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Recent problems solved by 'stanbon'
stanbon answered: 57274 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, >>NextMoney_Word_Problems/320229: Lee invests $10,000 in stocks and bonds. The stocks return 15% a year and the bonds return 10% a year. If the total return on the investment after one year is $1,100, how much did Lee invest each in stocks and bonds?
1 solutions
Answer 229346 by stanbon(57347)   on 2010-07-06 16:33:05 (Show Source):
You can put this solution on YOUR website!Lee invests $10,000 in stocks and bonds. The stocks return 15% a year and the bonds return 10% a year. If the total return on the investment after one year is $1,100, how much did Lee invest each in stocks and bonds?
--------------
Quantity Equation: s + b = 10,000
Interest Equation:0.15s + 0.10b = 1100
------------------------------------------------
Multiply thru 1st by 15;
Multiply thru 2nd by 100:
-------------------------------
15s + 15b = 15*10,000
15s + 10b = 110000
----------------------------
Subtract 2nd from 1st and solve for "b":
5b = 40,000
b = $8000 (amt. invested in bonds)
---
Since s + b = 10,000, s = $2000 (amt. invested in stocks)
=================================
Cheers,
Stan H.
===============
|
Expressions-with-variables/320219: Solve by substitution method
7x+8y=36
X=60-8y
Thank you
1 solutions
Answer 229335 by stanbon(57347) on 2010-07-06 16:11:54 (Show Source):
You can put this solution on YOUR website!Solve by substitution method
7x+8y=36
X=60-8y
-----
Substitute for "x" and solve for "Y":
7(60-8y) + 8y = 36
---
7*60 - 56y + 8y = 36
-48 = -384
-------
y = 8
---
Since x = 60-8y, x = 60-8*8 = -4
============================
Cheers,
Stan H.
============================
|
Equations/320216: Solve using multiplication principle
-3/4x=-5/6
It makes no sense to me!
Thank you
1 solutions
Answer 229324 by stanbon(57347) on 2010-07-06 16:01:41 (Show Source):
You can put this solution on YOUR website!Solve using multiplication principle
(-3/4)x=(-5/6)
---
Multiply both sides by -4/3 to get:
-----
x = (-4/3)(-5/6)
---
x = 20/18
---
x = 10/9
===============
Cheers,
Stan H.
============
|
Quadratic_Equations/320183: Please explain how I may obtain the needed answer.
I have
(x+3)^2=-25
I thought
(X+3)*(x+3)=X^2+6x+9= -25 and moved into quadratic form by adding 25 to both sides. like so,
x^2+6x+34=0 then solve for X.
At this point I usually give the brain a break and solve using the TI89.
Problem is that it keeps telling me false instead of the needed, {-3+5i,-3-5i}
Can anyone tell me where I went wrong?
Thanks
1 solutions
Answer 229289 by stanbon(57347) on 2010-07-06 14:07:55 (Show Source):
You can put this solution on YOUR website!The sum of squares factors as follows:
a^2 + b^2 = (a+bi)(a-bi)
=================================
(x+3)^2=-25
---
(x+3)^2 + 25 = 0
Factor:
[x+3+5i][x+3-5i] = 0
x = -3-5i or x = -3+5i
========================
Not sure what your TI89 is doing.
========================
Cheers,
Stan H.
============
|
Linear-equations/320184: I have a question that is a T/F question. Can anyone explain? Thanks in advance for your wisdom!
The equations y = 3x – 6 and y = 2x + 4 are independent. True or false and why.
1 solutions
Answer 229288 by stanbon(57347) on 2010-07-06 14:04:05 (Show Source):
You can put this solution on YOUR website!Yes, they are independent because the lines do not
have the same slope and therefore are not parallel
and are not dependent.
==========================
Cheers,
Stan H.
