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Recent problems solved by 'stanbon'
stanbon answered: 57288 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, >>Next
Proportions/289294: 35 out of 50 bike injuries in the state last year were head injuries. Of each 10 bike injuries how many are to the head?
I tried to figure the proportion but can't quite get it...
THANKS! 1 solutions
Answer 209585 by stanbon(57361) on 2010-04-06 18:46:17 (Show Source):
You can put this solution on YOUR website!35 out of 50 bike injuries in the state last year were head injuries.
Of each 10 bike injuries how many are to the head?
I tried to figure the proportion but can't quite get it...
-----------------------
head/bike injuries = head/bike injuries
---
x/10 == 35/50
---
x = 10(35/50)
x = 7
========================
Cheers,
Stan H.
========================
|
Quadratic_Equations/289278:  1 solutions
Answer 209583 by stanbon(57361) on 2010-04-06 18:23:58 (Show Source):
You can put this solution on YOUR website!y=-3x^2+6x+1
------------------------
Find the x-intercepts:
Quadratic Formula:
x = [-6 +- sqrt(36-4*-3*1)]/-6
-------
x = [-6 +- sqrt(48)]/-6
---
x = [-6 +-4sqrt(3)]/-6
---
x = 1 +- (2/3)sqrt(3)
---
Find the y-intercept:
y = 0+0+1
y = 1
----
y=-3x^2+6x+1
Find the vertex:
x = -b/2a = -6/(-6) = 1
f(1) = -3+6+1 = 4
Vertex at (1,4)
---------------------
Graph:

================================================
Cheers,
Stan H.
|
Probability-and-statistics/289273: How much pizza is left if 7 people ate 3/8 each of 4 pizzas? 1 solutions
Answer 209581 by stanbon(57361) on 2010-04-06 18:04:31 (Show Source):
You can put this solution on YOUR website!How much pizza is left if 7 people ate 3/8 each of 4 pizzas?
--------------------
The 7 people ate 7(3/8) = 21/8 pizza
----------------
The 4 pizzas can be written as 32/8 pizza
----------------
Then 32/8 - 21/8 = 11/8 pizza (amount of pizza that is left)
===================
Cheers,
Stan H.
===================
|
Length-and-distance/289185: The circle x^2+y^2-6x-8y=0 intersects the y axis at A& B and is a tangent to the x axis at C.
(a) write down the coordinates of pt C
(b) find the length of the chord AB
i figured that a line or something touches (6,8) i think because of -6x and -8y
thx!!!! 1 solutions
Answer 209537 by stanbon(57361) on 2010-04-06 15:00:55 (Show Source):
You can put this solution on YOUR website!The circle x^2+y^2-6x-8y=0 intersects the y axis at A& B and is a tangent to the x axis at C.
--------------
Complete the square to find the center and radius of the circle:
x^2-6x+9 + y^2-8y+16 = 25
(x-3)^2 + (y-4)^2 = 25
center at (3,4); radius = 5
-----------------
Draw the picture of that circle putting the center at (3,4)
and making the radius = 5.
------
y-intercepts = ?
Let x = 0 and solve for "y":
y^2-8y = 0
y(y-8) = 0
y = 0 or y = 8
---
The y-intercepts are (0,0) and (0,8)
The chord AB has length = 8
---------------------------------------
(a) write down the coordinates of pt C
Note: The circle is not tangent to the x-axis.
C is directly below (3,4)
C is (3,0) if it is on the x-axis
--------------------------
(b) find the length of the chord AB: 8
==============================================
Cheers,
Stan H.
==============================================
|
Miscellaneous_Word_Problems/289183: A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle?
Can you all help me with this one??? Thank you :) 1 solutions
Answer 209529 by stanbon(57361) on 2010-04-06 14:44:31 (Show Source):
You can put this solution on YOUR website! A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle?
