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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
percentage/691346: I am having a problem with percentages. How do you divide a large number into a smaller one? such as getting 35% of 50%
1 solutions
Answer 426641 by stanbon(57967)   on 2012-12-08 08:34:20 (Show Source):
You can put this solution on YOUR website!getting 35% of 50%
-----
Comment: That is not a division problem.
----
Equation:
x = 0.35*0.50 = 0.175
===============
Division of 35% and 50% looks like this:
35%/50% = [35/100]/[50/100] = 35/50 = 7/10 = 0.7
==========================
Cheers,
Stan H.
|
Numbers_Word_Problems/691347: Find 2 consecutive odd numbers such that the second is 3 times the first? I know the answer but I dont know how to work it.
1 solutions
Answer 426640 by stanbon(57967) on 2012-12-08 08:29:50 (Show Source):
You can put this solution on YOUR website!Find 2 consecutive odd numbers such that the second is 3 times the first?
----
1st: 2x-1
2nd: 2x+1
-----
Equation:
2x+1 = 3(2x-1)
2x+1 = 6x-3
4x = 4
x = 1
-----
1st: 2*1-1 = 1
2nd: 2*1+1 = 3
==================
Cheers,
Stan H.
|
test/691324: What annual rate of interest compounded yearly is required to double an investment in 4 years?
1 solutions
Answer 426638 by stanbon(57967) on 2012-12-08 08:23:25 (Show Source):
You can put this solution on YOUR website!What annual rate of interest compounded yearly is required to double an investment in 4 years?
------
A(t) = P(1+(r/n))^(nt)
---
Your problem requires that (1+(r/n))^(nt) = 2
------
(1 + (r/1))^(1*4) = 2
---
(1+r)^4 = 2
---
4*log(1+r) = log(2)
log(1+r) = (1/4)*0.3010
---
log(1+r) = 0.0753
---
1+r = 10^0.0753
1+r = 1.1892..
rate = 0.1892.. = 18.92%
============================
Cheers,
Stan H.
==============
|
Trigonometry-basics/690928: If sin theta = 5/6, and theta is in quadrant 2, find the exact value of:
a) cos theta and b) sin(theta + pi/6)
1 solutions
Answer 426618 by stanbon(57967) on 2012-12-07 21:28:06 (Show Source):
You can put this solution on YOUR website!If sin (t) = 5/6, and theta is in quadrant 2,
find the exact value of:
a) cos(t)
Since sin(t) = y/r, y = 5 and r = 6
Then x = sqrt[r^2-y^2] = sqrt(11)
------
Note: Remember; cos is negative in the QII
------------
So cos(t)= x/r = -sqrt(11)/6
=====================
b) sin(t + pi/6) = sin(t)*cos(pi/6) + cos(t)*sin(pi/6)
----
= (5/6)(sqrt(3)/2) + (-sqrt(11)/6)(1/2)
----
= (5sqrt(3) - sqrt(11))/12
================================
Cheers,
Stan H.
|
Trigonometry-basics/691247: A ladder 3 metres long leans against a wall . It reaches 2 metres up the wall. What angle does the ladder make with the ground?
can you please help me? thanks in advance
1 solutions
Answer 426617 by stanbon(57967) on 2012-12-07 21:16:59 (Show Source):
You can put this solution on YOUR website!A ladder 3 metres long leans against a wall . It reaches 2 metres up the wall. What angle does the ladder make with the ground?
----
Draw the picture.
You have a right triangle:
hypotenuse = 3 meters
height = 2 meters
----
Let the angle opposite the height be "x":
Equation:
sin(x) = 2/3
x = sin^-1(2/3) = 0.7297 radians or 41.81 degrees
=======
Cheers,
Stan H.
