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stanbon answered: 57214 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 , 57180..57209 , 57210..57239, >>Next

Trigonometry-basics/150756: csc^2 pi/6 - cot^2 pi/6. Use identity to find of the value of the expression (no calculator)
1 solutions

Answer 110688 by stanbon(57282) About Me  on 2008-08-04 14:47:48 (Show Source):
You can put this solution on YOUR website!
csc^2 pi/6 - cot^2 pi/6. Use identity to find of the value of the expression
--------------------
Identity:
csc^2x -cot^2x = 1
-------------
Therefore, csc^2 pi/6 - cot^2 pi/6 = 1
================
Cheers,
Stan H.


Quadratic_Equations/150746: 1. Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour, and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).

a. Does the graph of this equation open up or down? How did you determine this?

b. Describe what happens to the tickets sales as time passes?
c. Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.)

d. Will tickets peak or be at a low during the middle of the sale? How do you know?

e. After how many days will the peak or low occur?

f. How many tickets will be sold on the day when the peak or low occurs?

g. What is the point of the vertex? How does this number relate to your answers in parts e and f?

h. How many solutions are there to the equation ? How do you know?

i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?

1 solutions

Answer 110683 by stanbon(57282) About Me  on 2008-08-04 14:20:35 (Show Source):
You can put this solution on YOUR website!
You need to post the quadratic equation.
Cheers,
Stan H.


Numeric_Fractions/150745: 1. Which of the following is a correct statement
A. 0.03>30% B. 0.03=3/10 C. 0.30<3/10 D. 30%=3/10
1 solutions

Answer 110667 by stanbon(57282) About Me  on 2008-08-04 12:03:02 (Show Source):
You can put this solution on YOUR website!
Which of the following is a correct statement
A. 0.03>30%
false
---------------------
B. 0.03=3/10
false
---------------------
C. 0.30<3/10
false
----------------
D. 30%=3/10
30/100 = 3/10
true
==============
Cheers,
Stan H.


Rational-functions/150689: y= M + A/N + A
A = any coefficient
M = degree of the numerator
N = degree of the denominator
If M = N, the horizontal asymptote is the ratio of its coefficient
So, what if M < N and M > N, how do you find the horizontal asymptote?
1 solutions

Answer 110660 by stanbon(57282) About Me  on 2008-08-04 10:08:34 (Show Source):
You can put this solution on YOUR website!
y= M + A/N + A
A = any coefficient
M = degree of the numerator
N = degree of the denominator
If M = N, the horizontal asymptote is the ratio of its coefficient
So, what if M < N and M > N, how do you find the horizontal asymptote?
-------------
If M < N the ratio is 0; the horizontal asymptote is y = 0
Example: y = (x+2)/(x^2+4) ; ratio = 0/1 = 0
graph%28400%2C300%2C-10%2C10%2C-2%2C2%2C%28x%2B2%29%2F%28x%5E2%2B4%29%29
---------------------
If M > N the ratio is "undefined"; divide to find the slant asymptote.
Example: y = (x^2+4)/(x+2) ; ratio = 1/0 = undefined
Dividing you get y = (x-2) + 8/(x^2+4)
graph%28400%2C300%2C-20%2C10%2C-20%2C10%2C%28x%5E2%2B4%29%2F%28x%2B2%29%29
==================
Cheers,
Stan H.


Rational-functions/150690: You investigate how long it would take you and a friend to fold 1000 origami cranes. You take 2 minutes to fold 1 crane. Let x represent the number of minutes it might take a friend to fold 1 crane.

Question: The expression 60/1000x is your friend's work rate per hour. Explain why.
1 solutions

Answer 110646 by stanbon(57282) About Me  on 2008-08-04 07:21:26 (Show Source):
You can put this solution on YOUR website!
You investigate how long it would take you and a friend to fold 1000 origami cranes.
You take 2 minutes to fold 1 crane.
Therefore your rate is (1/2) crane/minute
------------------------------------------
Let x represent the number of minutes it might take a friend to fold 1 crane.
Then her rate is 1/x crane/minute
--------------------------------------
Question: The expression 60/1000x is your friend's work rate per hour. Explain why.
(1/x)(crane/min)(60 min/1 hr) = 60/x (crane/hr)
================
Comment: I don't agree with the 60/1000x answer.
================
Cheers,
Stan H.


Radicals/150709: rationalize denominator 6/12

1 solutions

Answer 110645 by stanbon(57282) About Me  on 2008-08-04 07:12:47 (Show Source):
You can put this solution on YOUR website!
Something is missing in your posting.
Cheers,
Stan H.


Surface-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(57282) About Me  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(57282) About Me  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(57282) About Me  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(57282) About Me  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/150686: Solve 3x^2 + 19x-14=0 using the quadratic formula

1 solutions

Answer 110625 by stanbon(57282) About Me  on 2008-08-03 21:39:27 (Show Source):
You can put this solution on YOUR website!
Solve 3x^2 + 19x-14=0 using the quadratic formula
------------------------
x = [-19 +- sqrt(19^2 - 4*3*-14)]/6
x = [-19 +- sqrt(529)]/6
x = [-19 +- 23]/6
x = 2/3 or x = -7
====================
Cheers,
Stan H.


Quadratic_Equations/150687: This question is from textbook Intermediate Algebra
write the rational expression Y 3/7 as a root
thank you
1 solutions

Answer 110624 by stanbon(57282) About Me  on 2008-08-03 21:35:38 (Show Source):
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write the rational expression Y 3/7 as a root
-------------------
Y^(3/7) means "the 7th root of (Y^3)"
==============================
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(57282) About Me  on 2008-08-03 19:50:08 (Show Source):
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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(57282) About Me  on 2008-08-03 19:30:13 (Show Source):
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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(57282) About Me  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(57282) About Me  on 2008-08-03 17:32:08 (Show Source):
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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(57282) About Me  on 2008-08-03 17:00:29 (Show Source):
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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(57282) About Me  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.


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(57282) About Me  on 2008-08-03 16:47:49 (Show Source):
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Ans: All of the above.
Cheers,
Stan H.


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(57282) About Me  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.


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(57282) About Me  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.


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(57282) About Me  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.


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(57282) About Me  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.


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(57282) About Me  on 2008-08-02 22:13:28 (Show Source):
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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.


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(57282) About Me  on 2008-08-02 22:09:24 (Show Source):
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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.


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(57282) About Me  on 2008-08-02 22:05:14 (Show Source):
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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.


Probability-and-statistics/150572: Find Q1, Q2, and Q3 for the data set below:
5.4
2.0
6.8
3.1
2.9
4.7
2.1
5.0
1.9
3.4
Can anyone help?
1 solutions

Answer 110525 by stanbon(57282) About Me  on 2008-08-02 22:00:18 (Show Source):
You can put this solution on YOUR website!
Find Q1, Q2, and Q3 for the data set below:
5.4
2.0
6.8
3.1
2.9
4.7
2.1
5.0
1.9
3.4
---------------------
I ran the data using a TI calculator:
Q1: 2.1
Q2: 3.25
Q3: 5
--------------
Cheers,
Stan H.


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(57282) About Me  on 2008-08-02 15:10:37 (Show Source):
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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.


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(57282) About Me  on 2008-08-02 14:59:08 (Show Source):
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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.


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(57282) About Me  on 2008-08-02 14:50:51 (Show Source):
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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.


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(57282) About Me  on 2008-08-02 14:32:52 (Show Source):
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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.