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Recent problems solved by 'stanbon'
stanbon answered: 57288 problems
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53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 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 , 57240..57269 , 57270..57299, >>NextProbability-and-statistics/522249: If a card is drawn at random from a standard 52-card deck, what is the probability that the card drawn is one of the following?
(a) a club
(b) a black card
(c) a jack
1 solutions
Answer 346762 by stanbon(57361)   on 2011-10-27 15:42:37 (Show Source):
You can put this solution on YOUR website!If a card is drawn at random from a standard 52-card deck, what is the probability that the card drawn is one of the following?
(a) P(a club) = 13/52 = 1/4
------------------------------------
(b) P(a black card) = 26/52 = 1/2
-------------------------------------
(c) P(a jack) = 4/52 = 1/13
==============================
Cheers,
Stan H.
===========
|
Probability-and-statistics/522253: If a couple plans on haveing 4 children, what is the probability that there will atleast have one boy? assume boys and girls are equally likely. is that probability high enough for the couple to be very confident that they will atleast get one boy?
1 solutions
Answer 346761 by stanbon(57361) on 2011-10-27 15:40:05 (Show Source):
You can put this solution on YOUR website!If a couple plans on having 4 children, what is the probability that there will at least have one boy? assume boys and girls are equally likely. is that probability high enough for the couple to be very confident that they will atleast get one boy?
---
P(at least one boy) = 1 - P(4 girls) = 1 - (1/2)^4 = 15/16
----------------------------
Cheers,
Stan H.
===========================
|
Probability-and-statistics/522259: assume that adults have IQ scores that are normally distributed with a mean of 101 and standard deviation of 15. Find quartile 3 which is the IQ score seperating the top 25% from the others
1 solutions
Answer 346760 by stanbon(57361) on 2011-10-27 15:38:05 (Show Source):
You can put this solution on YOUR website!assume that adults have IQ scores that are normally distributed with a mean of 101 and standard deviation of 15. Find quartile 3 which is the IQ score seperating the top 25% from the others
---
Find the z-value that has a left-tail of 0.75.
invNorm(0.75) = 0.6745
----
Find the corresponding score value using x = zs+u
----
x = .6745*15+101 = 111.12
=============================
Cheers,
Stan H.
=============================
|
Probability-and-statistics/522264: The appropriate decision rule for a one-tailed test, lower tail critical, at the .05 level of significance, is to reject if
a. z ≤ -1.65.
b. z ≥ -1.65.
c. z ≤1.65.
d. z ≥1.65
1 solutions
Answer 346758 by stanbon(57361) on 2011-10-27 15:35:18 (Show Source):
You can put this solution on YOUR website!The appropriate decision rule for a one-tailed test, lower tail critical, at the .05 level of significance, is to reject if
a. z ≤ -1.65.
b. z ≥ -1.65.
c. z ≤1.65.
d. z ≥1.65
--------------
The reject interval is (-oo< z < -1.645)
=============
Cheers,
Stan H.
|
Permutations/522278: A true/false test has 15 questions. Assuming that we do not care about the score of the test, in how many different ways can the test be completed?
1 solutions
Answer 346756 by stanbon(57361) on 2011-10-27 15:31:52 (Show Source):
You can put this solution on YOUR website!A true/false test has 15 questions. Assuming that we do not care about the score of the test, in how many different ways can the test be completed?
-----
Each question can be answered in 2 ways: true or false.
---
# of ways the test can be completed = 2^15 = 32768
===============
Cheers,
Stan H.
===============
|
Functions/522270: f(x)=9x^4-25^2 how to find the zero of the function algebraically
1 solutions
Answer 346754 by stanbon(57361) on 2011-10-27 15:29:23 (Show Source):
You can put this solution on YOUR website!f(x)=9x^4-25^2 how to find the zero of the function algebraically
-------
solve (3x^2-25)(3x^2+25) = 0
x^2 = 25/3 or x^2 = -25/3
-----
x = +/-5sqrt(3)/3 or x = +/-5sqrt(3)i/3
===============================================
Cheers,
Stan H.
====================
|
Probability-and-statistics/522235: A pair of dice is rolled. What is the probability of each of the following? (Round your answers to three decimal places.)
