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Recent problems solved by 'stanbon'
stanbon answered: 57894 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 , 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, >>Next
Linear-systems/537702: i need to solve the system y=4x+12 and y=-2x+6
1 solutions
Answer 352955 by stanbon(57967)   on 2011-11-28 12:27:15 (Show Source):
You can put this solution on YOUR website!i need to solve the system y=4x+12 and y=-2x+6
Since you have 2 expressions for "y", equate them
and solve for "x":
4x+12 = -2x+6
6x = 18
x = 3
---
Now solve for "y":
y = 4x+12
y = 4*3+12
y = 24
--------
Cheers,
stan H.
==============
|
Square-cubic-other-roots/537700: Im having trouble with square roots, cubed roots and so forth. For examble the cubed root of 81. How do i figure out what would be taken out the radical sign and what would be left under the radical sign.
1 solutions
Answer 352954 by stanbon(57967) on 2011-11-28 12:25:22 (Show Source):
You can put this solution on YOUR website! Im having trouble with square roots, cubed roots and so forth. For examble the cubed root of 81. How do i figure out what would be taken out the radical sign and what would be left under the radical sign.
----
The best thing to do would be to make a short list of
the squares of 1,2,3.....9,10
and the cubes of 1,2,3,...9,10
---
Keep the list handy when you have square root or
cube root problems. After a while you will begin
to recognize square and cube roots.
Cheers,
Stan H.
|
Travel_Word_Problems/537699: the lenght of a tennis court is 24ft more than twice the width. the area is 2106 sq feet, find the lenth and width of the tennis court.
1 solutions
Answer 352953 by stanbon(57967) on 2011-11-28 12:22:00 (Show Source):
You can put this solution on YOUR website!the length of a tennis court is 24ft more than twice the width.
Let width be "x"
Then length is "2x+24"
------
the area is 2106 sq feet, find the length and width of the tennis court.
----
Equation:
x(2x+24) = 2106
2x^2+24x-2106 = 0
x^2+12x-1053 = 0
Factor:
(x-27)(x+39) = -
Positive solution:
x = 27 ft (width)
2x+24 = 78 ft (length)
==============
Cheers,
Stan H.
==============
|
Triangles/537697: how can i solve this problem?
in triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 20 greater than that of angle A. Find the measure of the angles.
thanks a lot
1 solutions
Answer 352951 by stanbon(57967) on 2011-11-28 12:15:46 (Show Source):
You can put this solution on YOUR website!in triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 20 greater than that of angle A. Find the measure of the angles.
---
Let Angle A be "x" degrees
Then Angle C is "6x" degrees
And Angle B is "x+20" degrees
-----------------
Equation:
x + 6x + x+20 = 180
8x = 160
x = 20 degrees (Angle A)
6x = 120 degrees (Angle C)
x+20 = 40 degrees (Angle B)
-----------------------------
Cheers,
Stan H.
=========
|
Linear-equations/537686: Hello,
helping daughter with below problem.. can u pls help!
simplify: 8-14*3/7+2
possible answers 1)4 2)6 3)7 4) 3
Thank you!
1 solutions
Answer 352950 by stanbon(57967) on 2011-11-28 12:12:25 (Show Source):
You can put this solution on YOUR website!simplify: 8-14*3/7+2
possible answers 1)4 2)6 3)7 4) 3
---
Rule of operation:
1st: scan from left to right performing mult and division where they occur.
That gives you: 8-42/7+2 followed by 8-6+2
----------------------------------------------------
2nd: scan from left to right performing addition and subtraction where they occur
That gives you: 2+2 followed by 4 as the final answer
================
Cheers,
Stan H.
==================
|
Equations/537638: Tim wants air conditioning in his room. The air conditioner costs $45. Each day the electricity costs $2. Write an expression that can be used to find the cost to run the air conditioner for d days
If Tim spent $85 to cool his room, how many days did he run the air conditioner?