===========
dependent: one is a multiple of the other
independent: intersect at one point because slopes differ.
inconsistent: parallel lines
consistent: not parallel
==================
|
Probability-and-statistics/320119: A leasing firm claims that the mean number of miles driven annually, , in its leased cars is less than miles. A random sample of cars leased from this firm had a mean of annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is miles. Assume that the population is normally distributed. Is there support for the firm's claim at the level of significance?
Perform a one-tailed test. Then fill in the table below.
What is the null hypothesis?
What is the alternative hypothesis?
What is the type of test statistic (Z, T, Chi Square). If T what is the degree of freedom?
What is the value of the test statistic (round at least 3 decimal places)
What is the critical value at the 0.05 level of significance (round at least 3 decimal places)
Can we support the leasing firms claim that the mean number of miles driven annually is less than 13280 miles?
1 solutions
Answer 229287 by stanbon(57347) on 2010-07-06 13:58:50 (Show Source):
You can put this solution on YOUR website!A leasing firm claims that the mean number of miles driven annually, , in its leased cars is less than miles. A random sample of cars leased from this firm had a mean of annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is miles. Assume that the population is normally distributed. Is there support for the firm's claim at the level of significance?
Perform a one-tailed test. Then fill in the table below.
What is the null hypothesis?
What is the alternative hypothesis?
What is the type of test statistic (Z, T, Chi Square). If T what is the degree of freedom?
What is the value of the test statistic (round at least 3 decimal places)
What is the critical value at the 0.05 level of significance (round at least 3 decimal places)
Can we support the leasing firms claim that the mean number of miles driven annually is less than 13280 miles?
=====================================
Read your posted problem. Notice that there are numbers missing from
the text. I asked the site manager to look at what appears to be dropped
numbers. Here is his feedback:
"As far as I can tell, the numbers really are missing and there is no
indication that they exist but in some unreadable format."
----
If you are using a non-standard way of posting your numbers, you
might want to change that.
=========================================
Cheers,
Stan H.
======================
|
Travel_Word_Problems/320177: •A car and a bus set out at 2 p.m. from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car.
1 solutions
Answer 229284 by stanbon(57347) on 2010-07-06 13:20:55 (Show Source):
You can put this solution on YOUR website!A car and a bus set out at 2 p.m. from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car.
---------------------
Bus DATA:
rate = x mph ; time = 2 hrs ; distance = 2x miles
---------------
Car DATA:
rate = 2x-30 ; time = 2 hrs ; distance = 2(2x-30) = 4x-60 miles
-------------------------------------
Equation:
car distance - bus distance = 20 miles
4x-60-2x = 20
2x = 80
x = 40 mph (bus speed)
----------------------------
Car rate = 2x-30 = 2*40-30 = 50 mph
================
Cheers,
Stan H.
|
Numbers_Word_Problems/320171: Please help me solve this word problem: A town census shows population of 2400 in 1980 and 3600 in 1990. If the exponential rate of population increase continues, what will be the population in 2010?
1 solutions
Answer 229282 by stanbon(57347) on 2010-07-06 13:07:50 (Show Source):
You can put this solution on YOUR website!A town census shows population of 2400 in 1980 and 3600 in 1990. If the exponential rate of population increase continues, what will be the population in 2010?
A town census shows population of 2400 in 1980 and 3600 in 1990. If the exponential rate of population increase continues, what will be the population in 2010?
-----
You have two points: (0,2400) and (10,3600) where x is # of years after 1980.
----------------------------
Form: y = ab^x
---
Using the 1st point you get:
2400 = ab^0
2400 = a
--------------------
Using that result and the 2nd point you get:
3600 = 2400*b^10
3/2 = b^10
b = (1.5)^(1/10) = 1.0414
------------------------------
If the exponential rate of population increase continues, what will be the population in 2010?
---
y = 2400*(1.0414)^30
y = 8100
===============
Cheers,
Stan H.
|
Probability-and-statistics/320118: A leasing firm claims that the mean number of miles driven annually, , in its leased cars is less than miles. A random sample of cars leased from this firm had a mean of annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is miles. Assume that the population is normally distributed. Is there support for the firm's claim at the level of significance?
