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Recent problems solved by 'stanbon'
stanbon answered: 57255 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, >>NextMoney_Word_Problems/735325: which of the following will earn more money in 3 years
a. $3000 at 5.5% simple interest
b. $3000 at 5.6% compound interest
1 solutions
Answer 449393 by stanbon(57323)   on 2013-04-08 18:44:58 (Show Source):
You can put this solution on YOUR website!which of the following will earn more money in 3 years
a. $3000 at 5.5% simple interest
A(t) = P(1+rt)
A(3) = 3000(1+0.055*3) = 3000*(1.165) = $3495
--------
b. $3000 at 5.6% compound interest
A(t) = P(1+(r/n))^(nt)
A(t) = 3000(1+(0.056/1)^(1*3)
A(t) = 3000(1.056)^3 = $3532.75
-----------------------------------
Cheers,
Stan H.
===================
|
Probability-and-statistics/735169: Correction to previous submission:
Heights of men on a baseball team have a bell shaped distribution with a mean of 168 cm and a standard deviation of 5 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?
a. 153 cm and 183 cm
b. 158 cm and 178 cm
1 solutions
Answer 449310 by stanbon(57323) on 2013-04-08 14:15:59 (Show Source):
You can put this solution on YOUR website!Heights of men on a baseball team have a bell shaped distribution with a mean of 168 cm and a standard deviation of 5 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?
a. 153 cm and 183 cm
(153-168)/5 = -3
(183-168)/5 = 3
---
Using Chybyshev, at least (1-(1/3)^2) = 0.8888.. = 89% of the data
lies between 153 and 183
================================
b. 158 cm and 178 cm
(158-168)/5 = -2
(178-168)/5 = +2
---
Using Chybyshev, at leas (1-(1/2)^2) = 0.75 = 75% of the data
lies between 158 and 178
=============================
Cheers,
Stan H.
=============================
|
Probability-and-statistics/735198: I need help with the following questions please:
Problem 1)
A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis for a test of significance.
Problem 2)
At one school, the average amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. Formulate the null and alternative hypotheses for the study described.
Problem 3)
A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?
Problem 4)
A two-tailed test is conducted at the 5% significance level. What is the right tail percentile required to reject the null hypothesis?
Problem 5)
What is the difference between an Type I and a Type II error? Provide an example of both.
Thanks
1 solutions
Answer 449309 by stanbon(57323) on 2013-04-08 14:07:00 (Show Source):
You can put this solution on YOUR website!Problem 1)
A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis for a test of significance.
Ho: p >= 0.001
Ha: p < 0.001 (claim)
--------------------------------
Problem 2)
At one school, the average amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. Formulate the null and alternative hypotheses for the study described.
Ho: u >= 18.4
Ha: u < 18.4 (claim)
===========================
Problem 3)
A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?
Ans: p < 2.5% or p > 97.5%
--------------------------------
Problem 4)
A two-tailed test is conducted at the 5% significance level. What is the right tail percentile required to reject the null hypothesis?
Ans: < 2.5%
Problem 5)
What is the difference between an Type I and a Type II error? Provide an example of both.
Type I: You reject Ho when in fact it is true.
Type II: You fail to reject Ho when in fact it is false.
I'll leave the examples to you.
Cheers,
Stan H.
|
Linear-systems/735196: A bourbon that is 54-proof is 27% alcohol by volume while one that is 81-proof is 40.5% alcohol. How many liters of 54-proof bourbon must be mixed with 1.0-L of 81-proof bourbon to produce a 66-proof bourbon? Give your answer to three decimal places.
1 solutions
Answer 449308 by stanbon(57323) on 2013-04-08 13:52:04 (Show Source):
You can put this solution on YOUR website!A bourbon that is 54-proof is 27% alcohol by volume while one that is 81-proof is 40.5% alcohol. How many liters of 54-proof bourbon must be mixed with 1.0-L of 81-proof bourbon to produce a 66-proof bourbon? Give your answer to three decimal places.
------
Equation:
alcohol + alcohol = alcohol
0.27x + 0.405*1 = 0.33(x+1)
--------
270x + 405 = 330x + 33
------
60x = 372
x = 6.200 L (amt of 54 proof needed)
================
Cheers,
Stan H.
|
Graphs/735084: Would you please help me to solve this:
Graph the function y= 2/x. Draw a chart to show at least four ordered pairs that are on the graph.
(This is the 2nd time that I am submitting this problem without receiving any answer, could anyone help pls.)
Thanks
1 solutions
Answer 449273 by stanbon(57323) on 2013-04-08 07:31:51 (Show Source):
You can put this solution on YOUR website!Graph the function y= 2/x. Draw a chart to show at least four ordered pairs that are on the graph.
