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Recent problems solved by 'stanbon'
stanbon answered: 57146 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, >>Next
Mixture_Word_Problems/445544: Find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 30 quarts of 5% butter milk
1 solutions
Answer 306909 by stanbon(57214)   on 2011-05-05 14:21:01 (Show Source):
You can put this solution on YOUR website!Find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 30 quarts of 5% butter milk
-----
Equation:
fat + fat = fat
0.06x + 0.03(30-x) = 0.05*30
----
Multiply thru by 100.
----
6x + 3*30 - 3x = 5*30
---
3x = 2*30
---
x = 20 quarts (amt. of 6% butterfat milk needed)
=====================
Cheers,
Stan H.
=====================
|
expressions/445529: 2y/x+((2x-y)/y)
1 solutions
Answer 306902 by stanbon(57214) on 2011-05-05 14:05:38 (Show Source):
You can put this solution on YOUR website![2y/x]+((2x-y)/y)
---------
lcm = xy
----
Rewrite each fraction with the lcm as its denominator:
[(2y^2/lcm] + [(2x^2-xy)/lcm]
---------------
Combine the numerators over the lcm:
---------------
= [2y^2-xy+2x^2]/xy
----
Cheers,
Stan H.
========
|
Unit_Conversion_Word_Problems/445532: The length of a rectangle is 5 more than its width. If perimeter is 58ft, what are length and width?
1 solutions
Answer 306895 by stanbon(57214) on 2011-05-05 13:54:05 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is 5 more than its width.
If perimeter is 58ft, what are length and width?
-------------------
Let width be "W".
Then length = "W+5".
-------
Perimeter = 2(width + length)
58 = 2(W + W+5)
29 = 2W+5
2W = 24
W = 12 ft (width)
---
length = W+5 = 17 ft
========================
Cheers,
Stan H.
|
Money_Word_Problems/445530: If $3000 is deposited in a bank account paying 4% compounded monthly, what amount will be in the account after 4 years? How much interest will be earned during the 4 years?
The amount after 4 years will be $________.
1 solutions
Answer 306892 by stanbon(57214) on 2011-05-05 13:47:32 (Show Source):
You can put this solution on YOUR website!If $3000 is deposited in a bank account paying 4% compounded monthly, what amount will be in the account after 4 years? How much interest will be earned during the 4 years?
-----------
A(t) = P(1+(r/n))^(nt)
------
A(4) = 3000(1+(0.04/12))^(12*4)
------
A(4) = 3000(1.1732)
---
A(4) = $3519.60
-------------------------
Amount of interest = $519.60
-------------------------
=================
Cheers,
Stan H.
===================
|
Probability-and-statistics/445516: A safety light is designed so that the times between flashes are normally distributed with a mean of 4.00 seconds and a standard deviation of .50 seconds.
a. Find the probability that an individual time is greater than 4.50 seconds
b. Find the probability that the mean for 50 randomly selected times is greater than 4.50 seconds
c. Is part a or b more significant (being light) due to the importance of a sample OR SINGLE strobe?
1 solutions
Answer 306883 by stanbon(57214) on 2011-05-05 12:36:17 (Show Source):
You can put this solution on YOUR website!A safety light is designed so that the times between flashes are normally distributed with a mean of 4.00 seconds and a standard deviation of .50 seconds.
a. Find the probability that an individual time is greater than 4.50 seconds
----
z(4.5) = (4.5-4)/0.5 = 1
P(x >4.5) = P(z > 1) = 0.1587
-------------------------------------
b. Find the probability that the mean for 50 randomly selected times is greater than 4.50 seconds
z(4.5) = (4.5-4)/[0.5/sqrt(50)} = 7.0711
P(x > 4.5) = P(z > 7.0711) = 7.737x10^-13
-------------------------------------
c. Is part a or b more significant (being light) due to the importance of a sample OR SINGLE strobe?
I don't understand that question.
===========================
Cheers,
Stan H.
|
Probability-and-statistics/445511: Given an experiment of drawing two cards from a standard deck of 52 where the first card is not replaced before the second card is drawn:
1 solutions
Answer 306879 by stanbon(57214) on 2011-05-05 12:26:41 (Show Source):
You can put this solution on YOUR website! Given an experiment of drawing two cards from a standard deck of 52 where the first card is not replaced before the second card is drawn:
--------------------------
What is the question?
Cheers,
Stan H.
|
Probability-and-statistics/445317: Suppose the population of a country changes due to births, deaths, and immigration. The annual birth rate is 3.5 births per 1000 people, the death rate is 7.2 deaths per 1000 people, the immigration rate into the country is 9.3 per 1000, and the emigration rate out of the country is 4.6 per 1000. Find the net growth rate as a percentage.
