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Recent problems solved by 'stanbon'
stanbon answered: 57279 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, >>NextFinance/148479: Question
The equation y= -1777x + 27,153 can be used to predict the number y of gun deaths, in the U.S. x years after 2000, that is, x=0 corresponds to 2003, x=y corresponds to 2004, and so on... Predict the number of gun deaths in 2004 and 2007.
In what year will the number of gun deaths be 11,160?
What number of gun deaths predicted for 2004??? and What number gun deaths predicted for 2007?
1 solutions
Answer 108847 by stanbon(57352)   on 2008-07-16 14:34:33 (Show Source):
You can put this solution on YOUR website!The equation f(x)= -1777x + 27,153 can be used to predict the number y of gun deaths, in the U.S. x years after 2000, that is, x=3 corresponds to 2003, x=4 corresponds to 2004, and so on...
-------------------------------------
Predict the number of gun deaths in 2004 and 2007.
f(4) = -1777*4 + 27153 = 20045
f(7) = -1777*7 + 27153 = 14714
----------------------
In what year will the number of gun deaths be 11,160?
11,160 = -1777x + 27153 ; x=9
Year = 2009
====================
Cheers,
Stan H.
|
Travel_Word_Problems/148505: Approximate speed car traveling when brakes are suddently applied, use equation S=4.47L½. S= speed of car in miles per hour and L = length of skid marks left by the tires in feet. If 196-foot long skid marks were left by the car, at what speed was it traveling when the breaks were applied?
1 solutions
Answer 108841 by stanbon(57352) on 2008-07-16 14:14:45 (Show Source):
You can put this solution on YOUR website!Approximate speed car traveling when brakes are suddently applied,
use equation S=4.47L½.
S= speed of car in miles per hour and
L = length of skid marks left by the tires in feet.
If 196-foot long skid marks were left by the car, at what speed was it traveling when the breaks were applied?
================
Let L = 196 and solve for S
----------
S = 4.47sqrt(196) = 62.58 mph
================
Cheers,
Stan H.
|
Rate-of-work-word-problems/148509: Suppose it takes Tom and Dick 2 hours to do a certain job, it takes Tom and Harry 3 hours to do the same job. It takes Dick and Harry 4 hours to do this same job.
How long will it take Tom, Dick, and Harry to do the same job together?
So, just for organizing:
T + D = 2hrs
T + H = 3hrs
D + H = 4hrs
T+D+H = ? hrs
Therefore: (I think, but I'm sure it's most probably right)
1/T + 1/D =1/2
1/T + 1/H =1/3
1/D + 1/H =1/4
1/T + 1/D + 1/H =1/x
So far, I got to T=12/5 and D=12
using reciprocals and the first equation, the sum is 6/12 or 1/2; so far so good.
But I've tried using it to solve for the H one.. and it doesn't quite work.. so when I get to the last equation I still have two variables, H and X.
1 solutions
Answer 108838 by stanbon(57352) on 2008-07-16 14:05:26 (Show Source):
You can put this solution on YOUR website!Suppose it takes Tom and Dick 2 hours to do a certain job, it takes Tom and Harry 3 hours to do the same job. It takes Dick and Harry 4 hours to do this same job.
How long will it take Tom, Dick, and Harry to do the same job together?
So, just for organizing:
T + D = 2hrs
T + H = 3hrs
D + H = 4hrs
T+D+H = ? hrs
Therefore: (I think, but I'm sure it's most probably right)
1/T + 1/D =1/2
1/T + 1/H =1/3
1/D + 1/H =1/4
1/T + 1/D + 1/H =1/x
So far, I got to T=12/5 and D=12
using reciprocals and the first equation, the sum is 6/12 or 1/2; so far so good.
-----------------------
You only need the 1st three equations.