----
------
Points:
If x = -2 y = 2/(-2) = -1 giving you (-2,-1)
If x = -4 y = 2/(-4) = -1/2 giving you (-4,-1/2)
If x = 4 y = 2/4 = 1/2 giving you (4, 1/2)
If x = 2 y = 2/2 = 1 giving you (2,1)
==============
Cheers,
Stan H.
|
Sequences-and-series/735081: help me to find the sum 3+11+19+...+787.
1 solutions
Answer 449272 by stanbon(57323) on 2013-04-08 07:27:52 (Show Source):
You can put this solution on YOUR website!help me to find the sum 3+11+19+...+787.
----
Find "n":
787 = a + (n-1)d when a = 3 ; d = 8
---
787 = 3 + (n-1)8
784 = (n-1)8
n-1 = 98
n = 99
======
Sum = (n/2)(a+last)
Sum = (99/2)(3+787)
Sum = 39105
=================
Cheers,
Stan H.
===============
|
Exponential-and-logarithmic-functions/734781: log x + log 4 =1 please help with this
log x - log 9 =3
(1/2)^3x =8^2
1 solutions
Answer 449133 by stanbon(57323) on 2013-04-07 13:57:54 (Show Source):
You can put this solution on YOUR website!log x + log 4 =1
log(4x) = 1
4x = 10^1
4x = 10
x = 5/2
--------------------
log x - log 9 =3
log(x/9) = 3
x/9 = 10^3
x/9 = 1000
x = 9000
-------------------
(1/2)^3x =8^2
---
(2^-1)^(3x) = (2^3)^2
------
2^(-3x) = 2^(6)
---
-3x = 6
x = -2
===========
Cheers,
Stan H.
===========
|
Triangles/734771: If one side is fifteen and the other two sides are equal to each other, what's the smallest possible value for the other two sides?
1 solutions
Answer 449131 by stanbon(57323) on 2013-04-07 13:32:09 (Show Source):
You can put this solution on YOUR website!If one side is fifteen and the other two sides are equal to each other, what's the smallest possible value for the other two sides?
----------
Draw the picture.
Sketch the 15 side
Sketch two other equal sides that are both x long
-----------
Solve 2x> 15
x > 7.5
----
Note: By the way; there is no "smallest" number that is greater
than 7.5 because Real Number values are continuous
------------------
Cheers,
Stan H.
==================
|
Sequences-and-series/734773: determine whether the sequence is arithmetic if it is find the common difference 3,5/2,2,3/2,1,1/2
1 solutions
Answer 449130 by stanbon(57323) on 2013-04-07 13:26:44 (Show Source):
You can put this solution on YOUR website!determine whether the sequence is arithmetic if it is find the common difference 3,5/2,2,3/2,1,1/2
-------
Subtract the pairs as they progress to see if there is a common difference:
(5/2)-3 = -1/2
----
2-(5/2) = -1/2
----
(3/2)- 2 = -1/2
----
1-(3/2) = -1/2
----
(1/2)-1 = -1/2
---
It is arithmetic and the common difference is -1/2
=======================
Cheers,
Stan H.
=========================
|
test/734774: How do you find the slope of the line passing through these given points? (2,5) and (3,6). (6,1) and (-6,1). (4,6) and (4,8)
1 solutions
Answer 449127 by stanbon(57323) on 2013-04-07 13:23:21 (Show Source):
You can put this solution on YOUR website!How do you find the slope of the line passing through these given points? (2,5) and (3,6). (6,1) and (-6,1). (4,6) and (4,8)
----
slope = (change in y)/(corresponding change in x)
-----
Example using (3,6) (6,1)
---
slope = (1-6)/(6-3) = -5/3
===============================
Cheers,
Stan H.
|
Functions/734766: The graph of g(x) results when the graph of f(x) = |x| is shifted 3 units to the left.
Which is the equation of g(x)?
1 solutions
Answer 449122 by stanbon(57323) on 2013-04-07 13:03:56 (Show Source):
You can put this solution on YOUR website!The graph of g(x) results when the graph of f(x) = |x| is shifted 3 units to the left.
Which is the equation of g(x)?
------
g(x) = |x+3|
=============
Cheers,
Stan H.
|
Evaluation_Word_Problems/734765: Find three consecutive positive odd intergers such that the square of the smallest exceeds twice the largest by 7 | ONLY AN ALGEBRAIC SOLUTION WILL BE ACCEPTED?|
1 solutions
Answer 449120 by stanbon(57323) on 2013-04-07 12:58:22 (Show Source):
You can put this solution on YOUR website!Find three consecutive positive odd intergers such that the square of the smallest exceeds twice the largest by 7
------------------
1st: 2x-3
2nd: 2x-1
3rd: 2x+1
-------
Equation:
(2x-3)^2 = 2(2x+1)+7
------
4x^2 -12x + 9 = 4x+9
---
4x^2 -16x = 0
Factor:
4x(x-4) = 0
x = 0 or x = 4
----
If x = 0::
1st: -3
2nd: -1
3rd: 1
----
If x = 4
1st: 5
2nd: 7
3rd: 9
-----
Since you want positive odd only the x=4 set is acceptable.