Perform a one-tailed test. Then fill in the table below.
What is the null hypothesis?
What is the alternative hypothesis?
What is the type of test statistic (Z, T, Chi Square)
What is the value of the test statistic (round at least 3 decimal places)
What is the critical value at the 0.05 level of significance (round at least 3 decimal places)
Can we support the leasing firms claim that the mean number of miles driven annually is less than 13280 miles?
1 solutions
Answer 229280 by stanbon(57347) on 2010-07-06 12:48:53 (Show Source):
|
Numbers_Word_Problems/320098: you are given a two -digit positive integer. if reverse the digits of your number. The result is a number which is 20% larger than your number . what is your number ?
1 solutions
Answer 229237 by stanbon(57347) on 2010-07-06 09:18:34 (Show Source):
You can put this solution on YOUR website!given a two -digit positive integer. if reverse the digits of your number. The result is a number which is 20% larger than your number . what is your number ?
-----------------
Let the number be 10t+u
The reverse is 10u+t
-----------------------------
Equation:
10u+t = 1.20(10t+u)
---
10u + t = 12t + 1.2u
11t = 8.8u
t/u = 8.8/11
t/u = 0.8
t = 0.8u
-----------------
To get a whole digit, u must be 5
Then t = 0.8*5 = 4
---
Number = 10t+u = 45
=========================
Cheers,
Stan H.
===========================
|
Linear-systems/320080: y-3x=a
3x-y=2
what is a to make these equation a dependent system of linear equation
1 solutions
Answer 229234 by stanbon(57347) on 2010-07-06 09:12:36 (Show Source):
You can put this solution on YOUR website!y-3x=a
3x-y=2
what is a to make these equation a dependent system of linear equation
------
Rearrange:
y = 3x+a
y = 3x-2
---
Ans: a = -2
===================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/320100: At Halloween party, Fancy is throwing darts at jack-o-lanterns and witches. She gets 5 points for every jack-o-lantern she hits and 8 points for every witch. She has hit 13 jack-olanterns and witches altogether and has 80 points. How many jack-o-lanterns and how many witches has she hit?
1 solutions
Answer 229233 by stanbon(57347) on 2010-07-06 09:10:11 (Show Source):
You can put this solution on YOUR website!At Halloween party, Fancy is throwing darts at jack-o-lanterns and witches. She gets 5 points for every jack-o-lantern she hits and 8 points for every witch. She has hit 13 jack-olanterns and witches altogether and has 80 points. How many jack-o-lanterns and how many witches has she hit?
---
Hit Equation: j + w = 13
Points Equat:5j +8w = 80
-----------------------------
Multiply thru 1st Eq. by 5:
5j + 5w = 5*13
5j + 8w = 80
---------------------
Subtract 1st from end and solve for "w":
3w = 80-5*13
3w = 15
w = 5 (# of witches hit)
---
Since j+w = 13, w = 8 (# of jacko's hit)
=============================================
Cheers,
Stan H.
|
Probability-and-statistics/319933: Forecasters' interest rate predictions over the period 1982-1990 were studied to see whether the predictions corresponded to what actually happened. The 2x2 contingency table below show the frequencies of actual and predicted interest rate movements. At a = .10, is the actual change independent of the predicted change? (Date are from R.A. Kolb and H. O. Steckler, "Howe Well Do Analysis Forecast Interest Rates?" Journal of Forecasting 15, no. 15 (1990), pp. 385-394).
Forecasted Change Rate Fell Rates Rose Row Total
Rates would fall 7 12 19
Rates would rise 9 6 15
Col. Total 16 18 34
1 solutions
Answer 229232 by stanbon(57347) on 2010-07-06 09:05:20 (Show Source):
You can put this solution on YOUR website!Ho: row and column ae independent
Ha: they are not
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I ran a Chi-Sq test of the 2x2 matrix and got:
test stat: Chi-Sq = 1.8044
p-value: 0.1792
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Since P-value is greater than 5%, fail to reject Ho.