Three equations with three unknows yields an answer:
1/T + 1/D + 0 = 1/2
1/T + 0 +1/H =1/3
o +1/D + 1/H =1/4
-------------
1/T = 7/24
1/D = 5/24
1/H = 1/24
----------------
So T time = 24/7 = 3 3/7 days
D time = 24/5 = 4 4/5 days
H time = 24 days
==========================
Cheers,
Stan H.
|
Quadratic_Equations/148462: Find all the errors in the following solution to an equation:
7/x = 8/x+3 +1
7(x+3) = 8x + 1
7x + 3 = 8x
-x = -3
x= 3
1 solutions
Answer 108797 by stanbon(57352) on 2008-07-16 08:36:55 (Show Source):
You can put this solution on YOUR website!Find all the errors in the following solution to an equation:
7/x = 8/x+3 +1
7(x+3) = 8x + 1
7x + 3 = 8x
-x = -3
x= 3
----------------
I'll do it the right way and let you find the errors:
7/x = 8/x+3 +1
Multiply thru by x(x+3) to get:
7(x+3) = 8x + x(x+3)
7x+21 = 8x + x^2 + 3x
7x+21 = 11x + x^2
x^2 + 4x -21 = 0
(x+7)(x-3) = 0
x = -7 or x = 3
=================
Cheers,
Stan H.
|
Graphs/148456: Assume it costs 25 cents to mail a letter weighing once ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let L(x) be the cost of mailing a letter weighing x ounces. Solve and graph y=L(x).
I started by doing y=L(x)+20 then I plugged in points for x. Am I headed in the right direction with this?
1 solutions
Answer 108795 by stanbon(57352) on 2008-07-16 08:31:30 (Show Source):
You can put this solution on YOUR website!Assume it costs 25 cents to mail a letter weighing once ounce or less, and then 20 cents for each additional ounce or fraction of an ounce.
Let L(x) be the cost of mailing a letter weighing x ounces. Solve and graph
y=L(x).
I started by doing y=L(x)+20 then I plugged in points for x. Am I headed in the right direction with this?
---------------------
The 20 gets added every time you add an ounce, so the 20 is the slope.
---------
L(x) = 20(x-1)+25
-------------
Cheers,
Stan H.
|
Numbers_Word_Problems/148461: The sum of the digits of a two-digit number is 7. The original two-digit number is 3 less than 4 times the number with its digits reversed. Find the original two-digit number.
1 solutions
Answer 108794 by stanbon(57352) on 2008-07-16 08:20:22 (Show Source):
You can put this solution on YOUR website!The sum of the digits of a two-digit number is 7.
The original two-digit number is 3 less than 4 times the number with its digits reversed.
Find the original two-digit number.
----------------
Let the original number be 10t+u where t is the tens digit and u is the units digit.
--------
EQUATIONS:
t + u = 7
10t+u = 4(10u+t)-3
------------
Rearrange:
t + u = 7
6t -39u = -3
----------------
Modify:
6t + 6u = 42
6t - 39u = -3
---------------
Subtract to solve for "u":
45u = 45
u = 1
--------
Substitute into t+u = 7 to solve for "t":
t+1 = 7; t=6
------------------
Original Number: 61
======================
Cheers,
Stan H.
|
Travel_Word_Problems/148457: This question is from textbook
A plane flying the 3458 mi. trip from New York City to London has a 50 mph tailwind. The flight's point of no return is the point at which the flight time required to return to New York is the same as the time required to continue on to London. If the speed of the plane in still air is 360 mph, how far is New York from the point of no return.
1 solutions
Answer 108793 by stanbon(57352) on 2008-07-16 08:14:43 (Show Source):
You can put this solution on YOUR website!A plane flying the 3458 mi. trip from New York City to London has a 50 mph tailwind.
The flight's point of no return is the point at which the flight time required to return to New York is the same as the time required to continue on to London.
If the speed of the plane in still air is 360 mph, how far is New York from the point of no return.
