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Recent problems solved by 'stanbon'
stanbon answered: 57314 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, >>NextProbability-and-statistics/537116: On hot, sunny, summer days Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probabilities to the number of tubes she will rent on a randomly selected day.
X 25 50 75 100 Total
P(x) 0.20 0.40 0.30 0.10 1.00
Based on this data, what is the daily average number of tubes she will rent?
1 solutions
Answer 352722 by stanbon(57387)   on 2011-11-27 11:46:20 (Show Source):
You can put this solution on YOUR website!X 25 50 75 100 Total
P(x) 0.20 0.40 0.30 0.10
Based on this data, what is the daily average number of tubes she will rent?
----
Average: 0.20*25 + 0.40*50 + 0.30*75 + 0.10*100 = 57.5
=======================
Cheers,
Stan H.
=======================
|
Polynomials-and-rational-expressions/537080: the ratio of the sum of 2 positive integers to their difference is 7:5. If the sum of the 2 number is at most 25, find all possible values for the pair of numbers
1 solutions
Answer 352720 by stanbon(57387) on 2011-11-27 11:04:54 (Show Source):
You can put this solution on YOUR website!the ratio of the sum of 2 positive integers to their difference is 7:5. If the sum of the 2 number is at most 25, find all possible values for the pair of numbers
------
Equations:
(x+y)/(x-y) = 7/5
x + y <=25
---------
Solve the equality:
5x+5y=7x-7y
12y = 2x
y = x/6
-----
And:
x+y = 25
(25)/(x-y) = 7/5
125 = 7x-7y
y = x-(125/7)
----
x-y = (125/7)
x+y = 25
---
Add and solve for "x":
----
2x = 300/7
x = 150/7
----
Solve for "y":
x+y = 25
y = 25-(150/7)
y = 25/7
----
Equality solution: (150/7 , 25/7)
---
Inequality solution:
Since x+y <= 25
y <= 25-(150/7) <= 25/7
---
===========
Cheers,
Stan H.
===========
|
Age_Word_Problems/537070: The present age of a woman is 30years older than her daughter.15years ago, she was twice as old as her daughter.How old is her daughter at present.How old would the woman be 12years from now?
1 solutions
Answer 352712 by stanbon(57387) on 2011-11-27 10:04:18 (Show Source):
You can put this solution on YOUR website!The present age of a woman is 30years older than her daughter.15years ago, she was twice as old as her daughter.How old is her daughter at present.
Equations:
w = d + 30
(w-15) = 2(d-15)
----
Substitute for "w" and solve for "d":
d+30-15 = 2d-30
d = 45 yrs (daughter's age now)
---
Solve for "w";
w = d + 30
w = 45+30 = 75 yrs (woman(mother)age now)
========================
How old would the woman be 12years from now?
Ans: 75+12 = 87 yrs
========================
Cheers,
Stan H.
==============
|
Travel_Word_Problems/537056: if a driver drives at a speed of 24 km/hour , he reaches his destination 5 minutes too late . but if he drives at a speed of 30km/hour , he reaches his destination 4 minutes too soon . how far is his destination?
1 solutions
Answer 352709 by stanbon(57387) on 2011-11-27 09:34:51 (Show Source):
You can put this solution on YOUR website!if a driver drives at a speed of 24 km/hour , he reaches his destination 5 minutes too late . but if he drives at a speed of 30km/hour , he reaches his destination 4 minutes too soon . how far is his destination?
------
Late DATA:
rate = 24 km/hr ; distance = x km ;time=d/r= x/24 hrs = 60(x/24)= 2.5x minutes
---
Early DATA:
rate = 30 km/hr ; distance = x km ;time=d/r = x/30 hrs = 60x/30 = 2x mi2.5nutes
==============
Equation:
Late time - Early time = 9 minutes
2.5x - 2x = 9
0.5x = 9
x = 18 km
----
Cheers,
Stan H.
===============
|
Polynomials-and-rational-expressions/536968: z-4/z-8-z+1/z+8+z-72/z^2-64 Perform the indicated operations and simplify. I have tried this a dozen times and keep getting different answers. Can you Please Help me?
