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Recent problems solved by 'stanbon'
stanbon answered: 57182 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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209, >>NextProportions/549935: Word problem:
Mrs. Carter owns a shop specializing in tea. She combines 1 lb. Darjeeling with 3 lbs. Earl Grey to get a 4lb mixture of 25% Darjeeling. SHe chooses to change the mixture to 50% Darjeeling. How much Darjeeling should she add to bring the mixture to 50%?
I do not understand how to set this up.
1 solutions
Answer 358204 by stanbon(57250)   on 2011-12-22 21:54:26 (Show Source):
You can put this solution on YOUR website!Mrs. Carter owns a shop specializing in tea.
She combines 1 lb. Darjeeling with 3 lbs. Earl Grey to get a 4lb mixture of 25% Darjeeling.
SHe chooses to change the mixture to 50% Darjeeling. How much Darjeeling should she add to bring the mixture to 50%?
------
Equation:
Dar + Dar = Dar
0.25*4 + x = 0.50(4+x)
Multiply thru by 100 to get:
25*4 + 100x = 50*4 + 50x
50x = 25*4
x = 2 lb (amt. of Darjeeling she must add)
==============================================
Cheers,
Stan H.
================
|
Miscellaneous_Word_Problems/549906: Write an equation that can be used to solve the problem. Solve the equation and answer the question. Naomi Ericson and Ricky Mendoza work for a computer software company. Together they can write a particular computer program in 17 hours. Naomi can write the program by herself in 13.04 hours. How long will it take Ricky to write the program alone?
I have no idea how to do this one.
1 solutions
Answer 358203 by stanbon(57250) on 2011-12-22 21:49:17 (Show Source):
You can put this solution on YOUR website!Naomi Ericson and Ricky Mendoza work for a computer software company. Together they can write a particular computer program in 17 hours. Naomi can write the program by herself in 13.04 hours. How long will it take Ricky to write the program alone?
-----
Comment:
If Naomi can do it in 13.04 hours alone why do they require
15 hrs to do it when they both work at it?
=================
Cheers,
Stan H.
|
Equations/549933: Seven inches are equivalent to 17.78 cm. Find the equation converting length in cm to length in inches. What is the length in inches of a 96.2 cm bar?
1 solutions
Answer 358201 by stanbon(57250) on 2011-12-22 21:40:39 (Show Source):
You can put this solution on YOUR website!Seven inches are equivalent to 17.78 cm. Find the equation converting length in cm to length in inches. What is the length in inches of a 96.2 cm bar?
------
(96.2 cm)(7/17.78)(in/cm)
-----
= (96.2*7)/(17.78) in
-----
= 37.98 inches
=========================
Cheers,
Stan H.
============
|
Linear_Algebra/549930: when Marvin was 2 km. upstream from where he started his canoe trip, he passed a log floating with the current. After paddling upstream for one more hour, he paddled back and reached his starting point just as the log arrived.
How fast was the current flowing?
1 solutions
Answer 358199 by stanbon(57250) on 2011-12-22 21:28:18 (Show Source):
You can put this solution on YOUR website!when Marvin was 2 km. upstream from where he started his canoe trip, he passed a log floating with the current. After paddling upstream for one more hour, he paddled back and reached his starting point just as the log arrived.
How fast was the current flowing?
-------
Draw the picture:
Upstream DATA:
time = 1Downstream DATA:
distance = p-c+2 km ; rate = p+c km/h ; time = (p-c+2)/(p+c) hrs
---------
Log DATA:
rate = c km/h ; distance 2 km ; time = d/r = 2/c hrs
--------------------------------------------------------
Equation:
time up + time down = 2/c hrs
1 hr + (p-c+2)/(p+c) hr = 2/c hr
-----
Multiplthru by c(p+c) to get:
c(p+c) + c(p-c+2) = 2(p+c)
-----
cp + c^2 + cp-c^2+2c = 2p+2c
----
2cp = 2p
cp = p
current speed is 1 km/hr
=============================
Cheers,
Stan H.