------------
With the wind data:
rate = 360+50 = 410mph ; distance = x mi ; time = d/r = x/410
-------------------
Again the wind data:
rate = 360-50 =310 mph ; distance = (3458-x) mi ; time = d/r = (3458-x)/310
------------
EQUATION:
After going x miles from NY, time to go the remaining miles with the wind
equals time to return x miles against the wind.
time with = time against
x/310 = (3458-x)/410
410x = 310*3458 - 310x
720x = 310*3458
x = 1488.86 miles from NY is the point of no return
==============
Cheers,
Stan H.
|
Travel_Word_Problems/148460: A biker rode the first 20 miles of a trip at a constant rate. For the next 16 miles, the biker reduced his speed by 2 mph. The total time for the 36 miles was 4 hours. Find the rate of the biker for each leg of his trip.
1 solutions
Answer 108792 by stanbon(57352) on 2008-07-16 07:18:35 (Show Source):
You can put this solution on YOUR website!A biker rode the first 20 miles of a trip at a constant rate. For the next 16 miles, the biker reduced his speed by 2 mph. The total time for the 36 miles was 4 hours. Find the rate of the biker for each leg of his trip.
-------------------
1st Part DATA:
distance = 20 mi ; rate = x mph ; time = d/r = 20/x hrs
-------------------
2nd Part DATA:
distance = 16 mi ; rate = (x-2) mph ; time = d/r = 16/(x-2) hrs
--------------------
EQUATION:
time + time = 4 hrs
(20/x) + (16/(x-2)) = 4
Divide thru by 4 to get:
(5/x) + 4/(x-2) = 1
Multiply thru by x(x-2) to get:
5(x-2) + 4x = x^2-2x
9x-10 = x^2-2x
x^2-11x+10 = 0
(x-10)(x-1) = 0
x = 10 or x = 1
Then x-2 = 8 mph or x-2 = -1
-----------
Only x-2=8 mph is realistic for the speed on the 2nd leg of the journey
So the speed on the 1st leg is 10 mph
===================
Cheers,
Stan H.
|
Linear-equations/148459: I NEED HELP COULD ANYONE SHOW ME HOW THESE ARE DONE? QUESTION READS FIND THE EQUATION OF THE LINE DETERMINED BY THE GIVEN INFORMATION. 1. M=1; P=(-7,0) 2. P1=(4,-5); P2=(11,2) 3. P1=(0,6); P2=(-2,3) 4. M=2; P=(0,1)
1 solutions
Answer 108790 by stanbon(57352) on 2008-07-16 07:11:56 (Show Source):
You can put this solution on YOUR website!FIND THE EQUATION OF THE LINE DETERMINED BY THE GIVEN INFORMATION. 1. M=1; P=(-7,0) 2. P1=(4,-5); P2=(11,2) 3. P1=(0,6); P2=(-2,3) 4. M=2; P=(0,1)
-----------------
Line equations look like this: y = mx + b
m is the slope
b is the y-intercept; it is the value of y when x = 0.
----------------
1. M=1; P=(-7,0)
You are told the slope is 1 and y = 0 when x = -7
Put those numbers into y = mx + b to solve for "b":
0 = 1*-7 + b
b = 7
EQUATION: y = x + 7
------------------------
2. P1=(4,-5); P2=(11,2) 3. P1=(0,6); P2=(-2,3)
These cannot be worked because you only have one point to work with
------------------------
4. M=2; P=(0,1)
slope = 2
1 = 2*0 + b
b = 1
EQUATION:
y = 2x + 1
=================
Cheers,
Stan H.
|
Equations/148430: Two angles of a triangle measure 21 degrees and 86 degrees. What is the measure of the third angle?
Could you please show how you got it.
Thank you
1 solutions
Answer 108782 by stanbon(57352) on 2008-07-15 22:34:07 (Show Source):
You can put this solution on YOUR website!Two angles of a triangle measure 21 degrees and 86 degrees. What is the measure of the third angle?
--------------
The three angles always add up to 180 degrees.
Let the 3rd angle have measure "x".
EQUATION:
x + 21 + 86 = 180
x + 107 = 180
x = 73 degrees
================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/148431: Can you tell me if this formula is written correctly?
