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Recent problems solved by 'stanbon'
stanbon answered: 57351 problems
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2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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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, >>NextInverses/747659: Hi, I need your help a problem word:
Five times the reciprecal of a number equals the sum of 3/2 the reciprecal of the number and 7/6. What is the number?
Thank you.
1 solutions
Answer 455048 by stanbon(57424)   on 2013-05-11 19:51:39 (Show Source):
You can put this solution on YOUR website!Five times the reciprecal of a number equals the sum of 3/2 the reciprecal of the number and 7/6. What is the number?
------
Equation:
5(1/x) = (3/2)(1/x) + (7/6)
----------------------
Multiply thru by 6x to get:
-----
30 = 9 + 7x
---
7x = 21
x = 3
--------------
Cheers,
Stan H.
==============
|
Trigonometry-basics/747509: Hi, Im stuck on this problem. The directions are: "The terminal side of an angle of t radians lies in the given quadrant on the given line. Find sin t, cos t, and tan t. "
The actual problem is : quadrant 3; line 
My first thought was to graph the line and then find a point on the terminal ray and thought I could build from that. Turns out that I have no clue how to even do that. Could you help me solve this problem?
1 solutions
Answer 454969 by stanbon(57424) on 2013-05-11 11:13:48 (Show Source):
You can put this solution on YOUR website!"The terminal side of an angle of t radians lies in the given quadrant on the given line. Find sin t, cos t, and tan t. "
The actual problem is : quadrant 3; line
--------
2y-4x = 0
------
y = 2x
-----
Points for QIII:
(0,0) and (-1,-2)
---
x = -2 ; y = -1
---
Solve for "r":
r = sqrt[2^2+1^2] = sqrt(5)
-------
sin = y/r = -1/sqrt(5) = -sqrt(5)/5
----
cos = x/r = -2/sqrt(5) = -2sqrt(5)/5
----
tan = y/x = 1/2
====================
Cheers,
Stan H.
====================
|
Probability-and-statistics/747455: a committee of 5 students is to be selected at random from a group consisting of 6 boys and 7 girls. what is the probability that at most three girls out of 5 will include in this committee?
1 solutions
Answer 454938 by stanbon(57424) on 2013-05-11 06:08:24 (Show Source):
You can put this solution on YOUR website!a committee of 5 students is to be selected at random from a group consisting of 6 boys and 7 girls. what is the probability that at most three girls out of 5 will include in this committee?
----
P(at most 3) = 1 - [P(4) + P(5)]
= 1 - [(7C4*6C1)/13C5 + (7C5)/13C5]
-----
= 1 - [(210+ 21)/1287]
----
= 1 - [0.1795]
----
= 0.8205
=============
Cheers,
Stan H.
|
test/747419: If the age of father and son is 84.The age of father is three times of son then find the age of father and son.also show in graph.
1 solutions
Answer 454907 by stanbon(57424) on 2013-05-10 22:14:07 (Show Source):
You can put this solution on YOUR website!If the age of father and son is 84.The age of father is three times of son then find the age of father and son.also show in graph.
-------
Equations:
f + s = 84
f = 3s
----
Substitute for "f" and solve for "s":
3s+s = 84
4s = 84
s = 21 (son's age now)
-----
Solve for "f":
f = 3s
f = 3*21
f = 63 (father's age now)
=============================
cheers,
Stan H.
==========
|
expressions/747410: 3{[6(x-4)+5]-2[5(x+8)-3]} The directions says to simplify the problem. I have tried everything but nothing I do allows me to come up with the right.
1 solutions
Answer 454906 by stanbon(57424) on 2013-05-10 22:10:00 (Show Source):
You can put this solution on YOUR website!3{[6(x-4)+5]-2[5(x+8)-3]}
-------------
= 3{[6x-24+5]-2[5x+40-3]}
-------------
= 3{6x-19-10x+74}
-----
= 3{-4x+55}
-----
= -12x+165
======================
Cheers,
Stan H.
======================
|
Rectangles/747377: Calculate the length of the shorter of the two sides of a rectangle which has an area of 31.20 m2 and a perimeter of 23.80 m.
1 solutions
Answer 454886 by stanbon(57424) on 2013-05-10 18:30:29 (Show Source):
You can put this solution on YOUR website!Calculate the length of the shorter of the two sides of a rectangle which has an area of 31.20 m2 and a perimeter of 23.80 m.