==============
|
Trigonometry-basics/691248: A surveyor measures the angle of elevation of eye level to the top of a building 60 metres. If he is standing 40 metres away from the building and is 1.6 metres tall. How tall is the building?
can you please help me out i dont really get this question? thanks in advance
for the first question it is the distance from his eye to the top of the building is 60 meters
1 solutions
Answer 426616 by stanbon(57967) on 2012-12-07 21:13:21 (Show Source):
You can put this solution on YOUR website!A surveyor measures the angle of elevation of eye level to the top of a building 60 metres. If he is standing 40 metres away from the building and is 1.6 metres tall. How tall is the building?
can you please help me out i dont really get this question? thanks in advance
for the first question it is the distance from his eye to the top of the building is 60 meters
------
Draw the picture:
You have a right triangle
hypotenuse = 60 meters
base = 40 meters
height = sqrt(60^2-40^2) = sqrt(3200) = 40sqrt(2) meters
----
Total height of the building is 1.6 meters + 40sqrt(2) meters
-----
Approximate answer: 1.6+40sqrt(2) = 58.169 meters (height of the bldg)
=================
Cheers,
Stan H.
=================
|
Trigonometry-basics/691270: Solve the equation in the interval [0, 2pi.) 2 cos2 θ = 2 − cos 2θ
I think I'm supposed to use either a double or half- angle formula, but I'm not positive..
1 solutions
Answer 426613 by stanbon(57967) on 2012-12-07 21:01:41 (Show Source):
You can put this solution on YOUR website!Solve the equation in the interval [0, 2pi.)
2 cos2 θ = 2 − cos 2θ
----
2cos(2x) = 2 - cos(2x)
----
3cos(2x) = 2
cos(2x) = 2/3
2x = cos^-1(2/3)
2x = 0.7859
x = 0.3929
=================
Cheers,
Stan H.
==================
|
Trigonometry-basics/690825: 1.)Using radians, find the period of each function. Then graph.
a.) y=cos(4theta+5pi/3) b.)y=2tan(theta/2-5pi/6)
2.) Find the exact value of each trigonometric.
a.) tan-17pi/6 b.) cot-720 degrees
1 solutions
Answer 426552 by stanbon(57967) on 2012-12-07 15:46:15 (Show Source):
You can put this solution on YOUR website!1.)Using radians, find the period of each function. Then graph.
a.) y=cos(4(theta)+5pi/3)
Period for the cos is (2pi)/4 = pi/2
----------------------------------
b.)y=2tan((1/2)theta -5pi/6)
Period for the tan = pi/(1/2) = 2pi
-----------------------------------
2.) Find the exact value of each trigonometric.
a.) tan(-17pi/6) = tan(-12/6)pi - (7/6)pi) = tan[(5/6)pi)= -1/sqrt(3)
----------------------------
b.) cot(-720 degrees) = cot(-(2(360)) = cot(0) = 0
===================
Cheers,
Stan H.
|
Trigonometry-basics/690908: please help me figure out the rest of this equation. i have done the first step but am confused on how to place/write out the sine function with amplitude of 4, period of pi, and y-intercept of -3
I only have y=4sin
I would greatly appreciate your help and time, thank you.
1 solutions
Answer 426549 by stanbon(57967) on 2012-12-07 15:37:01 (Show Source):
You can put this solution on YOUR website!sine function with amplitude of 4, period of pi, and y-intercept of -3
------
y = asin(bx)+c
a = |4| = 4
---
Since period = 2(pi)/b = pi
b = 2
---
y-int = a*sin(b*0)+c = -3
a*0+c = -3
c = -3
---------------------
Equation:
y = 4sin(2x)-3
----
=====================
Cheers,
Stan H.
|
Trigonometry-basics/691184: The following problems give an expression for one of the three functions sin , cos, or tan ,with (theta) in the fi rst quadrant. Find expressions for the other two functions. Your answers will be algebraic expressions of x.
(a) sin (theta) = 3/x
(b) x = 4 cos (theta)
(c) tan (theta) = x
1 solutions
Answer 426543 by stanbon(57967) on 2012-12-07 15:30:05 (Show Source):
|
Inequalities/691182: please help me figure out this question.