My worksheet said to type a formula to evaluate the given polynomial at the points x = -2 and y = -3
The polynomial is 1 - x^2y + 6xy^2 - x^3y^3 + 12y^5
The formula I have written is =1*(-2)^2+6*(-3)^2-(-3)^2+3-(-3)+12+(-3)^5
1 solutions
Answer 108781 by stanbon(57352) on 2008-07-15 22:31:13 (Show Source):
You can put this solution on YOUR website!evaluate the given polynomial at the points x = -2 and y = -3
The polynomial is 1 - x^2y + 6xy^2 - x^3y^3 + 12y^5
The formula I have written is:
1 - (-2)^2*(-3) + 6*(-2)(-3)^2 - (-2)^3(-3)^3 + 12(-3)^5
= 1 - 4*-3 + 6*-2*9 - -8*-27 + 12*243
= 1 + 12 - 108 + 216 + 2916
= 3037
============================
Cheers,
Stan H.
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Graphs/148434: solve the inequality. write answer in interval notation.
100 < or equal to 10(5x-2) < or equal to 200
for what values of x is the perimeter of the rectangle from 40 to 60 feet?
length:x+3
width: 2x
1 solutions
Answer 108779 by stanbon(57352) on 2008-07-15 22:15:21 (Show Source):
You can put this solution on YOUR website!write answer in interval notation.
100 < or equal to 10(5x-2) < or equal to 200
Divide thru by 10 to get:
10 <= 5x-2 <=20
Add 2 along the line
12 <= 5x <= 22
Divide thru by 5 to get:
2.2 <= x <= 4.4
==================
for what values of x is the perimeter of the rectangle from 40 to 60 feet?
length:x+3
width: 2x
--------
40 <= perimeter <=60
40 <= 2(2x+x+3) <=60
20 <= 3x+3 <= 30
17 <= 3x <= 27
(17/3) <= x <= 9
==========================
Cheers,
Stan H>
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Probability-and-statistics/148331: This question is from textbook
Probability is not my high point. I have tried to come up with an answer, but I need assistance, please. Here is the question:
A sample of 20 pages was taken without replacement from the 1,591-page phone directory
Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in
square millimeters) are shown below:
0 260 356 403 536 0 268 369 428 536
268 396 469 536 162 338 403 536 536 130
(a) Construct a 95 percent confidence interval for the true mean.
(b) Why might normality be an issue here?
(c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence?
(d) If this is not a reasonable requirement, suggest one that is.
Thank you!
1 solutions
Answer 108773 by stanbon(57352) on 2008-07-15 20:00:58 (Show Source):
You can put this solution on YOUR website!A sample of 20 pages was taken without replacement from the 1,591-page phone directory
Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text).
The data (in square millimeters) are shown below:
0 260 356 403 536 0 268 369 428 536
268 396 469 536 162 338 403 536 536 130
---------
x-bar = 346.5 ; s = 170.378
(a) Construct a 95 percent confidence interval for the true mean.
I'm assuming you want a Z-Interval:
E = 1.96[170.378/sqrt(20] = 74.6715
95% CI: (x-bar-E, x-bar+E) = (346.5-74.6715 , 346.5+74.6715)
(b) Why might normality be an issue here?
These 20 samples gathered in the way described is probably not a random
sample.
----------------
(c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence?
E = z
n = [2.326s/E]^2
n = [2.326*170.378/10]^2 = 1571 when rounded up.
---------------------
(d) If this is not a reasonable requirement, suggest one that is.
You would get a smaller "n" if you increase the size of E or
decrease the size of z* by requiring less confidence.
------------------
Cheers,
Stan H.
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Polynomials-and-rational-expressions/148396: Divide:
-x^3 + 75x - 250 / x + 10
I started with x + 10 outside the division box and -x^3 + 75x - 250 inside the box. but when I started to divide them out it wasnt working.
1 solutions
Answer 108771 by stanbon(57352) on 2008-07-15 19:26:56 (Show Source):
You can put this solution on YOUR website!Divide:
-x^3 + 75x - 250 / x + 10
---------------------
Using synthetic division:
-10)....-1....0....75....-250
..........-1...-10.. 175..|..-1000
Remainder: -1000
Quotient: -x^2 -10x +175
===========================
Cheers,
Stan H.
