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Recent problems solved by 'stanbon'
stanbon answered: 57178 problems
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54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>NextSurface-area/150722: WHAT HAPPENS TO THE AREA WHEN THE LENGTH OF A SIDE OF A SQUARE IS DOUBLED?..
WHAT HAPPENS TO THE AREA WHEN THE LENGTH OF A SIDE IS TRIPLED?..
1 solutions
Answer 110644 by stanbon(57246)   on 2008-08-04 07:10:20 (Show Source):
You can put this solution on YOUR website!WHAT HAPPENS TO THE AREA WHEN THE LENGTH OF A SIDE OF A SQUARE IS DOUBLED?..
Before change: Area = L*W
After change: Area = (2L)*W = 2(L*W)
So the area has doubled.
---------------------------
WHAT HAPPENS TO THE AREA WHEN THE LENGTH OF A SIDE IS TRIPLED?..
Before change : Area = L*W
After change: Area = (3L)*W = 3(L*W)
So the area is 3 times what it was originally
=======================
Cheers,
Stan H.
|
Mixture_Word_Problems/150721: A 100 KILOGRAM MIXTURE OF 0.69 KG. OF PINTO BEANS AND 0.89 KG. KIDNEY BEANS IS VALUED AT 81.00. HOW MANY KILOGRAMS OF EACH DOES IT CONTAIN?.
1 solutions
Answer 110643 by stanbon(57246) on 2008-08-04 07:07:23 (Show Source):
You can put this solution on YOUR website!A 100 KILOGRAM MIXTURE OF 0.69 KG. OF PINTO BEANS AND 0.89 KG. KIDNEY BEANS IS VALUED AT 81.00. HOW MANY KILOGRAMS OF EACH DOES IT CONTAIN?.
----------------
Quantity equation : p + k = 100
Value equation: 0.69p + 0.89k = 81
-------------------
solve by any method to get:
p = 40 and k = 60
======================
Cheers,
Stan H.
|
Rational-functions/150719: hi
i am studying for my final and i would like to know something. this is the task:
tamika invests $3000 in a 5-yr cd that pays 5.35% interest compounded monthly. how much will she have in the acc. at the end of the 5 yr period?
I used the formula A=P(1+r/n)nt
so I got A = 3000(1+0.535/12)60 (that is an exponent)
now, i first divided 0.535 by 12 and then +1 so I get 1.044583333... and i took that by 60 exponential. I get 13.69574101
on the answer sheet it is written like this:
A=3000(1+0.535/12)60
3000(1.305916985) = 3917.75
how do i get the 1.3059...etc? how do i calculate the braces with the 60 exponential part? what i did was calculating the braces first and then take it exponential 60.
1 solutions
Answer 110642 by stanbon(57246) on 2008-08-04 07:01:55 (Show Source):
You can put this solution on YOUR website!tamika invests $3000 in a 5-yr cd that pays 5.35% interest compounded monthly. how much will she have in the acc. at the end of the 5 yr period?
I used the formula A=P(1+r/n)nt
so I got A = 3000(1+0.535/12)60 (that is an exponent)
now, i first divided 0.535 by 12 and then +1 so I get 1.044583333... and i took that by 60 exponential. I get 13.69574101
on the answer sheet it is written like this:
A=3000(1+0.535/12)60
3000(1.305916985) = 3917.75
how do i get the 1.3059...etc? how do i calculate the braces with the 60 exponential part? what i did was calculating the braces first and then take it exponential 60.
----------------------
Your mistake is changing 5.35% to 0.535.
You should have 5.35% = 0.0535
----------------------
After that your procedure is correct.
----------------------
Cheers,
Stan H.
|
Equations/150714: Hello E-Tutors:)
Could someone lead me in the right direction with this college
system of equations and inequality problem? The text book shows
how to solve something similiar but it only displays an equation
with two variables. Whereas this problem contains three variables.
That throws me for a loop.