1 solutions
Answer 352940 by stanbon(57967) on 2011-11-28 09:38:36 (Show Source):
You can put this solution on YOUR website! Tim wants air conditioning in his room. The air conditioner costs $45. Each day the electricity costs $2. Write an expression that can be used to find the cost to run the air conditioner for d days
---
Cost(d) = 45 + 2*d
-----
If Tim spent $85 to cool his room, how many days did he run the air conditioner?
Solvd: 45+2d = 85
2d = 40
d = 20 (# of days)
======================
Cheers,
Stan H.
======================
|
Equations/537639: Tammy wants to rent a movie form the video store. The membership fee is $15 per month, plus $4 per movie. Write an expression that can be used to find the cost to rent v videos.
Tammy spent $103 at the video store, how many videos did she rent?
1 solutions
Answer 352939 by stanbon(57967) on 2011-11-28 09:36:02 (Show Source):
You can put this solution on YOUR website!Tammy wants to rent a movie from the video store. The membership fee is $15 per month, plus $4 per movie.
Write an expression that can be used to find the cost to rent v videos.
Cost(v) = 15 + 4*v
-----
Tammy spent $103 at the video store, how many videos did she rent?
Solve 15+4v = 103
4v = 88
v = 22 videos
=================
Cheers,
Stan H.
=================
|
Miscellaneous_Word_Problems/537621: form an equivalent division problem for 5 divided by 1/3 by multiplying both the dividend and divisor by 3 then find the quotient
1 solutions
Answer 352938 by stanbon(57967) on 2011-11-28 09:33:25 (Show Source):
You can put this solution on YOUR website!form an equivalent division problem for 5 divided by 1/3 by multiplying both the dividend and divisor by 3 then find the quotient
-------------
x = 5/(1/3)
---
x = (5*3)/[(1/3)*3]
---
x = 15/1
---
x = 15
==========
Cheers,
Stan H.
==========
|
Probability-and-statistics/537501: A six-letter permutation is selected at random from the letters ABCDEF. How many of the possible permutations begin with with D
1 solutions
Answer 352888 by stanbon(57967) on 2011-11-27 21:39:48 (Show Source):
You can put this solution on YOUR website!A six-letter permutation is selected at random from the letters ABCDEF. How many of the possible permutations begin with with D
----
Ans: 5! = 120
======================
Cheers,
stan H.
|
Probability-and-statistics/537502: A committee of four people are to be chosen from six Democrats and four Republicans. Find the probability that two are Democrats and two are Republicans. Express your answer as a fraction reduced to lowest terms
1 solutions
Answer 352887 by stanbon(57967) on 2011-11-27 21:37:30 (Show Source):
You can put this solution on YOUR website!A committee of four people are to be chosen from six Democrats and four Republicans. Find the probability that two are Democrats and two are Republicans. Express your answer as a fraction reduced to lowest terms
----
# of ways to succeed: 6C2*4C2 = 15*6 = 90 ways
---
# of randomly chosen committee: 10C4 = 210
---
P(2Dems and 2Reps) = 90/210 = 9/21 = 3/7
========================
Cheers,
Stan H.
========================
|
Probability-and-statistics/537503: A 28 year old can buy a one-year life insurance policy of $25,000 for $150. Past history indicates that the probability of a person dying at age 28 is 0.003. Determine the company's expected gain per policy.
1 solutions
Answer 352886 by stanbon(57967) on 2011-11-27 21:32:47 (Show Source):
You can put this solution on YOUR website!A 28 year old can buy a one-year life insurance policy of $25,000 for $150. Past history indicates that the probability of a person dying at age 28 is 0.003. Determine the company's expected gain per policy.
-------------------------------------------
Let "x" be the company's gain:
----------
E(x) = 0.997*150 - 0.003(25000-150) = $75
==============
Cheers,
Stan H.
==============
|
Probability-and-statistics/537506: 1. What percentage of the area of the standard normal distribution is between z=-1.00 and z=+1.00? How do you know this?
2. Find the z-score for the standard normal distribution where:
Area is about equal to 0.95 to the left of z.