=================
|
Age_Word_Problems/549915: This christmas, your brother Jeff will be 2 years from being twice as old as his siter Megan. The sum of Jeff's age and 3 times Megan's age is 66. How old is Megan?
1 solutions
Answer 358198 by stanbon(57250) on 2011-12-22 21:15:47 (Show Source):
You can put this solution on YOUR website! This christmas, your brother Jeff will be 2 years from being twice as old as his siter Megan. The sum of Jeff's age and 3 times Megan's age is 66. How old is Megan?
-----------------
j = 2m-2
j + 3m = 66
----
Substitute for "j" and solve for "m":
2m-2 +3m = 66
5m = 68
m = 13 3/5 years Megan's age now)
-----------------
Solve for "j":
j = 2m-2
j = 2(68/5)-(10/5)
j = 126/6 = 25 1/6 years (Jeff's age now)
======================
Cheers,
Stan H.
======================
|
Exponential-and-logarithmic-functions/549870: How do I make the equation y=ab^x with two points, (5,4) and (7,9)?
1 solutions
Answer 358154 by stanbon(57250) on 2011-12-22 16:46:49 (Show Source):
You can put this solution on YOUR website!How do I make the equation y=ab^x with two points,
(5,4) and (7,9)?
--------------------
Solve for a and b:
Using (7,9) you get 9 = ab^7
---
Using (5,4) you get 4 = ab^5
--------------------------------
Divide the lower into the higher equation:
(9/4) = b^2
b = 3/2
------------------------
Substitute for "b" and solve for "a":
9 = ab^7
9 = a(3/2)^7
---
a = 9/(3/2)^7 = 0.5267
------------------------------
Equation:
y = (0.5267)(3/2)^x
=========================
Cheers,
Stan H.
=========================
|
Equations/549876: Please help me : Find the standard form of the equation of the line that passes through point (1,-4) and is parallel to the line 4x-y=2
1 solutions
Answer 358150 by stanbon(57250) on 2011-12-22 16:34:35 (Show Source):
You can put this solution on YOUR website!Please help me : Find the standard form of the equation of the line that passes through point (1,-4) and is parallel to the line 4x-y=2
---
Solve for "y" to find the slope of the given line:
y = 4x-2
slope = 4
----------------
Form:
y = mx + b
-4 = 4*1+b
b = -8
------------
Equation:
y = 4x-8
----------------------
Cheers,
Stan H.
=============
|
Equations/549873: Write the slope-intercept form of the equation of the line passing through point (-4,0) and parallel to the line y=3x+2
a. y=3x+12 b. y=-3x+4 c. y=-3x-12 d. y=3x-4
1 solutions
Answer 358149 by stanbon(57250) on 2011-12-22 16:30:29 (Show Source):
You can put this solution on YOUR website!Write the slope-intercept form of the equation of the line passing through point (-4,0) and parallel to the line y=3x+2
-------
slope = 3
Form: y = mx + b
0 = 3*(-4) + b
b = 12
-----
Equation:
y = 3x +12
=====================
Cheers,
Stan H.
=====================
a. y=3x+12 b. y=-3x+4 c. y=-3x-12 d. y=3x-4
|
Quadratic_Equations/549834: Express f(x)=4x^2-12x+5 in factored form and determine the x intercepts, the vertex and sketch the graph of the function
1 solutions
Answer 358136 by stanbon(57250) on 2011-12-22 14:54:39 (Show Source):
You can put this solution on YOUR website!Express f(x)=4x^2-12x+5 in factored form and determine the x intercepts, the vertex and sketch the graph of the function
-------------------
Factor: 4x^2-12x+5
---
= 4x^2-10x-2x+5
---
= 2x(2x-5)-(2x-5)
----
f(x) = (2x-5)(2x-1)
=========================
x-intercepts: x = 5/2 ; x = 1/2
---
Vertex:::
x = -b/2a = 12/8 = 3/2
f(3/2) = 4(3/2)^2-12(3/2)+5 = 4(9/4)-18+5 = -4
Vertex: ((3/2),-4)
------------------------
Graph:
-----------------
Cheers,
Stan H.
