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Recent problems solved by 'stanbon'
stanbon answered: 57911 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899 , 57900..57929, >>Next
Mixture_Word_Problems/405328: It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 70 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength?
1 solutions
Answer 286301 by stanbon(57984)   on 2011-02-06 21:10:40 (Show Source):
You can put this solution on YOUR website!It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 70 liters of 20% solution. How many liters of this should be drained and replaced with 100% antifreeze to get the desired strength?
----
Equation:
anti -anti + anti = anti
0.20*70-0.20x+1x = 0.40*70
----
Multiply thru 100 to get:
20*70 - 20x + 100x = 40*70
---
80x = 20*70
x = (1/4)*70
x = 17.5 liters should be removed and replaced.
===
cheers,
Stan H.
==========
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Probability-and-statistics/405240: At a particular school with 200 male students, 58 play football, 40 play basketball, and 8 play both.What is the probability that a randomly selected male student plays neither sport?
1 solutions
Answer 286300 by stanbon(57984) on 2011-02-06 21:00:31 (Show Source):
You can put this solution on YOUR website!At a particular school with 200 male students, 58 play football, 40 play basketball, and 8 play both.What is the probability that a randomly selected male student plays neither sport?
-----------------------
8 play both leaving 192
58-8 = 50 play football leaving 142
40-8 = 21 play basketball leaving 121
---
P(no play) = 121/200 = 0.6050
======================
Cheers,
Stan H.
============
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Probability-and-statistics/405241: The Gallup Poll reported that 52% of Americans used a seat belt the last time they got into a car. If 4 people are selected at random, find the probability that they all used a seat belt the last time they got into a car?.
1 solutions
Answer 286299 by stanbon(57984) on 2011-02-06 20:54:52 (Show Source):
You can put this solution on YOUR website!The Gallup Poll reported that 52% of Americans used a seat belt the last time they got into a car. If 4 people are selected at random, find the probability that they all used a seat belt the last time they got into a car?.
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Ans: 0.52^4 = 0.0731
----
Cheers,
Stan H.
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Probability-and-statistics/405244: If 28% of US medical degrees are conferred to women, find the probability that 3 randomly selected medical school graduates are men. Would you consider this event likely or unlikely to occur?
1 solutions
Answer 286298 by stanbon(57984) on 2011-02-06 20:49:14 (Show Source):
You can put this solution on YOUR website! If 28% of US medical degrees are conferred to women, find the probability that 3 randomly selected medical school graduates are men. Would you consider this event likely or unlikely to occur?
--------
72% of med degrees are conferred on men.
---
P(3 men) = 0.72^3 = 0.3732
======================
Cheers,
Stan H.
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Probability-and-statistics/405245: If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities.
a- both are spades
b- both are the same suit
c-both are kings
1 solutions
Answer 286297 by stanbon(57984) on 2011-02-06 20:45:45 (Show Source):
You can put this solution on YOUR website!If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities.
a- P(both are spades) = 13C2/52C2 = 0.0588
------
b- P(both are the same suit)= 4*0.0588 = 0.2353
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c-P(both are kings) = 8C2/52C2 = (8*7)/(52*51) = 0.0211
=====================
Cheers,
Stan H.
===============
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Probability-and-statistics/405274: Trudy Jones recently completed her certification examination and learned that her z-score was –2.5. The examining board also informed her that a failure to pass would be all scores that were 1 or more standard deviations below the mean and that those with scores higher than 2 standard deviations above the mean would receive a special commendation award. Trudy can, therefore, conclude that she
1 solutions
Answer 286296 by stanbon(57984) on 2011-02-06 20:36:12 (Show Source):
You can put this solution on YOUR website! Trudy Jones recently completed her certification examination and learned that her z-score was –2.5. The examining board also informed her that a failure to pass would be all scores that were 1 or more standard deviations below the mean and that those with scores higher than 2 standard deviations above the mean would receive a special commendation award. Trudy can, therefore, conclude that she FAILED.
Her score is 2 and 1/2 standard deviations below the mean.
=======
Cheers,
Stan H
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Equations/405314: please solve using the multiplication method
-3/4x=-5/6
type answer as an integer or fraction
1 solutions
Answer 286295 by stanbon(57984) on 2011-02-06 20:10:39 (Show Source):
You can put this solution on YOUR website!please solve using the multiplication method
-3/4x=-5/6
type answer as an integer or fraction
----
(-4/3)(-3/4)x = (-4/3)(-5/6)
---
x = 20/18
---
x = 10/9
======
Cheers,
Stan H.