1 solutions
Answer 306788 by stanbon(57214) on 2011-05-04 22:17:19 (Show Source):
You can put this solution on YOUR website!Suppose the population of a country changes due to births, deaths, and immigration.
--------------------------------
The annual birth rate is 3.5 births per 1000 people, the death rate is 7.2 deaths per 1000 people, the immigration rate into the country is 9.3 per 1000, and the emigration rate out of the country is 4.6 per 1000. Find the net growth rate as a percentage.
---
(3.5+7.2+9.3-4.6) = 15.4 births per 1000
============================================
Cheers,
Stan H.
|
Expressions-with-variables/445312: Select any two integers between -12 and +12 which will become solutions to a system of two equations.
Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution and equations should not be the same as those of other students or the textbook. There are infinite possibilities.
Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps.
I have never taken a math class higher than Pre-algebra, and that was 35 years ago. I am taking a course online and am having difficulty intrpreting the material.
1 solutions
Answer 306786 by stanbon(57214) on 2011-05-04 22:11:10 (Show Source):
You can put this solution on YOUR website!Select any two integers between -12 and +12 which will become solutions to a system of two equations.
Write two equations that have your two integers as solutions. Show how you built the equations using your integers.
----
Let x = 3
Let y = -2
-----
Form 2 equations in x and y:
----------------------------------
2x + y = 4
-x +2y = -7
-------------------
Solve the system:
Multiply the bottom equation by 2:
2x + y = 4
-2x +4y = -14
----------------------
Add the 2 equations and solve for "y":
5y = -10
y = -2
---
solve for "x":
2x+y = 4
2x - 2 = 4
2x = 6
x = 3
------------------
Solution: x= 3 ; y = -2
==============================
Cheers,
Stan H.
Your solution and equations should not be the same as those of other students or the textbook. There are infinite possibilities.
Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps.
|
Probability-and-statistics/445279: From a standard 52-card deck, how many 5-card poker hands can be dealt consisting of each of the following
five clubs
three kings and a pair
1 solutions
Answer 306776 by stanbon(57214) on 2011-05-04 21:41:57 (Show Source):
You can put this solution on YOUR website!From a standard 52-card deck, how many 5-card poker hands can be dealt consisting of each of the following
five clubs
Ans: 13C5 =
-----
three kings and a pair
Ans: 4C3*12*4C2 = 4*12*6 = 288
======================================
Cheers,
Stan H.
|
logarithm/445257: Solve the equation with a graphing calculator.Round to the nearest thousands.
log2(x+3)=2x+1
Use change of base formula
1 solutions
Answer 306774 by stanbon(57214) on 2011-05-04 21:31:03 (Show Source):
You can put this solution on YOUR website!Solve the equation with a graphing calculator.Round to the nearest thousands.
log2(x+3)=2x+1
Use change of base formula
----------------------
[log(x+3)/log(2)] = (2x+1)
------
Using your calculator:
Let the left side of the equation be Y1.
Let the right side of the equation be Y2
----
----
Find the intersection of the 2 graphs to find "x":
I get x = 0.378108
==============
Cheers,
Stan H.
|
logarithm/445242: what is log (11 to the 6th power times 12) to the second power
1 solutions
Answer 306766 by stanbon(57214) on 2011-05-04 20:56:42 (Show Source):
You can put this solution on YOUR website!what is log (11 to the 6th power times 12) to the second power
----
= log(11^6 *12)^2
----
= log(4.519337x10^14)
---
= 14log(10) + log(4.519337)
---
= 14.655075
================
Cheers,
Stan H.
===========
|
Functions/445223: Which of the following is the domain of the function G(F(x))?
F(x) = x + 6, G(y) =4/(square root)y
G(F(x)) =4/(square root)x+6
A. All numbers less than -6
B. All numbers less than or equal to -6
C. All numbers greater than -6
D. All numbers greater than or equal to -6
1 solutions
Answer 306761 by stanbon(57214) on 2011-05-04 20:36:03 (Show Source):
You can put this solution on YOUR website!Which of the following is the domain of the function G(F(x))?
F(x) = x + 6,
Domain of F is "all Real Numbers"
Its Range is also "all Real Numbers"
which are handed on to "G"
----
G(y) = 4/(square root(x)
----------------
G(F(x)) = G(x+6) = 4/sqrt(x+6)
------------
Note: x+6 must be >= 0
x must be >= -6
============================
Cheers,
Stan H.
