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Recent problems solved by 'stanbon'
stanbon answered: 57279 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 , 57240..57269 , 57270..57299, >>Nexttest/684800: X=-2 show graphing and steps please
1 solutions
Answer 424210 by stanbon(57352)   on 2012-11-25 18:08:54 (Show Source):
You can put this solution on YOUR website!X=-2 show graphing and steps please
----
x = -2 ; y can be any value:
Plot (-2,2) and (-2,5)
Draw a line thru those 2 points.
----
You have a vertical line passing thru
ALL points where x = -2.
---------------------
Cheers,
Stan H.
=====================
|
Probability-and-statistics/684704: 9 friends including Ann,Barry,Claire . 5 tickets are available. How many ways can a group of 5 be selected if at least 1 of Ann,Barry,Claire must be included
1 solutions
Answer 424196 by stanbon(57352) on 2012-11-25 17:11:30 (Show Source):
You can put this solution on YOUR website!9 friends including Ann,Barry,Claire . 5 tickets are available. How many ways can a group of 5 be selected if at least 1 of Ann,Barry,Claire must be included
-------
Pick 4 of the six: 6C4 = 6C2 = 15 ways
---
Pick 1 of the 3:: 3C1 = 3
----
Ans: Total # of ways = 15*3 = 45 ways
--------------
Cheers,
Stan H.
==============
|
Probability-and-statistics/684732: Suppose we want to determine the (binomial) probability(p) of getting 6 heads in 15 flips of a 2-sided coin. Using the Binomial Probabilities Table in Appendix B of the text, what values of n, x and p would we use to look up this probability, and what would be the probability?
1 solutions
Answer 424194 by stanbon(57352) on 2012-11-25 16:44:54 (Show Source):
You can put this solution on YOUR website!Suppose we want to determine the (binomial) probability(p) of getting 6 heads in 15 flips of a 2-sided coin. Using the Binomial Probabilities Table in Appendix B of the text, what values of n, x and p would we use to look up this probability, and what would be the probability?
------
n = 15
p = 1/2
x = 6
----
P(x = 6) = 15C6(1/2)^6*(1/2)^9 = 15C6/2^15 = 5005/32768 = 0.1527
============
Cheers,
Stan H.
|
Probability-and-statistics/684743: The chance of winning a lottery game is 1 in approximately 21 million. Suppose you buy a $1 lottery ticket in anticipation of winning the $8 million grand prize. Calculate your expected net winnings for this single ticket. Interpret the result.
Find µ= E (x)
1 solutions
Answer 424193 by stanbon(57352) on 2012-11-25 16:41:00 (Show Source):
You can put this solution on YOUR website!The chance of winning a lottery game is 1 in approximately 21 million. Suppose you buy a $1 lottery ticket in anticipation of winning the $8 million grand prize. Calculate your expected net winnings for this single ticket. Interpret the result.
-------
Random "winning" values::::::::::: 8x10^6-1::::::::::::::::: -1
Probabilities::::::::::::::::::::: 1/21x10^6::::: (21x10^6-1)/(21x10^6)
-------
E(x) = [8x10^6-1 - 21x10^6-1]/21x10^6
---
= -0.62
-----
You can expect to lose 62 cents on each dollar you spend on the lottery.
=========================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/684726: your teacher is giving youa test worth 100 points containing 40 questions.there are 2-point and 4-point questions on the test. how many of each type of question are on the test?
1 solutions
Answer 424188 by stanbon(57352) on 2012-11-25 16:16:29 (Show Source):
You can put this solution on YOUR website!your teacher is giving youa test worth 100 points containing 40 questions.there are 2-point and 4-point questions on the test. how many of each type of question are on the test?
---------
Equations:
Quantity Eq: t + f = 40
Points Eq:: 2t +4f = 100
---------------------------
Modify:
t + f = 40
t + 2f = 50
----
Subtract and solve for "f":
f = 10 (# of 4-point questions)
----
Solve for "t" using t + f = 40
t + 10 = 40
t = 30 (# of 2-point questions)
==================
Cheers,
Stan H.