----------------
Equations:
L + W = 23.8/2 = 11.9
LW = 31.2
----------------------------
Substitute for "L" and solve for "W":
(11.9-W)W = 31.2
-----
W^2 -11.9W + 31.2
-----
Solve for "W":
W = 3.9 or W = 8
----
Shorter side = 3.9 meters
==========================
Cheers,
Stan H.
|
Probability-and-statistics/747210: Scores on a standardized test are normally distributed with a mean of 246 and a standard deviation of 22. Students who score at least 2.4 standard deviations above the mean receive a certificate. What is the minimum score required to receive the certificate?
1 solutions
Answer 454883 by stanbon(57424) on 2013-05-10 18:11:42 (Show Source):
You can put this solution on YOUR website!Scores on a standardized test are normally distributed with a mean of 246 and a standard deviation of 22. Students who score at least 2.4 standard deviations above the mean receive a certificate. What is the minimum score required to receive the certificate?
-------------------------
Use the form x = z*s+u
---
x = 2.4*22+246 = 298.8
===================
Cheers,
Stan H.
===================
|
Probability-and-statistics/747332: Suppose you have data that is normally distributed with a mean of 36 and a standard deviation of 7 find the percent of data between 29 and 57
1 solutions
Answer 454878 by stanbon(57424) on 2013-05-10 18:05:27 (Show Source):
You can put this solution on YOUR website!Suppose you have data that is normally distributed with a mean of 36 and a standard deviation of 7 find the percent of data between 29 and 57
--------------------------------
z(57) = (57-36)/7 = 3
z(29) = (29-36)/7 = -1
-----
P(29<= x <=57) = P(-1<= z <=3) = normalcdf(-1,3) = 0.8400
==============================
Cheers,
Stan H.
==================
|
Probability-and-statistics/747359: I'm preparing notes for final exam, want to have clear understanding of these problems, can someone help with it?
Assume that a normal distribution has a mean of 25 and a standard deviation of 2.5. Use the 68-95-99.7 Rule to find the percentage of values in the distribution of:
A) Above 30
B) Below 22.5
C) Between 20 and 30
D) Between 25 and 32.5
1 solutions
Answer 454874 by stanbon(57424) on 2013-05-10 17:58:32 (Show Source):
You can put this solution on YOUR website!Assume that a normal distribution has a mean of 25 and a standard deviation of 2.5. Use the 68-95-99.7 Rule to find the percentage of values in the distribution of:
A) Above 30
(30-25)/2.5 = 5/2.5 = 2
So 30 is 2 standard deviations above the mean.
Percentage above 30 = (100-95)/2 = 2.5% = 0.025
----------------------------------------------------
B) Below 22.5
(22.5-25)/2.5 = -1
So 22.5 is 1 standard deviation below the mean.
Percentage below 22.5 = (100-68)/2 = 16% = 0.16
----------------------------------------------------
Comment: Hope you can figure out "C" and "D"
C) Between 20 and 30
D) Between 25 and 32.5
------------
Cheers,
Stan H.
|
Probability-and-statistics/747374: If 80% of job applicants are able to pass a computer literacy test, find the mean, standard deviation and variance of the number of people who pass the exam in a sample of 150 applicants.
1 solutions
Answer 454867 by stanbon(57424) on 2013-05-10 17:44:42 (Show Source):
You can put this solution on YOUR website!If 80% of job applicants are able to pass a computer literacy test, find the mean, standard deviation and variance of the number of people who pass the exam in a sample of 150 applicants.
----
mean = np = 150*0.8
std = sqrt(npq) = sqrt(150*0.8*0.2)
variance = (std)^2
======================
Cheers,
Stan H.
|
logarithm/747371: Knowing that x = 2 and log(base a)y = 3 calculate the numerical value of the following
a) log(base a)x^3y^2
b) log(base a) (a^3x^2/y^2)
Can you please help me out? Thanks so much in advance
Can you also show me the steps it would really help me understand:)
1 solutions
Answer 454865 by stanbon(57424) on 2013-05-10 17:37:44 (Show Source):
You can put this solution on YOUR website!Knowing that x = 2 and log(base a)y = 3 calculate the numerical value of the following
a) log(base a)x^3y^2
---
= loga(x^3)+loga(y^2)
---
= 3loga(x) + 2loga(y)
---
= 3loga(2) + 2loga(3)
---
= loga(8) + loga(9)
---
= loga(72)
=====================================
b) log(base a) (a^3x^2/y^2)
----
= loga(a^3) + loga(x^2) - loga(y^2)
----
= 3 + 2loga(2) -2loga(3)
----
= 3 + loga(4) - loga(9)
---
= 3 + loga[4/9]
======================
Cheers,
Stan H.
