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Recent problems solved by 'stanbon'
stanbon answered: 57231 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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, >>NextNumeric_Fractions/442210: Your cap size is based on the circumference of your head (in inches). For a certain range of head circumferences c, cap size s can be modeled by the following equation:
s=c-1/3
If you wear a size 7 cap, what is your head circumference? Please show all of your work.
thank you!
1 solutions
Answer 304991 by stanbon(57299)   on 2011-04-28 20:08:36 (Show Source):
You can put this solution on YOUR website!cap size s can be modeled by the following equation:
s=(c-1)/3
If you wear a size 7 cap, what is your head circumference?
-----------------------
size = (circumference - 1)/3
-------
7 = (c-1)/3
c-1 = 21
c = 22 cm
=========================================
Cheers,
Stan H.
|
logarithm/442186: Solve the following equation for x in terms of q:
2^(3x-1)=7(x-q)
1 solutions
Answer 304987 by stanbon(57299) on 2011-04-28 19:54:40 (Show Source):
You can put this solution on YOUR website!Solve the following equation for x in terms of q:
2^(3x-1)=7(x-q)
----------------------
Take the log of both sides:
(3x-1)*log(2) = log[7x-7q]
Solve for "x":
3x-1 = [log(7x-7q)/log(2)]
---
x = {[log(7x-7q)/log(2)]+1}/3
--
x = {[log2(7x-7q)]+1}/3
====================================
Cheers,
Stan H.
|
Travel_Word_Problems/442182: John ran a meter in 1 1/2 minutes. What was his speed in meters per hour?
1 solutions
Answer 304984 by stanbon(57299) on 2011-04-28 19:47:50 (Show Source):
You can put this solution on YOUR website!John ran a meter in 1 1/2 minutes. What was his speed in meters per hour?
--------------------
1 meter/(1.5 minutes)[60 minutes/1 hr]
-----
=[1*60]/[1.5*1](meters/hr)
-----
= 40 meters/hr
====================
Cheers,
Stan H.
|
Evaluation_Word_Problems/442173: if four hens lay 9 eggs in 7 days, how many days will it take four dozen hens to lay 27 dozen eggs?
1 solutions
Answer 304981 by stanbon(57299) on 2011-04-28 19:39:57 (Show Source):
You can put this solution on YOUR website!if four hens lay 9 eggs in 7 days, how many days will it take four dozen hens to lay 27 dozen eggs?
--------------------------------
hens and days are inversely related
days and eggs are directly related
------
d = k*e/h
----
Solve for "k" using "four hens lay 9 eggs in 7 days":
7 = k*9/4
---
k = 28/9
-----------
Equation:
d = (28/9)*e/h
------
how many days will it take four dozen hens to lay 27 dozen eggs?
d = (28/9)27/48
----
d = 28*3/48
---
days = 1 3/4 days
=======================
Cheers,
Stan H.
|
Exponents/442176: How many ways can 5 children line up to get on the school bus if jenny always gets on third?
1 solutions
Answer 304979 by stanbon(57299) on 2011-04-28 19:31:43 (Show Source):
You can put this solution on YOUR website!How many ways can 5 children line up to get on the school bus if jenny always gets on third?
-----------------------
Ans: 4! = 4*3*2*1 = 24
=========================
Cheers,
Stan H.
|
Probability-and-statistics/442174: Find the mean, variance and standard deviation of the binominal distribution with thte given values, n=124, p=0.72
1 solutions
Answer 304976 by stanbon(57299) on 2011-04-28 19:26:15 (Show Source):
You can put this solution on YOUR website!Find the mean, variance and standard deviation of the binominal distribution with thte given values, n=124, p=0.72
----------------
mean = np = 124*0.72 = 89.28
-----
variance = npq = 89.28*0.28 = 24.998..
-----
std = sqrt(npq) = 4.99984..
==============================
Cheers,
Stan H.
|
Equations/442163: I dont know what section I need, but can someone help me with the following problem? I have no clue where to even begin. Thank you.
Find f(x+h)-f(x)/h for the following function:
3x-2
1 solutions
Answer 304975 by stanbon(57299) on 2011-04-28 19:22:17 (Show Source):
You can put this solution on YOUR website!Find f(x+h)-f(x)/h for the following function:
f(x) = 3x-2
f(x+h) = 3(x+h)-2 = 3x + 3h -2
-----
f(x+h)-f(x) = 3h
-----------------------
[f(x+h)-f(x)]/h = 3h/h = 3
============================================
Cheers,
Stan H.
|
Probability-and-statistics/442025: suppose a contestant in a spelling bee has a 93% chance of spelling any given word correctly. what is the probability that he or she spells the first five words in a bee correctly and then misspells the sixth word
1 solutions
Answer 304936 by stanbon(57299) on 2011-04-28 15:56:48 (Show Source):
You can put this solution on YOUR website!suppose a contestant in a spelling bee has a 93% chance of spelling any given word correctly. what is the probability that he or she spells the first five words in a bee correctly and then misspells the sixth word
---
P = 0.93^5*0.07 = 0.0490
=============================
Cheers,
Stan H.
|
Age_Word_Problems/442018: If children's tickets to the zoo cost $22 each, then how much does it cost to buy "x" children's tickets? (what does the total cost equal to?)
