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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, >>NextMiscellaneous_Word_Problems/459758: PLEASE HELP ME PLEASE IM SOOOO STUCK ON THIS :) THANK YOU:
AN AIRCRAFT FLEW 4 HOURS WITH THE WIND. THE RETURN TRIP TOOK 5 HOURS AGAINST THE WIND. IF THE SPEED OF OF THE PLANE IN STILL AIR IS 384 MILES PER HOUR MORE THAN THE WIND SPEED, FIND THE SPEED OF THE WIND SPEED AND THE SPEED OF THE PLANE IN STILL AIR,
THANK YOU!!!
1 solutions
Answer 315283 by stanbon(57984)   on 2011-06-10 15:57:46 (Show Source):
You can put this solution on YOUR website!AN AIRCRAFT FLEW 4 HOURS WITH THE WIND. THE RETURN TRIP TOOK 5 HOURS AGAINST THE WIND. IF THE SPEED OF OF THE PLANE IN STILL AIR IS 384 MILES PER HOUR MORE THAN THE WIND SPEED, FIND THE SPEED OF THE WIND SPEED AND THE SPEED OF THE PLANE IN STILL AIR,
------------------
With wind DATA:
time = 4 hrs ; distance = x miles ; rate = d/t = x/4 mph
----------------------------------
Against wind DATA:
time = 5 hrs ; distance = x miles ; rate = d/t = x/5 mph
------------------
Let wind speed be "w".
Let speed of the plane in still air = "p".
---
Equation:
p + w = x/4
p - w = x/5
p = w + 384
-----------------------
Substitute for "p" and solve for w and x:
w + 384 + w = x/4
w + 384 - w = x/5
-------
2w + 384 = x/4
384 = x/5
x = 1920 miles
----
Solve for "w":
2w + 384 = 1920/4
2w = 96
wind speed = 48 mph
---
Solve for "p":
p = w + 384
plane speed in still air = 48+384 = 432 mph
=============================================
Cheers,
Stan H.
===========
|
Permutations/459759: From a group of 5 men and 4 women, a comittee of 6 is to be selected. How many different selections can be formed having exactly 4 men and 2 women?
1 solutions
Answer 315279 by stanbon(57984) on 2011-06-10 15:41:27 (Show Source):
You can put this solution on YOUR website!From a group of 5 men and 4 women, a comittee of 6 is to be selected. How many different selections can be formed having exactly 4 men and 2 women?
----
Ans: 5C4*4C2 = 5*6 = 30
===============================
Cheers,
Stan H.
|
Rational-functions/459754: Hello. Could you please help me?
I have to identify whether these are linear or quadratic
1. f(x) = 3x
2. f(x) = (x-3)^2 -6
3. if x is 1 then f(x)is 8,if x is 2 then f(x) is 11, if x is 3 then f(x) is 14
4. if x is 1 then f(x) is 8, if x is 2 then f(x) is 9, if x is 3 then f(x) is 11,
if x is 4 then f(x) is 14
1 solutions
Answer 315278 by stanbon(57984) on 2011-06-10 15:39:45 (Show Source):
You can put this solution on YOUR website!identify whether these are linear or quadratic
1. f(x) = 3x:::linear
2. f(x) = (x-3)^2 -6:::quadratic
3. if x is 1 then f(x)is 8,if x is 2 then f(x) is 11, if x is 3 then f(x) is 14
Plot the points (1,8),(2,11),(3,14)
You'll they are not in a line.
------------------------------------
Look at "change in y" over "change in x" and you will see that
the slopes are not the same for all the pairs of points.
----------------------------------------
4. if x is 1 then f(x) is 8, if x is 2 then f(x) is 9, if x is 3 then f(x) is 11, if x is 4 then f(x) is 14
Points are (1,8),(2,9),(3,11),(4,14)
Plot and look.
Check the slopes.
Cheers,
Stan H.
|
Rational-functions/459753: Please help!
I have to simplify 1. (3+2i)+ (-5-3i)
2. (6-3i) - (2+i)
3. (3+i)(3-i)
4. ( 5+ 2i) (3+i)
1 solutions
Answer 315273 by stanbon(57984) on 2011-06-10 15:25:14 (Show Source):
You can put this solution on YOUR website!simplify
1. (3+2i)+ (-5-3i) = (2-5)+(2-3)i = -3-i
----------------------------------------------
2. (6-3i) - (2+i)
= 6-2 -3-1
= 4 - 4i
----------------------------------------------
3. (3+i)(3-i)
= 9-3i+3i-(-1)
= 10
-------------------------
4. (5+ 2i) (3+i)
= 15+5i+6i-2
= 13+11i
=============
Cheers,
Stan H.
|
Rational-functions/459752: How do I simplify each expression? 1. i^7 2. i^32 and write the definition for i = and i^2 =
1 solutions
Answer 315269 by stanbon(57984) on 2011-06-10 15:20:53 (Show Source):
You can put this solution on YOUR website!How do I simplify each expression? 1. i^7 2. i^32 and write the definition for i = and i^2 =
---
sqrt(-1) = i
i^2 = -1
i^3 = -i
i^4 = 1
----
Then the cycle repeats over and over again.