1 solutions
Answer 352679 by stanbon(57387) on 2011-11-26 23:04:48 (Show Source):
You can put this solution on YOUR website!(z-4)/(z-8)-(z+1)/(z+8)+(z-72)/(z^2-64)
------
least common denominator: z^2-64
----
Rewrite each term with the lcd as its denominator:
[(z-4)(z+8)]/lcd - [(z+1)(Z-8)]/lcd + [(z-72)]/lcd
-----
Combine the numerators over the lcd:
[z^2+4z-32 - [z^2-7z-8] + z-72]/lcd
----
[z^2+4z-32-z^2+7z+8+z-72]/lcd
----
= [12z-96]/[z^2-64]
----
= [12(z-8)]/[z^2-64]
---
= 12/(z+8]
===============
Cheers,
Stan H.
|
Word_Problems_With_Coins/536971: Your piggy bank has a total of 20 coins in it; some are dimes and some are nickels. If you have a total of $1.25, how many nickels do you have?
1 solutions
Answer 352668 by stanbon(57387) on 2011-11-26 21:58:36 (Show Source):
You can put this solution on YOUR website!Your piggy bank has a total of 20 coins in it; some are dimes and some are nickels. If you have a total of $1.25, how many nickels do you have?
----
Equation:
Quantity: n + d = 20
Value::: 5n+10d = 125 cents
-------------------------------
Multiply thru Quantity by 5:
5n + 5d = 5*20
5n +10d = 125
----
Subtract and solve for "d":
5d = 25
d = 5 (# of dimes)
-----------------------
Solve for "n":
n + d = 20
n + 5 = 20
n = 15 (# of nickels)
===========================
Cheers,
Stan H.
|
Probability-and-statistics/536908: Claim: The proportion of brown M&Ms more than 22%. A simple random sample of 150 M&Ms contains 26% brown.
I have to identify the null and alternative hypothesis and identify the sampling distribution (normal, t, chi-square) of the test statistic or state that none of the sampling distributions would work.
I am stuck on this simple question and not sure why so any help would be great.
Thanks.
SS
1 solutions
Answer 352658 by stanbon(57387) on 2011-11-26 20:38:52 (Show Source):
You can put this solution on YOUR website!Claim: The proportion of brown M&Ms more than 22%. A simple random sample of 150 M&Ms contains 26% brown.
I have to identify the null and alternative hypothesis and identify the sampling distribution (normal, t, chi-square) of the test statistic or state that none of the sampling distributions would work.
------
Ho: p <= 0.22
Ha: p > 0.22
----------
test statistic: z(0.26) = (0.26-0.22)/sqrt[0.22*0.78/150] = 1.1826
Distribution: Normal
========================
Cheers,
Stan H.
|
Probability-and-statistics/536917: I'd appreciate some help with this problem. It is too complex for me to even begin to understand, thank you in advance!!
"In a class of 36 students, what is the probability that at least 2 people have the same birthday? Assume that there are 365 days in a calendar year. *
1 solutions
Answer 352657 by stanbon(57387) on 2011-11-26 20:29:54 (Show Source):
You can put this solution on YOUR website!"In a class of 36 students, what is the probability that at least 2 people have the same birthday? Assume that there are 365 days in a calendar year. *
------
Use Google to search for "Probability the birthday problem".
Cheers,
Stan H.
=========
|
Probability-and-statistics/536921: I am not sure how to solve this problem. I'd appreciate the help, thank you!!
"A scoring possibility in a game of Yahtzee with five 6-sided dice is called a "three of a kind," where three numbers are the same and the remaining two numbers are both different (eg: 5 5 5 1 4 or 2 5 2 3 2). Find the probability of rolling a three of a kind.
1 solutions
Answer 352655 by stanbon(57387) on 2011-11-26 20:25:03 (Show Source):
You can put this solution on YOUR website!"A scoring possibility in a game of Yahtzee with five 6-sided dice is called a "three of a kind," where three numbers are the same and the remaining two numbers are both different (eg: 5 5 5 1 4 or 2 5 2 3 2). Find the probability of rolling a three of a kind.
---
Pick a number: 6 ways
Pick 3 of that number on 5 dice: 5C3 = 10 ways
Pick another number: 5 ways
Pick yet another number: 4 ways
Total # of ways to succeed: 6*10*5*4 = 1200
---
# of possible outcomes: 6^5 = 7776
---
Probability of "three of a kind" = 1200/7776 = 0.1543
=======================================
Cheers,
Stan H.
|
Probability-and-statistics/536931: Every week, Emily and Jacod each write one story for an online magazine. Emily is paid 200 dollars plus 5% of the advertising revenue for her story. Jacob is paid 150 dollars plus 10% of the advertising revenue for his story. If they both generated the same amount of advertising revenue, and received equal paychecks for the week, how much in dollars was each paid?
