure the percent concentration of alcohol in a person’s bloodstream. In most states, a BAC of 0.08 percent means person is not allowed to drive. Each hour after drinking, a person’s ABC may decrease by 15%. If a person has BAC of 0.18, how many hours will he need to wait he can legally drive?
1 solutions
Answer 313755 by stanbon(57424) on 2011-06-04 06:38:44 (Show Source):
You can put this solution on YOUR website!In most states, a BAC of 0.08 percent means person is not allowed to drive. Each hour after drinking, a person’s ABC may decrease by 15%. If a person has BAC of 0.18, how many hours will he need to wait he can legally drive?
--------------------
Start 0.18
After 1 hr: 0.18-0.15*0.18 = (1-0.15)0.18 = 0.85*0.18
After 2 hr: 0.85^2*0.18
etc.
----
Solve:
0.85^n(0.18) < 0.08
---
0.85^n < 0.08/0.18 = 0.4444
n > log(0.4444)/log(0.85)
n > 4.9899
n >= 5 hrs.
=================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/457198: When writing an inequality for a word problem, do the units have to be converted to have the same value (dollars and cents) before writing the expression? This was one of our homework questions
A cell phone company has offered you two different rates. The first rate is $35 per month and 5 cents per phone call (time does not matter). The second offer is $55 per month and 2 cents per call. Set up the inequality to model this problem and find where it is less expensive to go with the second plan.
This is the inequality I came up with: 35 + 5x < 55 + 2x, but I'm not sure if that's correct. Since the price per call is in cents and not whole dollars, would I need to somehow convert that value before trying to write up the inequality? And if so, would it be something like: 35 + .05x < 55 + .02x ? Any help on this would be greatly appreciated. Thank you.
1 solutions
Answer 313705 by stanbon(57424) on 2011-06-03 20:14:38 (Show Source):
You can put this solution on YOUR website!35 + .05x < 55 + .02x
---
Yes, you need the decimals so everything
is stated in terms of dollars.
---
But you need to reverse the inequality
because you want the 2nd plan to be
less expensive:
----------
Solve: 35 + .05x > 55 + .02x
---
0.03x > 20
x > 20/0.03
x > 666.67
---
2nd plan is less expensive if 667 phone calls are made.
========================================================
Cheers,
Stan H.
===========
|
percentage/457205: Interest question, please help
$5400 is invested, part of it at 10% and part of it at 7%. For a certain year the total yield is $468. How much was invested at each rate? Thanks for your help.
1 solutions
Answer 313703 by stanbon(57424) on 2011-06-03 20:08:27 (Show Source):
You can put this solution on YOUR website!Interest question, please help
$5400 is invested, part of it at 10% and part of it at 7%. For a certain year the total yield is $468. How much was invested at each rate?
-----------------
Quantity Equation: x + y = 5400 dollars
Interest Equation:0.10x + 0.07y = 469 dollars
-------------------------------------------
Multiply thru 1st by 10
Multiply thru 2nd by 100
--------------------------------
10x + 10y = 54000
10x + 7y = 46900
---------------------------
Subtract and solve for "y":
3y = 7100
y = $2366.67 (amt. invested at 7%)
---
Solve for "x":
x+ y = 5400
x = 5400-2366.67
x = $2633.33 (amt. invested at 10%)
=======================================
Cheers,
Stan H.
=============
|
Coordinate-system/457208: I can't seem to get this
Write an equation in standard form for a line passing through the pair of points.
( 7, 8) and ( 7, -8)
Any help would be appreciated
1 solutions
Answer 313702 by stanbon(57424) on 2011-06-03 20:02:25 (Show Source):
You can put this solution on YOUR website!( 7, 8) and ( 7, -8)
-----------------
slope = (-8-8)/(7-7) = -16/0
which is "not defined".
----
Notice that both points have x=7.
Plot those two points and you will get
a vertical line passing thru all the
points where x=7
--------------------
Equation of the line: x = 7
===============================
Cheers,
Stan H.
==========
|
Complex_Numbers/457212: How can I simplify 1+2i/2-3i
1 solutions
Answer 313701 by stanbon(57424) on 2011-06-03 19:58:49 (Show Source):
You can put this solution on YOUR website!simplify 1+2i/2-3i
----
Multiply numerator and denominator
by the conjugate of 2-3i, which is 2+3i.
----
You get: [(1+2i)(2+3i)]/[(2-3i)(2+3i)]
====
= [2+5i-6]/[4 + 0i + 9]
------
= (-4+5i)/13
================
Cheers,
Stan H.
