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Recent problems solved by 'stanbon'
stanbon answered: 57911 problems
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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 , 57900..57929, >>Next
test/384799: y vaires directly as x and inversely as the sqaure of z. y=96 when x=64 and z=4. Find y when x=75 and z=5.
1 solutions
Answer 272385 by stanbon(57984)   on 2010-12-12 11:38:24 (Show Source):
You can put this solution on YOUR website! y varies directly as x and inversely as the square of z.
---
y = kx/z^2
Solve for "k" using the following:
y=96 when x=64 and z=4.
96 = k*64/4^2
96 = 4k
k = 24
---
Equation for this Problem:
y = 24*x/z^2
----
Find y when x=75 and z=5.
y = 24*75/5^2
y = 24*3
y = 72
===============
Cheers,
Stan H.
===============
|
Quadratic_Equations/384795: A ball is thrown straight up into the air. The approximate height h of the ball after t seconds can be appromimately modeled by the function h=-16t^2+55t.What is the maximum height that the ball reaches?
1 solutions
Answer 272384 by stanbon(57984) on 2010-12-12 11:34:07 (Show Source):
You can put this solution on YOUR website! A ball is thrown straight up into the air. The approximate height h of the ball after t seconds can be appromimately modeled by the function
h(t) =-16t^2+55t. What is the maximum height that the ball reaches?
-----
Max occurs when t = -b/(2a) = -55/(2*-16) = 55/32
----
Height at that time = h(55/32) = 47.27 ft.
==========================
Cheers,
Stan H.
|
Probability-and-statistics/384749: A test is composed of six multiple choice questions where each question has 4 choices. If the answer choices for each question are equally likely, find the probability of answering 3 OR 4 questions correctly
1 solutions
Answer 272383 by stanbon(57984) on 2010-12-12 11:29:55 (Show Source):
You can put this solution on YOUR website!A test is composed of six multiple choice questions where each question has 4 choices. If the answer choices for each question are equally likely, find the probability of answering 3 OR 4 questions correctly
-----------
Binomial Problem with n=6 and p = 1/4
----
P(3 or 4) = P(3) + P(4)
==
6C3*(1/4)^3*(3/4)3 + 6C4*(1/4)^4*(3/4)^2
=========================================
= 0.1318 + 0.0330
======================
Cheers,
Stan H.
|
Complex_Numbers/384769: z=r(cos theta + i sin theta) show:
a) {z}=r
b) 1/z = 1/r(cos theta - i sin theta)
1 solutions
Answer 272380 by stanbon(57984) on 2010-12-12 11:02:06 (Show Source):
You can put this solution on YOUR website! z=r(cos theta + i sin theta) show:
a) {z}=r
z = r(cos^2+sin^2)
= r*1
= r
---------------
b) 1/z = 1/r(cos theta - i sin theta)
That is an identity if z = r(cis(theta))
---
What are you expected to show?
Cheers,
Stan H.
|
Complex_Numbers/384772: perform the indicated operation, using polar form.
4cis pie * 3cis(-pie over 2)
b) 2(cos pie + i sin pie) * 5( cos 3pie over 4 + i sin 3pie over 4)
1 solutions
Answer 272379 by stanbon(57984) on 2010-12-12 10:57:55 (Show Source):
You can put this solution on YOUR website!perform the indicated operation, using polar form.
4cis (pie) * 3cis(-pie over 2) = 12*cis(pi/2)
b) 2(cos pie + i sin pie) * 5( cos 3pie over 4 + i sin 3pie over 4)
= 10(cis(pi + (3/4)pi))
= 10(cis((7/4)pi)
=====================
Cheers,
Stan H.
|
Mixture_Word_Problems/384774: The chemistry lab at the University of Hardwoods keeps two acidic solutions on hand. One is 20% acid and the other is 35% acid. How much 20% acid solution and how much 35% acid solution should be used to prepare 25 liters of a 26% acid solution?