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Linear-equations/405309: how do i solve this problem -3=x+y
1 solutions
Answer 286294 by stanbon(57984) on 2011-02-06 20:07:14 (Show Source):
You can put this solution on YOUR website!how do i solve this problem -3=x+y
---
You don't solve it.
You might graph it by
plotting two points and
draw a line thru them:
y = -x-3
----
If x = 0, y = -3
If x = -3, y = 0
----
Plot (0,-3) and (-3,0) to get:
=====================
Cheers,
Stan H.
============
|
Sequences-and-series/405300: I really need help with this question, I would appreciate any input, thankyou!
A culture of bacteria has 20 cells in it. The number of cells doubles every 30 minutes. Write the first 5 terms of this sequence and explain where this sequence is arithmetic or geometric and justify your answer.
1 solutions
Answer 286291 by stanbon(57984) on 2011-02-06 19:55:25 (Show Source):
You can put this solution on YOUR website!A culture of bacteria has 20 cells in it. The number of cells doubles every 30 minutes. Write the first 5 terms of this sequence and explain where this sequence is arithmetic or geometric and justify your answer.
------
20,40,80,160,320,...
----
Geometric with a = 20 and r = 2
=============================
Cheers,
Stan H.
==========
|
Rate-of-work-word-problems/405292: office has an old copying machine and a new one. together it takes both machines 4 hours to copy all financial reports. alone it takes the old copier 15 hours longer than the new one to make all copies . how long will it take the new copying machine to make all the copies
1 solutions
Answer 286290 by stanbon(57984) on 2011-02-06 19:51:18 (Show Source):
You can put this solution on YOUR website!office has an old copying machine and a new one.
together it takes both machines 4 hours to copy all financial reports.
alone it takes the old copier 15 hours longer than the new one to make all copies .
how long will it take the new copying machine to make all the copies
-------------------------
New copier DATA:
time = x hrs/job ; rate = 1/x job/hr
-----
Old copier DATA:
time = (x+15) hrs/job ; rate = 1/(x+15)job/hr
----
Together DATA:
time = 4 hrs/job ; rate = 1/4 job/hr
==========================================
Equation:
rate + rate = together rate
1/x + 1/(x+15) = 1/4
Multiply thru by 4x(x+15) to get:
4(x+15) + 4x = x(x+15)
---
4x + 60 + 4x = x^2+15x
---
x^2 + 7x - 60 = 0
x^2+12x-5x-60 = 0
x(x+12)-5(x+12) = 0
(x+12)(x-5) = 0
Positive solution:
x = 5 hrs (time for the new machine)
x+15 = 20 hrs (time for the old machine)
==================================
Cheers,
Stan H.
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Equations/405291: solve using multiplication method
-2x>1/9
what is the solution set
1 solutions
Answer 286287 by stanbon(57984) on 2011-02-06 19:36:50 (Show Source):
You can put this solution on YOUR website! solve using multiplication method
-2x>1/9
what is the solution set
------
Multiplying or Dividing by a negative reverses the inequality:
(-1/2)(-2)x > (-1/2)(1/9)
---
x < -1/18
=================
Cheers,
Stan H.
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|
Mixture_Word_Problems/405276: Is there a formula to combine like solution concentrations to make 100%
For Instance if you have a 123% pigment solution and an 87% pigment solution, how do combine them to make a 100% solution?
1 solutions
Answer 286285 by stanbon(57984) on 2011-02-06 19:31:20 (Show Source):
You can put this solution on YOUR website!Is there a formula to combine like solution concentrations to make 100%
For Instance if you have a 123% pigment solution and an 87% pigment solution, how do combine them to make a 100% solution?
---
There is no such thing as a 123% pigment solution.
---
Let's try the math as if there was such a thing:
pigment + pigment = pigment
1.23x + 0.87y = 1.00(x+y)
Multiply thru by 100 to get:
123x + 87y = 100x+100y
23x = 23y
x = y
---
That means 1.23x + 0.87x = 1*(x+x)
2x = 2x
x = x
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So no matter what quantity of 123% solution you
add to 87% solution you get 100% solution.
=======================
Cheers,
Stan H.
============
Stan H.
|
Polynomials-and-rational-expressions/405234: Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
3x – 15y = -12
3x + 24y = -12
1 solutions
Answer 286257 by stanbon(57984) on 2011-02-06 18:19:02 (Show Source):
You can put this solution on YOUR website!3x – 15y = -12
3x + 24y = -12
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Subtract and solve for "y":
39y = 0
y = 0
----
Solve for "x":
3x -15y = -12
3x - 0 = -12
x = -4
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Solution; (-4,0)
====================
Cheers,
Stan H.
