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Recent problems solved by 'stanbon'
stanbon answered: 57178 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>NextEquations/127341: This question is from textbook
Can you help me solve this problem Please.
David has fourteen thousand dollars to invest and he invest nine thousand in a mutual fund that pays twelve per cent annual simple interest. If he wants to make at least twenty two hundred dollars in yearly interest, at what minimum rate does the remainder of the money need to be invested? Thanks so much. Sharon
1 solutions
Answer 93293 by stanbon(57246)   on 2008-02-16 21:08:24 (Show Source):
You can put this solution on YOUR website!David has fourteen thousand dollars to invest and he invest nine thousand in a mutual fund that pays twelve per cent annual simple interest. If he wants to make at least twenty two hundred dollars in yearly interest, at what minimum rate does the remainder of the money need to be invested?
-------------
12% investment DATA:
Amount = 9000 dollars ; interest = 0.12(9000) = 1080 dollars
----------------------
x% investment DATA:
Amount:5000 ; interest 5000x dollars
------------------------
EQUATIOn:
1080 + 5000x >= 2200
5000x >= 1120
x >= 22.4%
=============
Cheers,
Stan H.
|
Linear-equations/127303: What is the solution to the sysytem of equations y=2x and y=-x+3?
Thank You for your time!!
1 solutions
Answer 93259 by stanbon(57246) on 2008-02-16 16:08:06 (Show Source):
You can put this solution on YOUR website!What is the solution to the sysytem of equations y=2x and y=-x+3?
--------------
Substitute to get:
2x = -x+3
3x = 3
x = 1
--------
Substitute to solve for "y":
y = 2*1 = 2
-----------
Cheers,
Stan H.
|
Probability-and-statistics/127279: A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail?
1 solutions
Answer 93256 by stanbon(57246) on 2008-02-16 16:04:59 (Show Source):
You can put this solution on YOUR website!A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail?
Prob(both fail) =0.2*0.2 = 0.04
------------------------------------
Prob(neither will fail) = 0.8*0.8 = 0.64
---------------------------------------
Prob(one will fail) = 1-P(none will fail)-Prob(both will fail) = 1-0.68
= 0/32
================
Cheers,
Stan H.
|
Probability-and-statistics/127276: Given a mean (8.0 hours) and a standard deviation (4.5 hours) of a population, calculate the probability of an event that falls between 5 to 10 hours. This question is due on day 5.
1 solutions
Answer 93247 by stanbon(57246) on 2008-02-16 15:35:54 (Show Source):
You can put this solution on YOUR website!Given a mean (8.0 hours) and a standard deviation (4.5 hours) of a population, calculate the probability of an event that falls between 5 to 10 hours. This question is due on day 5.
-----------------
Find the z-score of 5 and of 10:
z(5) = (5-8)/4.5 = -3/4.5 = -1/1.5 = -0.667
z(10)= (10-8)/4.5 = 2/4.5 = 0.4444
-------------
Use your z-chart or your calculator to find the following:
Probability (5<=x<=10) = P(-0.667 <= z <= 0.444) = 0.4191
===============
Cheers,
Stan H.
|
Rational-functions/127226: Write the following rule as a formula using function notation: Tuition cost in dollars is sixty-five times the number of credit hours.
Write the following rule as a formula using function notation: Tuition cost in dollars is sixty-five times the number of credit hours.
Thank you all, for your God given talent that helps us less fortunate.
1 solutions
Answer 93208 by stanbon(57246) on 2008-02-16 08:15:54 (Show Source):
You can put this solution on YOUR website!The answer that I have come up with is: (e -1).2:
The problem is what are the exact evaluation of, (integral sign), 2xe^(x^2) dx over the intervals (0, 1). I feel this is not correct, can you verify that for me please?
Answer: e^x^2 evaluated at 1 minus e^x^2 evaluated at 0
= e-1
----------------------
Also please, I have determined that In x is not the correct completion of the formula, (integral sign), (1/x). Is that correct, or should I do more research on this subject?
Answer: ln(x) + C because you want the indefinite integral, and C might
always be part of the function that was differentiated to arrive at
an answer of ln(x).