1 solutions
Answer 352885 by stanbon(57967) on 2011-11-27 21:28:15 (Show Source):
You can put this solution on YOUR website!1. What percentage of the area of the standard normal distribution is between z=-1.00 and z=+1.00? How do you know this?
----
P(-1 < z < 1) = normalcdf(-1,1) = 0.6827
==============================================
2. Find the z-score for the standard normal distribution where:
Area is about equal to 0.95 to the left of z.
invNorm(0.95) = 1.645
=========================
Cheers,
Stan H.
==========
|
Probability-and-statistics/537493: The odds against Dr Thomas winning the school golf tournament are 5:2. What is the probability of Thomas winning
1 solutions
Answer 352883 by stanbon(57967) on 2011-11-27 21:23:09 (Show Source):
You can put this solution on YOUR website!The odds against Dr Thomas winning the school golf tournament are 5:2. What is the probability of Thomas winning
---
odds against winning = P(lose)/P(win) = 5/2
---
Equations:
2*P(lose) - 5*P(win) = 0
P(lose) + P(win) = 1
--------
Multiply thru the lower equation by 2 to get:
2lose -5win = 0
2lose+ 2win = 2
---
Subtract and solve for P(win)
7win = 2
P(win) = 2/7
===================
Cheers,
Stan H.
===================
|
Probability-and-statistics/537484: A cookie company has 34 varieties of cookies. They decide to make sample boxes with 6 different cookies each. How many different sample boxes could they make
1 solutions
Answer 352880 by stanbon(57967) on 2011-11-27 21:09:10 (Show Source):
You can put this solution on YOUR website!A cookie company has 34 varieties of cookies. They decide to make sample boxes with 6 different cookies each. How many different sample boxes could they make
----
Ans: 34C6 = (34*33*32*31*30*29)/(1*2*3*4*5*6) = 1,344,904 sample boxes
===========
Cheers,
Stan H.
|
Sequences-and-series/537470: Find the sum of the sequence algebraically.
5k+3 is the common difference
k=1 is the starting term
Number of terms is 5
1 solutions
Answer 352878 by stanbon(57967) on 2011-11-27 20:56:16 (Show Source):
You can put this solution on YOUR website!Find the sum of the sequence algebraically.
5k+3 is the common difference
k=1 is the starting term
Number of terms is 5
------
a(5) = 1 + 4(5k+3) = 20k+13
-----
S(5) = (5/2)(1 + 20k+13)
---
S(5) = (5/2)(20k+14)
---
S(5) = 5(10k+7)
--
S(5) = 50k+35
==================
Cheers,
Stan H.
==================
|
Quadratic-relations-and-conic-sections/537430: how do i solve and graph this parabola x2+y2+6x-8y=11?
how do i solve this y2/4-x2/25=1
how do i solve this equation 4x2+y2=16
how do i solve this (x-1,782,000,000)2/3.42(10)23 + (y-356,400,000)2/1.368(10)22
1 solutions
Answer 352864 by stanbon(57967) on 2011-11-27 20:08:31 (Show Source):
You can put this solution on YOUR website!how do i solve and graph this parabola x2+y2+6x-8y=11?
It is not a parabola; it is a circle:
Complete the square on the x and on the y terms:
(x^2+6x+9) + (y^2-8y+16) = -11+9+16
(x+3)^2+ (y-4)^2= 14
Center at (-3,4); radius = sqrt(14)
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how do i solve this y^2/4-x^2/25=1
Hyperbola with center at (0,0) ; opening up and down;
y-intercept at (0,2) and (0,-2)
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how do i solve this equation 4x^2+y^2=16
Ellipse:
x^2/(1/4) + y^2/16 = 1
Center at (0,0); semi-major axis = 4 ; semi-minor axis = 1/2
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Cheers,
Stan H.
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Numbers_Word_Problems/537420: a 23 inch piece of string is to be cut into two pieces so that the length of the longer piece is three more than four times the shorter piece. If x represents the length of the shorter piece, find the lengths of both pieces.