=====================
Cheers,
Stan H.
=====================
|
Functions/734761: Use the function to answer the question.
f(x) = 10x-5
What is the value of f –1(–4)?
1 solutions
Answer 449118 by stanbon(57323) on 2013-04-07 12:53:40 (Show Source):
You can put this solution on YOUR website!Use the function to answer the question.
f(x) = 10x-5
What is the value of f –1(–4)?
----
Find the value of x which makes y = -4
----
Solve 10x-5 = -4
10x = 1
x = 1/10
-----
Therefore f^(-1)(-4) = 1/10
---------------------------
Cheers,
Stan H.
|
Functions/734764: Use the functions to answer the question.
f(x) = 2x+5;g(x)=3x^2
Which is equal to (f°g)(x)?
1 solutions
Answer 449117 by stanbon(57323) on 2013-04-07 12:48:54 (Show Source):
You can put this solution on YOUR website!Use the functions to answer the question.
f(x) = 2x+5;g(x)=3x^2
Which is equal to (f°g)(x)?
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fog(x) = f[g(x)] = f[3x^2] = 2(3x^2)+5 = 6x^2+5
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Cheers,
Stan H.
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Mixture_Word_Problems/734624: in a chemical process, the temperature T is to be kept within 10 C of 100 C. Express this restriction as an absolute value inequality.
1 solutions
Answer 449061 by stanbon(57323) on 2013-04-06 23:33:41 (Show Source):
You can put this solution on YOUR website!in a chemical process, the temperature T is to be kept within 10 C of 100 C. Express this restriction as an absolute value inequality.
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|T-100| <= 10
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Cheers,
Stan H.
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Linear-equations/734625: Find a linear equation in the form y=mx+b that models the quantity y after x days.
a. A quantity y is initially 750 and increases at a rate of 4 per day
b. A quantity is initially 2300 and decreases at a rate of 50 per day
c.A quantity y is initially 17, 875 and remains constant
1 solutions
Answer 449060 by stanbon(57323) on 2013-04-06 23:31:04 (Show Source):
You can put this solution on YOUR website!Find a linear equation in the form y=mx+b that models the quantity y after x days.
a. A quantity y is initially 750 and increases at a rate of 4 per day
Y = 4x + 750
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b. A quantity is initially 2300 and decreases at a rate of 50 per day
y = -50x + 2300
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c.A quantity y is initially 17,875 and remains constant
y = 17,875
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Cheers,
Stan H.
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Expressions-with-variables/734618: show me how to simplify this expression
2y 5
-------- + -----
y(2y - 1) 2y - 1
1 solutions
Answer 449059 by stanbon(57323) on 2013-04-06 23:23:33 (Show Source):
You can put this solution on YOUR website!show me how to simplify this expression
2y 5
-------- + -----
y(2y - 1) 2y - 1
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least common denominator: y(2y-1)
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Rewrite both fractions with the lcm as the denominator:
-----
[2y/lcm] + [5y/lcm]
----
Combine the numerators over the lcm:
= 7y/(y(2y-1))
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Cancel the common "y" factor:
----
= 7/(2y-1)
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Cheers,
Stan H.
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Probability-and-statistics/734579: Please help with this question.
Question: There are 8 light switches on the wall that connect to 8 different color lights inside the room. Each switch can either be in the on position or off position.
a.) How many different lighting configurations are possible?
b.) If you wanted to turn 3 of the lights on, how many choices of 3 lights could you make?
c.) If you needed to pick one light to use for an event on Thursday and another light for an event on Tuesday, how many choices for the two lights could you make?
1 solutions
Answer 449041 by stanbon(57323) on 2013-04-06 20:59:08 (Show Source):
You can put this solution on YOUR website!Question: There are 8 light switches on the wall that connect to 8 different color lights inside the room. Each switch can either be in the on position or off position.
a.) How many different lighting configurations are possible?
Ans: 2^8 = 256
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b.) If you wanted to turn 3 of the lights on, how many choices of 3 lights could you make?
Ans: 8C3 = (8*7*6)/(1*2*3) = 56
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c.) If you needed to pick one light to use for an event on Thursday and another light for an event on Tuesday, how many choices for the two lights could you
make?
8*2 = 56 if order makes a difference
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8C2 = 28 if order does not make a difference
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Cheers,
Stan H.