The perimeter of a rectangular swimming pool is not to exceed 70 ft. The
length is to be twice the width. what widths, w, will meet these conditions?
thank you for helping me out(:
1 solutions
Answer 426541 by stanbon(57967) on 2012-12-07 15:19:36 (Show Source):
You can put this solution on YOUR website!The perimeter of a rectangular swimming pool is not to exceed 70 ft. The
length is to be twice the width. what widths, w, will meet these conditions?
-----
P <= 70 ft.
L = 2W
-----
Inequality:
2(L+W) <= 70
L+W <= 35
------
2W+W <= 35
3W <= 35
Width <= 11 2/3 feet
----
Length = 2W <= 23 1/3 feet
==============================
Cheers,
Stan H.
==============
|
Trigonometry-basics/691155: A surveyor measures the angle of elevation of eye level to the top of a building 60 metres. If he is standing 40 metres away from the building and is 1.6 metres tall. How tall is the building?
can you please help me out i dont really get this question? thanks in advance
1 solutions
Answer 426540 by stanbon(57967) on 2012-12-07 15:15:37 (Show Source):
You can put this solution on YOUR website!A surveyor measures the angle of elevation of eye level to the top of a building 60 metres.
----
Note: Your 1st sentence is confusing. Are you saying the
distance from his eye to the top of the building is 60 meters?
Cheers,
Stan H.
|
Trigonometry-basics/691159: A ladder 3 metres long leans against a wall . It reaches 3 metres up the wall. What angle does the ladder make with the ground?
can you please help me? thanks in advance
1 solutions
Answer 426539 by stanbon(57967) on 2012-12-07 15:13:34 (Show Source):
You can put this solution on YOUR website!A ladder 3 metres long leans against a wall . It reaches 3 metres up the wall. What angle does the ladder make with the ground?
------
Draw the picture.
You have a right triangle with
hypotenuse = 3 metres
height = 3 meters
------
Let the angle opposite the height be "x".
Equation:
sin(x) = 3/3 = 1
---
x is a 90 degree angle.
-----
Note: Your hypotenuse cannot be as long as your height.
------
Cheers,
Stan H.
|
Trigonometry-basics/691180: The following problems give an expression for one of the three functions sin , cos, or tan ,with (theta) in the fi rst quadrant. Find expressions for the other two functions. Your answers will be algebraic expressions of x.
(a) sin = 3=x
(b) x = 4 cos
(c) tan = x
1 solutions
Answer 426538 by stanbon(57967) on 2012-12-07 15:09:48 (Show Source):
You can put this solution on YOUR website!The following problems give an expression for one of the three functions sin , cos, or tan ,with (theta) in the fi rst quadrant. Find expressions for the other two functions. Your answers will be algebraic expressions of x.
(a) sin = 3/x
Since sin = opp/hyp, opp = 3 and hyp = x
Then adj = sqrt[x^2-3^2] = sqrt[x^2-9]
cos = sqrt(x^2-9)/x
tan = (3/x)/[(x^2-9)]/x] = 3/(x^2-9)
---------------------------------------
(b) x = 4 cos
cos = x/4
Since cos = adj/hyp, adj = x and hyp = 4
Then opp = sqrt[4^2-x^2]
---
sin = opp/hyp = sqrt(16-x^2)/4
tan = opp/adj = sqrt(16-x^2)/x
======================================
(c) tan = x/1
Since tan = opp/adj, opp = x and adj = 1
---
Then hyp = sqrt(x^2+1]
sin = x/sqrt(x^2+1)
cos = 1/sqrt(x^2+1)
===========================
Cheers,
Stan H.
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Trigonometry-basics/691033: Explain how you would compute the values of the six trigonometric functions of any real number with the help of the coordinate plane?