1 solutions
Answer 272377 by stanbon(57984) on 2010-12-12 10:54:30 (Show Source):
You can put this solution on YOUR website! One is 20% acid and the other is 35% acid. How much 20% acid solution and how much 35% acid solution should be used to prepare 25 liters of a 26% acid solution?
----------------
Quantity Eq: x + y = 25 liters
----
Acid Eq::0.20x + 0.35y = 0.26*25
--------------------------------------
Multiply the Quantity Eq. by 20
Multiply the Acid Eq. by 100
-------------------------------------
20x + 20y = 20*25
20x + 35y = 26*25
----
Subtract and solve for "y":
15y = 6*25
y = 2*5 = 10 liters (amt. of 35% solution needed in the mixture)
---
Siince x+y = 25, x = 15 liters (amt. of 20% solution needed in the mixture)
========================
Cheers,
Stan H.
|
Travel_Word_Problems/384773: Two boys on bicycles start from the same place and ride in opposite directions. One rides twice as fast as the other one. in 3 hours, they are 27 kilometers apart. what is the rate of speed for each boy?
1 solutions
Answer 272375 by stanbon(57984) on 2010-12-12 10:49:11 (Show Source):
You can put this solution on YOUR website!Two boys on bicycles start from the same place and ride in opposite directions. One rides twice as fast as the other one. in 3 hours, they are 27 kilometers apart. what is the rate of speed for each boy?
----
1st rider data:
rate = x kmh ; time = 3 hrs ; distance = 3x km
---
2nd rider data:
rate = 2x kmh ; time = 3 hrs ; distance = 3(2x) = 6x km
-----
Equation:
distance + distance = 27 km
3x + 6x = 27
9x = 27
x = 3 km/h (1st rider's speed)
---
2x = 6 km/h (2nd rider's speed)
===================================
cheers,
Stan H.
|
Complex_Numbers/384770: express in polar form, using the smallest non-negative value for the argument.
-1/2 + radical 3/2 i
1 solutions
Answer 272371 by stanbon(57984) on 2010-12-12 10:35:36 (Show Source):
You can put this solution on YOUR website!express in polar form, using the smallest non-negative value for the argument.
-1/2 + radical 3/2 i
-----------------
r = sqrt[(1/2)^2 + (sqrt(3)/2)^2] = sqrt[1/4 + 3/4] = 1
-------
theta = arctan[(sqrt(3)/2)/(1/2)] = arctan[sqrt(3)] = 60 degrees
--
But the point is in the 2nd Quadrant so theta = 120 degrees or (2pi/3)
---
Polar Form: 1(cos(2pi/3)+isin(2pi/3))
============================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/384766: A man is 5 times as old as his grandson. If he is sixty years older than the grandson, find their ages?
1 solutions
Answer 272368 by stanbon(57984) on 2010-12-12 10:27:28 (Show Source):
You can put this solution on YOUR website!A man is 5 times as old as his grandson. If he is sixty years older than the grandson, find their ages?
----------------
Equations:
f = 5g
f = g+60
----
Substitute and solve for "g":
5g = g+60
4g = 60
g = 15 (grandson's age now)
----
f = 5g = 75 (grandpa's age now)
===============
cheers,
Stan H.
|
Probability-and-statistics/384760: In a distribution of scores with a mean of 35 and a standard deviation of 4, which event is more likely: that a randomly selected score will be between 29 and 31 or a randomly selected score will be between 40 and 42?
1 solutions
Answer 272366 by stanbon(57984) on 2010-12-12 10:19:40 (Show Source):
You can put this solution on YOUR website!In a distribution of scores with a mean of 35 and a standard deviation of 4, which event is more likely: that a randomly selected score will be between 29 and 31 or a randomly selected score will be between 40 and 42?
--------
Figure the number of standard deviations the intervals
are from the mean.