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Finance/148397: Here's a hard one...HELP
In 1991, th elife expectancy of males in a certain country was 70.4 years. In 1998, it was 74.2 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991.
The linear function E(t) that fits the data is??
E(t) = ??t + ??
(round to the nearest tenth)
Use the function to predict the life expectancy of males in 2003.
E(12)=???
(round to the nearest tenth)
1 solutions
Answer 108769 by stanbon(57352) on 2008-07-15 19:22:18 (Show Source):
You can put this solution on YOUR website!In 1991, the life expectancy of males in a certain country was 70.4 years.
In 1998, it was 74.2 years.
Let E represent the life expectancy in year t and let t represent the number of years since 1991
-----------
You have two points relating t and E: (0,70.4) and (7,74.2)
slope = (74.2-70.4)/7 = 3.8/7 = 19/35
intercept: 70.4
------------------------
The linear function E(t) that fits the data is??
E(t) =(19/35)t + 70.4
(round to the nearest tenth)
Use the function to predict the life expectancy of males in 2003.
E(12)= (19/35)*12 + 70.4 = 76.9 years
(round to the nearest tenth)
===================
Cheers,
Stan H.
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Finance/148400: On three consecutive passes, a football team gains 7 yards, loses 15 yards, and gains 15 yards. What number represents the total next yardage???
The total net yardage is ?? yards.
Thanks..
1 solutions
Answer 108766 by stanbon(57352) on 2008-07-15 19:15:29 (Show Source):
You can put this solution on YOUR website!On three consecutive passes, a football team gains 7 yards, loses 15 yards, and gains 15 yards. What number represents the total next yardage???
The total net yardage is ?? yards.
---------------------------------------
7-15+15 = 7 yrd net gain.
===============
Cheers,
Stan H.
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Probability-and-statistics/148409: This question is from textbook
the probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probabilty that they do not play is 1. What is the probablity that San Francisco plays in the next Super Bowl?
1 solutions
Answer 108763 by stanbon(57352) on 2008-07-15 19:10:39 (Show Source):
You can put this solution on YOUR website!the probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probabilty that they do not play is 1. What is the probablity that San Francisco plays in the next Super Bowl?
-----------------
P(plays) = 9*P(not plays)
P(plays) + P(not plays) = 1
--------------
Substitute to solve for P(plays)
---------------
9*P(not plays) + P(not plays) = 1
10P(not plays) = 1
P(not plays) = 0.1
--------
Substitute to solve for P(plays)
P(plays) = 9*0.1 = 0.9
==========================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/148392: Not understanding the polynomials, please help. What is the number of terms, the degree of the polynomial,the leading coefficient and is the ploynomial ascending or descending.
1-x^2+6xy^2-x^3y^3+12y^5
1 solutions
Answer 108756 by stanbon(57352) on 2008-07-15 16:54:29 (Show Source):
You can put this solution on YOUR website!What is the number of terms: 5
the degree of the polynomial: 5
the leading coefficient: 12
is the polynomial ascending or descending: ascending
-----------------------------
1-x^2+6xy^2-x^3y^3+12y^5
--------------------------
Cheers,
Stan H.
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Circles/148387: What is the area of a circle whose circumference is 12pi
1 solutions
Answer 108754 by stanbon(57352) on 2008-07-15 16:49:21 (Show Source):
You can put this solution on YOUR website!What is the area of a circle whose circumference is 12pi
----------------
Circumference = 2pi(r)
12pi = 2pi(r)
r = 6
-----------
Area = (pi)r^2
Area = 36pi sq units
=======================
Cheers,
Stan H.
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Triangles/148390: if the sides of a triangle are 13, 14 and 15 cm long, then the altitude drawn to the 24 cm side is 12 cm long. how long are the other two altitudes?> which side has the longest altitude?