Problem: The students from algebra class go for coffee together
every day. On Monday, Jordan paid $5.45 for three cartons of milk,
four cups of coffee, and seven doughnuts. On Tuesday, Ryan paid $5.30
for four milks, two coffees, and eight doughnuts. On Wednesday, Zack
paid $5.15 for two milks, five coffees, and six doughnuts.
1. Set up a system of equations to model this scenario.
I think this is right, but have no idea how to solve three layers,
with 3 different variables.
m=milk
c=coffee
d=doughnut
3m + 4c + 7d = 5.45
4m + 2c + 8d = 5.30
2m + 5c + 6d = 5.15
2. Determine the cost of one carton milk, one coffee, and one doughnut
by solving they system.
3. If on Thursday, Taylor had to pay for five milks, two coffees, and nine
doughnuts how much did he spend?
Think, I can get this one if I learn how to solve the second question.
Thank you in advance for sharing your valuable skills with us,
mishap mathematicians. :0)
Grateful,
Jai
1 solutions
Answer 110641 by stanbon(57246) on 2008-08-04 06:54:40 (Show Source):
You can put this solution on YOUR website!3m + 4c + 7d = 5.45
4m + 2c + 8d = 5.30
2m + 5c + 6d = 5.15
-------------------------
subtract 3rd equation from 1st to get:
m - c + d = 0.30
4m + 2c + 8d = 5.30
2m + 5c + 6d = 5.15
-----------------------
subtract 4 times 1st from 2nd;
subtract 2 times 1st from 3rd:
m - c + d = 0.30
0 + 6c + 4d = 4.10
0 + 7c + 4d = 4.55
----------------------
interchange 2nd and 3rd to get:
m - c + d = 0.30
0 + 7c + 4d = 4.55
0 + 6c + 4d = 4.10
------------------------
subtract 3rd from 2nd to get:
m - c + d = 0.30
0 + c + 0 = 0.45
0 + 6c + 4d = 4.10
----------------------
At this point you can see that c = 0.45
-------------
Subtitute that into the 3rd equation to solve for "d":
6(0.45) + 4d = 4.10
2.7 + 4d = 4.10
4d = 1.40
d = 0.35
----------------
Substitute the values of c and d into the 1st equation to solve for "m":
m - 0.45 + 0.35 = 0.30
m - 0.10 = 0.30
m = 0.40
-----------------
one mild costs 40 cents
one coffee costs 45 cents
one doughnut costs 35 cents
============================
Cheers,
Stan H.
|
Quadratic_Equations/150656: How do you completly factor a^2 - 10ab + 3b^2, what's the answer?
1 solutions
Answer 110617 by stanbon(57246) on 2008-08-03 19:50:08 (Show Source):
You can put this solution on YOUR website!a^2 - 10ab + 3b^2
--------------------
Using the Quadratic formula you get:
a = [10b +- sqrt(100b^2 - 4*3b^2)]/2
a = [10b +- sqrt(88b^2)/2
a = [10b +- sqrt(22)b]
If these are the zeroes of the trinomial, then , by the factor Theorem,
the factors are:
-----------------------------
Factors:
(a - [10b + sqrt(22)b]) * (a - [10b - sqrt(22)b])
===========================
Cheers,
Stan H.
|
Square-cubic-other-roots/150678: sqrt3 sqrt3
----- - -----
sqrt6 -1 sqrt6 + 1
sqrt9x^2 = x + 6
I am having a hard time figuring these out. Can you help?(sqrt means square root)
1 solutions
Answer 110615 by stanbon(57246) on 2008-08-03 19:30:13 (Show Source):
You can put this solution on YOUR website!sqrt3 sqrt3
----- - -----
sqrt6 -1 sqrt6 + 1
------------------------
To subtract fractions you need to have a common denominator on the fractions.