The 29 to 31 interval is from (6/4)-(4/4) or 3/2 to 1 standard
deviations to the left. P(29< x <31) = 0.0918
-----
the 40 to 42 interval is from (5/4) to (7/4) standard deviations
to the right. P(40< x <42) = 0.0656
======================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/384637: ***I NEED THE STEPS TO SOLVE THIS PROBLEM SO THAT I CAN BETTER UNDERSTAND IT...PLEASE HELP***
ANSWER: 10,125 WATTS
PROBLEM: POWER OF WIND ROTOR
The power (P) generated by a wind rotor is directly proportional to the product of the square of the area (A) swept out by the blades and the third power of the wind velocity (v). Suppose the diameter of the circular area swept out by the blades is 10ft, and P=3000 watts when v=20mi/hr. Find the power generated when the wind velocity is 30mi/hr.
THANK YOU!!!
1 solutions
Answer 272281 by stanbon(57984) on 2010-12-11 22:30:25 (Show Source):
You can put this solution on YOUR website!The power (P) generated by a wind rotor is directly proportional to the product of the square of the area (A) swept out by the blades and the third power of the wind velocity (v).
---
P = k*A^2*V^3
Solve for "k using the following.
------
Suppose the diameter of the circular area swept out by the blades is 10ft, and P=3000 watts when v=20mi/hr.
---
3000 = k*(pi*5^2)^2*20^3
---
3000 = k*(6168.5)*8000
---
k = 3000/49348000
---
k = 0.00006079
---------------------
Equation for this windmill:
P = 0.00006079274*A^2*V^3
------
Find the power generated when the wind velocity is 30mi/hr.
P = 0.00006079274(pi*5^2)(30)^3
---
P = 10125 watts
===================
Cheers,
Stan H.
|
Rectangles/384636: in an isosceles triangle the measure of one angle is three times the measure of one of the congruent angles. Find the measure of each angle
1 solutions
Answer 272275 by stanbon(57984) on 2010-12-11 22:18:36 (Show Source):
You can put this solution on YOUR website!In an isosceles triangle the measure of one angle is three times the measure of one of the congruent angles.
Find the measure of each angle
------------------------------------
Let each congruent angle be "x"
Equation:
x + x + 3x = 180
5x = 180
x = 36 degrees (size of each of the congruent angle)
3x = 108 degrfees (size of the largest angle)
=======================
Cheers,
Stan H.
|
Linear-equations/384618: Given the linear equation y = -6x – 2, find the y-coordinates of the points (-1, ), (-2, ), and (1, ). Please show all of your work. Plot these points and graph the linear equation.
1 solutions
Answer 272264 by stanbon(57984) on 2010-12-11 21:18:36 (Show Source):
You can put this solution on YOUR website!Given the linear equation y = -6x – 2, find the y-coordinates of the points
(-1, ), (-2, ), and (1, ). Please show all of your work. Plot these points and graph the linear equation.
----------------------
y = -6x – 2
If x = -1, y = 6-2 = 4
----
If x = -2, y = 12-2 = 10
----
If x = 1, y = -6-2 = -8
-----
============================================
cheers,
Stan H.
|
Linear-equations/384621: Find the x- and y-intercepts for the equation. Please show all of your work. Then graph the equation and submit your graph through the dropbox.
y = -2x – 6
1 solutions
Answer 272260 by stanbon(57984) on 2010-12-11 21:13:40 (Show Source):
You can put this solution on YOUR website!Find the x- and y-intercepts for the equation. Please show all of your work. Then graph the equation and submit your graph through the dropbox.
y = -2x – 6
-----
x-intercept ?
Let y = 0, then -2x = 6, and x = -3
---
y-intercept ?
Let x = 0, then y = -6
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Plot (-3,0) and (0,-6) and draw a line thru them to get:
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=========================================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/384605: I am having a nightmare with this one. Can someone please help me.
A 75-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 15 ft longer that the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.