============
|
Graphs/405228: Suppose it takes you 6.8 hours to fly about 2800 miles from Miami, Florida to Seattle, Washinghton. At the same time, your friend flies from Seattle to miami. His plane travels with the same average air speed, but his fight takes only 5.6 hours. Find the average airspeed of the planes. Find the average wind speed?
1 solutions
Answer 286255 by stanbon(57984) on 2011-02-06 18:14:18 (Show Source):
You can put this solution on YOUR website!Suppose it takes you 6.8 hours to fly about 2800 miles from Miami, Florida to Seattle, Washinghton.
------------------------------
At the same time, your friend flies from Seattle to miami. His plane travels with the same average air speed, but his fight takes only 5.6 hours.
------------------------------
Find the average airspeed of the planes. Find the average wind speed?
----------------------
Miam to Seat DATA:
distance = 2800 miles ; time = 6.8 hrs ; rate = 2800/6.8 mph
-------
Seat to Miam DATA:
distance = 2800 miles ; time = 5.6 hrs ; rate = 2800/5.6 mph
----------
Equation:
Let p = plane speed; and w = wind speed.
---
p + w = 2800/5.6
p - w = 2800/6.8
---
2p = 911.76
p = 455.88 mph (speed of the plane in still air)
---
Solve for "w":
p + w = 2800/5.6
455.88 + w = 500
w = 44.12 mph (speed of the wind)
======================================
Cheers,
Stan H.
==================
|
Probability-and-statistics/405211: in a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females and 12 of the juniors are males. If a student is selected at random, find the probability of selecting the following.
a. A junior or a female
b. A senior or a female
c. A junior or a senior
1 solutions
Answer 286254 by stanbon(57984) on 2011-02-06 17:59:26 (Show Source):
You can put this solution on YOUR website!in a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females and 12 of the juniors are males.
---
class #: 18 jun and 10 sen = 28 students
females: 6 senior: 6 juniors
males::: 4 senior ; 12 juniors
==============================
If a student is selected at random, find the probability of selecting the following.
a. P(A junior or a female) = P(junior)+P(female)-P(junior AND female)
= (18+12-6)/28
= 24/28
= 6/7
-------------
b. P(A senior or a female) = P(senior)+P(female)-P(senior AND female)
= (10+12-6)/28
= 16/28
= 4/7
==============
Cheers,
Stan H.
==============
c. A junior or a senior
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Probability-and-statistics/405192: X has a noral distribution with a mean of 80.0 . and a standard deviation of 3.5. Find the following probabilities:
(A) P(x < 75.0)
(B) P(78.0 < x < 83.0)
(C) P(x > 85.0)
1 solutions
Answer 286253 by stanbon(57984) on 2011-02-06 17:42:24 (Show Source):
You can put this solution on YOUR website!X has a noral distribution with a mean of 80.0 . and a standard deviation of 3.5. Find the following probabilities:
(A) P(x < 75.0)
(B) P(78.0 < x < 83.0)
(C) P(x > 85.0)
----
Find the z-value of each x-value using the given mean and std.
---
A) P(x < 75)
z(75) = (75-80)/3.5 = -5/3.5 = -1.4286
---
P(x < 75) = P(z < -1.4286) = 0.0766
=================
Cheers,
Stan H.
=============
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Equations/405203: please help
solve using elimination method
3r-5s=-15
5r+3s=43
1 solutions
Answer 286248 by stanbon(57984) on 2011-02-06 17:34:27 (Show Source):
You can put this solution on YOUR website!solve using elimination method
3r-5s=-15
5r+3s=43
--------
Multiply 1st by 5 and 2nd by 3 to get:
15r - 25s = -75
15r + 9s = 129
---------
Subtract the top from the bottom and solve for "s":
34s = 204
s = 6
----
Solve for "r":
3r-5s = -15
3r - 5*6 = -15
3r = 15
r = 5
=======
Solution: r = 5; s=6
==========================
Cheers,
Stan H.
===========
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Radicals/405189: √2(2√7 - 4√4) I tried setting it equal to 0 and squaring both sides but all that did was give me 28 is = to 32 and I know that is wrong
1 solutions
Answer 286242 by stanbon(57984) on 2011-02-06 17:28:32 (Show Source):
You can put this solution on YOUR website!√2(2√7 - 4√4) I tried setting it equal to 0 and squaring both sides ----
------
It's not an equation.
= 2sqrt(14) - 4sqrt(8)
---
= 2sqrt(14) - 8sqrt(2)
===========================
Cheers,
Stan H.