================
|
Polynomials-and-rational-expressions/457210: Hi I am really confused on how to complete this problem. I am in a study plan and very stuck in a section. I need to know where they are getting certain numbers so i can complete the rest of these assignments...
9th rt b^2 * sqrt b^9
I get this
b^2/9 b^9/2=b^2/18 b^9/18
from here I am confused. It shows in help that it is b^85/18. Where are they getting 85.
The next confusion is after this it shows b^4+13/18. Where are they getting 4+13..
Can anyone help. It would be wonderful. Thank You
1 solutions
Answer 313699 by stanbon(57424) on 2011-06-03 19:55:29 (Show Source):
You can put this solution on YOUR website!9th rt b^2 * sqrt b^9
I get this
b^2/9 b^9/2=b^2/18 b^9/18
-------------------
If what you say is correct you should add the
exponents to get b^(11/9)
---
from here I am confused. It shows in help that it is b^85/18.
---
To get 85/18 you would nee 9/2 + 2/9 = (81+4)/18 = 85/18
---
Maybe your problem is not what you posted but rather:
sqrt(b^9)* 9th rt. of b^2
which would give you
b^(9/2) * b^(2/9) = b^(9/2 + 2/9) = b^(85/18)
==============================================
Cheers,
Stan H.
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Mixture_Word_Problems/457199: Another problem I need help with
Suppose for a certain company C(x)= 35x + 300,000 represents the total function, and R(x)=55x represents the total revenue function. Find the total function and break even point.
1 solutions
Answer 313692 by stanbon(57424) on 2011-06-03 18:56:03 (Show Source):
You can put this solution on YOUR website!Suppose for a certain company C(x)= 35x + 300,000 represents the total cost function, and R(x)=55x represents the total revenue function. Find the total profit function and break even point.
---------------------------------------
Profit = Revenue - Cost
----
P(x) = 55x -(35x+300,000)
-----
P(x) = 20x - 300,000
-----------------------------
Break Even occurs when there is zero profit.
----
Solve 20x-300,000 = 0
20x = 300,000
x = 15000
-------------
Cheers,
Stan H.
===============
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Quadratic_Equations/457191: How do you change a problem such as, 2x^2=-6+8x, into a quadratic equation that can be solved using the quadratic formula?
1 solutions
Answer 313690 by stanbon(57424) on 2011-06-03 18:41:47 (Show Source):
You can put this solution on YOUR website!2x^2=-6+8x,
------------------
Rearrange:
2x^2-8x+6 = 0
----
Divide thru by 2 to get:
x^2 - 4x + 3 = 0
------------------------
Use the quadratic formula:
x = [4 +- sqrt(16-4*3)]/2
----
x = [4 +- sqrt(4)]/2
----
x = [4 +- 2]/2
----
x = (6/2) or x = (2/2)
---
x = 3 or x = 1
=========================
Cheers,
Stan H.
==================
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Linear-systems/457193: how do u solve this equation ok so here is the sentance complete the solution of t he eqation find the value of y when x=28
x+3y=28 please help me solve this problem!
1 solutions
Answer 313684 by stanbon(57424) on 2011-06-03 18:26:25 (Show Source):
You can put this solution on YOUR website!find the value of y when x=28
x+3y=28 please help me solve this problem!
---------------
Substitute for "x" and solve for "y":
-----
x+3y = 28
28 + 3y = 28
3y = 0
y = 0
============
Cheers,
Stan H.
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Trigonometry-basics/457189: use the law of sines to
side b= 40cm
angle A=120
angle C=58
1 solutions
Answer 313681 by stanbon(57424) on 2011-06-03 18:22:24 (Show Source):
You can put this solution on YOUR website!use the law of sines to
side b= 40cm
angle A=120
angle C=58
--------------------
angle B = 180-(58+120) = 2 degrees
---------------------------------------
Solve a/sin(120) = 40/sin(2)
----
Solve c/sin(58) = 40/sin(2)
===============================
Cheers,
Stan H.
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test/457190: There are a total 108 offensive players on a football team. There are twice as many runners than passing players. Write two equations and then slove for both equation. How many runners are there and how many passing people are there?
1 solutions
Answer 313680 by stanbon(57424) on 2011-06-03 18:14:05 (Show Source):
You can put this solution on YOUR website!There are a total 108 offensive players on a football team. There are twice as many runners than passing players. Write two equations and then solve for both equation. How many runners are there and how many passing people are there?
---
Equations:
r + p = 108 players
r = 2p
----
Substitute for "r" and solve for "P":
2p + p = 108
3p = 108
p = 36 (# of passers)
----
solve for "r":
r + p = 108
r + 36 = 108
r = 72 (# of runners)
========================
Cheers,
Stan H.
