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Recent problems solved by 'stanbon'
stanbon answered: 57214 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>NextExponential-and-logarithmic-functions/606080: simplify
this one is hard to write but it looks like
4^log base4 x
i think you take the 4(the 4 that is in front) and put it above the x.
then it would be log base 4 x^4
do you put the 4 equal to the x or the way I did it above?
Thank you 1 solutions
Answer 381910 by stanbon(57282) on 2012-05-01 22:05:34 (Show Source):
|
Rational-functions/606082: Find The Function Of G(X)Whose Graph Can Be Obtained By Translating The Graph Of Y=5x+7 Up 4 Units And To The Right 2 Units 1 solutions
Answer 381909 by stanbon(57282) on 2012-05-01 22:03:49 (Show Source):
You can put this solution on YOUR website!Find The Function Of G(X)Whose Graph Can Be Obtained By Translating The Graph Of Y=5x+7 Up 4 Units And To The Right 2 Units
-----
y = 5(x-2) + 7 + 4
---
y = 5x-10+11
---
y = 5x+1
=============
Cheers,
Stan H.
=============
|
Travel_Word_Problems/606073: Two mopeds leave town at the same time in opposite directions. One travels 25 kilometers per hour and the other one travels at 45 kilometers per hour. In how many hours will they be 210 miles apart? 1 solutions
Answer 381908 by stanbon(57282) on 2012-05-01 22:01:56 (Show Source):
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Age_Word_Problems/606066: Heather is 15 years older than Kim. In 10 years heather will be twice as old as Kim will be. How old is heather now 1 solutions
Answer 381903 by stanbon(57282) on 2012-05-01 21:32:32 (Show Source):
You can put this solution on YOUR website!Heather is 15 years older than Kim. In 10 years heather will be twice as old as Kim will be. How old is heather now
-----
Equations:
h = k + 15
(h+10) = 2(k+10)
----
Substitute for "h" and solve for "k":
k+15 + 10 = 2k + 20
k + 25 = 2k + 20
k = 5 (Kim's age now)
------
Solve for "h":
h = k + 15
h = 5 + 15 = 20 yrs (Heather's age now)
===================
Cheers,
Stan H.
======================
|
real-numbers/606067: To rationalize 4+3i/1+2i, multiply the numerator and the denominator by?
a. 2+i
b. 4-i
c.10/3+5/3 i
d. 1-2i 1 solutions
Answer 381901 by stanbon(57282) on 2012-05-01 21:29:08 (Show Source):
You can put this solution on YOUR website!To rationalize 4+3i/1+2i, multiply the numerator and the denominator by?
a. 2+i
b. 4-i
c.10/3+5/3 i
d. 1-2i
---------------------
Ans: 1-2i
=================
Cheers,
Stan H.
|
Probability-and-statistics/605958: Four cards with "girl" printed on them and five cards with "boy" printed on them are shuffled and placed face-down on a table. A card is drawn, and without replacing it, a second card is drawn. What is the probability that both cards have "girl" written on them 1 solutions
Answer 381900 by stanbon(57282) on 2012-05-01 21:16:31 (Show Source):
You can put this solution on YOUR website!Four cards with "girl" printed on them and five cards with "boy" printed on them are shuffled and placed face-down on a table. A card is drawn, and without replacing it, a second card is drawn. What is the probability that both cards have "girl" written on them
-------
# of ways to succeed: 4C2 = 6
# of random pairs: 9C2 = 36
------
P(2 girl cards) = 6/36 = 1/6
================================
Cheers,
Stan H.
|
Probability-and-statistics/605985: Question One:
Scores on a test are normally distributed with a mean of 541 and a standard deviation of 120. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score below 181. 1 solutions
Answer 381898 by stanbon(57282) on 2012-05-01 21:14:23 (Show Source):
You can put this solution on YOUR website!Scores on a test are normally distributed with a mean of 541 and a standard deviation of 120. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score below 181.
----
Find the number of standard deviations 181 is to the left of the mean:
(541-181)/120 = 3
-------
Draw a normal curve.
According to the "Rule" only 0.3% of the people are
outside the 99.7% limits.
---
Only 0.3%2 = 0.15% or 0.0015 of the people are below 181.