======================
|
expressions/747366: what is the excluded value p when -3 over 2p to the second power - p
1 solutions
Answer 454863 by stanbon(57424) on 2013-05-10 17:23:41 (Show Source):
You can put this solution on YOUR website!what is the excluded value p when -3 over 2p to the second power - p
------
-3/(2p^2-p)
-----
The denominator cannot be zero.
----
Solve:
2p^2-p = 0
p(2p-1) = 0
---
p = 0 or 2p-1 = 0
---
p = 0 or 2p = 1
----
p = 0 or p = 1/2
--------------------
p = 0 or p = 1/2
Those are the excluded values.
Cheers,
Stan H.
==============
|
Graphs/747367: Sketch the graph. y = − 1/3x+5/3
1 solutions
Answer 454861 by stanbon(57424) on 2013-05-10 17:15:24 (Show Source):
You can put this solution on YOUR website!Sketch the graph.
y = − 1/3x+5/3
----
y = (-x+5)/3
Plot 2 points and draw a line thru them.
---
Let x = 2 then y = 3/3 = 1 giving you point (2,1)
------
Let x = -1 thn y = 6/3 = 2 giving you point (-1,2)
-------
Cheers,
Stan H.
==================
|
Rational-functions/747361: Find an equation of variation where y varies jointly as w and the square of x and inversely as z, and y=16 when w=5, x=4, and z=10
1 solutions
Answer 454859 by stanbon(57424) on 2013-05-10 17:07:32 (Show Source):
You can put this solution on YOUR website!Find an equation of variation where y varies jointly as w and the square of x and inversely as z, and y=16 when w=5, x=4, and z=10
--------
y = k*w*x^2/z
------
16 = k*5*16/10
160 = 80k
k = 2
------
Equation:
y = [2wx^2]/z
=============
|
Exponential-and-logarithmic-functions/747347: At the beginning of an experiment, a scientist has 244 grams of radioactive goo. After 240 minutes, her sample has decayed to 3.8125 grams. what is the half life of goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. How many grams of goo will remain after 47 minutes.
1 solutions
Answer 454856 by stanbon(57424) on 2013-05-10 16:29:28 (Show Source):
You can put this solution on YOUR website!At the beginning of an experiment, a scientist has 244 grams of radioactive goo. After 240 minutes, her sample has decayed to 3.8125 grams. what is the half life of goo in minutes?
----
A(t) = Ao*(1/2)^(t)
------
3.8125 = 244*(1/2)^(240/k)
-----
0.0157 = (1/2)^(240/k)
---
(240/k) = log(0.0157)/log(0.5) = 5.9953
---
k = 240/5.9953
----
k = 6 minutes
---------
Find a formula for G(t), the amount of goo remaining at time t. How many grams of goo will remain after 47 minutes.
---
A(47) = 244*(1/2)^(47/6)
---
A(47) = 244*(1/2)^7.833
A(47) = 1.0698 grams
=========================
Cheers,
Stan H.
===================
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Probability-and-statistics/747311: On the daily run of an express bus, the average number of passengers is 48. The
standard deviation is 3. Assume the variable is normally distributed. Find the probability that the bus will have fewer than 42?
more than 48?
1 solutions
Answer 454813 by stanbon(57424) on 2013-05-10 13:42:22 (Show Source):
You can put this solution on YOUR website!On the daily run of an express bus, the average number of passengers is 48. The
standard deviation is 3. Assume the variable is normally distributed.
Find the probability that the bus will have
a) fewer than 42?
z(42) = (42-48)/3 = -2
P(x < 42) = P(z < -2) = 0.0228
----------------
b) more than 48?
z(48) = (48-48)/3 = 0
P(x > 48) = P(z > 0) = 0.5000
===================================
Cheers,
Stan H.
=================
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Permutations/747297: In Minnesota, license plates have 3 letters followed by 3 numbers or vice versa. You can repeat no more than two letters in any order. How many possible license plates are there?