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Cheers,
Stan H.
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Probability-and-statistics/320005: Find the point estimate of the population proportion if 85 out of 205 people like chocolate.
I'm not sure if I'm going in the right direction?
85/205 = 0.415
1 - 0.415 = 0.585
1 solutions
Answer 229226 by stanbon(57347) on 2010-07-06 08:56:47 (Show Source):
You can put this solution on YOUR website!Find the point estimate of the population proportion if 85 out of 205 people like chocolate.
I'm not sure if I'm going in the right direction?
85/205 = 0.415
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You are correct.
Cheers,
Stan H.
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Probability-and-statistics/320058: One bag contains 4 red marbles, a second bag contains 2 blue marbles, and a third bag contains 5white marbles. How many total possible ways when 1 marble from each bag be picked?
1 solutions
Answer 229225 by stanbon(57347) on 2010-07-06 08:54:34 (Show Source):
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Expressions-with-variables/320036: the amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 300 seconds with an average speed of 4 feet per second. find the average speed of the swimmer if it takes 400 seconds to finish the race.
possible answers: A)2 feet per second B)4 feet per second C)5 feet per second D)3 feet per second
1 solutions
Answer 229183 by stanbon(57347) on 2010-07-05 23:12:03 (Show Source):
You can put this solution on YOUR website!the amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer.
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t = k/s
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A swimmer finishes a race in 300 seconds with an average speed of 4 feet per second.
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Find "k"
300 = k/4
k = 1200
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Equation for this swimmer:
t = 1200/s
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find the average speed of the swimmer if it takes 400 seconds to finish the race.
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400 = 1200/s
s = 1200/400
s = 3 ft per second
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Cheers,
Stan H.
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possible answers: A)2 feet per second B)4 feet per second C)5 feet per second D)3 feet per second
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Travel_Word_Problems/320019: A boat goes 15 miles per hour in still water. If it can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current?
1 solutions
Answer 229181 by stanbon(57347) on 2010-07-05 23:08:09 (Show Source):
You can put this solution on YOUR website! A boat goes 15 miles per hour in still water. If it can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current?
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Down-stream DATA:
distance = 12 miles ; rate c + 15 mph ; time = 12/(c+15) hrs.
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Up-stream DATA:
distance 9 miles ; rate = 15-c mph ; time = 9/(15-c) hrs.
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Equation:
time = time
12/(15+c) = 9/(15-c)
12(15-c) = 9(15+c)
12*15 - 12c = 9*15 + 9c
21c = 3*15
c = 15/7 = 2 1/7 mph (speed of the current)
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Cheers,
Stan H.
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Square-cubic-other-roots/320028: True or false? The square root of A^2 = -A if A is negative.
1 solutions
Answer 229175 by stanbon(57347) on 2010-07-05 22:53:46 (Show Source):
You can put this solution on YOUR website!True or false? The square root of A^2 = -A if A is negative.
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Solve sqrt[(-2)^2] = sqrt[4] = 2, which is -(-2)
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Ans: True
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Cheers,
Stan H.
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Square-cubic-other-roots/320030: Explain why the equation x^2 = 4 has two real number solutions, while the equation the square root of x = 2 has only one real number solution.
1 solutions
Answer 229174 by stanbon(57347) on 2010-07-05 22:50:48 (Show Source):
You can put this solution on YOUR website!Explain why the equation x^2 = 4 has two real number solutions, while the equation the square root of x = 2 has only one real number solution.
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Solve x^2 = 4
x^2-4 = 0
Factor:
(x-2)(x+2) = 0
x = 2 or x = -2
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Solve sqrt(x) = 2
Square both sides to get:
x = 4
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Cheers,
Stan H.
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Equations/319977: There are approximately 4lbs of muscle for every 7lbs of body weight of a certain animal. For a 175 lb. animal, how much of the weight is muscle?