1 solutions
Answer 272256 by stanbon(57984) on 2010-12-11 21:06:05 (Show Source):
You can put this solution on YOUR website!A 75-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge.
Draw this right triangle with hypotenuse = 75 ft
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The horizontal distance that it spans is 15 ft longer that the height that it reaches on the side of the bridge.
Let the height be of the triangle be x ft.
Then the horizontal distance is (x+15) ft
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Find the horizontal and vertical distances spanned by this brace.
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Use Pythgoras to find the missing sides of your triangle:
75^2 = x^2 + (x+15)^2
x^2 + x^2+30x+225 = 75^2
2x^2 + 30x - 5400 = 0
x^2 + 15x -2700 = 0
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(x-45)(x+60) = 0
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Positive solution:
x = 45 ft (vertical distance of the brace)
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x+15 = 60 ft (horizontal distance of the brace)
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Cheers,
Stan H.
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Rational-functions/384603: I need help dividing the following:
3y+12/8y^3 ÷ 9y+36/16y^3
1 solutions
Answer 272253 by stanbon(57984) on 2010-12-11 20:44:22 (Show Source):
You can put this solution on YOUR website!I need help dividing the following:
[3y+12/8y^3] ÷ [9y+36/16y^3]
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[3(y+4)/8y^3]
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Cancel all factors common to a numerator and a denominator to get:
[1/1]
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= 2/3
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cheers,
Stan H.
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Probability-and-statistics/384596: A person is picked at random from the group of l00 blood donors, broken down by blood type and gender as follows:
Male =blood type A is 20. type b is 8, type AB is l6, type O is 11
Female =blood type A is l5, type B is 6, type AB is l0, type O is l4
(a) What is the probability that the person selected is a FEMALE?
(b) What is the probability that the person selected has blood type O?
(c) Given that the person selected is a MALE, what is the probability that their blood type is AB?
(d) Given that the person's blood type is A, what is the probability that the person is a FEMALE/
(e) What is the probability that the person selected has blood type B or is a male?
(b)
1 solutions
Answer 272250 by stanbon(57984) on 2010-12-11 20:39:03 (Show Source):
You can put this solution on YOUR website!A person is picked at random from the group of l00 blood donors, broken down by blood type and gender as follows:
Male =blood type A is 20. type b is 8, type AB is l6, type O is 11
Female =blood type A is l5, type B is 6, type AB is l0, type O is l4
(a) What is the probability that the person selected is a FEMALE?:: 0.45
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(b) What is the probability that the person selected has blood type O?::0.25
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(c) Given that the person selected is a MALE, what is the probability that their blood type is AB? 0.16/0.55
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(d) Given that the person's blood type is A, what is the probability that the person is a FEMALE? 0.15/0.35
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(e) What is the probability that the person selected has blood type B or is a male? 0.14 + 0.55 - -0.08 = 0.61
===================================
cheers,
stan H.
0 solutions
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Circles/384597: What is the radius of a circle with an area of 615.44 inches?
1 solutions
Answer 272242 by stanbon(57984) on 2010-12-11 20:20:10 (Show Source):
You can put this solution on YOUR website!What is the radius of a circle with an area of 615.44 inches?
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Area = pi*r^2
615.44 = pi*r^2
r^2 = 615.44/pi
r^2 = 195.9
r = 13.1 inches
====================
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/384592: If X units of a product cost C dollars to manufacture and ear revnue for of R dollars, the value of X where the expressions for C and R are equal is called the break-even quanity, the number of that produce zero profit. Find the break even quantity when C=12x+7200 and R=18x
How many units must be produced and sold in order to break even?
1 solutions
Answer 272240 by stanbon(57984) on 2010-12-11 20:14:12 (Show Source):
You can put this solution on YOUR website!Find the break even quantity when C=12x+7200 and R=18x
How many units must be produced and sold in order to break even?
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Solve: C = R
12x+7200 = 18x
6x = 7200
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x = 1200 (# of units needed to break even)
=================================================
Cheers,
Stan H.