==================
|
Money_Word_Problems/684727: the number of grams of a certain radioactive substance present after t hours is given by the equation Q=Q(0)e^-0.45t, where Q(0) represents the initial number of grams. how long will it take 2500 grams to be REDUCED to 1250 grams?
1 solutions
Answer 424186 by stanbon(57352) on 2012-11-25 16:05:58 (Show Source):
You can put this solution on YOUR website!the number of grams of a certain radioactive substance present after t hours is given by the equation Q=Q(0)e^-0.45t, where Q(0) represents the initial number of grams. how long will it take 2500 grams to be REDUCED to 1250 grams?
--------
Solve for "t":
1250 = 2500*e^(-0.45t)
----
e^(-0.45t) = 0.5
---
Take the log of both sides:
-0.45t = ln(0.5) = -0.6931
t = 1.54 hours
=================
Cheers,
Stan H.
|
Functions/684721: Find the domain of the rational function:
(y+5)/(y^2-5y)
1 solutions
Answer 424182 by stanbon(57352) on 2012-11-25 15:58:58 (Show Source):
You can put this solution on YOUR website!Find the domain of the rational function:
(y+5)/(y^2-5y)
----
The denominator cannot be zero.
Solve:
y^2-5y = 0
Factor:
y(y-5) = 0
y = 0 or y = 5
----
Ans: Domain is All Real Numbers except y = 0 and y = -5.
=============
Cheers,
Stan H.
=================
|
Probability-and-statistics/684633: If you answer 5 multiple choice questions (each having four selection), what is the probability of getting all 5 correct?
1 solutions
Answer 424162 by stanbon(57352) on 2012-11-25 14:27:02 (Show Source):
You can put this solution on YOUR website!If you answer 5 multiple choice questions (each having four selection), what is the probability of getting all 5 correct?
-----
Binomial Problem with n = 5 ; p(correct) = 1/4
---
P(x=5) = 5C5(1/4)^5*(3/4)^0 = (1/4)^5 = 0.00009766
-----------
Cheers,
Stan H.
=============
|
Probability-and-statistics/684501: A panel of 5 politicians is to be chosen from a group of 15 politicians
a) In how many ways can the panel be chosen?
Now suppose that the group of politicians consists of 8 Democrats, 4 Republicans, and 3 Independents. In how many ways can the panel of 5 politicians be chosen if the panel must consist of 2 Democrats, 2 Republicans, and 1 Independent?
1 solutions
Answer 424160 by stanbon(57352) on 2012-11-25 14:19:37 (Show Source):
You can put this solution on YOUR website!A panel of 5 politicians is to be chosen from a group of 15 politicians
a) In how many ways can the panel be chosen?
Ans: 15C5 = (15*14*13*12*11)/(1*2*3*4*5) = 3003
-------
Now suppose that the group of politicians consists of 8 Democrats, 4 Republicans, and 3 Independents.
In how many ways can the panel of 5 politicians be chosen if the panel must consist of 2 Democrats, 2 Republicans, and 1 Independent?
-
Ans: 8C2*4C2*3C1 = 28*6*3 = 504 ways
=================
Cheers,
Stan H.
===================
|
Quadratic_Equations/684406: I want to first say, thank you for your service, and that this is not homeowrk for me but a study review for an exam so your help would be amazing so I can prepare well for it.
Find the distance PQ and the coordinates of the midpoint for the following ordered pairs.
1) p(-3,9), Q(2,7)
2)p(2x,-4x), Q(4x,2x^2)
Find the x-intercept and y-intercept for each line. use the intercepts to graph the equations
3) x/2+y/3=1
4)4x-5y=20
Graph the linear inequality
5)2x-y less then and equal to 1
6)x/2+y/4>1
7) x<2y
1 solutions
Answer 424084 by stanbon(57352) on 2012-11-24 18:18:05 (Show Source):
You can put this solution on YOUR website!Find the distance PQ and the coordinates of the midpoint for the following ordered pairs.