------
So i^7 = i^(4+3) = i^4*i^3 = 1*i^3 = = -i
------------------
i^32 = i(4*8) = (i^4)^8 = 1^8 = 1
--------------------
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/459703: A game at a carnival has 75 rubber ducks floating in water. The ducks are numbered 1 to 75, with numbers written on their undersides so they can’t be seen. To play, you select a duck and see what number it has. If the number is less than 60, you win a consolation prize. If the number is at least 60 but less than or equal to 70, you win a stuffed duck. If the number is greater than 70 you win a giant, stuffed banana. What is the probability you win a stuffed duck? What is the probability you don’t win a duck or a banana?
1 solutions
Answer 315234 by stanbon(57984) on 2011-06-10 12:21:34 (Show Source):
You can put this solution on YOUR website!A game at a carnival has 75 rubber ducks floating in water.
The ducks are numbered 1 to 75, with numbers written on their undersides so they can’t be seen.
To play, you select a duck and see what number it has.
If the number is less than 60, you win a consolation prize:::Prob = 59/75
---------------------------------------
If the number is at least 60 but less than or equal to 70, you win a stuffed duck::::Prob = 11/75
---------------------------------------
If the number is greater than 70 you win a giant, stuffed banana:::Prob = 4/75.
---------------------------------------
What is the probability you win a stuffed duck?:::Prob = 11/75
---------------------------------------
What is the probability you don’t win a duck or a banana?:::Prob = 59/75
========================
Cheers,
Stan H.
========================
|
Linear-equations/459669: how do I find the x and y intercept in: y=-8x
thanks
Paola
1 solutions
Answer 315232 by stanbon(57984) on 2011-06-10 12:15:05 (Show Source):
You can put this solution on YOUR website!how do I find the x and y intercept in: y=-8x
-----
The y axis is the line where x is always zero.
So you let x = 0 and solve for "y" to get the y-intercept.
In you case you get y = -8*0 = 0
So the y-intercept is (0,0)
---
Similary the x-axis is the line where y is always zero.
So you let y = 0 and you solve for "x".
You get -8x = 0
x = 0
So the x-intercept is (0,0)
============
Ans: (0,0) is the x and the y intercept.
Cheers,
Stan H.
=================
|
Triangles/459667: If I'm given a right triangle with the bottom part measuring 30...how do I find the other two sides measurements?
1 solutions
Answer 315207 by stanbon(57984) on 2011-06-10 10:25:22 (Show Source):
You can put this solution on YOUR website!If I'm given a right triangle with the bottom part measuring 30...how do I find the other two sides measurements?
---
You have to know another side or another angle.
Cheers,
Stan H.
|
Probability-and-statistics/459584: Assume that the population of heights of female college students is approximately normally distributed with mean m of 67.16 inches and standard deviation s of 4.82 inches. A random sample of 92 heights is obtained. Show all work.
(A) Find the mean and standard error of the x distribution
(B) Find P(x > 67.75)
1 solutions
Answer 315205 by stanbon(57984) on 2011-06-10 10:23:47 (Show Source):
You can put this solution on YOUR website!Assume that the population of heights of female college students is approximately normally distributed with mean m of 67.16 inches and standard deviation s of 4.82 inches. A random sample of 92 heights is obtained. Show all work.
----------------
I'm going to assume you mean the x-bar distribution, which
is the probability distribution of the sample means.
------------------
(A) Find the mean and standard error of the x distribution
u(x-bar) = 67.16
s(x-bar) = 4.82/sqrt(92)
--------------------------------
(B) Find P(x-bar > 67.75)
t(67.75) = (67.75-67.16)/[4.82/sqrt(92)] = 1.17
----
P(x-bar > 67.75) P(t > 1.17 when df = 91) = tcdf(1.17,100,91) = 0.12
=================================================
cheers,
Stan H.
==========
|
Linear_Equations_And_Systems_Word_Problems/459637: Real life situation that could be modeled by a function:
Conversion from a fahrenheit to celsius is given by a function f(C)=5/9 F -32
what is the answer?