1 solutions
Answer 352649 by stanbon(57387) on 2011-11-26 20:07:59 (Show Source):
You can put this solution on YOUR website!Every week, Emily and Jacod each write one story for an online magazine. Emily is paid 200 dollars plus 5% of the advertising revenue for her story. Jacob is paid 150 dollars plus 10% of the advertising revenue for his story. If they both generated the same amount of advertising revenue, and received equal paychecks for the week, how much in dollars was each paid?
-----
Equation:
200 + 0.05a = 150 + 0.10a
0.05a = 50
5a = 5000
a = $1,000.00 (advertising revenue)
======================
Cheers,
Stan H.
==================
|
Linear-equations/536929: If the line defined by the equation -4x+2y=8 crosses another line with the equation y+(2/3)x+b at the point (3,a), what is the value of b?
1 solutions
Answer 352638 by stanbon(57387) on 2011-11-26 19:55:27 (Show Source):
You can put this solution on YOUR website!If the line defined by the equation -4x+2y=8 crosses another line with the equation y=(2/3)x+b at the point (3,a), what is the value of b?
------------
If (3,a) satisfies both equations you get:
-12+2a = 8
a = 2 + b
---
Substitute for "a" and solve for "b":
-12 + 2(2+b) = 8
2+b = 10
b = 8
==============
Cheers,
Stan H.
==============
|
Linear-equations/536363: solve by graphing
7x-6y=30
6y-7y=-30
1 solutions
Answer 352280 by stanbon(57387) on 2011-11-24 11:39:09 (Show Source):
You can put this solution on YOUR website!pipe A cn fill a cistern in 6hrs & pipe B cn fill it in 8hrs. both pipes r opened simultaneously bt after 2hrs pipeA is closed. how many hrs willB take to fill the remaining partbof cistern
---------------------------
A time = 6 hrs/job ; rate = 1/6 job/hr
-------
B time = 8 hrs/job ; rate = 1/8 job/hr
-------
Together rate = 1/6 + 1/8 = (14/48) = 7/24 job/hr
-----------------------------------------
Note: work done = rate*time
-----------------------------------------------------
Equation:
work + work = 1 job
2(7/24) + (1/8)x = 1
14 + 3x = 24
3x = 14
x = 4 1/3 hrs (time for "B" to finish the job)
=================
Cheers,
Stan H.
==================
|
Probability-and-statistics/536358: Hi -
Claim: The standard deviation is greater than 5.2 lbs. When a simple random sample of 21 items is taken from a normally distributed population, s - 6.8 lbs.
I have to identify the null and alternative hypothesis, identify the sampling distribution (normal, t, chi-square) of the test statistic.
Thanks! Happy Thanksgiving!
-SS
1 solutions
Answer 352278 by stanbon(57387) on 2011-11-24 11:02:52 (Show Source):
You can put this solution on YOUR website!Claim: The standard deviation is greater than 5.2 lbs. When a simple random sample of 21 items is taken from a normally distributed population, s - 6.8 lbs.
I have to identify the null and alternative hypothesis, identify the sampling distribution (normal, t, chi-square) of the test statistic.
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Ho: sigma <= 5.2
Ha: sigma > 5.2 (clsim)
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chi-square
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Cheers,
Stan H.
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Probability-and-statistics/536349: Claim: heights of a new variety of corn vary less than those of an older variety. The standard deviation of heights for the population of the old corn variety is 3.5 inches and the population has a normal distribution. A simple random sample of new corn variety provides the following data: n = 36, s = 1.2.
I have to identify null hypothesis, the alternative hypothesis, and identify the sampling distriubtion of the test statistic (normal, t, chi-square).
Any help would be greatly appeciated!
-SS
1 solutions
Answer 352277 by stanbon(57387) on 2011-11-24 10:59:00 (Show Source):
You can put this solution on YOUR website! Claim: heights of a new variety of corn vary less than those of an older variety. The standard deviation of heights for the population of the old corn variety is 3.5 inches and the population has a normal distribution. A simple random sample of new corn variety provides the following data: n = 36, s = 1.2.
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Ho: sigma(new)-sigma(old)>= 0
Ha: sigma(new)-sigma(old) < 0 (claim)
I have to identify null hypothesis, the alternative hypothesis, and identify the sampling distriubtion of the test statistic (normal, t, chi-square).