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Linear-equations/384593: write an equation of the line that passes through (2,3) & (-3,4)
1 solutions
Answer 272238 by stanbon(57984) on 2010-12-11 20:10:17 (Show Source):
You can put this solution on YOUR website! write an equation of the line that passes through (2,3) & (-3,4)
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slope = m = (4-3)/(-3-2) = -1/5
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Form: y = mx + b
Substitute to solve for "b":
3 = (-1/5)2 + b
3 = -2/5 + b
b = 15/5 + 2/5
b = 17/5
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/384578: Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2325 . What was the rate charged per hour by each mechanic if the sum of the two rates was $150 per hour?
1 solutions
Answer 272233 by stanbon(57984) on 2010-12-11 19:58:03 (Show Source):
You can put this solution on YOUR website! Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2325 . What was the rate charged per hour by each mechanic if the sum of the two rates was $150 per hour?
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Let 1st mechanic rate be "x dollars per hour"
Let 2nd mechanic rate be "y dollars per hour"
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Equations:
Value Eq: 20x + 5y = 2325
Rate Eq: x + y = 150 per hour
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Multiply thru the Rate equation by 20 to get:
20x + 20y = 20*150
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Subtract that from the value equation and solve for "y":
-15y = 2325 - 20*150
-15y = -675
y = $45
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Substitute to solve for "x"
x + 45 = 150
x = $105
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Cheers,
Stan H.
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Expressions-with-variables/384580: I have done the following equations and I need to know "For what value is this equation undefined?"
6000/200-2x75%=120 million
6000/200-2x90%=300 million
6000/200-2x99%-3000million
1 solutions
Answer 272232 by stanbon(57984) on 2010-12-11 19:37:14 (Show Source):
You can put this solution on YOUR website!
"For what value is this equation undefined?"
6000/200-2x75%=120 million
6000/200-2x90%=300 million
6000/200-2x99%-3000million
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The denominator is (200-2x)
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The fraction is undefined when 200-2x is zero.
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Solve: 200-2x =0
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2x = 200
x = 100
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Undefined when x = 100.
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/384565: Can someone help me with this problem on porportions. I am lost and do not know what to do.
The ratio of men to women at a certain company is 5 to 4. How many employees does the company have if there are 72 female employees?
Thank you
1 solutions
Answer 272228 by stanbon(57984) on 2010-12-11 19:00:48 (Show Source):
You can put this solution on YOUR website!The ratio of men to women at a certain company is 5 to 4. How many employees does the company have if there are 72 female employees?
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5 to 4 is the same as 5x to 4x where 5x is the # of men.
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Equation:
5x + 4x = 72
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9x = 72
x = 8
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# of men = 5x = 5*8 = 40
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# of women = 4x = 4*8 = 32
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Cheers,
Stan H.
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Money_Word_Problems/384570: A store mixes Brazillian coffee worth $10 per kilogram and Venezulen coffee worth $12 per kilogram. The mixture is to sell for $11 per kilogram. Find out how much of each should be used to make a 132-kilogram mixture?
1 solutions
Answer 272225 by stanbon(57984) on 2010-12-11 18:52:22 (Show Source):
You can put this solution on YOUR website!A store mixes Brazilian coffee worth $10 per kilogram and Venezulen coffee worth $12 per kilogram. The mixture is to sell for $11 per kilogram. Find out how much of each should be used to make a 132-kilogram mixture?
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Equations:
Quantity Eq: b + v = 132 kg
Value Eq.:: 10b+12v = 11*132
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Multiply thru the 1st Eq by 10 to get:
10b + 10v = 10*132
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Subtract that from the Value Eq and solve for "v":
2v = 132
v = 66 kg (amt. of Venezualen coffee needed for the mixture)
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Since b+v = 132, b = 132-66 = 66 kg (amt. of Brazilian coffee in the mix)
================================================
Cheers,
Stan H.
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