===================
Cheers,
Stan H.
|
Probability-and-statistics/606006: Two cards are drawn from a well-shuffled deck of 52 playing cards. Let X denote the number of aces drawn. Find P(X = 2). (Round your answer to three decimal places.) 1 solutions
Answer 381896 by stanbon(57282) on 2012-05-01 21:08:25 (Show Source):
You can put this solution on YOUR website! Two cards are drawn from a well-shuffled deck of 52 playing cards. Let X denote the number of aces drawn. Find P(X = 2).
----------------------
Number of ways to succeed: 4C2 = 6
---
Number of random pairs: 52C2 = (52*51)/(1*2) = 26*51 =
----
P(x = 2 aces) = 6/52C2 = 6/1326 = 3/663 = 1/221
---------------------------------------------------
Cheers,
Stan H.
|
Finance/605776: What is the probability of getting at least 3 tails when tossing a coin 6 times? 1 solutions
Answer 381800 by stanbon(57282) on 2012-05-01 11:16:26 (Show Source):
You can put this solution on YOUR website!What is the probability of getting at least
3 tails when tossing a coin 6 times?
---------------
Binomial Problem with n = 6 and p(tail) = 1/2
----
P(3<= x <=6) = 1 - binomcdf(6,1/2,2) = 0.6563
==================
Cheers,
Stan H.
============
|
logarithm/605773: Please help me solve this equation:
log(x+3)=2+log(x) 1 solutions
Answer 381799 by stanbon(57282) on 2012-05-01 11:12:13 (Show Source):
You can put this solution on YOUR website!Please help me solve this equation:
log(x+3)=2+log(x)
----
log(x+3) - log(x) = 2
----
log[(x+3)/x] = 2
----
(x+3)/x = 10^2
---
x+3 = 100x
99x = 3
x = 1/33
===============
Cheers,
Stan H.
=====================
|
Finance/605770: If 2 fair dice (6 sides) are rolled, what is the probability of the sum being at least 10? 1 solutions
Answer 381798 by stanbon(57282) on 2012-05-01 11:09:23 (Show Source):
You can put this solution on YOUR website!If 2 fair dice (6 sides) are rolled, what is the probability of the sum being at least 10?
----
Successful pairs:
4/6 ; 5/5 ; 6/4
5/6 ; 6/5
6/6
--------------
Ans: 6/36 = 1/6
=====================
cheers,
Stan H.
|
Finance/605762: Find the amount of interest earned for a deposit of $24,677.23 at 9.72% compounded monthly for 32 months. 1 solutions
Answer 381795 by stanbon(57282) on 2012-05-01 11:06:10 (Show Source):
You can put this solution on YOUR website!Find the amount of interest earned for a deposit of $24,677.23 at 9.72% compounded monthly for 32 months.
-------------------------
Interest = value after 32 months - initial deposit
----
Value after 32 mths.: 24677.23(1 + (0.0972/12))^(12*(32/12))
------
= 24677.23(1.0081^(32) = 24677.23*1.2945
= 31945.68
----
Interest = 31945.68-24677.23 = 7268.45
========================
Cheers,
Stan H.
========================
|
Probability-and-statistics/605750: If a couple plans to have eight children, find the probability that they are all of the same gender (assuming that probability of having a girl is 0.5) 1 solutions
Answer 381792 by stanbon(57282) on 2012-05-01 10:56:07 (Show Source):
You can put this solution on YOUR website! If a couple plans to have eight children, find the probability that they are all of the same gender (assuming that probability of having a girl is 0.5)
-----
Ans: (1/2)^8 = 1/256
============
Cheers,
Stan H.
===============
|
Probability-and-statistics/605759: In a certain game, there is a 0.7 probability that you win $20 and 0.3 probability that you lose $40. Find the expected value. 1 solutions
Answer 381791 by stanbon(57282) on 2012-05-01 10:54:07 (Show Source):
You can put this solution on YOUR website! In a certain game, there is a 0.7 probability that you win $20 and 0.3 probability that you lose $40. Find the expected value.
---------------
E(x) = 0.7*20 + 0.3*40 = 14+12 = $26.00
========================================
Cheers,
Stan H.
|
Travel_Word_Problems/605488: Kathryn drove her rig 3 hours before dawn and 4 hours after dawn. Her average speed was 6 miles per hour more in the dark and she covered 410 miles altogether. What was her speed after dawn in miles per hour?