----------------
Equations:
d = L + 3.6
d = W + 7.1
---------------------
length = d-3.6 ft
width = d-7.1 ft
---------------------
Cheers,
Stan H.
|
Length-and-distance/289179: if the diagonal of a rhombus are 12 and 16 then a side of the rhombus will measure?
a) 10
b) 12
c) 16
d) 20
and how did you do it? 1 solutions
Answer 209527 by stanbon(57361) on 2010-04-06 14:39:09 (Show Source):
You can put this solution on YOUR website!if the diagonal of a rhombus are 12 and 16 then a side of the rhombus will measure?
Draw a rhombus (all sides are equal)
The diagonal are perpendicular bisectors of one-another.
---
Diagonal pieces are 6,6 and 8,8.
Use Pythgoras:
side^2 = 6^2 + 8^2
side = sqrt[100]
side = 10
-------------
Cheers,
Stan H.
=======================
a) 10
b) 12
c) 16
d) 20
=======================
|
expressions/289141: Using a standard American keyboard, how do I enter a square root symbol ? How do I enter an exponent ? How do I enter a pi symbol ? How do I enter a greater than or less than symbol ? How do I enter does not equal symbol ? If you can add any other 'problematic' keyboard entries it would be greatly appreciated.
1 solutions
Answer 209508 by stanbon(57361) on 2010-04-06 12:45:24 (Show Source):
You can put this solution on YOUR website! Using a standard American keyboard,
how do I enter a square root symbol ?:: use "sqrt"
How do I enter an exponent ?::: use ^(power) or "to the---power"
How do I enter a pi symbol ?::: use 3.14 or (22/7)
How do I enter a greater than or less than symbol ?::: use > or "greater than"
; use < or "less than"
How do I enter does not equal symbol ?::: use "is not equal to"
How to enter e ::: use 2.1828..
If you can add any other 'problematic' keyboard entries it would be greatly appreciated.
====================
Cheers,
Stan H.
|
Linear-equations/289137: solve by substitution
I need help finding the response to these sentences
2m+n=16
m-3n=15 1 solutions
Answer 209502 by stanbon(57361) on 2010-04-06 12:36:18 (Show Source):
You can put this solution on YOUR website!2m+n=16
m-3n=15
-----
Comment: It's up to you to decide which variable
you are going to eliminate.
If you want to eliminate the "n" terms,
Multiply thru the 1st equation by 3, then add the two equations:
6m + 3n = 48
m - 3n = 15
--------------
7m = 63
m = 9
----
Substitute into either of the original equations and solve for "n":
9-3n = 15
-3n = 6
n = -2
-------------------
Cheers,
Stan H.
=====================
|
Equations/289131: In testing an engine, various mixtures of gasoline and methanol are being tried. How much of a 90% gasoline mixture and a 75% gasoline mixture are needed for 1200 L of an 85% gasoline mixture? 1 solutions
Answer 209500 by stanbon(57361) on 2010-04-06 12:32:16 (Show Source):
You can put this solution on YOUR website!How much of a 90% gasoline mixture and a 75% gasoline mixture are needed for 1200 L of an 85% gasoline mixture?
--------------
Equation:
gas + gas = gas
0.90x + 0.75(1200-x) = 0.85*1200
----
Multiply thru by 100 and solve for "x":
90x + 75*1200 - 75x = 85*1200
15x = 10*1200
x = (2/3)1200
x = 800 L (amt. of 90% gasoline needed in the mixture)
---
1200-x = 400 L (amt. of 75% gasoline needed in the mixture)
====================================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/289107: a 90% antifreeze solution is to be mixed with a 75% solution to make 30 liters of an 80% solution. How many liters of the 90% and 75% solutions should be used? 1 solutions
Answer 209471 by stanbon(57361) on 2010-04-06 11:19:42 (Show Source):
You can put this solution on YOUR website!A 90% antifreeze solution is to be mixed with a 75% solution to make 30 liters of an 80% solution.
How many liters of the 90% and 75% solutions should be used?