1 solutions
Answer 315184 by stanbon(57984) on 2011-06-10 08:46:36 (Show Source):
You can put this solution on YOUR website!Real life situation that could be modeled by a function:
Conversion from a fahrenheit to celsius is given by a
function C(F)=(5/9)(F -32)
what is the answer?
-----
If 32 degrees Fahrenheit is the freezing temperature in Maryland,
what is the freezing temperature in Berlin where Cencisus is used?
-----------
Cheers,
Stan H.
|
Evaluation_Word_Problems/459638: I have another one, I don't have a clue
f(x)=(x^2-6x)^2-35(X^2-6x)-200
Thank you
1 solutions
Answer 315183 by stanbon(57984) on 2011-06-10 08:40:40 (Show Source):
You can put this solution on YOUR website!f(x)=(x^2-6x)^2-35(X^2-6x)-200
------------
I suppose you are asked to solve for "x":
---
Let x^2-6x = w
---
Your problem becomes:
w^2 - 35w - 200 = 0
(w+5)(w-40) = 0
w = -5 or w = 40
---
Then solve for "x" using
x^2-6x = -5 or x^2-6x = 40
===============================
Cheers,
Stan H.
==================
|
Graphs/459639: A linear graph is created to predict the path of a storm.
The line has a slope of -3/2. If one of the points on the line is (4,3) what is another point on the line.
A. (-3,0)
B. (0,9)
C. (0, 2)
D. (4, 0)
Could someone hlep me please with this problem... I am so confused!
1 solutions
Answer 315182 by stanbon(57984) on 2011-06-10 08:36:11 (Show Source):
You can put this solution on YOUR website!A linear graph is created to predict the path of a storm.
The line has a slope of -3/2. If one of the points on the line is (4,3) what is another point on the line.
----
What does a slope of -3/2 mean?
It means "when x increases by 2, y decreases by 3"
Also if x decreases by 2, y will increase by 3.
--------------------------------------------
Starting at the point (4,3)
Decrease x by 2; then y will increase by 3 to get (2,6)
Decrease x by 2 again; then y will increase by 3 to get (0,9)
==============================================
Cheers,
Stan H.
===============
A. (-3,0)
B. (0,9)
C. (0, 2)
D. (4, 0)
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Evaluation_Word_Problems/459636: you provide great, can someone help me with these problems
Find all x intercepts of the given f(x) =-9sqrt x + 18
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Find the quadratic equatioin that fits the following set of data points
((3,66),(-4,38),(-1-10))
Thank you
1 solutions
Answer 315180 by stanbon(57984) on 2011-06-10 08:29:48 (Show Source):
You can put this solution on YOUR website!Find all x intercepts of the given f(x) = -9sqrt x + 18
y = 0 for all x-intercepts
Solve -9x^2+18 = 0
Divide thru by -9 to get:
x^2-2 = 0
x^2 = 2
x = +/-sqrt(2)
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Find the quadratic equation that fits the following set of data points
((3,66),(-4,38),(-1-10))
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Form: ax^2 + bx + c = y
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Substitute for (x,y) and solve for a,b,c:
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Using (3,66): 9a + 3b + c = 66
Using(-4,38): 16a- 4b + c = 38
Using(-1,-10):: a - b + c = -10
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Use any method you know to solve the system to get:
a = 5
b = 9
c = -6
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Equation: y = 5x^2+9x-6
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Cheers,
Stan H.
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Linear_Algebra/459627: the endpoint of segment AB are A(-1,-5)and B (9,11) . Find the coordinates of the point 7/8 of the way from A to B
1 solutions
Answer 315178 by stanbon(57984) on 2011-06-10 08:21:22 (Show Source):
You can put this solution on YOUR website!the endpoint of segment AB are A(-1,-5)and B (9,11) . Find the coordinates of the point 7/8 of the way from A to B
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Let (x,y) be the point you are looking for.
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From A to B the x distance is 9--1 = 10
and the y distance is 11--5 = 16
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(7/8)of the 10 = 70/8 = 8.75
(7/8) of the 16 = 14
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Add 8.75 to the x-coordinate of A to get -1+8.75 = 7.75
Add 14 to the y-coordinate of A to get -5+14 = 9
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Ans: (x,y) = (7.75,9)
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/459628: The height, in feet, of an arrow is given by the equation h= -16tsquared +70t +7 where "t" is in seconds. How long will it take for the arrow to hit the ground? Please round your solution to the nearest tenth of a second.
1 solutions
Answer 315174 by stanbon(57984) on 2011-06-10 08:12:29 (Show Source):
You can put this solution on YOUR website!The height, in feet, of an arrow is given by the equation
h(t) = -16tsquared +70t +7 where "t" is in seconds.