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Probability-and-statistics/734582: Please help. I'm not understanding this questions
The scores on a national test were normally distributed with a mean of 83 and a standard deviation of 8
To the nearest percent, what percentage of test takers scored between 70 and 90
15% of test takers scored below what test score? (Round to nearest test score)
1 solutions
Answer 449039 by stanbon(57323) on 2013-04-06 20:51:46 (Show Source):
You can put this solution on YOUR website!The scores on a national test were normally distributed with a mean of 83 and a standard deviation of 8
To the nearest percent, what percentage of test takers scored between 70 and 90
z(70) = (70-83)/8 = -13/8
z(90) = (90-83)/8 = 7/8
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P(70< x <90) = P(-13/8 < z < 7/8) = normalcdf(-13/8,7/8) = 0.7571 = 75.71%
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15% of test takers scored below what test score? (Round to nearest test score)
Draw the picture:
Find the z-score with a left tail of 15%
invNorm(0.15) = -1.0364
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Find the corresponding score value:
x = z*s + u
x = -1.0364*8+83 = 74.71
==============================
Cheers,
Stan H.
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Linear-equations/734578: What is the Equation of a line containing these points?
(4,5) and (12,11)
1 solutions
Answer 449036 by stanbon(57323) on 2013-04-06 20:33:06 (Show Source):
You can put this solution on YOUR website!What is the Equation of a line containing these points?
(4,5) and (12,11)
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slope = (11-5)/(12-4) = 6/8 = 3/4
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Form: y = mx + b
Solve for "b":
5 = (3/4)4 + b
b = 2
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Equation:
y = (3/4)x + 2
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Cheers,
Stan H.
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Inequalities/734576: Select the values of x that are solutions to the inequality 0 > x^2 + 5x -2
1 solutions
Answer 449032 by stanbon(57323) on 2013-04-06 20:20:18 (Show Source):
You can put this solution on YOUR website!Select the values of x that are solutions to the inequality 0 > x^2 + 5x -2
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The parabola opens up.
Find the x-intercepts:
x = [-5 +- sqrt(25-4*-2)]/2
x = [-5+sqrt(33)]/2 or x = [-5-sqrt(33)]/2
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The solution set is the x-values between those two x-intercepts.
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Cheers,
Stan H.
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Exponential-and-logarithmic-functions/734573: The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on advertising are given by the following.
S = 10(1 – e^kx)
When $450 is spent on advertising 2600 units are sold. solve for k.
Estimate the number of units that will be sold if advertising expenditures are raised to $550
1 solutions
Answer 449031 by stanbon(57323) on 2013-04-06 20:11:29 (Show Source):
You can put this solution on YOUR website! The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on advertising are given by the following.
S = 10(1 – e^(kx))
-----------------------------------
When $450 is spent on advertising 2600 units are sold. solve for k.
450 = 10(1-e^(26k)
----
45 = 1-e^(26k)
e^(26k) = -44
---
Note: No power of e can result in a negative result.
So, can't solve for "k".
Cheers,
Stan H.
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Estimate the number of units that will be sold if advertising expenditures are raised to $550
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Rational-functions/734401: Simplify the complex fraction.
1) 2x+12/3x-15/2x^2-6x-20/x^2-10x+25
thanks!
1 solutions
Answer 448915 by stanbon(57323) on 2013-04-06 10:59:03 (Show Source):
You can put this solution on YOUR website!2x+12/3x-15/2x^2-6x-20/x^2-10x+25
Factor:
[2(x+6)/3(x-5)]/[2(x-5)(x+2)/(x-5)^2]
------------------------
Invert the denominator and multiply:
[2(x+6)/3(x-5)]*{(x-5)^2/[2(x-5)(x+2)]}
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[2(x+6)/3] * {(x-5)^2/[2(x-5)^2*(x+2)]}
---------
Cancel 2,(x-5)^2 to get:
-------------------------------
[(x+6)/3]*{1/[(x+2)}
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= (x+6)/[3(x+2)]
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Cheers,
Stan H.
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Finance/734396: an investor invested a total of $2300 in two mutual funds. one fund earned a 7% profit while the other earned a 2% profit. if the investors total profit was $66, how much was invested in each mutual fund?
1 solutions
Answer 448914 by stanbon(57323) on 2013-04-06 10:48:58 (Show Source):
You can put this solution on YOUR website!an investor invested a total of $2300 in two mutual funds. one fund earned a 7% profit while the other earned a 2% profit. if the investors total profit was $66, how much was invested in each mutual fund?
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Quantity Equation: a + b = 2300 dollars
Profit Equation: 7a +2b = 6600
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Multiply Quantity Eq through by 2:
2a + 2b = 2*2300
7a + 2b = 6600
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Subtract and solve for "a":
5a = 2000
a = $500.00 (amt invested at 7%
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b = 2300-500 = $1800.00 (amt invested at 2%)
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Cheers,
Stan H.
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