1 solutions
Answer 304933 by stanbon(57299) on 2011-04-28 15:52:07 (Show Source):
You can put this solution on YOUR website!If children's tickets to the zoo cost $22 each, then how much does it cost to buy "x" children's tickets? (what does the total cost equal to?)
----
total cost = (unit price)(# of units)
= $22x
============================
Cheers,
Stan H.
|
Graphs/442009: Hello! I need some help trying to solve parts a and b. I've already used the quadratic formula to find the two zeros (.5 and 2) but I am having trouble moving forward. Thank you so much!!
An espresso stand finds that its weekly profit is a function of the price, x, it charges per cup. If x is in dollars, the weekly profit is P(x) = -2900x^2 + 7250x - 2900 dollars.
a) Approximate the maximum profit and the price per cup that produces that profit.
b) Which function, P(x - 2) or P(x) - 2, gives a function that has the same maximum profit? What price per cup produces that maximum profit?
1 solutions
Answer 304931 by stanbon(57299) on 2011-04-28 15:44:09 (Show Source):
You can put this solution on YOUR website!Hello! I need some help trying to solve parts a and b. I've already used the quadratic formula to find the two zeros (.5 and 2) but I am having trouble moving forward. Thank you so much!!
An espresso stand finds that its weekly profit is a function of the price, x, it charges per cup. If x is in dollars, the weekly profit is P(x) = -2900x^2 + 7250x - 2900 dollars.
--
Note that value is the average of 0.5 and 2: (0.5+2)/2 = 1.25
--------------------------------------------------------------------
a) Approximate the maximum profit and the price per cup that produces that profit.
Maximum for a quadratic always where x = -b/2a = -7250/(2(-2900)) = $1.25
Then max profit = f(1.25) = $1631.30
---------------------------------
b) Which function, P(x - 2) or P(x) - 2, gives a function that has the same maximum profit? What price per cup produces that maximum profit?
---
P(x-2) moves all point 2 to the right and changes the price to x = $3.25.
=====================
Cheers,
Stan H.
|
Polygons/442003: a pyramid wit a volum of 44 1/3cm has a height of 19cm what is the area of the base
1 solutions
Answer 304928 by stanbon(57299) on 2011-04-28 15:23:17 (Show Source):
You can put this solution on YOUR website!a pyramid with a volume of 44 1/3cm has a height of 19cm what is the area of the base
----
Volume = (1/3)(base area)(height)
(133/3) = (1/3)(base area)(19)
---
133 = 19*base area
---
base area = 7 sq cm
========================
Cheers,
Stan H.
|
Travel_Word_Problems/441992: leave home at 4pm on sunday return 36 hours later what day and time would it be email gwengraham@juno.com
1 solutions
Answer 304927 by stanbon(57299) on 2011-04-28 15:18:46 (Show Source):
You can put this solution on YOUR website!leave home at 4pm on sunday
return 36 hours later
what day and time would it be
----
36 hrs = 24 hr + 12 hr
= 1 day + 12 hr
---
4pm sunday + 36 hrs gets you to monday 4pm + 12 hr
---------
= 4am on Tuesday.
====================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/441996: Rationalize the denominator. Assume that all expressions under radicals represent positive numbers: 2 - sqrt(a)/4 + sqrt(a)
1 solutions
Answer 304924 by stanbon(57299) on 2011-04-28 15:09:48 (Show Source):
You can put this solution on YOUR website!Rationalize the denominator. Assume that all expressions under radicals represent positive numbers: (2 - sqrt(a))/(4 + sqrt(a))
-------------------
Multiply numerator and denominator by 4-sqrt(a)
---------------------
=[(2-sqrt(a))(4-sqrt(a))]/[16-a]
-----
= [8 - 6 sqrt(a) + a]/[16-a]
-----
= [(8+a)-6sqrt(a)]/[16-a]
==============================
Cheers,
Stan H.
===========
|
Expressions-with-variables/441982: A manufactor determines that the profit in dollars for manufactoring n units is P=2n^2-10n-175 (Assume that n is a positive integer). How many units are produced when the profit is $425?
1 solutions
Answer 304921 by stanbon(57299) on 2011-04-28 15:05:20 (Show Source):
You can put this solution on YOUR website!A manufactor determines that the profit in dollars for manufactoring n units is P=2n^2-10n-175 (Assume that n is a positive integer). How many units are produced when the profit is $425?