-------------
Least Common Denominator: (sqrt(6)-1)(sqrt(6)+1) = 6-1 = 5
------------------------
Rewrite the problem with lcm = 5
[(sqrt(3)(sqrt(6)+1) - sqrt(3)(sqrt(6)-1)]/5
[(sqrt(18) + sqrt(3)) - (sqrt(18)-sqrt(3))]/5
= [2sqrt(3)] / 5
= (2/5)*sqrt(3)
=====================
Cheers,
Stan H.
|
Travel_Word_Problems/150665: This question is from textbook
BY boat, Joseph can go 72 km upstream to a fishing hole in 4 hours. To go back he needs only 3 hours. What is his rate upstream and his rate downstream?
1 solutions
Answer 110605 by stanbon(57246) on 2008-08-03 18:54:13 (Show Source):
You can put this solution on YOUR website!BY boat, Joseph can go 72 km upstream to a fishing hole in 4 hours. To go back he needs only 3 hours. What is his rate upstream and his rate downstream?
----------------
Upstream DATA;
distance = 72 km ; time = 4 hrs ; rate = 72/4 = 18 kph
--------------
Downstream DATA:
distance = 72 km ; time = 3 hrs ; rate = 72/3 = 24 kph
------------------
Let b = boat speed ; Let c = current speed
EQUATIONS:
b+c = 24
b-c = 18
-----------
Add to get:
2b = 42
b = 21 (boat speed in still water)
Substitute into b+c = 24 to get:
21 + c = 24
c = 3 kph (current speed)
-----------
Upstream speed = 18 kph
Downstream speed = 24 kph
|
Linear_Equations_And_Systems_Word_Problems/150668: In 1995 the life expectancy of a male in a certain country was 62.6 years In 2001 it was 64.9 years Let E represent the life expectancy in year t and let t represent the number of years since 1995
The linear function E(t) that fits the data is
E(t)= t +
(round to the nearest tenth)
Use the function to predict the life expectancy of males in 2005
E(14)=
(round to the nearest tenth)
1 solutions
Answer 110598 by stanbon(57246) on 2008-08-03 17:32:08 (Show Source):
You can put this solution on YOUR website!In 1995 the life expectancy of a male in a certain country was 62.6 years In 2001 it was 64.9 years Let E represent the life expectancy in year t and let t represent the number of years since 1995
----------
You have two points: (0,62.6) and (6,64.9), where x is the number of years after
1995.
-------------------------------
slope: (64.9-62.6)/(6-0) = 2.3/6 = 23/60
-------------
intercept: when x = 0, y = 62.6
-----------------------------
Equation:
E(t) = (23/60)t + 62.6
---------------------------
The linear function E(t) that fits the data is
(round to the nearest tenth)
Use the function to predict the life expectancy of males in 2005
E(14)= (23/60)*14 + 62.6
E(14) = 68.0
(round to the nearest tenth)
---------------
Cheers,
Stan H.
|
Age_Word_Problems/150670: Can you please help me solve this problem:
Three years ago, Rica was thrice as old as Dandy. Three years hence, she will be twice as old. Find their present ages.
1 solutions
Answer 110596 by stanbon(57246) on 2008-08-03 17:00:29 (Show Source):
You can put this solution on YOUR website!Three years ago, Rica was thrice as old as Dandy. Three years hence, she will be twice as old. Find their present ages.
-----------------------
Let Rica's present age be "r". Let Dandy's present ate by "d".
-----------------------
EQUATIONS:
Three years ago: r-3 = 3(d-3)
Three years hence: r+3 = 2(d+3)
-----------------
Rearrange:
r - 3d = -6
r - 2d = 3
--------------
Subtract 1st from 2nd to get:
d = 9 (Dandy's age NOW)
-----------
Substitute into r-2d = 3
r -(2*9) = 3
r = 21 (Rita's age NOW)
================
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/150660: Hi
Please help me tell the difference between a logarithmic function and a logarithmic equation? I have to come up a a logarithmic function. I wanted to turn my exponential function into the logarithmic function. My expo function is f(x)=6^x. My answer is f=18, is that correct? Please help me with the log function. Thank you in advance.
1 solutions
Answer 110595 by stanbon(57246) on 2008-08-03 16:52:14 (Show Source):
You can put this solution on YOUR website!Please help me tell the difference between a logarithmic function and a logarithmic equation? I have to come up a a logarithmic function. I wanted to turn my exponential function into the logarithmic function. My expo function is f(x)=6^x. My answer is f=18, is that correct? Please help me with the log function. Thank you in advance.