===========
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Polynomials-and-rational-expressions/405186: solve and show the answer in interval notation:
3x-4<8 and 4x-1<13
i got:
3x-4<8
+4 +4
3x<12
x<4
4x-1<13
+1 +1
4x<14
x< 7/2
but professor marked it wrong. Please help
1 solutions
Answer 286234 by stanbon(57984) on 2011-02-06 16:48:04 (Show Source):
You can put this solution on YOUR website! solve and show the answer in interval notation:
3x-4<8 and 4x-1<13
i got:
3x-4<8
+4 +4
3x<12
x<4
4x-1<13
+1 +1
4x<14
x< 7/2
but professor marked it wrong.
----
The work you are showing is correct.
The problem involes "AND" so the
interval values must satisfy both
of the inequalities.
---
For x to be <4 AND <7/2 the values
would have to be <7/2.
---
Interval Solution: (-inf,7/2)
=============================
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Probability-and-statistics/405117: 22) A multiple-choice test has 48 questions, each with four response choices. If a student is simply guessing at the answers,
A) What is the probably of guessing correctly for any question?
¼ = 25%
b) On average, how many questions would a student get correct for the entire test?
c) What is the probability that a student would get more than 18 answers correct simply by guessing?
d) What is the probability that a student would get 18 or more answers correct simply by guessing?
1 solutions
Answer 286207 by stanbon(57984) on 2011-02-06 15:44:12 (Show Source):
You can put this solution on YOUR website!A multiple-choice test has 48 questions, each with four response choices. If a student is simply guessing at the answers,
---
Binomial Problem with n=48 and p(correct)=1/4 and p(wrong)=3/4
---------------------------------------------------------------
A) What is the probability of guessing correctly for any question?
¼ = 25%
-----------------------------
b) On average, how many questions would a student get correct for the entire test?
mean = np = 48*(1/4) = 12
------------------------------------
c) What is the probability that a student would get more than 18 answers correct simply by guessing?
P(19 <= x <= 48) = 1 - binomcdf(48,0.25,18) = 0.0184..
---------------------------------------
d) What is the probability that a student would get 18 or more answers correct simply by guessing?
P(18<= x <= 48) = 1 - binomcdf(48,0.25,17) = 0.0374..
==============
Cheers,
Stan H.
|
Probability-and-statistics/405115: 8) Find each of the following probabilities for a normal distribution.
a) p(z > -1.00) b) p(z> -0.80) c) p(z < 0.25) d) p(z < 1.25)
a)p(z > -1.00) = 0.5 – P(0 < Z < -1.00) = 0.5 - -
1 solutions
Answer 286205 by stanbon(57984) on 2011-02-06 15:35:53 (Show Source):
You can put this solution on YOUR website!8) Find each of the following probabilities for a normal distribution.
a) p(z > -1.00)
b) p(z> -0.80)
c) p(z < 0.25)
d) p(z < 1.25)
----
For each of these you should shade the area of the
standard normal curve you are finding.
------
a)p(z > -1.00) = 0.5 + P(-1 < Z < 0) = 0.5 - 0.341345
---
b)P(z > -0.80) = P(-0.8 < z < 0)+0.5 = 0.7881
---
c)P(z < 0.25) = 0.5 + P(0 < z < 0.25) = 0.5987
---------------
d)P(z < 1.35) = ?
----
You can do these using a TI-83 or better calculator
or using a z-chart, which can be found online.
------
Cheers,
Stan H.
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Probability-and-statistics/405100: I am so lost on this problem so I need help. Can somebody check to see if I am correct.
A real estate agent claims that the average price of a home sold in Bevear County, Pennsylvania, is $60,000. A random sample of 36 homes sold in the county is selected. Is there enough evidence to reject the agent's claim at a=0.05? Assuming a=$76,025
I need to
a. State the hypotheses and identify the claim
b. Find the critical value(s)
c. Compute the test value
d. Make a decision
e. Summarize the results
My answer that I got was
H0: = 60,000
Ha: ≠60,000
=(82495-60000)/(76024/36) = -1.78
Answer: Reject the null hypothesis
1 solutions
Answer 286200 by stanbon(57984) on 2011-02-06 15:23:03 (Show Source):
You can put this solution on YOUR website!A real estate agent claims that the average price of a home sold in Bevear County, Pennsylvania, is $60,000. A random sample of 36 homes sold in the county is selected. Is there enough evidence to reject the agent's claim at a=0.05? Assuming std = $76,025
I need to
a. State the hypotheses and identify the claim
b. Find the critical value(s)
c. Compute the test value
d. Make a decision
e. Summarize the results
My answer that I got was
H0: = 60,000
Ha: ≠60,000
test statistic: t = (82495-60000)/[76024/sqrt(36)] = -1.78
Comment: I guess you are saying the sample mean was $82495.