Example: The derivative of f(x) = ln(x) +2 is the same as the derivative
of f(x)= ln(x) + 5
So when you integrate ln(x) you should write ln(x)+C to cover all the
possible constants that might be part of the answer.
-----------
It's a different story when you take the definite integral from x=a to
x=b because you subtract out the constant that may have been part of
the function.
================
Cheers,
Stan H.
|
Linear-equations/127228: This is from a worksheet from the instructor: Write the following rule as a formula using function notation: Tuition cost in dollars is sixty-five times the number of credit hours.
1 solutions
Answer 93206 by stanbon(57246) on 2008-02-16 07:48:22 (Show Source):
|
Trigonometry-basics/127225: Hello. Please help me ASAP- I need to turn this in quick. So I have a worksheet that says that I need to discriminate the solutions of the quadratic equation: x squared + 5x + 3 + a. How do I do it and what does the direction mean?
Thanks.
1 solutions
Answer 93193 by stanbon(57246) on 2008-02-15 22:48:38 (Show Source):
You can put this solution on YOUR website!discriminate the solutions of the quadratic equation: x squared + 5x + 3 + a.
-----------------
The discriminant of a quadratic is b^2-4ac
---------------
Your quadratic has a = 1, b=5, c=3+a
-----------
Your discriminant is 5^2 -4*1*(3+a) = 25-12-4a = 13-4a
---------------------
When the discriminant is less than zero you have no Real Number solutions:
13-4a < 0
4a>13
a > 13/4
-----------
When the discriminant is equal to zero you have two equal Real number solutions:
13-4a = 0
4a = 13
a = 13/4
-------------
when the discriminant is greater than zero you have two unequal Real number
solutions:
13-4a >0
4a<13
a < 13/4
===============
Cheers,
Stan H.
|
Equations/127212: I need to express the following in the simplest form:
{a^2+6a-7} {2a^2+a-15} {a^2+5a-14}
-------- * --------- / ---------
{6a^2-7a-20} {a^2+2a-3} {3a^2-2a-8}
So far I have:
{(a+6)(a-1)} {3a+4}
---------- * -------- / ---------
{(a+3)(a-1)} {(a+7)}
1 solutions
Answer 93192 by stanbon(57246) on 2008-02-15 22:42:16 (Show Source):
You can put this solution on YOUR website!I need to express the following in the simplest form:
{a^2+6a-7} {2a^2+a-15} {a^2+5a-14}
-------- * --------- / ---------
{6a^2-7a-20} {a^2+2a-3} {3a^2-2a-8}
=====================================================================
Factor where you can; Cancel where you can:
{(a+7)(a-1)} * {(2a-5)(a+3)} / {(a+7)(a-2)}
------------ ------------ ------------
{(2a-5)(3a+4)} {(a+3)(a-1)} {(a-2)(3a+4)}
=====================================================================
Cancel (a-1),(2a-5),(a+3), (a-2)
{(a+7)} * 1 / {(a+7)}
--------- --- ------------
{(3a+4)} 1 {(3a+4)}
=============================
Invert the denominator and multiply to get:
Final Answer: 1
===================
Cheers,
Stan H.
|
Quadratic_Equations/127200: One root of the function y=x^2-10x+k is 5+2isqrt3. What is the value of k????
1 solutions
Answer 93191 by stanbon(57246) on 2008-02-15 22:20:57 (Show Source):
You can put this solution on YOUR website!One root of the function y=x^2-10x+k is 5+2isqrt3. What is the value of k????
-----------------
If 5+2sqrt(3)i is a root, so is 5-2sqrt(3)i.
----------------
Then the following product is a factor of the given polynomial:
(x-(5+2sqrt(3)i)(x-(5-2sqrt(3)i)
= ((x-5)-2sqrt(3)i)((x-5)+2sqrt(3)i)
Comment: Notice that the factors are in the form (a-b)(a+b).
So the product is a^2-b^2
-----------------------
= (x-5)^2 -(2sqr(3)i)^2
= x^2-10x+25+12
= x^2-12x+37
Comparing that to the original polynominal you see that
k = 37
===========
Cheers,
Stan H.
|
Mixture_Word_Problems/127218: My math teacher, unfortunately, never taught me how to do this kind of supposed "mixture" problem: With a tailwind, a jet flew 2000 miles in 8 hours, but the return trip against the wind required 10 hours. Find the jet's speed and the wind speed.