======================
Exponential Function : y = 6^x
Log Function : log(base 6) y = x
=====================
General form of a log function:
y = log(base a) b
====================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/150669:
Would you say a parabola would be considered a Symmetrical, second order, quadratic polynomial? I have a question asking :Parabolas are what kind of Polynomial?
() Symmetrical
()Second order
() Quadratic
() All of the above
I see all being a part of a parabola but only Quadratic is a polynomial, the second order part seems to fall under the quadratic and symmetrical seems to be just an axis that says there are two sides that mirror each other.
What is your take?
Shelly
1 solutions
Answer 110594 by stanbon(57246) on 2008-08-03 16:47:49 (Show Source):
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Probability-and-statistics/150654: A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
1 solutions
Answer 110593 by stanbon(57246) on 2008-08-03 16:46:27 (Show Source):
You can put this solution on YOUR website!A manufacturer wants to increase the absorption capacity of a sponge.
Based on past data, the average sponge could absorb 3.5 ounces.
After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9.
What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
-----------------
Ho: u = 3.5
Ha: u > 3.5
---------------
x-bar of the data = 3.76
---------------
Comment: The decision rule depends on whether you use a "t" or
a "z" critical value.
If "t" the decision rule is "reject Ho if t is above 2.821".
If "z" the decision rule is "reject Ho if z is above 2.326".
---------------
Cheers,
Stan H.
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Polynomials-and-rational-expressions/150602: Please help me find x.
-12x^3 + 52x^2 + 54x + 12 = 0
I don't know where to go from here? Please show work so I know how to do problems like this from now on, Thanks!
My work that I think is wrong...
-12(x^3 - (13/3)x^2 - (27/6)x - 1) = 0
Thanks again for your help!
1 solutions
Answer 110548 by stanbon(57246) on 2008-08-03 08:19:07 (Show Source):
You can put this solution on YOUR website!Please help me find x.
-12x^3 + 52x^2 + 54x + 12 = 0
x = -0.5481009, -0.3488316, or 5.2302657
-------------
I used a graphing calculator to find these zeroes.
-------------
Cheers,
Stan H.
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Quadratic_Equations/150609: (4 / x^6) ^3 I need to simplify it and I am pulling my hair out. Maybe I am too old for this! Can you possibly show me a detailed explanation?
1 solutions
Answer 110547 by stanbon(57246) on 2008-08-03 08:08:16 (Show Source):
You can put this solution on YOUR website!(4 / x^6) ^3 I need to simplify it
----------------------
= (4/x^6)(4/x^6)(4/x^6)
multiply the coefficients and add the exponents to get
= 64/x^18
================
Another way to do it:
(4/x^6)^3
= [4^3/x^(3*6)]
= 64/x^18
=====================
Cheers,
Stan H.
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Probability-and-statistics/150569: Find the value for the correlation coefficient r:
x 5, 1, 4, 2, 3
-------------------------
y 5, 10, 12, 4, 8
Can anyone help?
1 solutions
Answer 110533 by stanbon(57246) on 2008-08-02 22:20:07 (Show Source):
You can put this solution on YOUR website!Find the value for the correlation coefficient r:
x 5, 1, 4, 2, 3
-------------------------
y 5, 10, 12, 4, 8
==================================
I used a TI calculator on the data to get:
r = -0.09449...
Cheers,
Stan H.
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Inequalities/150576: You are taking a history course in which there will be four tests, each worth 100 poins. You have scores of 95, 99 and 100 on the first three tests. You must make a total of 360 in order to get an A. What scores on the last test will give you an A.
The solution is {s|s>___}
Simplify your answer.
1 solutions
Answer 110531 by stanbon(57246) on 2008-08-02 22:13:28 (Show Source):
You can put this solution on YOUR website!You are taking a history course in which there will be four tests, each worth 100 poins. You have scores of 95, 99 and 100 on the first three tests. You must make a total of 360 in order to get an A. What scores on the last test will give you an A.