1 solutions
Answer 352860 by stanbon(57967) on 2011-11-27 19:44:42 (Show Source):
You can put this solution on YOUR website! a 23 inch piece of string is to be cut into two pieces so that the length of the longer piece is three more than four times the shorter piece. If x represents the length of the shorter piece, find the lengths of both pieces.
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short piece: x
long piece: 4x+3
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Equation:
x + 4x+3 = 23
5x = 20
x = 4 (shorter)
4x+3 = 19 (longer)
Cheers,
Stan H.
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Linear-equations/537352: Janelle works two part time jobs. One pays $9 per hour, and the other pays $18 per hour. Next week she wants to earn at least $270 and can work at most 25 hours. She can only be scheduled for a maximum of 15 hours at the $18-per-hour-job. Write and graph a system of inequalities to represent this situation. List at least one possible solution from the solution set. Show or explain your work.
Please help! Thanks!
1 solutions
Answer 352836 by stanbon(57967) on 2011-11-27 18:39:01 (Show Source):
You can put this solution on YOUR website!Janelle works two part time jobs.
One pays $9 per hour, and the other pays $18 per hour.
Next week she wants to earn at least $270 and can work at most 25 hours.
She can only be scheduled for a maximum of 15 hours at the $18-per-hour-job.
----------------------------
Write and graph a system of inequalities to represent this situation.
Let x be number of hrs at $9 per hr
Let y be number of hrs at $18 per hr
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0<= x <=25
0<= y <= 25
Comment: These determine the restricted graphing area.
Draw a vertical line at x = 25
Draw a horizontal line at y = 25
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Hrs. worked: x + y <= 25
Earnings:::: 9x + 18y >= 270
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Solve each for "y":
y <= -x+25
Graph the boundary line and shade below it in the restricted graphing area.
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y >= (-1/2)x + 15
Graph the boundary line and shade above it in the restricted graphiing area.
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Ans: Find a point in the restricted area in the intersection
of the shaded areas.
Example: (10,14)
===========================
===========================
List at least one possible solution from the solution set. Show or explain your work.
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Cheers,
Stan H.
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real-numbers/537331: Freddie gets a car ride to the top of a hill, then rides his skateboard back down. The downhill ride takes 15 minutes longer than the uphill. If the car averages 32 mph, and Freddie rides his skateboard at 8 mph, find out how much time he spends skateboarding.
Let t=time spent driving to the top of the hill then, t+15=time going down the hill.
distance up=distance down
from the formula speed=distance/time(s=d/t), then d=st,
32t=8(t+15)
32t=8t+120
I can't get to the answer of 1/3 hour. I keep coming up with 1/4 hour.
1 solutions
Answer 352826 by stanbon(57967) on 2011-11-27 18:11:12 (Show Source):
You can put this solution on YOUR website!Freddie gets a car ride to the top of a hill, then rides his skateboard back down.
The downhill ride takes 15 minutes longer than the uphill.
If the car averages 32 mph, and Freddie rides his skateboard at 8 mph, find out how much time he spends skateboarding.
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Drive up DATA:
rate = 32 mph ; time = t hrs ; distance = 32t miles
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Skate down DATA:
rate = 8 mph ; time = t+(1/4) hrs ; distance = 8(t+(1/4)) miles
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Equation:
distance up = distance down:
32t = 8t+2
24t = 2
time = 1/12 hr = 5 minutes (time up)
time down = 5 min + 15 min = 20 min (time down)
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Total skate time = 20 min = 1/3 hr.
====================================
Cheers,
Stan H.
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Numbers_Word_Problems/537329: a woman has $1.70 in dimes and nickels. she has 2 more dimes than nickels. how many nickels does she have
1 solutions
Answer 352818 by stanbon(57967) on 2011-11-27 17:45:51 (Show Source):
You can put this solution on YOUR website! a woman has $1.70 in dimes and nickels. she has 2 more dimes than nickels. how many nickels does she have
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Equations:
Quantity: d = n + 2
Value: 5n + 10d = 170 cents
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Substitute for "d" and solve for "n":
5n + 10(n+2) = 170
n + 2(n+2) = 34
3n+4 = 34
n = 10 (number of nickels)
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Solve for "d":
d = n+2
d = 12 (number of dimes)
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Cheers,
Stan H.