1 solutions
Answer 229151 by stanbon(57347) on 2010-07-05 19:58:28 (Show Source):
You can put this solution on YOUR website!There are approximately 4lbs of muscle for every 7lbs of body weight of a certain animal. For a 175 lb. animal, how much of the weight is muscle?
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x/175 = 4/7
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x = 175(4/7)
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x = 100 lbs of muscle
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Cheers,
Stan H.
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Numbers_Word_Problems/319971: Please help me solve this word problem: A certain radioactive element decays at a rate of 4% per year. Find the half-life of the substance (i.e. the time it will take for one half of any given amount of the substance to decay).
1 solutions
Answer 229149 by stanbon(57347) on 2010-07-05 19:56:07 (Show Source):
You can put this solution on YOUR website!Please help me solve this word problem: A certain radioactive element decays at a rate of 4% per year. Find the half-life of the substance
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A(t) = ab^t
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(1/2)a = a(0.96)^t
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(1/2) = (0.96)^t
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Take the log:
t*log(0.96) = log(0.5)
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t = 16.98 years
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Cheers,
Stan H.
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Unit_Conversion_Word_Problems/319957: Gwen bought a new car. The selling price plus the 8% sales tax was $15,714. What was the selling price?
1 solutions
Answer 229145 by stanbon(57347) on 2010-07-05 19:47:44 (Show Source):
You can put this solution on YOUR website!Gwen bought a new car. The selling price plus the 8% sales tax was $15,714. What was the selling price?
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Let the selling price be "x".
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Equation:
x + 0.08x = 15714
1.08x = 15714
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x = $14,550
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Cheers,
Stan H.
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Inequalities/319960: Give an ordered pair(u,v) of numbers that satisfy the following equation.
6u-v=3
1 solutions
Answer 229141 by stanbon(57347) on 2010-07-05 19:25:55 (Show Source):
You can put this solution on YOUR website! Give an ordered pair(u,v) of numbers that satisfy the following equation.
6u-v=3
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v = 6u-3
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Let u = 0, then v = -3
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Ans: (0,-3)
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Cheers,
Stan H.
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test/319949: The owner of Nuts2U Snack Shack mixes cashews worth $6.25 a pound with peanuts
worth $2.00 a pound to get a half-pound mixed nut bag worth $1.70. How much of each kind of nut is included in the mixed bag?
1 solutions
Answer 229140 by stanbon(57347) on 2010-07-05 19:22:51 (Show Source):
You can put this solution on YOUR website! The owner of Nuts2U Snack Shack mixes cashews worth $6.25 a pound with peanuts
worth $2.00 a pound to get a half-pound mixed nut bag worth $1.70.
How much of each kind of nut is included in the mixed bag?
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Note: Something is wrong with your data. You cannot mix
6.25 and 2.00 nuts and get 1.70 nuts.
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Cheers,
Stan H.
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If you try to get a solution you end up with a negative quantity.
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Value Equation: 6.25c + 2.00p = 1.70(1/2)
Quantity Equation: c + p = 1/2
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Multiply thru the 1st by 100
Multiply thru the 2nd by 200
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625c + 200p = 170*(1/2)
200c + 200p = 200*(1/2)
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Subtract 2nd from 1st and solve for "c":
425c = -30(1/2)
c = -0.0353, which is unrealistic.
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Cheers,
Stan H.
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Pythagorean-theorem/319945: 1. Find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree.
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2. Solve the proportion:
     
Show that the answer is 
1 solutions
Answer 229138 by stanbon(57347) on 2010-07-05 19:05:55 (Show Source):
You can put this solution on YOUR website!The Question:find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree.
h:10=1:root 2
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Equation:
h/10 = 1/sqrt(2)
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h = 10/sqrt(2)
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h = 10sqrt(2)/2
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h = (10/2)sqrt(2)
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h=5 root 2
My Question: how do you get 1 after the equal sign?
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The "1" is the numerator of the right side of the equation.
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Cheers,
Stan H.
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