(a) the sum of the numbers shown uppermost is less than 7
1 solutions
Answer 346744 by stanbon(57361) on 2011-10-27 13:59:21 (Show Source):
You can put this solution on YOUR website!A pair of dice is rolled. What is the probability of each of the following? (Round your answers to three decimal places.)
(a) the sum of the numbers shown uppermost is less than 7
---
Count the ways to succeed:
sum of 2: 1 way
sum of 3: 2 ways
sum of 4: 3 ways
sum of 5: 4 ways
sum of 6: 5 ways
---# of ways to succeed: 15
---
P(sum less than 7) = 15/36
========================================
Cheers,
Stan H.
===============
|
Probability-and-statistics/522105: Find the z-scores for which 20% of the distribution’s area lies between -z and z.
A. -0.719, 0.719
B. -0.253, 0.253
C. -0.528, 0.528
D. -0.842, 0.842
1 solutions
Answer 346743 by stanbon(57361) on 2011-10-27 13:48:35 (Show Source):
You can put this solution on YOUR website!Find the z-scores for which 20% of the distribution’s area
lies between -z and z.
-------------------------------------------
Draw the picture so you can see the sense of the solution.
------
Find the z-value with a left tail of 40%
---
invNorm(0.4) = -0.2533
---------------------------
So the answer is "B".
=======================
Cheers,
Stan H.
=======================
A. -0.719, 0.719
B. -0.253, 0.253
C. -0.528, 0.528
D. -0.842, 0.842
|
Probability-and-statistics/522150: random sample of 200 measurements give a mean of 50 and standard deviation of 9. at 5% level of significance, test the hypothesis that the population mean is 52.
1 solutions
Answer 346739 by stanbon(57361) on 2011-10-27 13:29:10 (Show Source):
You can put this solution on YOUR website!random sample of 200 measurements give a mean of 50 and standard deviation of 9. at 5% level of significance, test the hypothesis that the population mean is 52.
--------
Ho: u = 52 (claim)
Ha: u is not equal to 52
----
sample mean = 50
z(50) = (50-52)/[9/sqrt(200)] = -3.1427
----
p-value = P(z<-3.1427) = 0.00083705
-------
Since the p-value is less than 5%, reject Ho.
The test results do not support the claim.
================
Cheers,
Stan H.
================
|
Probability-and-statistics/522173: A study conducted by the Corrections Department of a certain state revealed that 164,002 people out of a total adult population of 1,770,000 were under correctional supervision (on probation, parole, or in jail). What is the probability that a person selected at random from the adult population in that state is under correctional supervision? (Round your answer to four decimal places.)
1 solutions
Answer 346735 by stanbon(57361) on 2011-10-27 13:20:10 (Show Source):
You can put this solution on YOUR website!A study conducted by the Corrections Department of a certain state revealed that 164,002 people out of a total adult population of 1,770,000 were under correctional supervision (on probation, parole, or in jail). What is the probability that a person selected at random from the adult population in that state is under correctional supervision? (Round your answer to four decimal places.)
----
P(under correctional supervision) = 164,002/1770000 = 0.0927
==========
Cheers,
Stan H.
================
|
Probability-and-statistics/522174: Of the 106 first-degree murder cases from 2002 through the first half of 2004 in a certain superior court, 6 cases were thrown out of the system, 65 cases were plea-bargained, and 35 cases went to trial. What is the probability that a case selected at random has the following outcomes? (Round your answers to three decimal places.)
(a) settled through plea bargaining
(b) went to trial
1 solutions
Answer 346734 by stanbon(57361) on 2011-10-27 13:16:31 (Show Source):
You can put this solution on YOUR website!Of the 106 first-degree murder cases from 2002 through the first half of 2004 in a certain superior court, 6 cases were thrown out of the system, 65 cases were plea-bargained, and 35 cases went to trial. What is the probability that a case selected at random has the following outcomes? (Round your answers to three decimal places.)
(a) P(ettled through plea bargaining) = 65/106
-------------
(b) P(went to trial) = 35/106
===============================
Cheers,
Stan H.
==========
|
Probability-and-statistics/522192: A die is rolled 360 times. Find the mean, variance, and standard deviation of the number of 4s that will be rolled?