===============================
A. All numbers less than -6
B. All numbers less than or equal to -6
C. All numbers greater than -6
D. All numbers greater than or equal to -6
|
Linear_Equations_And_Systems_Word_Problems/445218: The new parking lot has spaces for 450 cars. The ratio of spaces for full-sized cars to compact cars is 11 to 4. How many spaces are for full-sized cars? How many spaces are for compact cars?
1 solutions
Answer 306750 by stanbon(57214) on 2011-05-04 20:13:00 (Show Source):
You can put this solution on YOUR website!The new parking lot has spaces for 450 cars. The ratio of spaces for full-sized cars to compact cars is 11 to 4. How many spaces are for full-sized cars? How many spaces are for compact cars?
---------------------
11 to 4 is the same as 11x to 4x where 4x is the number of compact cars.
----
Equation:
11x + 4x = 450
15x = 450
x = 30
----
# of compact cars = 4x = 4*30 = 120
# of full-sized cars = 11x = 11*30 = 330
========================================
Cheers,
Stan H.
|
test/445214: If cos θ = 3/5 and θ terminates in the first quadrant, find the exact value of sin 2θ.
1 solutions
Answer 306746 by stanbon(57214) on 2011-05-04 20:04:13 (Show Source):
You can put this solution on YOUR website!If cos θ = 3/5 and θ terminates in the first quadrant,
---
Since cos = x/r, x = 3 and r = 5
Then y = sqrt(5^2-3^2) = sqrt(16) = 4
So sin(theta) = 4/5
-------------------------------------------
find the exact value of sin 2θ
----
sin(2*theta) = 2sin(theta)*cos(theta)
----
= 2*(4/5)(3/5) = 24/25
===========================
Cheers,
Stan H.
=============
|
Probability-and-statistics/445207: A pizzeria has 6 meat toppings and 9 vegetable toppings. In how many different ways can a pizza with 2 meat toppings and 3 vegetable toppings be ordered from this pizzeria?
1 solutions
Answer 306743 by stanbon(57214) on 2011-05-04 19:56:44 (Show Source):
You can put this solution on YOUR website!A pizzeria has 6 meat toppings and 9 vegetable toppings. In how many different ways can a pizza with 2 meat toppings and 3 vegetable toppings be ordered from this pizzeria?
----------------------------
# of different pizzas = (6C2)(9C3) = 15*84 = 1260
===============
Cheers,
Stan H.
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decimal-numbers/445155: How does one convert 400.05% and 4.0555% into immproper and mixed fractions?
Thank you for your help.
1 solutions
Answer 306726 by stanbon(57214) on 2011-05-04 18:56:28 (Show Source):
You can put this solution on YOUR website!How does one convert 400.05% and 4.0555% into immproper and mixed fractions?
Thank you for your help.
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400.05% = 400.05/100 = [40005/100]/100
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= 40005/10000
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= 4 5/10000
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= 4 1/2000
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4.0555% = 4.0555/100
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Multiply numerator and denominator by 10,000
= [40555/1,000,000]
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= 8111/200,000
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Cheers,
Stan H.
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logarithm/445150: logb*4 X^3Y^2/Z^4
1 solutions
Answer 306723 by stanbon(57214) on 2011-05-04 18:41:51 (Show Source):
You can put this solution on YOUR website!logb*4 X^3Y^2/Z^4
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= logb(x^3y^2)-logb(z^4)
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= logb(x^3)+logb(y^2)-logb(z^4)
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= 3logb(x) + 2logb(y) - 4logb(z)
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Cheers,
Stan H.
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Probability-and-statistics/445106: Suppose that the average grade for all people who take this course in statistics is 83 with a standard deviation of 3.5.
If your particular class has an average of 89, can you conclude that your class is better than average at the 90 percent confidence level?
Label and describe each step of the hypothesis testing procedure, and be sure to specify whether this is a one-tailed or two-tailed test.
But with the sample size of 30.
1 solutions
Answer 306721 by stanbon(57214) on 2011-05-04 18:36:16 (Show Source):
You can put this solution on YOUR website!Suppose that the average grade for all people who take this course in statistics is 83 with a standard deviation of 3.5.
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If your particular class has an average of 89, can you conclude that your class is better than average at the 90 percent confidence level?
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Label and describe each step of the hypothesis testing procedure, and be sure to specify whether this is a one-tailed or two-tailed test.
But with the sample size of 30.
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Ho: u <= 83
Ha: u > 83 (the question)
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This Ha implies the need for a right-tail test.
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If you conduct a Z-test:
Critical value = invNorm(0.9) = 1.2816
test stat: z(89) = (89-83)/[3.5/sqrt(30)] = 9.3900
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Conclusion: Since the test stat is in the reject interval,
reject Ho.
The test results support a positive answer to the question.
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Cheers,
Stan H.
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