I need to know teh correct formula as well as how to find this answer. Thank you.
1 solutions
Answer 381711 by stanbon(57282) on 2012-04-30 19:22:58 (Show Source):
You can put this solution on YOUR website!Kathryn drove her rig 3 hours before dawn and 4 hours after dawn. Her average speed was 6 miles per hour more in the dark and she covered 410 miles altogether. What was her speed after dawn in miles per hour?
-----------------------
Before dawn DATA:
time = 3 hrs ; rate = x+6 mph ; distance = 3x+18 miles
----------------------------------
After dawn DATA:
time = 4 hrs ; rate = x mph ; distance = 4x miles
-----------------------------------------
Equation:
3x+18 + 4x = 410 miles
7x = 392 miles
x = 56 mph (speed after dawn)
===================================
Cheers,
Stan H.
|
Probability-and-statistics/605446: If the odds in favor of winning first prize in a sweepstake contest are 2500 to 1, what is the probability of winning first prize? 1 solutions
Answer 381709 by stanbon(57282) on 2012-04-30 19:13:07 (Show Source):
You can put this solution on YOUR website!If the odds in favor of winning first prize in a sweepstake contest are 2500 to 1, what is the probability of winning first prize?
------
Ans: P(winning) = 2500/2501
----------------------------------
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/605452: The problem is y^2-6y+16x+25=0. I have to find the vertex, the focus, the directrix and the axis. 1 solutions
Answer 381706 by stanbon(57282) on 2012-04-30 18:56:03 (Show Source):
You can put this solution on YOUR website!The problem is y^2-6y+16x+25=0.
I have to find the vertex, the focus, the directrix and the axis.
-----------------------------
Rearrange:
16x = -y^2+6y-25
16x = -(y^2-6y+25)
16x = -(y^2-6y+9)-25+9
--------
x = (-1/16)(y-3)^2 +(9/16)
That is a parabola opening to the left:
k = 3 ; h = 9/16
4p = -1/16
p = -1/64
-----------------
Vertex: (9/16 , 3)
Axis: y = 3
Focus: (9/16-1/64,3) = (35/64 , 3)
Directrix: x = 9/16+1/64 = 37/64
=========================================
Cheers,
Stan H.
=================
|
Linear-equations/605465: Graph the linear equation. 3x-4y= 24 1 solutions
Answer 381698 by stanbon(57282) on 2012-04-30 18:33:43 (Show Source):
You can put this solution on YOUR website!Graph the linear equation. 3x-4y= 24
---------------------
Let x = 0, then y = -6
Let y = 0, then x = 8
----------------------------
Plot (0,-6) and (8,0) and draw a line thru them to get:

===========================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/605463: I am trying to help me 12 year old with his word problems, but I think I am going in the wrong direction and will confuse him. The question is " Nine less eight times a number is one less than negative two times the difference of three times the number and six.
8n-9=3n + 6 - 1-2n
Please help --- am i on the right track?? Thanks so much! 1 solutions
Answer 381697 by stanbon(57282) on 2012-04-30 18:28:45 (Show Source):
You can put this solution on YOUR website!Nine less eight times a number is one less than negative two times the difference of three times the number and six.
-------
Equation:
Let the number be "x":
9 - 8x = -2(3x-6)-1
-----
9 - 8x = -6x+12-1
---
9 - 8x = -6x+11
2x = -2
x = -1
================
cheers,
Stan H.
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Geometry_Word_Problems/605461: A toy rocket is launched from a building 148 feet tall at an initial velocity of 222 feet per second.
(a)give the function that describes the height of the rocket in terms of time t.
(b) determine the time at which the rocket reaches its maximum height, and the maximum height in feet
(c) for what time intercal will the rocket be more than 834 feet above ground level?
(d) after how many seconds will it hit the ground? 1 solutions
Answer 381696 by stanbon(57282) on 2012-04-30 18:24:23 (Show Source):
You can put this solution on YOUR website!A toy rocket is launched from a building 148 feet tall at an initial velocity of 222 feet per second.