1 solutions
Answer 346732 by stanbon(57361) on 2011-10-27 13:10:18 (Show Source):
You can put this solution on YOUR website! A die is rolled 360 times. Find the mean, variance, and standard deviation of the number of 4s that will be rolled?
---
Binomial distribution with n=360 and p(4) = 1/6
----------------
mean = np = 360*(1/6) = 60
----
variance = npq = 60(5/6) = 50
----
std = sqrt(npq) = 5*sqrt(2)
=============================
Cheers,
Stan H.
=============
|
Probability-and-statistics/522208: blood pressure readings have a mean of 121 and a standard deviation of 15. Find the percentage of people with blood pressure readings above 136
1 solutions
Answer 346731 by stanbon(57361) on 2011-10-27 13:07:20 (Show Source):
You can put this solution on YOUR website!blood pressure readings have a mean of 121 and a standard deviation of 15. Find the percentage of people with blood pressure readings above 136
-------------------
z(136) = (136-121)/15 = 25/15 = 5/3
-----------
P(x > 136) = P(z > 5/3) = 0.0478
===================================
Cheers,
Stan H.
============
|
Numbers_Word_Problems/522210: "the sum of five and eight times a number is the same as fifty plus one-half the number. find the number."
1 solutions
Answer 346728 by stanbon(57361) on 2011-10-27 13:03:53 (Show Source):
You can put this solution on YOUR website! "the sum of five and eight times a number is the same as fifty plus one-half the number. find the number."
-----------------
Let the number be "x":
Equation:
5 + 8x = (x/2) + 50
----
(15/2)x = 45
---
x = (2/15)*45
---
x = 30
==========
Cheers,
Stan H.
==============
|
Probability-and-statistics/522060: In a certain group of computer personnel, 65% have insufficient knowledge of hardware, 45% have inadequate idea of software & 70% are in either one or both of the two categories. What is the percentage of people who do not know software among those who have a sufficient knowledge of hardware?
1 solutions
Answer 346686 by stanbon(57361) on 2011-10-27 07:19:55 (Show Source):
You can put this solution on YOUR website!In a certain group of computer personnel, 65% have insufficient knowledge of hardware, 45% have inadequate idea of software & 70% are in either one or both of the two categories. What is the percentage of people who do not know software among those who have a sufficient knowledge of hardware?
----
P(know soft |no hard) = P(soft AND hard)/P(hard) = 0.30/0.35 = 6/7
===========
Cheers,
Stan H.
==========
|
Probability-and-statistics/522062: A coin is tossed 300 times. What is the probability that heads will appear more than 140 times & less than 150 times?
1 solutions
Answer 346685 by stanbon(57361) on 2011-10-27 07:05:40 (Show Source):
You can put this solution on YOUR website!A coin is tossed 300 times. What is the probability that heads will appear more than 140 times & less than 150 times?
--------
Binomial Problem with n = 300 and p = 1/2
---
P(141<= x <=149) = binomcdf(300,1/2,149)-binomcdf(300,1/2,140) = 0.3407
==========
Cheers,
Stan H.
==========
|
Probability-and-statistics/522087: Four Students sit a typing test.
The probability that Anna passes the test is 1/2
The probablity that Boris passes the test is 4/9
Calulate the probabilty that both Anna and Boris pass the test. Give the answer in its simplest form?
1 solutions
Answer 346684 by stanbon(57361) on 2011-10-27 07:00:46 (Show Source):
You can put this solution on YOUR website!The probability that Anna passes the test is 1/2
The probablity that Boris passes the test is 4/9
Calulate the probabilty that both Anna and Boris pass the test. Give the answer in its simplest form?
-------------
The events are independent so you multiply to get:
P(both pass) = (1/2)(4/9) = 2/9
=================
Cheers,
Stan H.
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Age_Word_Problems/522088: ten years ago a mans age will be two and half times the age he was 20 years ago find his present age
1 solutions
Answer 346682 by stanbon(57361) on 2011-10-27 06:57:10 (Show Source):
You can put this solution on YOUR website!ten years ago a mans age will be two and half times the age he was 20 years ago find his present age
--------------
Let the man's age now be "x".
Equation:
x-10 = (2 1/2)(x-20)
x-10 = (5/2)x - 50
(3/2)x = 40
x = (2/3)40
x = 26 yrs 8 months
===========================
Cheers,
Stan H.