-----------------------------
Equation:
alcohol + alcohol = alcohol
0.9x + 0.75(30-x) = 0.30(80)
---
Multiply thru by 100 and solve for "x":
90x + 75*30 - 75x = 30*80
15x = 5*30
x = 6 liters (amt. of 90% antifreeze needed in the mixture)
---
30-x = 24 liters (amt. of 75% antifreeze needed in the mixture)
====================================
Cheers,
Stan H.
====================================
|
Polynomials-and-rational-expressions/289102: Missing ages. Molly’s age is twice Anita’s. If the sum of
the squares of their ages is 80, then what are their ages?
I started this problem and took 80 divided by two which gave me 40, then this is where i got stuck. Am i doing this right ro do i need to go about it differently? 1 solutions
Answer 209465 by stanbon(57361) on 2010-04-06 11:08:47 (Show Source):
You can put this solution on YOUR website!Missing ages. Molly’s age is twice Anita’s. If the sum of
the squares of their ages is 80, then what are their ages?
-----------------------------------
Equations:
m = 2a
m^2 + a^2 = 80
----
Substitute for "m" and solve for "a":
(2a)^2 + a^2 = 80
4a^2 + a^2 = 80
5a^2 = 80
a^2 = 16
a = 4 (Anita's age)
---
Since m = 2a, m = 8 (Molly's age)
===================================
Cheers,
Stan H.
===================================
|
Trigonometry-basics/289100: i must find the exact value of six trig functions of pi/4 radians.
sin pi/4 csc pi/4
cos pi/4 sec pi/4
tan pi/4 cot pi/4
please help me i have no idea how to do this. thank you i really appreciate any help. 1 solutions
Answer 209461 by stanbon(57361) on 2010-04-06 11:03:26 (Show Source):
You can put this solution on YOUR website!find the exact value of six trig functions of pi/4 radians.
Draw a 45/45/90 right triangle
Let the hypotenuse be 1.
Then, using Pytagoras, each side is sqrt(2)
----
sin (pi/4) = 1/sqrt(2)
csc pi/4 = sqrt(2)/1 = sqrt(2)
--------------------------------
cos (pi/4) = 1/sqrt(2)
sec (pi/4) = sqrt(2)
--------------------------------
tan (pi/4)= sqrt(2)/sqrt(2) = 1
cot (pi/4)= sqrt(2)/sqrt(2) = 1
==============================
Cheers,
Stan H.
==============================
|
Polynomials-and-rational-expressions/289099: The instruction tell me to factor completely given that the binomial following is the factor of the binomial. Please help i thought i had the hang of it it but guess not!!!
x3 + 2x2 - 5x - 6, x + 3 1 solutions
Answer 209459 by stanbon(57361) on 2010-04-06 10:57:05 (Show Source):
You can put this solution on YOUR website!The instruction tell me to factor completely given that the binomial following is the factor of the binomial. Please help i thought i had the hang of it it but guess not!!!
x3 + 2x2 - 5x - 6, x + 3
-----
Using synthetic division:
-3)....1....2....-5....-6
.......1...-1....-2...|..0
Quotient: x^2-x-2
---
Solve x^2-x-2 = 0
(x-2)(x+1) = 0
x = 2 or x = -1
===================
Cheers,
Stan H.
|
Surface-area/289072: What is the length of the diagonal of a square with area 40.5 square inches 1 solutions
Answer 209420 by stanbon(57361) on 2010-04-06 09:37:03 (Show Source):
You can put this solution on YOUR website!What is the length of the diagonal of a square with area 40.5 square inches
---
side^2 = 40.5
side = sqrt(40.5)
----
Use Pythagoras
---
diagonal = sqrt(side^2 + side^2)
d = sqrt(40.5 + 40.5)
d = sqrt(2(40.5))
d = sqrt(81)
d = 9 inches
====================
cheers,
Stan H.
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Linear-equations/289073: Please help me solve this equation. I have started the question but I am unsure if I am going in the right direction.