1 solutions
Answer 93190 by stanbon(57246) on 2008-02-15 22:13:40 (Show Source):
You can put this solution on YOUR website!With a tailwind, a jet flew 2000 miles in 8 hours, but the return trip against the wind required 10 hours. Find the jet's speed and the wind speed.
----------------------
With tailwind DATA:
Distance = 2000 miles ; Time = 8 hrs. ; Rate = 2000/8 = 250 mph
------------------
Return trip DATA:
Distance = 2000 miles ; Time = 10 hrs. ; Rate = 2000/10 = 200 mph
-------------------------------------
Let p be plane speed with no wind; Let w be the speed of the wind.
EQUATIONS:
p+w = 250 mph
p-w = 200 mph
---------
Add the two equations to solve for "p":
2p = 450
p = 225 mph (speed of the plane with no wind)
------------
Subsitute to solve for w:
225 + w = 250
w = 25 mph (speed of the wind)
================================
Cheers,
Stan H.
|
Quadratic_Equations/127201: At the beginning of a study , there are 50 grams of a substance present. After 17 days there are 38.7 grams remaining. What is the rate of decay ???? How much of the substance will be present after 40 days???? Assume the substance decays exponentially.
1 solutions
Answer 93186 by stanbon(57246) on 2008-02-15 22:03:12 (Show Source):
You can put this solution on YOUR website!At the beginning of a study , there are 50 grams of a substance present. After 17 days there are 38.7 grams remaining. What is the rate of decay ???? How much of the substance will be present after 40 days???? Assume the substance decays exponentially.
--------------------
You have two points: (0,50) and (17,38.7)
-------------
Equation form: y = ab^x
38.7 = ab^17
50 = ab^0
---------------
From the 2nd equation: a = 50
Substitute into the 1st equation to solve for "b":
38.7 = 50b^17
b^17 = 38.7/50
b^17 = 0.7740
Take the 17th root to get:
b = 0.9850
---------------
EQUATION:
y = 50*0.9850^x
------------------
How much of the substance will be present after 40 days?
y = 50*0.9850^40
y = 50*0.5473
y = 27.3643 grams
======================
Cheers,
Stan H.
|
Linear-equations/127216: This question is from textbook finite mathematics
Find an equation in the form y = mx + b
through (5, -1); slope = 2/3
1 solutions
Answer 93181 by stanbon(57246) on 2008-02-15 21:46:27 (Show Source):
You can put this solution on YOUR website!Find an equation in the form y = mx + b
through (5, -1); slope = 2/3
------------------------
You have the form and you are told the values of x,y, and m.
Solve for "b":
-1 = (2/3)*5 + b
-1 = (10/3) + b
b = -13/3
---------------
EQUATION:
y = (2/3)x-(13/3)
--------------------
Cheers,
Stan H.
|
Linear-equations/127211: This problem is not from a book. It is a an activity made by my instructor. Here is the problem:
You are considering going to spring semester at CGCC. You know that you will have to pay $65 per credit hour. You are on a limited budget, so you need to calculate the total cost based on the number of credit hours.
1. What are the input and output variables?
2. Write in words a rule that describes how to calculate the total tuition bill
1 solutions
Answer 93179 by stanbon(57246) on 2008-02-15 21:41:40 (Show Source):
You can put this solution on YOUR website!You are considering going to spring semester at CGCC. You know that you will have to pay $65 per credit hour. You are on a limited budget, so you need to calculate the total cost based on the number of credit hours.
1. What are the input and output variables?
input: number of credit hours
output: tuition cost
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2. Write in words a rule that describes how to calculate the total tuition bill
Tuition cost in dollars is sixty-five times the number of credit hours .
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Cheers,
Stan H.
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Expressions-with-variables/127157: the frequency(F) of vibration of a string varies directly as the square root of the tension(t) and inversely as the length(L) and diameter(d). if a string of 5 cm long, with a diameter of 0,05 cm vibrates at a frequency of 1300 v/s at a voltage of 16 kg, what will be the frequency of a rope 15 inches long and 0,08 cm in diameter at a voltage of 25 kg?