--------------------
Let x be the 4th test score.
----------------------
EQUATION:
95 + 99 + 100 + x > 360
x + 294 > 360
x > 66
==========
Cheers,
Stan H.
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Inequalities/150575: Most insurance companies will replace a vehicle any time an estimated repair exceeds 80% of its blue book value. Michelle's care had 9600 in repairs after an accident. What can be concluded about its blue book value?
The blue book value of Michelle's car ___,$___
Type an inequality symbol and then an integer.
1 solutions
Answer 110527 by stanbon(57246) on 2008-08-02 22:09:24 (Show Source):
You can put this solution on YOUR website!Most insurance companies will replace a vehicle any time an estimated repair exceeds 80% of its blue book value. Michelle's car had 9600 in repairs after an accident. What can be concluded about its blue book value?
Let the blue book value be "x".
9600 < 0.80x
x > $12000
--------------------------
The blue book value of Michelle's car ___,$___
Type an inequality symbol and then an integer.
Cheers,
Stan H.
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Inequalities/150574: 5(r-6) + 4 > 6(r + 3)- 28
The solution set is {r|r ___, ___
Type an inequality symbol, then and integer or fraction
1 solutions
Answer 110526 by stanbon(57246) on 2008-08-02 22:05:14 (Show Source):
You can put this solution on YOUR website! 5(r-6) + 4 > 6(r + 3)- 28
5r-30 + 4 > 6r+18-28
5r - 26 > 6r -10
r < -16
The solution set is {r|r < -16)}
Type an inequality symbol, then and integer or fraction
--------------------------------
Cheers,
Stan H.
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Rational-functions/150537: a bird species in danger of extinction has a population that is decreasing (A=A(base0)e^kt). five years ago the population was at 1400 and today only 1000 are still alive. once the population drops below 100, the situation is irreversible. When will this happen?
1 solutions
Answer 110500 by stanbon(57246) on 2008-08-02 15:10:37 (Show Source):
You can put this solution on YOUR website!a bird species in danger of extinction has a population that is decreasing (A=A(base0)e^kt). five years ago the population was at 1400 and today only 1000 are still alive. once the population drops below 100, the situation is irreversible. When will this happen?
----------------------------
A(t) = A(o) e^(kt)
Find "k":
1000 = 1400 e^(k*5)
(5/7) = e^(5k)
Take the ln to get:
5k = ln (5/7)
5k = -0.3365
k = -0.06729
---------------
Equation: A(t) = A(o) e^(-0.06729t)
----------
When will the population be 100?
100 = 1000 e^(-0.06729t)
0.10 = e^(-0.06729t)
-0.06729t = ln(0.10)
t = 31.22 years from 5 yrs. ago
OR
26.22 years from NOW
=======================
Cheers,
Stan H.
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Rational-functions/150535: After 50 times at bat, a major league baseball player has a batting average of 0.160. How many consecutive hits must the player get to raise his batting average to 0.250?
i tried solving this problem this way:
0.250 - 0.160 = 0.09
50/0.09 = 555.555....
1 solutions
Answer 110498 by stanbon(57246) on 2008-08-02 14:59:08 (Show Source):
You can put this solution on YOUR website!After 50 times at bat, a major league baseball player has a batting average of 0.160. How many consecutive hits must the player get to raise his batting average to 0.250?
-----------------------
After 50 times at bat he has 0.16*50 = 8 hits
-----------------
Let x be the number of hits he needs to be batting 0.250
EQUATION:
# hits/# at bat = (x + 8)/(50+x) = 0.250
x + 8 = (1/4)(50+x)
4x + 32 = 50 + x
3x = 18
x = 6 (# of consecutive hits he needs to be batting 0.250)
============================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/150534: How many pounds of hamburger that $1.60 per pound must be mixed with 70 pounds of hamburger that costs $2.10 per pound to make a mixture that costs $1.70 per pound?