=================
|
Angles/549850: Please help me Find the complimentary angle of the given angle 31 next to 2degrees over 5.
Thank you.
1 solutions
Answer 358134 by stanbon(57250) on 2011-12-22 14:48:23 (Show Source):
You can put this solution on YOUR website!Find the complimentary angle of the given angle 31 next to 2degrees over 5.
--------------------
Ans: 90 - 31 2/5 degrees = 58 3/5 degrees
============================================
Cheers,
Stan H.
|
Graphs/549849: using the graphing method how do you do y=3, x+y=5 Please help me and how to do it. Thank You.
1 solutions
Answer 358132 by stanbon(57250) on 2011-12-22 14:46:03 (Show Source):
You can put this solution on YOUR website!using the graphing method how do you do y=3, x+y=5 Please help me and how to do it.
-----
Graph y = 3 as a horizontal line passing thru all points where y = 3.
---
Solve x + y = 5 for "y":
y = -x+5
Plot two points:
(0,5) and (5,0)
Draw a line thru them.
--------------
Solution:
Find the point where y =3 meets y = -x+5
Answer: (2,3)
--------------------
Graph:
================
Cheers,
Stan H.
================
|
Exponential-and-logarithmic-functions/549847: You invest $800 in an account with an annual interest rate of 3.2%, compounded annually. How much in in the account after 15 years? Round your answer to the nearest whole number
1 solutions
Answer 358130 by stanbon(57250) on 2011-12-22 14:41:50 (Show Source):
You can put this solution on YOUR website!You invest $800 in an account with an annual interest rate of 3.2%, compounded annually. How much in in the account after 15 years? Round your answer to the nearest whole number
----
A(t) = Ao(1+(r/n))^(nt)
Ao = 800
n = 1
r = 0.032
t = 15
------
A(15) = 800(1.032)^(15)
A(15) = $1283
====================
Cheers,
Stan H.
=================
|
test/549839: Use binomial theorem to expand (x+5)^21 Plc show all work
1 solutions
Answer 358124 by stanbon(57250) on 2011-12-22 14:38:18 (Show Source):
You can put this solution on YOUR website!Use binomial theorem to expand (x+5)^21
-------
21C21*x^21*5^0 + 21C20*x^^20*5 + 21C19*x^19*5^2 etc...+21C0*x^0*5^21
--------------------------------------------------------------
Cheers,
Stan H.
|
test/549823: The length of a drawing of a tool is 3/8 of the length of the actual tool. If the length of the drawing of the tool is 6 inches, what is the length, in inches, of the actual tool?
a. 2 1/4
b. 8 1/4
c. 26
d. 18 1/4
e. 22
1 solutions
Answer 358102 by stanbon(57250) on 2011-12-22 13:25:49 (Show Source):
You can put this solution on YOUR website!The length of a drawing of a tool is 3/8 of the length of the actual tool. If the length of the drawing of the tool is 6 inches, what is the length, in inches, of the actual tool?
-----
drawing length = (3/8)(tool length)
----
6" = (3/8)(tool length)
---
tool length = (8/3)6 = 16 inches
======================
Cheers,
Stan H.
=============
|
Graphs/549802: Sorry, I pressed the wrong button before...
I am lost can someone help with this;
Given the restraints x + y <=5
y >= x
x >=0
and the objective Function C = x + y, find the maximum value?
1 solutions
Answer 358096 by stanbon(57250) on 2011-12-22 13:08:17 (Show Source):
You can put this solution on YOUR website!Given the restraints x + y <=5
y >= x
x >=0
and the objective Function C = x + y, find the maximum value?
----
Graph the line y = x
Shade the area above the line
----
Graph the line y = -x+5
Shade the area below the line
---
Shade the area to the right of x = 0 that is above y = x
and below y = -x+5.
---
Find the coordinates of the three vertices of the resulting
triangle: (0,0) ; (0,5), (2.5 , 2.5)
---
Evaluate C = x + y for each of those number pairs:
(0,0): C = 0
(0,5): C = 5
(2.5 2.5) C = 5
------------------------
Max for (0,5) and for (2.5 , 2.5)
====================================
Cheers,
Stan H.