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Linear-equations/521979: I need help solving the equation 7 + 2y = -14 I need to know how to solve it and graph it on a linear equation
1 solutions
Answer 346646 by stanbon(57361) on 2011-10-26 22:13:25 (Show Source):
You can put this solution on YOUR website!7 + 2y = -14 I need to know how to solve it and graph it on a linear equation
----
Subtract 7 from both sides:
2y = -21
Divide both sides by 2:
y = -10.5
-----
You need two points to graph the line:
(1,-10.5), (2,-10.5)
----
Plot the two points and draw a line thru them to see the graph.
-----
----------------
Cheers,
Stan H.
----------------
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Numbers_Word_Problems/521986: i have the same 100 digit as one digit. the value of my tens digit is 50.the value of my one digit is 4
1 solutions
Answer 346645 by stanbon(57361) on 2011-10-26 22:06:43 (Show Source):
You can put this solution on YOUR website!i have the same 100 digit as one digit. the value of my tens digit is 50.the value of my one digit is 4
------
Let the number be 100h + 10t+u:
---
Equations:
h = u
t = 5
u = 4
-----
Number: 454
=================
Cheers,
Stan H.
-----------------
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Rectangles/521985: The length of a rectangle is 8 more than 3 times the width, if the perimeter is 64, what are the measurements? The area?
1 solutions
Answer 346642 by stanbon(57361) on 2011-10-26 21:58:35 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is 8 more than 3 times the width, if the perimeter is 64, what are the measurements? The area?
-----
L = 3W + 8
---
Perimeter = 2(length + width)
64 = 2(3W+8 + W)
32 = 4W+8
4W = 24
Width = 6
---
Then Length = 3*6 + 8 = 26
----
Area = L*W
Area = 6*26 = 156
=======================
Cheers,
Stan H.
==============
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Mixture_Word_Problems/521982: A photographer wishes to mix 5 liters of 4% acetic acid solution with a 8% solution to get a 7% solution. How many liters of 8% solution must be added?
1 solutions
Answer 346641 by stanbon(57361) on 2011-10-26 21:55:19 (Show Source):
You can put this solution on YOUR website!A photographer wishes to mix 5 liters of 4% acetic acid solution with a 8% solution to get a 7% solution. How many liters of 8% solution must be added?
---
Equation:
acid + acid = acid
0.04*5 + 0.08x = 0.07(5+x)
-----
Multiply thru by 100 to get:
4*5 + 8x = 7*5 + 7*x
x = 3*5
x = 15 liters (amt. of 8% solution needed)
==============================================
Cheers,
Stan H.
===========
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Equations/521975: please help me solve this problem by substitution
(x-4y+z=6 & 2x+5y-z=7 & 2x-y-z=1)
What would x, y & z equal?
1 solutions
Answer 346639 by stanbon(57361) on 2011-10-26 21:52:48 (Show Source):
You can put this solution on YOUR website!x-4y+z =6
2x+5y-z=7
2x-y-z =1
------------------
Use any method you know to get:
x = 4
y = 1
z = 6
=============
Cheers,
Stan H.
=============
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Circles/521892: Write the equation of a circle with endpoints of the diameter at (2, -5) and (-4, 3).
Show your work for credit.
please please PLEASE help.:)
1 solutions
Answer 346612 by stanbon(57361) on 2011-10-26 20:28:22 (Show Source):
You can put this solution on YOUR website!Write the equation of a circle with endpoints
of the diameter at (2, -5) and (-4, 3).
---
The midpoint of the diameter is the center of the circle.
center = ?
x coordinate: (-4+2)/2 = -1
y coordinate: (3-5)/2 = -1
-----------------------------
center is at (-1,-1)
----
radius = ?
radius = sqrt[(3--1)^2 + (-4--1)^2] = sqrt[16+9] = 5
-----
Equation:
(x+1)^2 + (y+1)^2 = 25
===========================
Cheers,
Stan H.
============
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Numbers_Word_Problems/521875: Flying with the wind, an airplane can travel 1080 miles in 6 hours, but flying against the wind it goes only 1/3 the distance in half the time. Find the speed of the plane in still air and the wind speed.