1 solutions
Answer 110497 by stanbon(57246) on 2008-08-02 14:50:51 (Show Source):
You can put this solution on YOUR website!How many pounds of hamburger that costs $1.60 per pound must be mixed with 70 pounds of hamburger that costs $2.10 per pound to make a mixture that costs $1.70 per pound?
---------------------
Value Equation: 160x + 210*70 = 170(x+70)
160x + 210*70 = 170x + 170*70
10x = 40*70
x = 280 lbs. (Amt of 1.60 hamburger that must be added)
=====================
Cheers,
Stan H.
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Rational-functions/150528: Using the formula I=PRT to find simple interest on an account, find the ammount earned in 3 years if you deposited $500 into a saving account earning 6% per year.
1 solutions
Answer 110491 by stanbon(57246) on 2008-08-02 14:32:52 (Show Source):
You can put this solution on YOUR website!Using the formula I=PRT to find simple interest on an account, find the amount earned in 3 years if you deposited $500 into a saving account earning 6% per year.
------------------
I = 500*0.06*3 = $90
====================
Cheers,
Stan H.
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Probability-and-statistics/150513: The General Social Survey is an annual survey given to about 1,500 U.S. adults selected at random. Each year, the survey contains several questions meant to probe respondents' views of employment. A recent survey contained the question "How important to your life is having a fulfilling job?" Of the 261 college graduates surveyed, 107 chose the response "Very important." Of the 121 people surveyed whose highest level of education was high school or less, 34 chose the response "Very important." Based on these data, can we conclude, at the 0.05 level of significance, that there is a difference between the proportion p1 of all U.S. college graduates who would answer "Very important" and the proportion p2 of all U.S. adults whose highest level of education was high school or less who would answer "Very important"?
Perform a two-tailed test. Then answer the 6 questions below.
Carry your intermediate computations to at least three decimal places and round your answers the same way.
1) The null hypothesis
2) The alternative hypothesis
3) The type of test statistic (Z, t, chi-square, etc)
4) The value of the test statistic
5) The p-value
6) (YES OR NO) Can we conclude that there is a difference between the two populations in the proportions who would answer "very important"?
1 solutions
Answer 110490 by stanbon(57246) on 2008-08-02 14:29:05 (Show Source):
You can put this solution on YOUR website!The General Social Survey is an annual survey given to about 1,500 U.S. adults selected at random. Each year, the survey contains several questions meant to probe respondents' views of employment. A recent survey contained the question "How important to your life is having a fulfilling job?"
----------------------
Of the 261 college graduates surveyed, 107 chose the response "Very important." Of the 121 people surveyed whose highest level of education was high school or less, 34 chose the response "Very important."
----------------------
Based on these data, can we conclude, at the 0.05 level of significance, that there is a difference between the proportion p1 of all U.S. college graduates who would answer "Very important" and the proportion p2 of all U.S. adults whose highest level of education was high school or less who would answer "Very important"?
Perform a two-tailed test. Then answer the 6 questions below.
Ho: p(coll) - p(hs) =0
Ha: p(coll) - p(hs) is not equal to 0
---------------------------------------
Carry your intermediate computations to at least three decimal places and round your answers the same way.
1) The null hypothesis (above)
2) The alternative hypothesis (above)
3) The type of test statistic (Z, t, chi-square, etc)
I ran a 2-Prop Z-test
---------------------------
4) The value of the test statistic
z = 4.4029
----------------
5) The p-value: 0.000010688
---------------
6) (YES OR NO) Can we conclude that there is a difference between the two populations in the proportions who would answer "very important"?
Since p-value is less than alpha, reject Ho.
There is a difference in the proportions.
=======================
Cheers,
Stan H.
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Mixture_Word_Problems/150506: an airplane made a 2040-kilometer trip in the direction of the wind in 5 hours last tuesday. if the trip against the direction of the wind took an hour longer, find the rate of the plane in still air and the velocity of the wind.