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Probability-and-statistics/457084: The size of the box in a boxplot shows the ____________________ of the data set.
A)
difference between the mean and the median
B)
variance
C)
skewness
D)
interquartile range
1 solutions
Answer 313660 by stanbon(57424) on 2011-06-03 16:18:19 (Show Source):
You can put this solution on YOUR website!The size of the box in a boxplot shows the ____ of the data set.
-----------
Comment:
The box shows the spread of data between Q1 and Q3.
I don't like any of the option answers you have
listed.
-------------------------
Cheers,
Stan H.
================
A)
difference between the mean and the median
----------------
B)
variance
----------------
C)
skewness
----------------
D)
interquartile range
-------------------
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Probability-and-statistics/457143: The recovery rate from a flu is 0.9. If 4 people have this flu, what is the probability that:
a) all will recover?
b) at least 2 will recover?
c) exactly 2 will recover?
Assume independence.
Thanks so much for your help!
1 solutions
Answer 313659 by stanbon(57424) on 2011-06-03 16:12:36 (Show Source):
You can put this solution on YOUR website!The recovery rate from a flu is 0.9. If 4 people have this flu, what is the probability that:
a) all will recover?
Ans: (0.9)^4 =
--------------------------
b) at least 2 will recover?
Ans: P(2<= x <=4)
= 1 - P(0<= x <=2)
= 1-binomcdf(4,0.9,2)
= 1-0.0523
= 0.9477
====================
c) exactly 2 will recover?
Ans: P(x = 2) = 4C2(0.9)^2(0.1)^2 = binompdf(4,0.9,2) = 0.048600
====================================================================
Cheers,
Stan H.
================
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Probability-and-statistics/457091: The following distribution is not a probability distribution because
The following distribution is NOT a probability distribution because
X -2 -1 0 1 2
P(X) 0.13 0.19 0.42 0.16 0.27
A)
the values of the variable are negative.
B)
the probability values are not increasing.
C)
the probability values do not add to 1.
D)
the probability values are not discrete.
1 solutions
Answer 313657 by stanbon(57424) on 2011-06-03 16:03:25 (Show Source):
You can put this solution on YOUR website!The following distribution is NOT a probability distribution because
X -2 -1 0 1 2
P(X) 0.13 0.19 0.42 0.16 0.27
=============================================
Ans: C
-------------
Cheers,
Stan H.
===================
A)
the values of the variable are negative.
B)
the probability values are not increasing.
C)
the probability values do not add to 1.
D)
the probability values are not discrete.
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Probability-and-statistics/457101: hello here is a exam question i have on my practice paper
:
Emilia picks up a chocolate at random from a box.
All the chocolates in the box are identically wrapped.
The probability that she picks a caramel is 5/8.
Sophie picks a chocolate at random from a different box.
All the chocolates in Sophie's box are identically wrapped.
The probability that she picks up a caramel is denoted by P.
The probability that both Emilia and Sophie pick a caramel is 1/4
Emilia's box
P(emilia picks a caramal)=5/8
Sophies box
P(Sophie picks a caramel)=P
(a)Work out the value of P.
(b)calculate the probability that Neither emilia nor sophie picks a caramel
Please help me with these and tell me step step instructions what to do and tips
thanks so much for your time
1 solutions
Answer 313656 by stanbon(57424) on 2011-06-03 16:00:16 (Show Source):
You can put this solution on YOUR website! Emilia picks up a chocolate at random from a box.
All the chocolates in the box are identically wrapped.
The probability that she picks a caramel is 5/8.
Sophie picks a chocolate at random from a different box.
All the chocolates in Sophie's box are identically wrapped.
The probability that she picks up a caramel is denoted by P.
The probability that both Emilia and Sophie pick a caramel is 1/4
Emilia's box
P(emilia picks a caramal)=5/8
--------------------
Sophies box
P(Sophie picks a caramel)=P
--------------------
Note: The events are independent.
So, P(both pick caramel) = P(Emilia picks caramel)*P(Sophie picks caramel)
-----
(a)Work out the value of P.
Solve (5/8)P = (1/4)
p = (1/4)/(5/8)
P = 2/5
========================
(b)calculate the probability that Neither emilia nor sophie picks a caramel
P(Emelia does not pick caramel) = (3/8)
P(Sophie does not pick caramel) = (3/5)
P(neither picks are caramel) = (3/8)(3/5) = 9/40
===================================================
Cheers,
Stan H.
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