1) p(-3,9), Q(2,7)
d = sqrt[(9-7)^2+(2--3)^2] = sqrt[4+25] = sqrt(29)
-----------------------------------
2)p(2x,-4x), Q(4x,2x^2)
d = sqrt[(2x^2-2x)^2 + (4x--4x)^2] = sqrt[4x^4-8x^3+4x^2+64x^2]
= sqrt[4x^4-8x^3+68x^2]
-----------------------------------
Find the x-intercept and y-intercept for each line. use the intercepts to graph the equations
3) x/2+y/3=1
x-intercept: Let y = 0, then x = 2
y-intercept: Let x = 0, then y = 3
-----
Graph the line that passes thru (0,3) and (2,0)
-----------------------------------------
4)4x-5y=20
x-intercept: Let y = 0, then x = 5
y-intercept: Let x = 0, then y = -4
----
Graph the line that passes thru (0,-4) and (5,0)
--------------------------------------------------
Graph the linear inequality
5)2x-y less then and equal to 1
Graph the boundary y = 2x-1
Shade the half-plane above that boundary.
---------------------------------------------
6)x/2+y/4>1
y/4 > (-x/2)+1
y > -2x+4
Graph the boundary y = -2x+4 as a dashed line.
Shade the half-plane above that boundary.
--------------------------------
7) x<2y
y > (1/2)x
----
Draw the boudary y = (1/2)x as a dashed line.
Shade the half-plane above the boundary.
=============
Cheers,
Stan H.
|
Trigonometry-basics/684328: For each right triangle find all the missing values of the side lengths and angle measures.Show your work
a) Triangle PQR is right angled at Q , PQ is 24 cm, RQ is 10 cm , PQ is the hypotenuse which is unknown.
b) Triangle PRQ is right angled at R, PQ is 30 mm , RQ is 40 mm , PQ is 50 mm.
c) Triangle QRP is right angled at R , angle of P is 60 degrees, QP is 20 cm.
can you please explain this to me? thanks in advance
d) Triangle PQR is right angled at Q , QR is 1.125 dm, PR is 5.125 dm.
1 solutions
Answer 424053 by stanbon(57352) on 2012-11-24 16:17:16 (Show Source):
You can put this solution on YOUR website!For each right triangle find all the missing values of the side lengths and angle measures.Show your work
a) Triangle PQR is right angled at Q , PQ is 24 cm, RQ is 10 cm , PQ is the hypotenuse which is unknown.
PQ = sqrt[24^2+10^2] = sqrt(576] = 26
---------------------------------------------------
b) Triangle PRQ is right angled at R, PQ is 30 mm , RQ is 40 mm , PQ is 50 mm.
P is the angle opposite RQ
PQ is opposite R and is the hypotenuse
So P = sin^-1(40/50) = 53.13 degrees
And Q = sin^-1(30/50) = 36.87 degrees
-----------------------------
c) Triangle QRP is right angled at R , angle of P is 60 degrees, QP is 20 cm.
can you please explain this to me? thanks in advance
Draw the picture.
You have a right triangle with
hypotenuse is side opposite right angle R which is QP = 20 cm
P = 60 degrees is the angle opposite QR
Q = 90-60 = 30 degrees
------
QR is side opposite P, so sin(P) = QR/QP ; sin(60) = QR/20 ;
QR = 20*sin(60) = 17.32
PR is side opposite Q which is 30 degrees
PR = (1/2)*hypotenuse = (1/2)*20 = 10 cm
--------------------------------
---------------------------
d) Triangle PQR is right angled at Q , QR is 1.125 dm, PR is 5.125 dm.
Draw the picture and see if you can determine:
angle P =
angle R =
side PQ =
=================
Cheers,
Stan H.
==================
|
Trigonometry-basics/683572: i don't get the concept of exact trigonometric value
so the problem is
sin(data) =2/5
0degrees<(data)< 90degrees
cos(data)=?
please show all work and if possible, please explain how to solve these kind of problems
1 solutions
Answer 424046 by stanbon(57352) on 2012-11-24 15:52:34 (Show Source):
You can put this solution on YOUR website!sin(data) =2/5
0degrees<(data)< 90degrees
cos(data)=?