1 solutions
Answer 110472 by stanbon(57246) on 2008-08-02 09:10:42 (Show Source):
You can put this solution on YOUR website!an airplane made a 2040-kilometer trip in the direction of the wind in 5 hours last tuesday. if the trip against the direction of the wind took an hour longer, find the rate of the plane in still air and the velocity of the wind.
--------------
Let "p" and "w" represent the plane speed and the wind speed.
--------------
With-wind DATA:
distance = 2040 km ; time = 5 hrs ; rate = 2040/5 = 408 kph
--------------
Against-wind DATA:
distance = 2040 km ; time = 6 hrs ; rate = 2040/6 = 340 kph
--------------
EQUATIONS:
p + w = 408
p - w = 340
-------------
Add to get:
2p = 748
p = 374 kph (speed of the plane in still air)
------------
Substitute into p+w = 408 to solve for w:
374 + w = 408
w = 34 kph (speed of the wind)
==================================
Cheers,
Stan H.
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Mixture_Word_Problems/150505: a grocer mixes 12kg of one grade of beans with 10kg of another grade to obtain a blend worth 540 pesos. he then makes a second blend worth 610 pesos by mixing 8kg of the first grade with 15kg of the second grade. find the price per kilogram of each grade?
1 solutions
Answer 110471 by stanbon(57246) on 2008-08-02 09:02:56 (Show Source):
You can put this solution on YOUR website!a grocer mixes 12kg of one grade of beans with 10kg of another grade to obtain a blend worth 540 pesos. he then makes a second blend worth 610 pesos by mixing 8kg of the first grade with 15kg of the second grade. find the price per kilogram of each grade?
---------------------------------------
Let "a" be the price of 1st bean and "b" be the price of 2nd bean.
--------------------------------------
Value Equation: 12a + 10b = 540
Value Equation: 8a + 15b = 610
-------------------
Solve the system by substitution, elimination, or matrix to get:
a = 20 p
b = 30 p
==============
Cheers,
Stan H.
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Miscellaneous_Word_Problems/150502: This question is from textbook ARCO Master the Officer Candidate Tests
I'm not sure if there's a more specific category to file under.
"In a 3-hour examination of 350 questions, there are 50 mathematics problems. If twice as much time should be allowed for each mathematics problem as for each of the other questions, how many minutes should be spent on the mathematics problems?"
I've read but only understand parts of the solution in the back of the book. It is this:
x = number of minutes for each math problem
x(50) + x/2(300) = 180 [x/2 i don't understand]
x = 180/200
50(180/200) = 45 minutes per question
Also, can you please let me know how to search for problems of this type so I can practice more? Thank you.
1 solutions
Answer 110469 by stanbon(57246) on 2008-08-02 08:57:26 (Show Source):
You can put this solution on YOUR website!"In a 3-hour examination of 350 questions, there are 50 mathematics problems. If twice as much time should be allowed for each mathematics problem as for each of the other questions, how many minutes should be spent on the mathematics problems?"
I've read but only understand parts of the solution in the back of the book.
----------------------
It is this:
x = number of minutes for each math problem and there are 50 of them.
x/2 = number of minutes for each "other" problem and there are 300 or them.
-----------------------
Note: 3 hrs = 180 minutes
-----------------------
EQUATION:
time for math + time for others = 180
x(50) + (x/2)(300) = 180
50x + 150x = 180
200x = 180
x = (180/200) minutes is the time for EACH of the math problems
------------------------
50(180/200) = 45 minutes for ALL of the math problems
------------------------
Also, can you please let me know how to search for problems of this type so I can practice more? Thank you.
-------
May I suggest use Google on the internet and search for "algebra word problems".
You will find a multitude of sites.
======================
Cheers,
Stan H.