-------
p-value is 2*P(t < -1.78 when df=35) = 2*0.4188 = 0.0838
Note: You doube the probability that t is less that -1.78
because your test is a two-tail test.
---
Answer: Since the p-value is greater than 5%, fail to
Reject the null hypothesis.
====
Cheers,
Stan H.
|
Graphs/404966: Please can you help me in solving this equation as i tried to solve it but unable to do it.
4xy − x3 − 2 = 0
Use algebra to determine the exact values for the x-intercepts. Then give an approximation rounded to two decimal places.
(x, y) = (_________), ~(_______)
I know how to get the equation in slope intercept form: y= (x^3+2)/4x
But unable to understand how to work further.
1 solutions
Answer 286176 by stanbon(57984) on 2011-02-06 12:56:24 (Show Source):
You can put this solution on YOUR website!4xy − x3 − 2 = 0
Use algebra to determine the exact values for the x-intercepts. Then give an approximation rounded to two decimal places.
(x, y) = (_________), ~(_______)
I know how to get the equation in slope intercept form: y= (x^3+2)/4x
But unable to understand how to work further.
--------------
y = (x^3+2)/(4x)
---
To find the x-intercept, let y = 0 and solve for "x":
(x^3+2)/4x = 0
---
This fraction will be zero when the numerator is zero.
Solve x^3+2 = 0
x^3 = -2
x = (-2)^(1/3) is approximately -1.259921...
-----
---------
Cheers,
Stan H.
==============
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Percentage-and-ratio-word-problems/404979: I could really use some help with this:
"The sum of the numerator and denominator of a fraction is 40. If 3 is added to the numerator, and 2 added to the denominator, the new fraction is equal to 4/5.
What is the original fraction? "
1 solutions
Answer 286172 by stanbon(57984) on 2011-02-06 12:09:08 (Show Source):
You can put this solution on YOUR website!The sum of the numerator and denominator of a fraction is 40. If 3 is added to the numerator, and 2 added to the denominator, the new fraction is equal to 4/5.
What is the original fraction? "
-----------------
Let the original fraction be x/y.
---
Equations:
x + y = 40
(x+3)/(y+2) = 4/5
----
Modify the 2nd equation as follows:
5(x+3) = 4(y+2)
5x+15 = 4y+8
5x-4y = -7
------
Now, solve the system:
x+y = 40
5x-4y = -7
---
Multiply the 1st equation by 5:
5x + 5y = 5*40
5x-4y = -7
-----
Subtract the bottom eq. from the top and solve for "y":
9y = 207
y = 23
---
Solve for "x":
x + y = 40
x + 23 = 40
x = 17
-------
Original Fraction: 17/23
=============================
Cheers,
Stan H.
================
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Sequences-and-series/404802: what is the sum of the first 110 positive even integers?
1 solutions
Answer 286083 by stanbon(57984) on 2011-02-05 22:11:04 (Show Source):
You can put this solution on YOUR website!what is the sum of the first 110 positive even integers?
---
2+4+6+...+220
---
This is an arithmetic series with a(1)=2,
d = 2, n = 110
---
Sum = (110/2)(2+220)
= 55*224
---
= 12320
==============
Cheers,
Stan H.
==============
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Linear_Equations_And_Systems_Word_Problems/404777: A theater has a seating capacity of 720 and charges $2 for children (x), $4 for students (y), and $6 for adults (z). At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $3080. How many children attended the show?
1 solutions
Answer 286082 by stanbon(57984) on 2011-02-05 22:07:08 (Show Source):
You can put this solution on YOUR website!A theater has a seating capacity of 720 and charges $2 for children (x), $4 for students (y), and $6 for adults (z).
At a certain screening with full attendance, there were half as many adults as children and students combined.
The receipts totaled $3080.
How many children attended the show?
--------------------------
Equations:
People: x + y + z = 720
Quantity: z = (1/2)(x+y)
Values: 2x + 4y + 6z = 3080
===================================
Rearrange:
x + y + z = 720
x + y -2z = 0
x +2y +3z = 1540
----------------------
Use whatever method you know to get:
x = 140
y = 340
z = 240
========================
Cheers,
Stan H.
========================
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Graphs/404778: find the slope, if it exists, of the line containing the points -10, 1/2 and -7,1/2.
The slope is m=??
1 solutions
Answer 286079 by stanbon(57984) on 2011-02-05 21:56:53 (Show Source):
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