1 solutions
Answer 426536 by stanbon(57967) on 2012-12-07 15:04:46 (Show Source):
You can put this solution on YOUR website!Explain how you would compute the values of the six trigonometric functions of any real number with the help of the coordinate plane?
----
Example:
Try Real Number = "2"
Let sin(2) = opp/hyp = k/1
---
adj = sqrt[k^2-1^2]
----
So:
sin(2) = k
cos(2) = adj/hyp = (k^2-1)/1 = k^2-1
tan(2) = opp/adj = k/(k^2-1)
----
csc(2) = 1/k
sec(2) = 1/(k^2-1)
cot(2) = (k^2-1)/k
=====================
Cheers,
Stan H.
=====================
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Trigonometry-basics/691179: Use a calculator to find all solutions in the interval (0, 2π). Round the answers to two decimal places. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
sin x cos x = 0.078
1 solutions
Answer 426533 by stanbon(57967) on 2012-12-07 14:57:24 (Show Source):
You can put this solution on YOUR website!Use a calculator to find all solutions in the interval (0, 2π). Round the answers to two decimal places. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
sin x cos x = 0.078
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Note: sin(2x) = 2sin(x)cos(x)
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Your Problem:
(1/2)sin(2x) = 0.078
----
sin(2x) = 0.156
----
2x = sin^-1(0.156)
----
2x = 0.1566 radians
x = 0.0783 radians
==========================
Cheers,
Stan H.
=====================
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t e s t/691170: Evaluate (0.0025)^-1/4
how exactly do I do this question? thanks in advance
1 solutions
Answer 426529 by stanbon(57967) on 2012-12-07 14:47:38 (Show Source):
You can put this solution on YOUR website!Evaluate (0.0025)^-1/4
how exactly do I do this question?
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Note: 0.0025 = 25/10,000
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Your Problem:
(0.0025)^(-1/4)
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= [25/10,000)^(-1/4)
----
= (10,000/25)^(1/4)
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= (400)^(1/4)
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= 4.4721
===============
Cheers,
Stan H.
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Miscellaneous_Word_Problems/691171: A triangle contains two angles having measures of 91 degrees and 46 degrees. Find the measure of the third angle. The measure of the missing angle is ? degrees. (simplify your answer. Type and integer or a decimal.)
1 solutions
Answer 426524 by stanbon(57967) on 2012-12-07 14:38:25 (Show Source):
You can put this solution on YOUR website!A triangle contains two angles having measures of 91 degrees and 46 degrees. Find the measure of the third angle. The measure of the missing angle is x degrees.
-------------
Let the measure of the 3rd angle be "x":
Equation:
x + 91 + 46 = 180
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x + 137 = 180
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x = 43 degrees
=====================
Cheers,
Stan H.
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Probability-and-statistics/691116: A single card is drawn from an ordinary 52-card deck. Find the probability that the card is a face card, given it is a jack.
1 solutions
Answer 426500 by stanbon(57967) on 2012-12-07 13:09:27 (Show Source):
You can put this solution on YOUR website!A single card is drawn from an ordinary 52-card deck. Find the probability that the card is a face card, given it is a jack.
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P (face | jack) = P(face and jack)/p(jack) = (4/52)/(4/52) = 1
===============
Cheers,
Stan H.