---------------------
2n^2-10n-175 = 425
----
2n^2-10n-600 = 0
---
n^2-5n-300 = 0
----
(n-20)(n+15) = 0
---
Positive solution:
n = 20 units
================
Cheers,
Stan H.
|
Geometry_Word_Problems/441989: A man stands at the top of a 105 foot light house and sees a boat. The angle of depression to sight the boat is 37degrees, find the distance between the base of the light house and the boat.
1 solutions
Answer 304916 by stanbon(57299) on 2011-04-28 14:56:26 (Show Source):
You can put this solution on YOUR website!A man stands at the top of a 105 foot light house and sees a boat. The angle of depression to sight the boat is 37degrees, find the distance between the base of the light house and the boat.
----------------------
Draw the picture.
You have a right angle with height = 105 ft. and angle
opposite = 37 degrees.
---
tan(37) = height/dist
dist = height/tan(37)
dist = 105/0.7536
dist = 139.34 ft.
======================
Cheers,
Stan H.
|
Angles/441970: What is the measure of the reference angle Q=-260degrees
1 solutions
Answer 304910 by stanbon(57299) on 2011-04-28 14:46:28 (Show Source):
You can put this solution on YOUR website!What is the measure of the reference angle Q=-260degrees
------------------------
Draw the given angle.
Draw a vertical line from a point on the terminal side
of the angle to the x-axis.
The size of the acute angle at the base of the
resulting right angle is the measure of the reference
angle.
Ans: 80 degrees
---------------------
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/441884: Solve the following system of equations and state answer in coordinate pairs?x=2y and x^(2)+y^(2)=(5)/(16)
answers...(1/2,1/4)(-1/2,-1/4),(1/2,1/4)(-1/2,1/4), no solution
1 solutions
Answer 304903 by stanbon(57299) on 2011-04-28 14:28:13 (Show Source):
You can put this solution on YOUR website!Solve the following system of equations and state answer in coordinate pairs?x=2y and x^(2)+y^(2)=(5)/(16)
----
substitute for "x and solve for "y":
(2y)^2 + y^2 = (5/16)
---
5y^2 = 5/16
----
y^2 = 1/16
y = +(1/4) or y = -1/4
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Solve for "x":
x = 2y
If y = 1/4, x = 1/2; If y = -1/4, x = -1/2
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cheers,
Stan H.
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answers...(1/2,1/4)(-1/2,-1/4),(1/2,1/4)(-1/2,1/4), no solution
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Numbers_Word_Problems/441949: a coffee company wants a new favor of Cajun coffee. How many pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound.
1 solutions
Answer 304899 by stanbon(57299) on 2011-04-28 13:46:57 (Show Source):
You can put this solution on YOUR website!a coffee company wants a new favor of Cajun coffee. How many pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound.
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Value Equation: 10x + 4*30 = 5(x+30)
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10x + 4*30 = 5x + 5*30
5x = 30
x = 6 lbs. (amt of $10 coffee needed)
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Cheers,
Stan H.
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Probability-and-statistics/441876: In a multiple-choice test, each question has four options. students will get 4 points for each correct answer; lose 1 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer? Show your calculations for expected value. Show your work for full credit.
Please help!!!!!!!!!!!!!!!! I am lost, you guys are the best here and I have learned a lot but stuck on this one.
1 solutions
Answer 304897 by stanbon(57299) on 2011-04-28 13:42:39 (Show Source):
You can put this solution on YOUR website!In a multiple-choice test, each question has four options. students will get 4 points for each correct answer; lose 1 point for each incorrect answer; and receive no points for unanswered questions.
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A student does not know the correct answer for one question. Is it to her advantage or disadvantage to guess an answer? Show your calculations for expected value. Show your work for full credit.
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E(x) = 4(1/4) + (-1)(3/4) + 0(0) = 1-(3/4) = 1/4 point.
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The student should guess.
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Cheers,
Stan H.
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Functions/441943: the problem is (5x²y^3)²=
do i write it out twice like this
(5x²y^3) (5x²y^3) do i then foil that?
1 solutions
Answer 304895 by stanbon(57299) on 2011-04-28 13:35:32 (Show Source):
You can put this solution on YOUR website!the problem is (5x²y^3)²=
do i write it out twice like this
(5x²y^3) (5x²y^3) do i then foil that?
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Yes to the 1st question.
No to the 2nd. You only FOIL when you have binomials
to multiply.
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Your Problem:
= 25x^4y^6
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Cheers,
Stan H.
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Unit_Conversion_Word_Problems/441941: Here i my word problem......please help!
the amout of radioactive substance present, in grams, at time t i months is gven by the formula y=6000(2)^-0.3t. Find the numer of grams present in 3 years. If necessary, round to 3 decimal places.