(a)give the function that describes the height of the rocket
in terms of time t.
h(t) = -16t^2 + 222t + 148
======================================
(b) determine the time at which the rocket reaches its maximum height,
and the maximum height in feet
Vertex at time = -b/(2a) = -222/(2*-16) = 6.9375 seconds
-----------------------------------------
(c) for what time intercal will the rocket be more than 834 feet
above ground level?
Solve -16t^2+222t+148 = 834
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(d) after how many seconds will it hit the ground?
Solve -16t^2+222t+148 = 0
=============================
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/605457: red apples cost ,25,green apples cost .35.If you spent 7.65 on twice as may green apples as red apples, how many green apples did you buy 1 solutions
Answer 381695 by stanbon(57282) on 2012-04-30 18:13:58 (Show Source):
You can put this solution on YOUR website!red apples cost ,25,green apples cost .35.If you spent 7.65 on twice as may green apples as red apples, how many green apples did you buy
----------------------------
Equations:
g = 2r
0.25r + 0.35g = 7.65
---------
g = 2r
25r + 35g = 765
---------
Substitute for "g" and solve for "r":
25r + 35(2r) = 765
25r + 70r = 765
95r = 765
r =
----
Note: must be a whole number. Your data gives
an answer of # of red apples is 8.05...
=======================================
Cheers,
Stan H.
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Probability-and-statistics/605416: A fair coin is tossed 500times,find the probability that the number of heads will not differ from 250 by (1)more than 10 (2)more than 30 1 solutions
Answer 381682 by stanbon(57282) on 2012-04-30 16:44:53 (Show Source):
You can put this solution on YOUR website!A fair coin is tossed 500times,find the probability that the number of heads will not differ from 250 by (1)more than 10 (2)more than 30
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Binomial Problem with n = 500 and p(heads) = 1/2
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P(240<= x <= 260) = binomcdf(500,1/2,260) - binomcdf(500,1/2,240) = 0.6284
==============================
P(220<= x <= 280) = same procedure
======================================
Cheers,
Stan H.
=====================
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Equations/605421: Solve the system of equations
-6x − y = 1
7x + y = 0
x=
y= 1 solutions
Answer 381681 by stanbon(57282) on 2012-04-30 16:40:21 (Show Source):
You can put this solution on YOUR website!Solve the system of equations
-6x − y = 1
7x + y = 0
------
Add and solve for "x":
x = 1
---
solve for "y":
-6x - y = 1
-6 - y = 1
y = -7
================
Cheers,
Stan H.
========================
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Equations/605422: Solve the system of equations
-x + 6y = -6
3x − 29y = 28
x =
y = 1 solutions
Answer 381680 by stanbon(57282) on 2012-04-30 16:38:13 (Show Source):
You can put this solution on YOUR website!Solve the system of equations
-x + 6y = -6
3x − 29y = 28
----
Multiply thru the 1st eq. by 3:
-3x + 18y = -18
3x - 29y = 28
----------
Add and solve for "y":
-11y = 10
y = -10/11
--------------
solve for "x":
-x + 6y = -6
-x + 6(10/11) = -(66/11)
-x = -126/11
x = 126/11
=====================
cheers,
Stan H.
==============
x =
y =
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Travel_Word_Problems/605418: Okk I jonny travelled at 120 mph n his distance to cover was 12400. How long will it take little jonny to reach his destination 1 solutions
Answer 381677 by stanbon(57282) on 2012-04-30 16:33:55 (Show Source):
You can put this solution on YOUR website!120 mph n his distance to cover was 12400
------
time = distance/rate = 12400/120 = 103 1/3 hrs
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Cheers,
Stan H.
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test/605329: Hoe much soil containing 45% sand do you need to add to 1ft(cubed) of soil containing 15% sand in order to make a soil containing 35% sand? 1 solutions
Answer 381673 by stanbon(57282) on 2012-04-30 16:01:06 (Show Source):
You can put this solution on YOUR website!How much soil containing 45% sand do you need to add to 1ft(cubed) of soil containing 15% sand in order to make a soil containing 35% sand?
-------------------
Equation:
sand + sand = sand
0.45x + 0.15*1 = 0.35(x+1)
----
45x 15*1 = 35x + 35*1
-------
10x = 20
x = 2 cu. ft (amt of 45% soil needed)
=======================================
Cheers,
Stan H.
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