===============
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Probability-and-statistics/691129: CLAIMS FILED DURING YEAR FOR INSURANCE HAD MEAN OF NORMAL DISTRIBUTION =$4560.STD DEVIATION OF NORMAL DISTRIB WAS $1500. A SAMPLE OF 100 CLAIMS WAS SELECTED. FIND PROBABILITY THAT THE MEAN CLAIM FOR THE 100 SAMPLES WAS BETWEEN 4200 AND 4600 DOLLARS AND PROB IT WAS LESS THEN 4000 DOLLARS. PLEASE HELP ME
1 solutions
Answer 426497 by stanbon(57967) on 2012-12-07 13:04:31 (Show Source):
You can put this solution on YOUR website!CLAIMS FILED DURING YEAR FOR INSURANCE HAD MEAN OF NORMAL DISTRIBUTION =$4560.STD DEVIATION OF NORMAL DISTRIB WAS $1500. A SAMPLE OF 100 CLAIMS WAS SELECTED. FIND PROBABILITY THAT THE MEAN CLAIM FOR THE 100 SAMPLES WAS BETWEEN 4200 AND 4600 DOLLARS AND PROB IT WAS LESS THEN 4000 DOLLARS. PLEASE HELP ME
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std of means of samples of size n = 100 is 1500/sqrt(100) = 150
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z(4600) = (4600-4560)/150 = 40/150 = 4/15
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z(4200) = (4200-4560)/150 = -260/150 = -26/15
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P(4200<= x-bar <= 4600) = P(-26/15<= z <=4/15)
= normalcdf(-26/15,4/15)
= 0.5636
===============
Cheers,
Stan H.
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Mixture_Word_Problems/691126: Find how many quarts of 6% butterfat milk and 2% butterfat milk should be mixed to yield 40 quarts of 3% butterfat milk.
The mixture should contain __ quarts of the 6% butterfat milk
The mixture should contain___ quarts of the 2% butterfat mik
1 solutions
Answer 426493 by stanbon(57967) on 2012-12-07 12:58:04 (Show Source):
You can put this solution on YOUR website!Find how many quarts of 6% butterfat milk and 2% butterfat milk should be mixed to yield 40 quarts of 3% butterfat milk.
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Equation:
fat + fat = fat
0.02x + 0.06(40-x) = 0.03*40
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Multiply thru by 100 to get:
2x + 6*40 - 6x = 3*40
-4x = -3*40
x = 30 quarts (amt. of 2% solution needed)
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40-x = 10 quarts (amt. of 6% solution needed)
============================
Cheers,
Stan H.
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The mixture should contain __ quarts of the 6% butterfat milk
The mixture should contain___ quarts of the 2% butterfat mik
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Geometry_Word_Problems/691123: Mary bought 4 tapes and 5 cd's for a total of $83. Mark bought 6 tapes and 3 cd's for a total of $75 . How much are tapes and cd's?
1 solutions
Answer 426491 by stanbon(57967) on 2012-12-07 12:48:59 (Show Source):
You can put this solution on YOUR website!Mary bought 4 tapes and 5 cd's for a total of $83. Mark bought 6 tapes and 3 cd's for a total of $75 . How much are tapes and cd's?
-----
Equation:
4t + 5c = 83 dollars
6t + 3c = 75 dollars
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Multiply thru 1st by 3
Multiply thru 2nd by 5
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12t + 15c = 3*83
30t + 15c = 5*75
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Subtract and solve for "t":
18t = 126
t = $7 (price of each tape)
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Solve for "c" using 4t + 5c = 83 dollars
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4*7 + 5c = 83
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5c = 83-28
5c = 55
c = $11 (price of a cd)
============================
Cheers,
Stan H.
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Money_Word_Problems/691115: Melinda invested three times as much money at 9% yearly interest as she did at 7%. Her total yearly interest from the two investments was $170. How much did she invest at each rate?
I only set up this
9(.09x)+ .07x= 170
1 solutions
Answer 426490 by stanbon(57967) on 2012-12-07 12:41:13 (Show Source):
You can put this solution on YOUR website!Melinda invested three times as much money at 9% yearly interest as she did at 7%. Her total yearly interest from the two investments was $170. How much did she invest at each rate?
------
Quantity Equation: n = 3s
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Interest Eqution:: 0.09n + 0.07s = 170
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Substitute for "n" and solve for "s"
0.09(3s) + 0.07s = 170
Multiply thru by 100 to get:
27s + 7s = 17000
34s = 17000
s = $500.00 (amt. invested at 7%)
----
solve for "n" using n = 3s
n = $1500 (amt. invested at 9%)
===================
Cheers,
stan H.