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Chi-Square
================
Cheers,
Stan H.
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Rectangles/536339: The length of a table is 5 meters greater than the width. The area of the table is 104m squared. What is the lenth and width?
1 solutions
Answer 352274 by stanbon(57387) on 2011-11-24 10:43:17 (Show Source):
You can put this solution on YOUR website! The length of a table is 5 meters greater than the width. The area of the table is 104m squared. What is the leng
th and width?
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let width be W
then length is W+5
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Area = length * width
104 = w(w+5)
104 = w^2+5w
w^2+5w-104 = 0
Use Quadratic formula:
w = [-5+-sqrt(25-4*-104)]/2
Positive solution:
w = [-5+sqrt(441)]/2
etc.
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Cheers,
Stan H.
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Percentage-and-ratio-word-problems/536337: How much salt must be evaporated for 120 kg of solution which is 3% salt to make a solution of 5% salt?
1 solutions
Answer 352269 by stanbon(57387) on 2011-11-24 09:44:38 (Show Source):
You can put this solution on YOUR website!How much water must be evaporated for 120 kg of solution which is 3% salt to make a solution of 5% salt?
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Equation:l
water - water = water
0.97*120 - 1x = 0.95(120-x)
97(120)- 100X = 95*120-95X
2(120)=5X
X = 48 kg (amt. of water that must be evaporated)
Cheers,
Stan H.
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Equations/535455: please help me i dont understand how to do these six problems
1) 1-7x=-20
2) 1+5x=26
3) -6x+7=15
4) -3+4x=-47
5) 3x-2=13
6) -3x-4=-19
1 solutions
Answer 351894 by stanbon(57387) on 2011-11-21 20:50:23 (Show Source):
You can put this solution on YOUR website!1) 1-7x=-20
Add 7x to both sides
Add 20 to both sides
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1+20 = 7x
7x = 21
Divide both sides by 7 to get:
x = 3
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2) 1+5x=26
Subtract 1 from both sides to get:
5x = 25
Divide by 5 to get:
x = 5
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3) -6x+7=15
Add 6x to both sides
Subtract 15 from both sides
6x = 7-15
6x = -8
Divide both sides by 6
x = -4/3
==============================
4) -3+4x=-47
Add 3 to both sides:
4x = -44
Divide by 4 to get:
x = -11
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5) 3x-2=13
3x = 15
x = 5
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6) -3x-4=-19
-3x = -15
x = 5
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Cheers,
Stan H.
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Cheers,
Stan H.
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Mixture_Word_Problems/535441: A grocer mixes walnuts selling at 55 cents a pound and almonds selling at 70 cents a pound, making a mixture of 30 pounds to sell at 61 cents. How many pounds of walnuts should he use? Represent the walnuts with x and the almonds with y. transale the word statement in 2 equations. I tried this for about 30 minutes. so far i got x + y = 30 and 55x + 70y = 610.
1 solutions
Answer 351893 by stanbon(57387) on 2011-11-21 20:45:00 (Show Source):
You can put this solution on YOUR website!Quantity: x + y = 30
Value: 55x + 70y = 61*30
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Multiply thru Quantity by 55 to get:
55x + 55y = 55*30
55x + 70y = 61*30
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Subtract and solve for "y":
15y = 6*30
y = 12 lbs. (amt of 55 cent walnuts needed)
---
Solve for "x":
x + y = 30
y = 18 lbs. (amt of 70 cent almonds needed)
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Cheers,
Stan H.
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Graphs/535445: can you please help me figure out the slope of the line that is perpendicular to y=5x+10.....i am having some troubles with math this year and i really want to get a good grade, but this is what i am struggling on..thanks!
1 solutions
Answer 351892 by stanbon(57387) on 2011-11-21 20:35:38 (Show Source):
You can put this solution on YOUR website!figure out the slope of the line that is perpendicular to
y=5x+10
That line has a slope of 5
----
If 2 lines are perpendicular, the product of there slopes must be -1.
----
Solve 5*m = -1
m = -1/5
That is the slope you want.
Cheers,
Stan H.
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logarithm/535345: Hello everyone! I need help with logarithmic functions please! This is a hard topic for me and could use all the help I can.