1 solutions
Answer 93157 by stanbon(57246) on 2008-02-15 19:26:15 (Show Source):
You can put this solution on YOUR website!the frequency(F) of vibration of a string varies directly as the square root of the tension(t) and inversely as the length(L) and diameter(d). if a string of 5 cm long, with a diameter of 0,05 cm vibrates at a frequency of 1300 v/s at a voltage of 16 kg, what will be the frequency of a rope 15 inches long and 0,08 cm in diameter at a voltage of 25 kg?
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F=k*sqrt(t)/Ld
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Need to find "k"
1300 = k*sqrt(16)/(5*0.05)
1300 = k*(1/4)
k = 5200
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Equation to use in the next part:
F = 5200*sqrt(t)/(Ld)
F = 5200*sqrt(25)/(15 inches*0.08 cm)
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Comment: Did you mean to have a rope with length 15 inches or should
that be 15 cm?
You need to have the length and the diameter measured in cm's.
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Cheers,
stan H.
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Trigonometry-basics/126759: A ball is thrown vertically upward with an intitial velocity of 100 feet per second.
a) Determine a function h(t) that gives the height of the ball at time t seconds after it is thrown. The height function is h(t)=-16t^2+vt+h where v is the initial velocity of the ball and h is the initial height of the ball.
b) how long does it take the ball to reach its maximum height?
c) what is the maximum height the ball reaches?
1 solutions
Answer 93155 by stanbon(57246) on 2008-02-15 19:18:11 (Show Source):
You can put this solution on YOUR website!A ball is thrown vertically upward with an initial velocity of 100 feet per second.
a) Determine a function h(t) that gives the height of the ball at time t seconds after it is thrown. The height function is h(t)=-16t^2+vt+h where v is the initial velocity of the ball and h is the initial height of the ball.
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If you assume the ball was thrown upward from the ground the equation is
Ans: h(t)=-16t^2+100t because h=0.
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b) how long does it take the ball to reach its maximum height?
Maximum occurs when t = -b/2a = -100/(2*-16) = 3.125 seconds.
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c) what is the maximum height the ball reaches?
h(3.125) = -16(3.125)^2+100(3.125) = 156.25 feet
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Cheers,
Stan H.
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Rational-functions/127174: I’m not sure if I have determined the correct value. Could you please check my answer?
(The symbol of a long slim S comes first) (4/x) dx over intervals (1, 3) = 4 Is that correct or did I miss something? Thank you
Also, would this formula (the symbol of a long slim S) e^x dx be completed at e^x or do I need to go farther?
Thank you so much for your help again. You folks are awesome!
1 solutions
Answer 93153 by stanbon(57246) on 2008-02-15 19:09:26 (Show Source):
You can put this solution on YOUR website!The symbol of a long slim S comes first) (4/x) dx over intervals (1, 3) = 4 Is that correct or did I miss something? Thank you
Also, would this formula (the symbol of a long slim S) e^x dx be completed at e^x or do I need to go farther?
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That "long slim S" is an integral sign.
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int(4/x)dx evaluated from x=1 to x=3 is
4lnx evaluated at x=3 - 4lnx evaluated at x=1
You get: 4ln3-4ln1= 4(ln3-ln1) = 4(ln3-0) = 4ln3 = 4.3944...
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int(e^x) = e^x + C, where C is any constant.
You need the +C because your problem is an
indefinate integral.
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Cheers,
stan H.
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Trigonometry-basics/127177: a) The amount of money each member of a band earns playing at a graduation party varies inversely as the number of members in the band. If the band has five members, each member earns 70 dollars. Write an equation that models the relationship between the number of members in a band, n, and the amount each member earns, d.
b) Use the equation to calculate the amount each member earns if there are four members in the band.
1 solutions
Answer 93152 by stanbon(57246) on 2008-02-15 19:01:55 (Show Source):
You can put this solution on YOUR website!) The amount of money each member of a band earns playing at a graduation party varies inversely as the number of members in the band. If the band has five members, each member earns 70 dollars. Write an equation that models the relationship between the number of members in a band, n, and the amount each member earns, d.
d = k/n
Need to find "k":
70 = k/5
k = 350
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Equation to be used to work part b:
d = 350/n
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b) Use the equation to calculate the amount each member earns if there are four members in the band.
d = 350/4
d = $87.50
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Cheers,
Stan H.