Must show all work, can someone please assist me?
1 solutions
Answer 454810 by stanbon(57424) on 2013-05-10 13:37:03 (Show Source):
You can put this solution on YOUR website!In Minnesota, license plates have 3 letters followed by 3 numbers or vice versa. You can repeat no more than two letters in any order. How many possible license plates are there?
----
Pattern: LLLNN or NNNLL
# of ways to succeed:
with pattern LLLNN: 26^2*25*10^2
with pattern NNNLL: 10^3*26^2
----
Ans: Add to get the answer.
----
Note: Your "vice versa" can be interpreted in more than one way.
========
Cheers,
Stan H.
===============
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Permutations/747303: how many ways can you arrange 6 students in the front row if there are 30 total students?
1 solutions
Answer 454806 by stanbon(57424) on 2013-05-10 13:28:08 (Show Source):
You can put this solution on YOUR website!how many ways can you arrange 6 students in the front row if there are 30 total students?
----
Ans: 30! = 2.6525x10^32
==========================
Cheers,
Stan H.
================
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Radicals/747304: y/x + 2y/(x+4) = 3
express in terms of y
1 solutions
Answer 454805 by stanbon(57424) on 2013-05-10 13:25:59 (Show Source):
You can put this solution on YOUR website! y/x + 2y/(x+4) = 3
express in terms of y
------
y[(1/x) + 2/(x+4)] = 3
---
y[(x+4+2x)/(x(x+4)] = 3
----
y[(3x+4)/(x^2+4x)] = 3
---
y = [3x^2+12x]/(3x+4)
==========================
Cheers,
Stan H.
==========================
|
Polynomials-and-rational-expressions/747300: ((x+9)/(-2-x))/((x^2-2x-63)/(x^2-7x-18)) Im a little confused. Help please? Thank you.
1 solutions
Answer 454803 by stanbon(57424) on 2013-05-10 13:22:39 (Show Source):
You can put this solution on YOUR website!((x+9)/(-2-x))/((x^2-2x-63)/(x^2-7x-18))
--------
= (x+9)/(-(2+x))/((x^2-9x+7x-63)/(x^2-9x+2x-18))
--------------
= (x+9)/(-(2+x))/((x(x-9)+7(x-9))/(x(x-9)+2(x-9))
---------------
= (x+9)/(-(2+x))/(((x-9)(x+7))/((x-9)(x+2)))
---------------
= (x+9)/(-(2+x))]
----
Cancel all factors that are common to numerator and denominator.
-----
= [(x+9)/(-1)]
------
= -(x+9)/(x+7)
=================
Cheers,
Stan H.
=================
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�t�e�s�t/747193: Factor completely : 4x exponent3 +10x exponent2 +6x
1 solutions
Answer 454756 by stanbon(57424) on 2013-05-10 08:07:23 (Show Source):
You can put this solution on YOUR website!Factor completely : 4x exponent3 +10x exponent2 +6x
-------------
4x^3+10x^2+6x
----
= 2x(2x^2+5x+3)
----
Use the Quadratic formula to find roots of 2x^2+5x+3.
If these roots are r1 and r2 the factors are
----
= 2x(x-r1)(x-r2)
===================
Cheers,
Stan H.
====================
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Age_Word_Problems/747065: A father is 2 years younger than 3 times the age of his son. In 12 years, he will be 12 years younger than twice the age of his son will be. Find their present ages.
1 solutions
Answer 454679 by stanbon(57424) on 2013-05-09 20:53:56 (Show Source):
You can put this solution on YOUR website!A father is 2 years younger than 3 times the age of his son. In 12 years, he will be 12 years younger than twice the age of his son will be. Find their present ages.
----
Equations:
f = 3s-2
f+12 = 2(s+12)-12
---------
Substitute for "f" and solve for "s":
3s-2+12 = 2s+24-12
s+10 = 12
s = 2 yrs old (son's age now)
---
f = 3s-2 = 3*2-2 = 4 yrs old (father's age now)
----
Note: That doesn't make much sense.
-------
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/747061: A car salesman earns $18,000 a year, plus 8% of the amount of sales from the cars he sells. What is the minimum amount of sales he must make if he wants to earn at least $40,000 per year?
***I really just need help with how to set up the problem, i can do the work, i just don't know where to start. Please help!)