How long will it take for the arrow to hit the ground?
Please round your solution to the nearest tenth of a second.
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Height is zero when the arrow hits the ground.
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-16tsquared +70t +7 = 0
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t = [-70 +- sqrt(70^2-4*-16*7)]/(-32)
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t = [-70 +- sqrt(5348)]/(-32)
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Positive solution:
t = 4.47 seconds
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Cheers,
Stan H.
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t = [
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Volume/459629: how many square inches of paper is needed to cover a cube that is 12 inches on each side
1 solutions
Answer 315173 by stanbon(57984) on 2011-06-10 08:04:36 (Show Source):
You can put this solution on YOUR website!how many square inches of paper is needed to cover a cube that is 12 inches on each side
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There are 6 faces on the cube.
Each face is 12*12 = 144 sq in.
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You need 6*144 = 864 sq in.
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Cheers,
Stan H.
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Travel_Word_Problems/459630: you and your friend decide to have a race. your friend will ridw a bike for 15 seconds while you walk for the same 15 seconds. who will travel the longer distance?
1 solutions
Answer 315172 by stanbon(57984) on 2011-06-10 08:02:48 (Show Source):
You can put this solution on YOUR website!you and your friend decide to have a race. your friend will ridw a bike for 15 seconds while you walk for the same 15 seconds. who will travel the longer distance?
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Most probably the bike riders.
Cheers,
Stan H.
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Triangles/459631: 7. Which of the following could NOT be the lengths of the sides of a right triangle?
9 ft, 12 ft, 15 ft
5 in., 10 in., 15 in.
4 cm, 7.5 cm, 8.5 cm
1.5 m, 2 m, 2.5 m
1 solutions
Answer 315171 by stanbon(57984) on 2011-06-10 08:00:58 (Show Source):
You can put this solution on YOUR website!7. Which of the following could NOT be the lengths of the sides of a right triangle?
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In each set of numbers there is a longest and two shorter sides.
If longest^2 = shorter side^2 + other shorter side ^2
you have a right triangle. If not, you don't.
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Example: 15,12,9
15^2 = 225
9^2 + 12^2 = 81+144 = 225
So this is a right triangle.
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Cheers,
Stan H.
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9 ft, 12 ft, 15 ft
5 in., 10 in., 15 in.
4 cm, 7.5 cm, 8.5 cm
1.5 m, 2 m, 2.5 m
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Travel_Word_Problems/459570: A ball is thrown vertically upward from the top of a building 128 feet tall with an initial velocity of 112 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s=128+112t-16t^2
a) After how many seconds does the ball strike the ground?
b) After how many seconds will the ball pass the top of the building on its way down?
1 solutions
Answer 315130 by stanbon(57984) on 2011-06-09 22:51:30 (Show Source):
You can put this solution on YOUR website!A ball is thrown vertically upward from the top of a building 128 feet tall with an initial velocity of 112 feet per second. The distance s (in feet) of the ball from the ground after t seconds is
s(t) = 128+112t-16t^2
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a) After how many seconds does the ball strike the ground?
Let s(t) = 0 and solve for "t":
-16t^2+112t+128 = 0
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Divide thru by -16 to get:
t - 7t+ 8 = 0
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(t-8)(t+1) = 0
Positive solution:
time = 8 seconds
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b) After how many seconds will the ball pass the top of the building on its way down?
Let s(t) = 128
Solve: -16t^2+112t+128 = 128
-16t^2+112t = 0
t^2 - 7t = 0
t(t-7) = 0
Positive solution:
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time = 7 seconds
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Cheers,
Stan H.
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Sequences-and-series/459568: A department contains 8 men and 20 women. It needs to build a committee of 6.
a. How many ways can you build these committees?
Committees with only women?
Committees with one man?
Committees with two men?
Committees with three men?
b. How many ways are there to form a committee with 6 members if it must have more women than men?
1 solutions
Answer 315127 by stanbon(57984) on 2011-06-09 22:38:04 (Show Source):
You can put this solution on YOUR website!A department contains 8 men and 20 women. It needs to build a committee of 6.
a. How many ways can you build these committees?
Committees with only women?::: 20C6 = 38,760
Committees with one man?8C1*20C5 = 124,032
Committees with two men?:::8C2*20C4 = 135,660
Committees with three men?:::8C3*20C3 = 63840
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b. How many ways are there to form a committee with 6 members if it must have more women than men?
Comment: # of men could be 0 or 1 or 2
Cheers,
Stan H.
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Rational-functions/459564: Please help me solve this for a test I am taking! Thanks in advance.