===============
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Probability-and-statistics/549814: In your own line of work, give one example of a discrete
and one example of a continuous random variable, and describe why each is continuous or discrete. (Points : 4)
1 solutions
Answer 358093 by stanbon(57250) on 2011-12-22 13:00:51 (Show Source):
You can put this solution on YOUR website!In your own line of work, give one example of a discrete
and one example of a continuous random variable, and describe why each is continuous or discrete. (Points : 4)
----
discrete: the number of files in the 2nd drawer of your file case.
----
continuous: the time between your morning meeting and you 3rd cup
of coffee for the day.
---------
Cheers,
Stan H.
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Permutations/549805: In a shipment of 100 laptops, 6 are defective. If a person buys two laptops from that shipment, what is the probability that they are defective?
1 solutions
Answer 358090 by stanbon(57250) on 2011-12-22 12:57:52 (Show Source):
You can put this solution on YOUR website!In a shipment of 100 laptops, 6 are defective. If a person buys two laptops from that shipment, what is the probability that they are defective?
-----------------
P(2 defective) = 6C2/100C2 = 15/4900 = 0.0031
===============================
Cheers,
Stan H.
================================
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Polynomials-and-rational-expressions/549786: Show all work. A gardener wants to create a rectangular garden with length of 8x - 4y ft. and width of 6x - 6y ft. What is an algebraic expression for the area of the garden? Be sure to multiply this out, express in simplest correct mathematical form, and include units.
1 solutions
Answer 358087 by stanbon(57250) on 2011-12-22 12:53:24 (Show Source):
You can put this solution on YOUR website!Show all work. A gardener wants to create a rectangular garden with length of 8x - 4y ft. and width of 6x - 6y ft. What is an algebraic expression for the area of the garden? Be sure to multiply this out, express in simplest correct mathematical form, and include units.
---------------------------
8x-4y = 4(2x-y)
6x-6y = 6(x-y)
---------------------
Area = 24[2x^2-3xy+y^2
---
Area = (48x^2-72xy+24y^2) sq. ft.
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Probability-and-statistics/549642: List all the possible ways that the word GREAT could be arranged. How many possibilities did you find? Work out this same problem using the formula for permutations that you learned in this lesson. Did you miss any in your original count? Explain why the formula of permutations is helpful for most problems.
1 solutions
Answer 358041 by stanbon(57250) on 2011-12-22 11:04:17 (Show Source):
You can put this solution on YOUR website!List all the possible ways that the word GREAT could be arranged.
Ans: there are 5! = 120 ways
----------------------
How many possibilities did you find? Work out this same problem using the formula for permutations that you learned in this lesson. Did you miss any in your original count? Explain why the formula of permutations is helpful for most problems.
-----------------------
Cheers,
Stan H.
==================
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Probability-and-statistics/549771: in a certain department 40% of the students have internet facility 25% have printing facility and 15% have internet and printing facility student is selected at random from this department (i)if he has internet what is the probabilty that he also has printing facility ?
(ii) if he has printing facility what is the probabilty that he also has internet ?
1 solutions
Answer 358039 by stanbon(57250) on 2011-12-22 11:01:57 (Show Source):
You can put this solution on YOUR website!in a certain department 40% of the students have internet facility
25% have printing facility and
15% have internet and printing facility
-------------
A student is selected at random from this department
(i)if he has internet what is the probabilty that he also has printing facility ?
P(p | i) = P(p AND i)/P(i) = 0.15/0.4 = 0.375
---------------------------------
(ii) if he has printing facility what is the probabilty that he also has internet ?
P(i | p) = P(p AND i)/P(p) = 0.15/0.25 = 0.6
===================
Cheers,
Stan H.