1 solutions
Answer 454676 by stanbon(57424) on 2013-05-09 20:46:00 (Show Source):
You can put this solution on YOUR website!A car salesman earns $18,000 a year, plus 8% of the amount of sales from the cars he sells. What is the minimum amount of sales he must make if he wants to earn at least $40,000 per year?
-----------
Let the minimum amt. be "x":
Inequality:
18000 + 0.08x >= 40000
0.08x >= 22000
x >= $275,000
===================
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/747051: an automobile tank is 1/6 full of gasoline. when eight litres are added to the tank, it is 1/4 full of gasoline. how many litres of gasoline does the tank hold
1 solutions
Answer 454672 by stanbon(57424) on 2013-05-09 20:36:37 (Show Source):
You can put this solution on YOUR website!an automobile tank is 1/6 full of gasoline. when eight litres are added to the tank, it is 1/4 full of gasoline. how many litres of gasoline does the tank hold
------
Let the tank capacity be "x" litres.
-----
Equation:
(1/6)x + 8 = (1/4)x
--------
Multiply thru by 12 to get:
2x + 96 = 3x
x = 96 litres
=====================
Cheers,
Stan H.
|
�t�e�s�t/747054: Solve the system of equations by the addition method and check : 4x-3y=11
3x-y =7
1 solutions
Answer 454669 by stanbon(57424) on 2013-05-09 20:25:07 (Show Source):
You can put this solution on YOUR website!Solve the system of equations by the addition method and check :
4x-3y=11
3x-y =7
-----
Multiply thru the bottom equation by 3:
4x-3y = 11
9x-3y = 21
-----
Subtract and solve for "x":
5x = 10
x = 2
------
Solve for "y":
3x-y = 7
3*2 - y = 7
y = 6-7
y = -1
============
Cheers,
Stan H.
|
Inequalities/747052: Write an inequality equivalent to the following expression: All real numbers greater than 9.
1 solutions
Answer 454666 by stanbon(57424) on 2013-05-09 20:20:54 (Show Source):
You can put this solution on YOUR website!Write an inequality equivalent to the following expression: All real numbers greater than 9.
------
x > 9 where x is a Real Number
--------------------------------
Cheers,
Stan H.
|
Travel_Word_Problems/747049: Hi, I've been stuck on this word problem for a while, and I can't seem to figure ot where to start with it. I can't help feeling that it's right in front of me, but some help would be greatly appreciated. The word problem is this:
"Two cars left Hamilton at the same time, one travelling east and the other west. Their average speeds differ by 5 km/h. After two hours they are 210 km apart. What is the speed of each car?"
Thank you!
1 solutions
Answer 454665 by stanbon(57424) on 2013-05-09 20:17:25 (Show Source):
You can put this solution on YOUR website!Two cars left Hamilton at the same time, one travelling east and the other west. Their average speeds differ by 5 km/h. After two hours they are 210 km apart. What is the speed of each car?" --------
----
East-bound car DATA:
rate = x ; time = 2 hrs ; distance = 2x miles
----
West-bound car DATA:
rate = x-5 ; time = 2 hrs ; distance = 2(x-5)= 2x-10 miles
-------
Equation:
distance + distance = 210 km
2x + 2x-10 = 210 km
4x = 220
x = 55 km/hr (speed of the East-bound car.
-----
x-5 = 50 km/hr (speed of the West-bound car.
----------
Cheers,
Stan H.
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Human-and-algebraic-language/747047: One scoop of ice cream has 5 mg of cholesterol less than the amount of cholesterol in one hamburger. Together, they have 37 mg of cholesterol. How much cholesterol is in each food
1 solutions
Answer 454662 by stanbon(57424) on 2013-05-09 20:05:17 (Show Source):
You can put this solution on YOUR website!One scoop of ice cream has 5 mg of cholesterol less than the amount of cholesterol in one hamburger.
Let the amt. of cholesterol in one hamburger be "x".
Then amt in one scoop of icecream is x-5
----------------------------------------
Together, they have 37 mg of cholesterol.
Equation:
x + x-5 = 37 mg
2x = 42 mg
x = 21 mg
------------
How much cholesterol is in each food
hamburger = x = 21 mg
ice cream = (x-5) = 16 mg
---------------------------
Cheers,
Stan H.
===============
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