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Probability-and-statistics/150495: A study conducted by the research department of a pharmaceutical company claims that the annual spending (per person) for prescription drugs for allergy relief, m1 , is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine, m2 . A health insurance company conducted an independent study and collected data from a random sample of 255 individuals for prescription allergy relief medicine. The sample mean is found to be 17.8 dollars/year, with a sample standard deviation of 5.1 dollars/year. They have also collected data for non-prescription allergy relief medicine. An independent random sample of 245 individuals yielded a sample mean of 18.2 dollars/year, and a sample standard deviation of 4.3 dollars/year. Since the sample size is quite large, it is assumed that the population standard deviation of the sales (per person) for prescription and non-prescription allergy relief medicine can be estimated by using the sample standard deviation values given above. Is there sufficient evidence to reject the claim made by the research department of the company, at the 0.10 level of significance?
Perform a one-tailed test and answer the questions below.
Carry your intermediate computations to at least three decimal places and round your answers to three as well.
1) The null hypothesis
2) The alternative hypothesis
3) The type of test statistic (ex. Z, t, Chi-Square, etc.)
4) The value of the test statistic
5) The p value
6) YES or NO. Can we reject the claim that the mean spending on prescription allergy relief medication is greater than or equal to the mean spending on non-precription allergt relief medication?
1 solutions
Answer 110467 by stanbon(57246) on 2008-08-02 08:43:01 (Show Source):
You can put this solution on YOUR website!A study conducted by the research department of a pharmaceutical company claims that the annual spending (per person) for prescription drugs for allergy relief, m1 , is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine, m2.
Ho: u(m1) >= u(m2)
Ha: u(m1) < u(m2)
-----------------------------
A health insurance company conducted an independent study and collected data from a random sample of 255 (n1) individuals for prescription allergy relief medicine. The sample mean is found to be 17.8 (x1-bar) dollars/year, with a sample standard deviation of 5.1 dollars/year(s1).
------------------------------
They have also collected data for non-prescription allergy relief medicine. An independent random sample of 245 (n2) individuals yielded a sample mean of 18.2 dollars/year (x2-bar), and a sample standard deviation of 4.3 dollars/year(s2).
-------------------------------------
Since the sample size is quite large, it is assumed that the population standard deviation of the sales (per person) for prescription and non-prescription allergy relief medicine can be estimated by using the sample standard deviation values given above.
----------------------------------------
Is there sufficient evidence to reject the claim made by the research department of the company, at the 0.10 level of significance?
Perform a one-tailed test and answer the questions below.
Carry your intermediate computations to at least three decimal places and round your answers to three as well.
1) The null hypothesis (above)
-----------
2) The alternative hypothesis (above)
-----------
3) The type of test statistic (ex. Z, t, Chi-Square, etc.)
That depends on your text. Some use "t" for all means-test; some use
t only if n < 30. Since n > 30 for both samples, use a z test statistic.
-------------------
4) The value of the test statistic
z = 2.3263
------------
5) The p value
I ran a 2-sample z test with a TI calculator and got
p-value = 0.1712 or greater than 17%
-----------------------------------
6) YES or NO. Can we reject the claim that the mean spending on prescription allergy relief medication is greater than or equal to the mean spending on non-precription allergt relief medication?
Since p-value is greater than 1%, fail to reject Ho.
======================
Cheers,
Stan H.
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Quadratic-relations-and-conic-sections/150501: solve the inequality and write the solution in interval notation
x+1/x+3 > 2
1 solutions
Answer 110466 by stanbon(57246) on 2008-08-02 08:08:15 (Show Source):
You can put this solution on YOUR website!solve the inequality and write the solution in interval notation
x+1/x+3 > 2
----------------
x cannot be -1
x cannot be -3
-----------------
Solve the equality by cross-multiplying:
x+1 = 2(x+3)
x+1 = 2x+6
x cannot be -5
-------------------
Draw a number line and plot -5, -3, -1 on it
--------------------
Since x=-5 yields equality test values on either side to find the solution set.
---------------------------------
Check x = -6; (-6+1)/(-6+3) >2; false, so no solutions in (-inf,-6)
Check x = -4: (-4+1)/(-4+3) >2; true, so solutions in (-5,-3)
Check x = -2: (-2+1)/(-2+3) >2; false, so no solutions in (-3,+inf)
-----------------------------------
Final Answer: -5 < x < -3
==============================
==============================
Cheers,
Stan H.
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