-------
sin(angle) = y/r
------------------------
Since sin(data) = 2/5,y = 2 and r = 5
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Solve for "x" using r^2 = x^2+y^2
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x = sqrt[r^2-y^2] = sqrt[25-4] = sqrt(21)
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Your Problem:
cos(data) = x/r = sqrt(21)/5
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Cheers,
Stan H.
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Trigonometry-basics/684320: In the right triangle ABC, AB is 10 m, AC is 24 m, BC is 26 m. Give all the possible names of each of the following ratios.
a) 10/26
b) 10/24
c) 24/26
d) 24/10
can you please explain this to me ? thanks in advance
1 solutions
Answer 424044 by stanbon(57352) on 2012-11-24 15:46:25 (Show Source):
You can put this solution on YOUR website!In the right triangle ABC, AB is 10 m, AC is 24 m, BC is 26 m. Give all the possible names of each of the following ratios.
a) 10/26
b) 10/24
c) 24/26
d) 24/10
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AB is opposite angle C
AC is opposite angle B
BC is opposite angle A
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Draw the right triangle with BC as the hypotenuse
AC as the base and AB as the height.
----
a) 10/26 = AB/BC = height/hypotenuse = sin(C) or cos(B)
b) 10/24 = AB/AC = height/base = tan(C)
c) 24/26 = AC/BC = base/hypotenuse = cos(C) or sin(B)
d) I'll leave this one to you
===============
Cheers,
Stan H.
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Trigonometry-basics/684350: Could someone please help a damsel in distress?
16-24x-9x^2
I would greatly appreciate it!
1 solutions
Answer 424039 by stanbon(57352) on 2012-11-24 15:29:03 (Show Source):
You can put this solution on YOUR website!16-24x-9x^2
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Assuming you want to solve this Quadratic,
use the Quadratic Formula:
a = -9, b = -24, c = 16
----
x = [24 +- sqrt(24^2 - 4*(-9)(16)]/(-18)
---
x = [24 +- sqrt(1152)]/-18
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x = [24 +- 33.94]/(-18)
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x = 57.94/-18 or x =
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x = -3.22... or x = 0.55...
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Cheers,
Stan H.
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Probability-and-statistics/684334: You walk into statistics class one Wednesday & find that you’re having a pop quiz looking at the exam, you find that there are 72 multiple-choice questions with three possible responses (A, B or C) for each, where only one is correct. The passing grade is set at 50%. Unluckily for you, you haven’t been to a single class before this, nor have you ever opened the textbook. Actually, you can’t even say for sure who the guy is at the front of the class. You will have to guess the answer on all the questions. What is the probability that you will pass the exam?
1 solutions
Answer 424036 by stanbon(57352) on 2012-11-24 15:17:44 (Show Source):
You can put this solution on YOUR website!You walk into statistics class one Wednesday & find that you’re having a pop quiz looking at the exam, you find that there are 72 multiple-choice questions with three possible responses (A, B or C) for each, where only one is correct. The passing grade is set at 50%. Unluckily for you, you haven’t been to a single class before this, nor have you ever opened the textbook. Actually, you can’t even say for sure who the guy is at the front of the class. You will have to guess the answer on all the questions. What is the probability that you will pass the exam?
--------
Note: 50% of 72 is 36
Binomial Problem with n = 72 ; p(correct) = 1/3
----
P(36<= x <=72) = 1-P(0<= x <= 35) = 1 - binomcdf(72,1/3,35) = 0.0025
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Cheers,
Stan H.
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Probability-and-statistics/684343: 1. Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 20 to 90. What is the probability that this experiment results in an outcome less than 30? (Points : 2)
1 solutions
Answer 424034 by stanbon(57352) on 2012-11-24 15:12:09 (Show Source):
You can put this solution on YOUR website!Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 20 to 90. What is the probability that this experiment results in an outcome less than 30?