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Probability-and-statistics/691029: A box contains 3 red, 5 black and 2 white balls. One ball is drawn randomly from the box. After putting the ball back into the box, one ball is again drawn randomly.
Find the probability that the 2 balls drawn are of different colours
1 solutions
Answer 426489 by stanbon(57967) on 2012-12-07 12:11:08 (Show Source):
You can put this solution on YOUR website!A box contains 3 red, 5 black and 2 white balls. One ball is drawn randomly from the box. After putting the ball back into the box, one ball is again drawn randomly.
Find the probability that the 2 balls drawn are of different colours
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# of ways to succeed: 10C2 - [3C2+5C2+2C2] = 45-[3+10+1] = 31
---
# of possible pairs: 10C2 = 45
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P(2 of different colors) = 31/45
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Cheers,
Stan H.
==================
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Probability-and-statistics/691076: Assume that a set of test scores is normally distributed with a mean of 80 and a standarddeviation of 15. use the 68-95-99.7 rule to find the following quantities.
1 solutions
Answer 426488 by stanbon(57967) on 2012-12-07 12:07:34 (Show Source):
You can put this solution on YOUR website!Assume that a set of test scores is normally distributed with a mean of 80 and a standarddeviation of 15. use the 68-95-99.7 rule to find the following quantities.
-----
What "following quantities"?
Cheers,
Stan H.
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Probability-and-statistics/691105: Mean rent in a city is $750 per month with a standard deviation of $50. The rents are normally distributed. You randomly select 36 apartments in this city. What is the probability that the mean price will be more than $725?
1 solutions
Answer 426487 by stanbon(57967) on 2012-12-07 12:06:01 (Show Source):
You can put this solution on YOUR website!Mean rent in a city is $750 per month with a standard deviation of $50. The rents are normally distributed. You randomly select 36 apartments in this city. What is the probability that the mean price will be more than $725?
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std for the means of samples of size 36 is 50/sqrt(36] = 50/6 = 25/3
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z(725) = (725-750]/(25/3] = -75/25 = -3
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P( x-bar > 725) = P( z > -3) = 0.9987
==============================================
Cheers,
Stan H.
=================
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Probability-and-statistics/691083: A local weight-loss company suggests that the average client loses 15 pounds during the first month. A consumer advocate group feels that the actual number of pounds lost is much less than this. To test the claim, they select 30 of the clients at random and obtain the following data: Pounds Lost During the 1st Month: 16 20 14 15 14 18 19 20 9 13 20 11 12 18 13 17 11 21 14 15 15 13 17 12 9 20 16 18 21 11 A hypothesis test is conducted. a. State the null and alternative hypotheses. b. The test statistic is t = 0.6107 with p-value = 0.7269. Based on this information, what is the conclusion of the hypothesis test? Justify your answer.
1 solutions
Answer 426481 by stanbon(57967) on 2012-12-07 11:20:48 (Show Source):
You can put this solution on YOUR website!A local weight-loss company suggests that the average client loses 15 pounds during the first month. A consumer advocate group feels that the actual number of pounds lost is much less than this. To test the claim, they select 30 of the clients at random and obtain the following data: Pounds Lost During the 1st Month: 16 20 14 15 14 18 19 20 9 13 20 11 12 18 13 17 11 21 14 15 15 13 17 12 9 20 16 18 21 11 A hypothesis test is conducted.
--------------------------
a. State the null and alternative hypotheses.
Ho: u >= 15 (claim)
Ha: u < 15
b. The test statistic is t = 0.6107 with p-value = 0.7269.
Based on this information, what is the conclusion of the hypothesis test? Justify your answer.
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Since the p-value is greater than 5%,fail to
reject Ho at the 5% level of significance.
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The average loss of weight is too high to deny that the average
loss is not at least 15 lbs.
===============================
Cheers,
Stan H.
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