Find the domain of the logarithmic function..
f(x)= log(x^2-17x+72)
1 solutions
Answer 351860 by stanbon(57387) on 2011-11-21 18:56:34 (Show Source):
You can put this solution on YOUR website!Find the domain of the logarithmic function..
f(x)= log(x^2-17x+72)
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x^2-17x+72 must be > 0
(x-9)(x-8) > 0
---
Draw a number line and plot x=8 and x=9
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Look for solutions in the intervals:
Try x = 0: -*- > 0 ; true, so solutions in (-oo,8)
Try x = 8.5: -*+ > 0 ; false
Try x = 9.5: +*+ > 0 ; true, so solutions in (9,+oo)
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Domain: (-oo,8)U(9,+oo)
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/535336: How do I solve 125x^3 + 343 = 0?
1 solutions
Answer 351857 by stanbon(57387) on 2011-11-21 18:37:31 (Show Source):
You can put this solution on YOUR website!solve 125x^3 + 343 = 0
Modify:
----
(5x)^3 + 7^3 = 0
---
Factor:
(5x+7)((5x)^2-(5x)(7)+7^2) = 0
----
(5x+7)(25x^2-35x+49) = 0
One of those factors must be zero:
If 5x+7 = 0
x = -7/5
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If 25x^2-35x+49 = 0
x = [35 +- sqrt(35^2 - 4*25*49)]/50
---
x = [35 +- sqrt(-3675)]/50
---
x = (7/10) +- (60.62/50)i
==============================
Cheers,
Stan H.
====================
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Functions/535330: How do you find f(x+h) for this function: f(x)=x^2-2x+5. I know you pug in (x+h0 for x.. but i don't understand how to solve it. If you could please help me that'd be great. :)
1 solutions
Answer 351850 by stanbon(57387) on 2011-11-21 18:22:02 (Show Source):
You can put this solution on YOUR website!How do you find f(x+h) for this function:
f(x)=x^2-2x+5
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f(x+h) = (x+h)^2 - 2(x+h) + 5
f(x+h) = x^2 +2hx + h^2 -2x -2h + 5
---
f(x+h) = x^2 +(2h-2)x + h^2-2h+5
===========================
Cheers,
Stan H.
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Probability-and-statistics/535295: Suppose you have 6 types of cereal. If you eat a bowl of cereal every morning for breakfast, how many ways can you eat breakfast in the next 4 days?
1 solutions
Answer 351845 by stanbon(57387) on 2011-11-21 18:14:34 (Show Source):
You can put this solution on YOUR website!Suppose you have 6 types of cereal. If you eat a bowl of cereal every morning for breakfast, how many ways can you eat breakfast in the next 4 days?
----
Assuming you have only one bowl of each cereal you get:
1st day: 6 choices
2nd day: 5 choices
3rd day: 4 choices
4th day: 3 choices
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Ans: 6*5*4*3 = 30*12 = 360 choices
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OR
Ans: 6P4 = 360
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Cheers,
Stan H.
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Probability-and-statistics/535317: please help me solve this probability question! "if 83% of seeds will sprout and 10 are selected at random, what is the probability that at least 8 will sprout"
1 solutions
Answer 351841 by stanbon(57387) on 2011-11-21 18:04:04 (Show Source):
You can put this solution on YOUR website!"if 83% of seeds will sprout and 10 are selected at random, what is the probability that at least 8 will sprout"
----
Binomial Problem with n = 10 and p(sprout) = 0.83
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P(8<= x <=10) = 1 - binomcdf(10,0.83,7) = 0.7659
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Cheers,
Stan H.
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Linear-equations/535314: graph the line passing through the given point with the given slope
(0,4),m=1
1 solutions
Answer 351839 by stanbon(57387) on 2011-11-21 17:58:50 (Show Source):
You can put this solution on YOUR website!graph the line passing through the given point with the given slope
(0,4),m=1
----
You are given the slope and the y-intercept:
y = 1*x + 4
---
y = x + 4
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Cheers,
Stan H.
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Numbers_Word_Problems/535313: if the sum of a number and eight is tripled, the result is 5 less than twice the number . Find the number.
could you show step by step please and thank you.
1 solutions
Answer 351835 by stanbon(57387) on 2011-11-21 17:53:51 (Show Source):
You can put this solution on YOUR website!if the sum of a number and eight is tripled, the result is 5 less than twice the number . Find the number.
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Equation:
3(x + 8) = 2x-5
3x + 24 = 2x-5
x = -29
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Cheers,
Stan H.
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