1 solutions
Answer 346605 by stanbon(57361) on 2011-10-26 20:16:19 (Show Source):
You can put this solution on YOUR website!Flying with the wind, an airplane can travel 1080 miles in 6 hours, but flying against the wind it goes only 1/3 the distance in half the time. Find the speed of the plane in still air and the wind speed.
-----------------------------------
With-wind: rate = distance/time = 1080/6 = 180 mph
Against-wind: rate = distance/time = 360/3 = 120 mph
---------------------------------------
Equations:
p + w = 180
p - w = 120
----
Add and solve for "p":
2p = 300
p = 150 (speed of the plane with no wind)
----
Solve for "w":
p + w = 180
150 + w = 180
w = 30 mph (speed of the wind)
================================
Cheers,
Stan H.
=============
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Numbers_Word_Problems/521871: The sum of two numbers is five times their difference. If one number exceeds the other by 7, find the numbers.
1 solutions
Answer 346603 by stanbon(57361) on 2011-10-26 20:09:39 (Show Source):
You can put this solution on YOUR website!The sum of two numbers is five times their difference. If one number exceeds the other by 7, find the numbers.
-----------------
Equations:
x+y = 5(x-y)
x = y + 7
--------------------
Substitute for "x" and solve for "y":
y+7+y = 5(y+7-y)
2y + 7 = 35
2y = 28
y = 14 (one of the numbers)
------
Solve for "x":
x = y + 7
x = 14+7
x = 21 (the other number)
================================
Cheers,
Stan H.
=============
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Age_Word_Problems/521863: I am 44 and my daughter is twelve what will our ages be when I am 3 times her age?
1 solutions
Answer 346602 by stanbon(57361) on 2011-10-26 20:05:26 (Show Source):
You can put this solution on YOUR website!I am 44 and my daughter is twelve what
will our ages be when I am 3 times her age?
----
Let the answer be "in x years".
------------------
Equation:
44+x = 3(12+x)
---
44+x = 36 + 3x
2x = 8
Ans: x = 4 years
---
In 4 years "I" will be 44+4 = 48
In 4 years the daughter will be 12+4 = 16
==============================================
Cheers,
Stan H.
============
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Travel_Word_Problems/521861: An elf steals a sleeping dragon's gold treasure and runs off at 16 mph. 3 hours after the theft, the dragon wakes up and sets off after the elf at 20 mph. How long will it take the dragon to capture his lunch?
Dragon dines on firey roasted elf in ________ hours.
1 solutions
Answer 346601 by stanbon(57361) on 2011-10-26 20:00:04 (Show Source):
You can put this solution on YOUR website!An elf steals a sleeping dragon's gold treasure and runs off at 16 mph.
---------------------------------
3 hours after the theft, the dragon wakes up and sets off after the elf at 20 mph.
-------------------------------------------
How long will it take the dragon to capture his lunch?
------------------------------------
Elf DATA:
rate = 16 mph ; time = x hrs ; distance = 16x miles
------
Dragon DATA:
rate = 20 mph ; time = x-3 hrs ; distance = 20(x-3) miles
----------------------
Equation:
elf distance = dragon distance
16x = 20(x-3)
16x = 20x - 60
4x = 60
x = 15 hrs (elf time)
x-3 = 12 hrs (dragon time)
==============================
Cheers,
Stan H.
================
Dragon dines on firey roasted elf in ________ hours.
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Percentage-and-ratio-word-problems/521852: A retired couple invested part of $11,400 at 6% interest and the rest at 7.5%. If their annual income from these investments is $783. Find the invested part at each rate?
1 solutions
Answer 346600 by stanbon(57361) on 2011-10-26 19:51:37 (Show Source):
You can put this solution on YOUR website!A retired couple invested part of $11,400 at 6% interest and the rest at 7.5%. If their annual income from these investments is $783. Find the invested part at each rate?
------
Equations:
x + y = 11,400
0.075x + 0.06y = 783
-----------------------------
Multiply thru 1st equation by 75
Multiply thru 2nd equation by 1000
-----
75x + 75y = 75*11400
75x + 60y = 783000
-----
Subtract and solve for "y":
15y = 72000
-----
y = $4800 (amt invested at 6%)
----------------
Solve for "x":
x + y = 11,400
x + 4800 = 11,400
x = $6600 (amt invest at 7.5%)
================================
Cheers,
Stan H.
=============
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