1 solutions
Answer 108753 by stanbon(57352) on 2008-07-15 16:45:59 (Show Source):
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Finance/148384: The mean life of a belted tire is given as 45000 km. The standard deviation is 2250 km.
What percent of the tires will have a life that exceeds 47250 km?
What percent of the tires will last longer than 40500 km?
1 solutions
Answer 108752 by stanbon(57352) on 2008-07-15 16:44:37 (Show Source):
You can put this solution on YOUR website!The mean life of a belted tire is given as 45000 km. The standard deviation is 2250 km.
What percent of the tires will have a life that exceeds 47250 km?
What percent of the tires will last longer than 40500 km?
--------------------------
Find the z-score for 47250 and for 40500.
z(47250) = (47250-45000)/2250 = 1
P(z> 1 ) = 0.15866...
-----------------------------
z(40500) = (40500-45000)/2250 = -4500/2250 = -2
P(z>-2) = 0.9772499...
======================
Cheers,
Stan H.
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Linear-systems/148379: 5 4 1 Solve the following literal equation for y.
___ - ____ = ___
a y b
1 solutions
Answer 108746 by stanbon(57352) on 2008-07-15 15:35:42 (Show Source):
You can put this solution on YOUR website!5 4 1 Solve the following literal equation for y.
___ - ____ = ___
a y b
------------------------------------------
Multiply thru by aby to get:
5by - 4ab = ay
5by-ay = 4ab
y(5b-a) = 4ab
y = (4ab)/(5b-a)
==================
Cheers,
Stan H.
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Exponential-and-logarithmic-functions/148317: Let f(x) = 1/x. Show that (f * f)(x) = x for all nonzero value of x.
Thank you for your help ahead of time.
It's very appeciated.
1 solutions
Answer 108716 by stanbon(57352) on 2008-07-15 07:05:24 (Show Source):
You can put this solution on YOUR website!Let f(x) = 1/x. Show that (f * f)(x) = x for all nonzero value of x.
--------------
Comment: (f*f)(x) means [f(x)*f(x)].
In your case that would be 1/x^2
I don't think you want that.
---------
I think what you want is fof(x) which means f[f(x)] = f(1/x)] 1/(1/x) = x
================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/148318: You and a friend have decided to go into the lawn mowing business. Having done a particular yard several times you note the following. Working together you and your friend can mow the yard in 3 hours. Working alone, it takes you 2 hours more than your friend to mow the yard. How long does it take your friend to mow the yard?
1 solutions
Answer 108715 by stanbon(57352) on 2008-07-15 07:01:21 (Show Source):
You can put this solution on YOUR website!You and a friend have decided to go into the lawn mowing business. Having done a particular yard several times you note the following. Working together you and your friend can mow the yard in 3 hours. Working alone, it takes you 2 hours more than your friend to mow the yard. How long does it take your friend to mow the yard?
-----------------------
Together:
Time = 3 hrs/job : Rate = 1/3 job//hr
----------
Friend:
Time = x hrs/job ; Rate = 1/x job/hr
----------
You:
Time = x+2 hrs/job ; Rate = 1/(x+2) job/hr
--------------
EQUATION:
rate + rate = together rate
1/x + 1/(x+2) = 1/3
Multiply thru by 3x(x+2)
3x+6 + 3x = x^2+2x
x^2-x-6 = 0
(x-3)(x+2) = 0
Positive answer:
x = 3 hrs (Your friend's time to do the job)
x+2 = 5 hrs ( Your time to do the job)
================
Cheers,
Stan H.
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logarithm/148320: Write as a single logarithm:
5/6log(x) + 12log(y) - 6logx - logy
1 solutions
Answer 108714 by stanbon(57352) on 2008-07-15 06:56:07 (Show Source):
You can put this solution on YOUR website!(5/6)log(x) + 12log(y) - 6logx - logy
Rearrange and factor to get:
[(5/6)-6]logx + 11logy
[-31/6]logx + 11logy
= log[x^(-31/6)*y^11]
= log[y^11/x^(31/6)]
========================
Cheers,
Stan H.
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