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Money_Word_Problems/127175: Hello I made a mistake earlier and was asked to repost this. I just can not deal with word problems. I always mess them up please help me solve this.
Everton college $1625 for an order of 45 calculators. the store paid $10 for each scientific calculator, The others all graphing calculators cost the store $57 each. How many of each type were ordered?
Thank you again...
1 solutions
Answer 93151 by stanbon(57246) on 2008-02-15 18:57:28 (Show Source):
You can put this solution on YOUR website!Everton college paid $1625 for an order of 45 calculators. The store paid $10 for each scientific calculator, The others all graphing calculatos cost the store $57 each. How many of each type were ordered?
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Let # of scientific calculators be "x" ; value of these is 10x dollars
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# of graphing calculators is "45-x" ; value is 57(45-x)= 2565 -57x dollars
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EQUATION:
value + value = 1625 dollars
10x + 2565-57x = 1625
-47x = -1240
x = 26.38..
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Comment: Something is wrong with your data. Since the value
of "x" is the number of scientific calculators, the value
of x should be a counting number, not a decimal.
Please check your data.
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Cheers,
Stan H.
shou
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Trigonometry-basics/127180: If i=radical -1 what is the value of i^223
1 solutions
Answer 93148 by stanbon(57246) on 2008-02-15 18:46:34 (Show Source):
You can put this solution on YOUR website!If i=radical -1 what is the value of i^223
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Dividing 223 by 4 you get 4*55 + 3
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i^223 = (i^4)^55 * i^3
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But i^4=1, so you get:
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i^223 = 1^55*i^3 = 1*i^3 = -i
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Cheers,
Stan H.
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Geometric_formulas/127096: Please help me. I need desperate help. Thank you
A sample of 20 pages was taken without replacement from the 1,591-page phone directory
Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured
(a display ad is a large block of multicolored illustrations, maps, and text). The data (in
square millimeters) are shown below:
0 260 356 403 536 0 268 369 428 536
268 396 469 536 162 338 403 536 536 130
a)Construct a 95 percent confidence interval for the true mean.
(b) Why might normality be an issue here?
c) What sample size would be needed to obtain an error of ±10 square millimeters
with 99 percent confidence?
(d) If this is not a reasonable requirement, suggest one that is.
1 solutions
Answer 93110 by stanbon(57246) on 2008-02-15 10:21:28 (Show Source):
You can put this solution on YOUR website!A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages.
On each page, the mean area devoted to display ads was measured
(a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below:
0 260 356 403 536 0 268 369 428 536
268 396 469 536 162 338 403 536 536 130
a)Construct a 95 percent confidence interval for the true mean.
The mean of the sample (or sample mean) is x-bar = 346.5
The sample standard deviation is s = 170.38
t* for 19 degrees of freedom on a two-tailed test with alpha = 5% is 2.093
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E=t= 2.093[170.38/sqrt(20)]= 0.0549
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95% C.I. is (346.5-0.0549,346.5+0.0549)
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(b) Why might normality be an issue here?
The C.I. is a statement about the population. The sample of 20 might not
have been randomly selected from the whole population.
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c) What sample size would be needed to obtain an error of ±10 square millimeters
with 99 percent confidence?
Formula: E = t
Solve for "n":
n =[t*s/E]^2
n = [1.96*170.38/10]^2 = 1116 when rounded up.
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(d) If this is not a reasonable requirement, suggest one that is.
Either raise the allowed error or lower the confidence requirement.
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Cheers,
Stan H.
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Geometric_formulas/127097: Please help me. Thankyou
Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86.
(a) Construct a 90 percent confidence interval for the proportion
of all kernels that would not pop.
(b) Check the normality assumption.
(c) Try the Very Quick
Rule. Does it work well here? Why, or why not?
(d) Why might this sample not be typical?
1 solutions
Answer 93109 by stanbon(57246) on 2008-02-15 10:20:10 (Show Source):
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Quadratic_Equations/127088: The graph of y=4^x is transformed and the new focal point is (16,7). What is the new function ? Can someone please explain to me how this is done ???
1 solutions
Answer 93098 by stanbon(57246) on 2008-02-15 08:19:38 (Show Source):
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