1 solutions
Answer 304893 by stanbon(57299) on 2011-04-28 13:29:50 (Show Source):
You can put this solution on YOUR website!the amount of radioactive substance present, in grams, at time t months is gven by the formula y=6000(2)^-0.3t. Find the number of grams present in 3 years. If necessary, round to 3 decimal places.
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y=6000(2)^-0.3t
f(36) = 6000*2^(-0.3*36)
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f(36) = 6000*2^(-10.8) =
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f(36) = 3.3653 grams
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Cheers,
Stan H.
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Probability-and-statistics/441923: In a sample of 60 mice, a biologist found that 46% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run that maze in 30 seconds or less?
1 solutions
Answer 304891 by stanbon(57299) on 2011-04-28 13:24:49 (Show Source):
You can put this solution on YOUR website!In a sample of 60 mice, a biologist found that 46% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run that maze in 30 seconds or less?
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I assume you want a 90% Confidence Interval.
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p-hat = 0.46
ME = 1.645*sqrt[0.46*0.54/60] = 0.1058
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90% CI: 0.46-0.1058 < p < 0.46+0.1058
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Cheers,
Stan H.
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Probability-and-statistics/441910: given the amount (oz) of juice in 10 randomly selected juice bottles are:
15.1, 15.6, 15.6, 15.9, 15.2, 15.9, 15.2,15.1, 15.8, 15.2.
construct a 94% confidence interval for the mean amount of the juice, u(with a wierd line), in the population of all such bottles. assume that the population has a normal distribution.
1 solutions
Answer 304890 by stanbon(57299) on 2011-04-28 13:23:40 (Show Source):
You can put this solution on YOUR website!In a sample of 60 mice, a biologist found that 46% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run that maze in 30 seconds or less?
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p-hat = 0.46
ME = 1.645*sqrt[0.46*0.54/60] = 0.1058
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90% CI: 0.46-0.1058 < p < 0.46+0.1058
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Cheers,
Stan H.
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Probability-and-statistics/441929: A study of 60 bolts of carpet showed that their average length was 150 yards. The standard deviation of the population is 10 yards. Which of the foloowing is the 99% confidence interval for the mean length per bolt of carpet?
(Please write out so I can learn how to answer this problem.) Thanks!
1 solutions
Answer 304887 by stanbon(57299) on 2011-04-28 13:18:07 (Show Source):
You can put this solution on YOUR website!A study of 60 bolts of carpet showed that their average length was 150 yards. The standard deviation of the population is 10 yards. Which of the following is the 99% confidence interval for the mean length per bolt of carpet?
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x-bar = 150
ME = 2.5758*10/sqrt(60) = 3.3254
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99% CI: 150-3.3254 < u < 150+3.3254
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Cheers,
Stan H.
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Probability-and-statistics/441918: A report states that 44% of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4 percentage with 92% confidence?
(Please help!! I need to see how to solve this answer. Thanks.)
1 solutions
Answer 304886 by stanbon(57299) on 2011-04-28 13:13:45 (Show Source):
You can put this solution on YOUR website!A report states that 44% of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4 percentage with 92% confidence?
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Since E = z*sqrt(pq/n)
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n = [z/E}^2*(pq)
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n = [1.7507/0.04]^2(0.44*0.56)
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n = 472 when rounded up
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Cheers,
Stan H.
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Probability-and-statistics/441846: Please show me how to do these probability problems!
An airline estimates that with probability 0.05 a passenger who purchased a ticket won’t take the designated flight. Suppose for a certain flight the airplane can carry 100 passengers and the airline sold 102 tickets.
11. Find the probability that exactly 101 passengers show up to take the flight (4 digits after decimal point).
12. Find the probability that exactly 102 passengers show up to take the flight (4 digits after decimal point).
13. Find the probability that no more than 100 passengers show up to take the flight so the airline doesn’t have to compensate some people and ask them to leave the plane (4 digits after decimal point).
1 solutions
Answer 304864 by stanbon(57299) on 2011-04-28 10:34:18 (Show Source):
You can put this solution on YOUR website!An airline estimates that with probability 0.05 a passenger who purchased a ticket won’t take the designated flight. Suppose for a certain flight the airplane can carry 100 passengers and the airline sold 102 tickets.
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11. Find the probability that exactly 101 passengers show up to take the flight (4 digits after decimal point).
P(x = 101) = 0.95^101 = 0.0056
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12. Find the probability that exactly 102 passengers show up to take the flight (4 digits after decimal point).
P(x = 102) = 0.95^102 = 0.0053
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13. Find the probability that no more than 100 passengers show up to take the flight so the airline doesn’t have to compensate some people and ask them to leave the plane (4 digits after decimal point).
P(0<= x <= 100) = binomcdf(102,0.95,100) = 0.9660
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Cheers,
Stan H.
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