Solve ( x2 – 2x )( x + 3) = -2x ( x + 1)
This is what I have so far.
x3+3x2-2x2-6x=-2x2-2x
x3+x2-6x=-2x2-2x
x3+x2+2x2-6x=-2x2+2x2-2x
x3+3x2-6x=-2x+2x
x3+3x2-4x=0
1 solutions
Answer 209414 by stanbon(57361) on 2010-04-06 09:32:05 (Show Source):
You can put this solution on YOUR website!Solve ( x^2 – 2x )( x + 3) = -2x ( x + 1)
This is what I have so far.
x^3+3x^2-2x^2-6x=-2x^2-2x
x^3+x^2-6x=-2x^2-2x
x^3+x^2+2x^2-6x=-2x
x^3+3x^2-4x=0
x(x^2+3x-4) = 0
x(x+4)(x-1) = 0
x = 0 or x = -4 or x = 1
==============================
cheers,
Stan H.
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Probability-and-statistics/289047: couple plan to have 4 children List the sample space assuming the outcome are equally likely using boy girl 1 solutions
Answer 209410 by stanbon(57361) on 2010-04-06 09:25:08 (Show Source):
You can put this solution on YOUR website!couple plan to have 4 children List the sample space assuming the outcome are equally likely using boy girl
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4 girls
gggg
---
3 girls
bggg
gbgg
ggbg
gggb
---
2 girls
ggbb
gbbg
bbgg
gbgb
bgbg
bggb
----
1 girl
gbbb
bgbb
bbgb
bbbg
---
0 girls
bbbb
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Cheers,
Stan H.
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Equations/288982: Hi all, I was hoing to get some help with the following:
I need to make t the subject of the following expression:
h^3 = ln(g /(t^2+1))
Help with steps and explanations would be great.
Thanks, -Nick. 1 solutions
Answer 209385 by stanbon(57361) on 2010-04-05 23:39:15 (Show Source):
You can put this solution on YOUR website! make t the subject of the following expression:
h^3 = ln(g /(t^2+1))
e^(h^3) = g/(t^2+1)
t^2+1 = g/e^(h^3)
t = sqrt{[g/e^(h^3)]-1}
============================
Cheers,
Stan H.
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Trigonometry-basics/288980: I have 2 very similar questions which i dont know what to do with!
1) sin(Sin^-1(3/5))+sin(Sin^-1(-3/5)
2) cos(Artan(4/3))-Arcos(5/13))
Thanks for the help. 1 solutions
Answer 209381 by stanbon(57361) on 2010-04-05 23:30:48 (Show Source):
You can put this solution on YOUR website!1) sin(Sin^-1(3/5))+sin(Sin^-1(-3/5)
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= (3/5) + (-3/5)
= 0
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2) cos(Artan(4/3))-Arcos(5/13))
---
= cos(arctan(4/3))cos(arccos(5/13)) + sin(arctan(4/3))sin(arccos(5/13))
---------
= (3/5)(5/13) + (4/5)(12/13)
---
= (3/13) + (48/65)
---
= (15 + 48)/65
= 63/65
==============================
Cheers,
Stan H.
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Travel_Word_Problems/288981: An airplane takes hours to travel a distance of against the wind. The return trip takes hours with the wind. What is the rate of the plane in still air and what is the rate of the wind?
Rate of the plane in still air:
rate of the wind: 1 solutions
Answer 209378 by stanbon(57361) on 2010-04-05 23:20:31 (Show Source):
You can put this solution on YOUR website!An airplane takes 5 hours to travel a distance of 3400km against the wind. The return trip takes4 hours with the wind. What is the rate of the plane in still air and what is the rate of the wind?