Use rational exponents to write as a single radical expression.
x^1/3*y^1/6*z^1/9
1 solutions
Answer 315123 by stanbon(57984) on 2011-06-09 22:26:48 (Show Source):
You can put this solution on YOUR website!Use rational exponents to write as a single radical expression.
x^1/3*y^1/6*z^1/9
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Convert to a common denominator of 18:
x^(6/18)*y^(3/18)*z^(2/18)
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= 18th root of [x^6y^3z^2]
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Cheers,
Stan H.
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Expressions-with-variables/459422: Find the value of
1) 32⅕ (32 to the power of 1/5)
2) 32 ⅖ (32 to the power of 2/5)
Thanks :)
1 solutions
Answer 315031 by stanbon(57984) on 2011-06-09 16:25:01 (Show Source):
You can put this solution on YOUR website!Find the value of
1) 32⅕ (32 to the power of 1/5)
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The "5" in the denominator of the exponent means,
"take the 5th root".
Ans: 32^(1/5) = 2
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2) 32 ⅖ (32 to the power of 2/5)
The "5" means 5th root.
The "2" means square.
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32^(2/5) = 2^2 = 4
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Cheers,
Stan H.
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Evaluation_Word_Problems/459404: hello,
Can someone help with this question
The height of building is 1332 ft how long would it take for an object to fall to the ground from the top. Use the s= 16t^2, where s is the distance, in feet, traveled by an object falling freely from rest in t seconds. Thank you
1 solutions
Answer 315029 by stanbon(57984) on 2011-06-09 16:22:13 (Show Source):
You can put this solution on YOUR website!The height of building is 1332 ft how long would it take for an object to fall to the ground from the top. Use the s= 16t^2
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16t^2 = 1332
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t^2 = 1332/16
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t = 9.12 seconds
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Cheers,
Stan H.
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Inequalities/459414: Can someone help me figure this out?
Solve the compound inequality:
x+11 < - 1 or x + 11> 1
1 solutions
Answer 315026 by stanbon(57984) on 2011-06-09 16:16:11 (Show Source):
You can put this solution on YOUR website!Solve the compound inequality:
x+11 < - 1 or x + 11> 1
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x < -11 or x > -10
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To see the solution:
Draw a number line and label x= -11 and x= -10
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Put an open circle around each of the points x = -11 and x = -10
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Draw a ray to the left from x = -11;
Draw a ray to the right from x = -10.
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That is the graph of the compound inequality.
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Cheers,
Stan H.
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Probability-and-statistics/459224: Seven runners are racing against each other in a track meet. In how many ways can these runners be in first, second, and third place (assume there cannot be any ties).
1 solutions
Answer 314952 by stanbon(57984) on 2011-06-09 05:44:17 (Show Source):
You can put this solution on YOUR website!Seven runners are racing against each other in a track meet. In how many ways can these runners be in first, second, and third place (assume there cannot be any ties).
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Ans: 7*6*5 = 210 ways
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Cheers,
Stan H.
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Probability-and-statistics/459221: a bag contains 3 red discs, 4 black discs and 5 yellow discs. 2 discs are picked one after the other without replacement. Find the probability that
a) the first disc is black and the second is red
b) the first and second discs are yellow
c) the first is red and e second is yellow
1 solutions
Answer 314951 by stanbon(57984) on 2011-06-09 05:42:51 (Show Source):
You can put this solution on YOUR website!a bag contains 3 red discs, 4 black discs and 5 yellow discs. 2 discs are picked one after the other without replacement. Find the probability that
a) the first disc is black and the second is red:::(4/12)(3/11)
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b) the first and second discs are yellow:::(5/12)(4/11)
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c) the first is red and e second is yellow:::(3/12)(5/11)
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Cheers,
Stan H.
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Rate-of-work-word-problems/459219: If it takes seven men 2.5 hours to clean up a street after a New Year's party, how long (in hour and minutes) would it take for three men to do the job?
1 solutions
Answer 314950 by stanbon(57984) on 2011-06-09 05:38:29 (Show Source):
You can put this solution on YOUR website!If it takes seven men 2.5 hours to clean up a street after a New Year's party, how long (in hour and minutes) would it take for three men to do the job?
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# of men and time to do the job are inversely related.
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t = k/m
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Solve for "k" using "it takes seven men 2.5 hours to clean up a street":
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2.5 = k/7
k = 17.5
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Equation:
t = 17.5/m
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How long (in hour and minutes) would it take for three men to do the job?
time = 17.5/3
time = 5.83 hrs
= 5 hr (0.83)60 min
= 5 hr 50 minutes
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Cheers,
Stan H.
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