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Travel_Word_Problems/537310: Bob roller blades 9 miles each morning. Today, he averaged 10 miles per hour for the first 6 miles but then slowed to 5 miles per hour for the rest of the trip. How long did the entire trip take?
1 solutions
Answer 352801 by stanbon(57967) on 2011-11-27 17:26:15 (Show Source):
You can put this solution on YOUR website!Bob roller blades 9 miles each morning. Today, he averaged 10 miles per hour for the first 6 miles but then slowed to 5 miles per hour for the rest of the trip. How long did the entire trip take?
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1st part DATA:
distance = 6 miles ; rate = 10 mph ; time = d/r = 6/10 hr
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2nd part DATA:
distance = 3 miles ; rate = 5 mph ; time = d/r = 3/5 hr
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Total time = (6/10) + (3/5) = 6/10 + 6/10 = 12/10 = 1.2 hr = 1hr 12 minutes
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Cheers,
Stan H.
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Numbers_Word_Problems/537262: Find three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number.
1 solutions
Answer 352772 by stanbon(57967) on 2011-11-27 16:03:59 (Show Source):
You can put this solution on YOUR website!Find three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number.
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1st: x-1
2nd: x
3rd: x+1
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Equation:
2(x-1+x)= 3(x+1)+10
4x-2 = 3x+13
x = 15
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1st: x-1 = 14
2nd: 15
3rd 16
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Cheers,
Stan H.
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Numbers_Word_Problems/537214: Two numbers have a difference of 3.The sum of their square is 89.Find the number.
1 solutions
Answer 352768 by stanbon(57967) on 2011-11-27 15:59:31 (Show Source):
You can put this solution on YOUR website!Two numbers have a difference of 3.The sum of their square is 89.
Find the numbers.
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Equatiions:
x -y = 3
x^2 + y^2 = 89
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x = y + 3
---
Substitute and solve for "y":
(y+3)^2 + y^2 = 89
y^2+6y+9 + y^2 = 89
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2y^2 + 6y -80 = 0
y^2 + 3y - 40 = 0
Factor:
y^2+8y-5y-40 = 0
y(y+8)-5(y+8) = 0
(y+8)(y-5)= 0
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y = 5 or y = -8
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Solve for "x":
x-y = 3
If x = 5, y = 2
If x = -8, y = -11
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Checking (5,2)
x -y = 3
ok
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x^2 + y^2 = 89
5^2+2^2 = 89
false
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Checking (-8,-11)
x-y = 3
-8--11 = 3
ok
---
x^2+y^2 = 89
64+121 = 89
false
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Cheers,
Stan H.
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Probability-and-statistics/537203: You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test.
a) what kind of probability does x have?
b) What is your expected score on the exam?
c) Compare the variance and standard deviation of x.
d) based on your answers to parts b and c, is it likely that you would score over 50 on this exam? explain your reasoning behind your answer
1 solutions
Answer 352760 by stanbon(57967) on 2011-11-27 14:53:09 (Show Source):
You can put this solution on YOUR website!You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test.
a) what kind of probability does x have?:::binomial with n = 100 and p = 1/5
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b) What is your expected score on the exam?
expected = np = 100*(1/5) = 20
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c) Compare the variance and standard deviation of x.
std = sqrt(100*1/5*4/5) = 4
var = std^2 = 16
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d) based on your answers to parts b and c, is it likely that you would score over 50 on this exam? explain your reasoning behind your answer
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z(50) = (50-20)/4 = 30/4 = 7 1/2 standard deviations
Since 50 is 7 1/2 standard deviations above the mean
it is highly unlikely a person would score over 50
with no study.
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Cheers,
Stan H.
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