----------------------------
Against the wind DATA:
distance = 3400 km ; time = 5 hr. ; rate = d/t = 3400/5 = 680 km/hr
=============
With the wind DATA:
distance = 3400 km ; time = 4 hr. ; rate = d/t = 3400/4 = 850 km/hr
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Equations:
plane speed - wind speed = 680 km/hr
plane speed + wind speed = 850 km/hr
----------------------
2(plane speed) = 1530
plane speed = 765 km/hr
---
Substitute and solve for "wind speed":
765 + wind speed = 850
wind speed = 85 km/hr
========================================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/288957: An arrow is shot directly upward from the top of a 112-foot tall building with an initial velocity of 96 feet per second. The height of the arrow above the ground after (t) seconds is given by the position function. s(t)=-16t^2+96t+112. After how many seconds will the arrow strike the ground? 1 solutions
Answer 209372 by stanbon(57361) on 2010-04-05 22:49:49 (Show Source):
You can put this solution on YOUR website!An arrow is shot directly upward from the top of a 112-foot tall building with an initial velocity of 96 feet per second. The height of the arrow above the ground after (t) seconds is given by the position function.
s(t)=-16t^2+96t+112. After how many seconds will the arrow strike the ground?
-------------------
Solve -16t^2 + 96t + 112 = 0
---
-16(t^2 - 6t + 7) = 0
Factor:
(t-6)(t+1) = 0
Positive solution:
t = 6 seconds
=====================
Cheers,
Stan H.
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Rate-of-work-word-problems/288966: An inlet pipe can fill a swimming pool in nine hours and an outlet pipe can empty a pool in 12 hours. Through an error both pipes were left open. How long will it take to fill the pool? 1 solutions
Answer 209367 by stanbon(57361) on 2010-04-05 22:39:49 (Show Source):
You can put this solution on YOUR website!An inlet pipe can fill a swimming pool in nine hours and an outlet pipe can empty a pool in 12 hours. Through an error both pipes were left open. How long will it take to fill the pool?
----------------------------------
Inlet DATA:
time = 9 hrs/job ; rate = 1/9 job/hr
------------------
Outlet pipe DATA:
time = 12 hr/job ; rate = 1/12 job/hr
--------------
Together DATA:
time = x hr./job ; rate = 1/x job/hr
============================================
Equation:
rate - rate = together rate
1/9 - 1/12 = 1/x
---
Multiply thru by 36x to get:
12x - 9x = 36
3x = 36
x = 12 hrs (time to fill the pool together)
===========================================
Cheers,
Stan H.
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Probability-and-statistics/288922: A multiple-choice test has three questions, each with four choices for the answer, of which only one of the choices is correct. What is the probability of guessing correctly on at least one of the questions? The answer is .578 but how do I get that?
A network executive has to decide on the programming line-up for Thursday night. If there are ten shows to choose from, how many six-show line-ups are possible? Answer s 151,200 how do I get that?
Find the probability of having exactly four girls in seven births. Assume no multiple births and that male and female births are equally likely and independent. Answer is.273 how do I get that?
Thanks-
1 solutions
Answer 209365 by stanbon(57361) on 2010-04-05 22:27:27 (Show Source):
You can put this solution on YOUR website!A multiple-choice test has three questions, each with four choices for the answer, of which only one of the choices is correct. What is the probability of guessing correctly on at least one of the questions? The answer is .578 but how do I get that?
---------------
Binomial Problem with n = 3 ; p = 1/4
P(at least one correct) = 1 - P(none correct)
= 1 - (3/4)^3
= 1 - 0.4219
= 0.5781
============================
A network executive has to decide on the programming line-up for Thursday night. If there are ten shows to choose from, how many six-show line-ups are possible? Answer s 151,200 how do I get that?
-------------
10P6 = 10!/(10-6)! = 10*9*8*7*6*5 = 151200
==================================================
Find the probability of having exactly four girls in seven births. Assume no multiple births and that male and female births are equally likely and independent. Answer is.273 how do I get that?
--------
P(4 girls in 7 births) = 7C4(1/2)^4(1/2)^3
= 35(1/2)^7
= 35/128
= 0.273
==============
Cheers,
Stan H.
==============
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Linear-systems/288924: my homework paper say to graph each equation and tell whether it is linear 1 solutions
Answer 209347 by stanbon(57361) on 2010-04-05 21:20:10 (Show Source):
You can put this solution on YOUR website!my homework paper say to graph each equation and tell whether it is linear
---
An equation is linear if you can write it in the form y = mx+b
where y is not zero.
=======================
Cheers,
Stan H.
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