===============
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Radicals/549764: I am having trouble can you help
Find a polynomial of degree 3 with roots 5, -2+4i
Find a polynomial of degree 4 with roots 3-2i, 2+i
thanks so much for your help
1 solutions
Answer 358033 by stanbon(57250) on 2011-12-22 10:30:22 (Show Source):
You can put this solution on YOUR website!Find a polynomial of degree 3 with Real Number coefficients and
with roots 5, -2+4i
-----
f(x) = (x-5)(x-(-2+4i))(x-(-2-4i))
---
f(x) = (x-5)((x+2)-4i)((x+2)+4i)
---
f(x) = (x-5)((x+2)^2+16)
---
f(x) = (x-5)(x^2+4x+20)
===============================
Find a polynomial of degree 4 with Real Number coefficients and
with roots 3-2i, 2+i
---
f(x) = (x-(3-2i))(x-(3+2i))(x-(2+i))(x-(2-i))
---
f(x) = ((x-3)^2+4)((x-2)^2+1)
===================================
Cheers,
Stan H.
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Probability-and-statistics/549661: a score that is 6 points below the mean corresponds to a z score of z= -0.50. what is the population standard deviation?
1 solutions
Answer 358028 by stanbon(57250) on 2011-12-22 10:22:51 (Show Source):
You can put this solution on YOUR website!a score that is 6 points below the mean corresponds to a z score of z= -0.50. what is the population standard deviation?
----
z = (distance from mean)/(standard deviation)
-----
-0.5 = -6/s
s = -6/-0.5
-----
s = 12
===========
Cheers,
Stan H.
============
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Probability-and-statistics/549662: for a sample with a mean of m=45, a score of x=59 corresponds to z= 2.00. what is the sample of standard deviation?
1 solutions
Answer 358027 by stanbon(57250) on 2011-12-22 10:20:02 (Show Source):
You can put this solution on YOUR website!for a sample with a mean of m=45, a score of x=59 corresponds to z= 2.00. what is the sample standard deviation?
------------------
Use z(x) = (x-m)/s and solve for "s":
----
2 = (59-45)/s
---
s = 14/2
---
s = 7
===============
Cheers,
Stan H.
|
Probability-and-statistics/549666: for each of the following, identify the exam score that should lead to the better grade. in each case, explain your answer.
a. a score of x=56, on a exam with u=50 and 0= 4, or a score of x=60 on an exam with u =50 and o =20.
b. a score of x =40 on a exam with u=45 and 0=2, or a score of x=60 on a exam with u=70 and o=20.
c. a score of x=62, on an exam with u=50 and o=8 or a score of x=23 on an exam with u=20 and o=2.
1 solutions
Answer 358026 by stanbon(57250) on 2011-12-22 10:17:13 (Show Source):
You can put this solution on YOUR website!for each of the following, identify the exam score that should lead to the better grade. in each case, explain your answer.
a. a score of x=56, on a exam with u=50 and 0= 4, or a score of x=60 on an exam with u =50 and o =20.
b. a score of x =40 on a exam with u=45 and 0=2, or a score of x=60 on a exam with u=70 and o=20.
c. a score of x=62, on an exam with u=50 and o=8 or a score of x=23 on an exam with u=20 and o=2.
----
For each of these, find the z-score using z(x)=(x-u)/sigma.
Then compare the z-scores to determine the highest grade.
--------------------------------------------
Cheers,
Stan H.
===========
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Probability-and-statistics/549668: for a population with u=50 and o=8,
find the z-score for each of the following x values. ( note: u should be able to find these values using the definition of a z score. u should not need to use a formula or do any serious calculations).
x=54
x=42
x=62
x=48
x=52
x=34
1 solutions
Answer 358025 by stanbon(57250) on 2011-12-22 10:13:42 (Show Source):
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Probability-and-statistics/549669: a sample has a mean of m=40 and a standard deviation of s=6. find the z-score for each of the following x values from this sample.
x=44
x=28
x=42
x=50
x=46
x=37
1 solutions
Answer 358024 by stanbon(57250) on 2011-12-22 10:10:10 (Show Source):
You can put this solution on YOUR website!a sample has a mean of m=40 and a standard deviation of s=6. find the z-score for each of the following x values from this sample.
Use the following formula to find each z-value.
z(x) = (x-m)/s
===================
Cheers,
Stan H.
===================
x=44
x=28
x=42
x=50
x=46
x=37
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