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Draw a picture of the distribution.
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You have a rectangle on the x-axis with base
running from 20 to 90.
So the base is 70
Therefore the height is 1/70
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Shade the area in the rectangle over the interval (20,30)
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Find the area of that shaded area:
base = 10
height = 1/70
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Area = P(20<= x <=30) = 10(1/70) = 1/7
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Cheers,
Stan H.
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Functions/684340: Find the equation of a straight line l1 which is perpendicular to l2:2x+3y-1=0 at the meeting point of l2 with the y-axis.
1 solutions
Answer 424033 by stanbon(57352) on 2012-11-24 15:07:07 (Show Source):
You can put this solution on YOUR website!Find the equation of a straight line l1 which is perpendicular to l2:2x+3y-1=0 at the meeting point of l2 with the y-axis.
----
Determine the slope of the given line:
2x + 3y - 1 = 0
3y = -2x+1
y = (-2/3)x + (1/3)
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Slope = -2/3
----
Any line perpendicular to it must have a slope of 3/2
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Equation Form: y = mx + b
You know m = 3/2 and y = 0 when x = 12
----
Solve for "b":
0 = (3/2)12 + b
b = -18
----
Equation:
y = (3/2)x - 18
====================
Cheers,
Stan H.
==============
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Functions/684337: Please help me solve: rewrite the equation so y is a function of x
-2y=2x+8
My answer was: y=-x-4 or y=-4-x
1 solutions
Answer 424031 by stanbon(57352) on 2012-11-24 14:59:26 (Show Source):
You can put this solution on YOUR website!Please help me solve: rewrite the equation so y is a function of x
-2y=2x+8
----
Divide both sides by -2 to get:
y = -x -4
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Cheers,
Stan H.
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�t�e�s�t/683064: a student says that the graph of y= ax2 + bx+ c gets wider as a incereases.
A. Error Analysis use examples to show that the student is wrong.
B.Writing Summarize the relationship between |a| and the width of the graph of y= ax2 + bx+ c
1 solutions
Answer 423450 by stanbon(57352) on 2012-11-19 21:33:14 (Show Source):
You can put this solution on YOUR website!a student says that the graph of y= ax2 + bx+ c gets wider as a incereases.
A. Error Analysis use examples to show that the student is wrong.
----
Compare y = x^2(red) to y = 9x^2(green)
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----------------
Cheers,
Stan H.
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Linear-equations/683060: I don't know what type of help I need. I am trying to solve the problem - the product of two numbers is 442. The sum of the two numbers is 43. Find the two numbers. I don't know if this is algebra or what it is. I tried timesing 43 by several numbers and I tried dividing 442 but I can't find an answer.
1 solutions
Answer 423448 by stanbon(57352) on 2012-11-19 21:28:35 (Show Source):
You can put this solution on YOUR website!the product of two numbers is 442. The sum of the two numbers is 43. Find the two numbers.
-------
Equations:
xy = 442
x+y = 43
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Substitute for "x" and solve for "y":
x = 43-y
----
So (43-y)y = 442
-y^2 +43y = 442
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y^2 - 43y +442 = 0
(y-17)(y-26) = 0
y = 17 or y = 26
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Solve for "x":
If y = 17, x = 43-17 = 26
If y = 26, x = 43-26 = 17
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Cheers,
Stan H.
===============
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Mixture_Word_Problems/683052: In a chemistry class, 4 liters of a 4% silver iodine solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?
1 solutions
Answer 423441 by stanbon(57352) on 2012-11-19 21:13:58 (Show Source):
You can put this solution on YOUR website!In a chemistry class, 4 liters of a 4% silver iodine solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?
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Equation:
active + active = active
0.04*4 + 0.10x = 0.06(4+x)
----
Multiply thru by 100 to get:
4*4 + 10x = 6*4 + 6x
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4x = 2*4
x = 2 liters (amt. of 10% solution needed)
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Cheers,
Stan H.
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