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Recent problems solved by 'stanbon'
stanbon answered: 57304 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, >>NextProbability-and-statistics/195602: plS help me!.. URgent..I need your cooperatioN!
#1 problem:
The Old Farmer's Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.
#2 problem:
Procter & Gamble reported that an American family of four washes an average of 1 ton (2000 pounds) of clothes each year. If the standard deviation of the distribution is 187.5 pounds, find the probability that the mean of a randomly selected sample of 50 families of four will be between 1980 and 1990 pounds.
#3 problem:
The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The standard deviation is 8 minutes. Assume the variable is normally distributed.
a.) Find the probability that a randomly selected adult will complete the test in less than 43 minutes.
b.) Find the probability that, if 50 randomly selected adult take the test, the mean time it takes the group to complete the test will be less than 43 minutes.
c.)Does it seem reasonable that an adult would finish the test in less than 43 minutes? Explain.
1 solutions
Answer 146695 by stanbon(57377)   on 2009-05-09 22:44:39 (Show Source):
You can put this solution on YOUR website!#1 problem:
The Old Farmer's Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.
#2 problem:
Procter & Gamble reported that an American family of four washes an average of 1 ton (2000 pounds) of clothes each year. If the standard deviation of the distribution is 187.5 pounds, find the probability that the mean of a randomly selected sample of 50 families of four will be between 1980 and 1990 pounds.
---------------
Find the z-values of 1980 and 1990
z(1980) = (1980-2000)/[187.5/sqrt(50)] = -0.7542
z(1990) = (1990-2000)/[187.5/sqrt(50)] = -0.37712
-----------
The P(1980 < xbar < 1990) = P(-0.7542 < z < -0.3771) = 0.1277
=====================================================================
#3 problem:
The average time it takes a group of adults to complete a certain achievement test is 46.2 minutes. The standard deviation is 8 minutes. Assume the variable is normally distributed.
a.) Find the probability that a randomly selected adult will complete the test in less than 43 minutes.
---
z(43) = (43-46.2)/8 = -0.4
---
P(x < 43) = P(z < -0.4) = 0.3446
=========================================================================
b.) Find the probability that, if 50 randomly selected adults take the test, the mean time it takes the group to complete the test will be less than 43 minutes.
---
z(43) = (43-46.2)/[8/sqrt(50)] = -2.8284
---
P(xbar < 43) = P(z < -2.8284) = 0.0023
==========================================================================
c.)Does it seem reasonable that an adult would finish the test in less than 43 minutes? Explain.
He has better than a 34% chance of doing that, as seen above.
Cheers,
Stan H.
|
Quadratic_Equations/195599: I have two questions.
1) Write a quadratic equation with the variable x having the given numbers. Write an equation in standard form ax^2+bx+c=0 solutions are -3,1
2) There is a cookbook open to two pages the product of the page numbers are 1190. Find the page numbers.
first page-
second page-
Thanks in advance
1 solutions
Answer 146693 by stanbon(57377) on 2009-05-09 21:56:27 (Show Source):
You can put this solution on YOUR website!1) Write a quadratic equation with the variable x having the given numbers. Write an equation in standard form ax^2+bx+c=0 solutions are -3,1
---
f(x) = (x+3)(x-1)
f(x) = x^2 + 2x -3
--------------------------------------------------------
2) There is a cookbook open to two pages the product of the page numbers are 1190. Find the page numbers.9
---
The page numbers are consecutive natural numbers:
1st : x
2nd : x+1
-----
Equation:
x(x+1) = 1190
x^2 + x - 1190 = 0
(x+35)(x-34) = 0
x = 34 (first page
x+1 = 35 (next page
=============================
Cheers,
Stan H.
|
Quadratic_Equations/195499: Set up a table of values (minimum 5 ordered pairs) equally arranged around the axis of symmetry x value to prepare to graph:
y=x^2-10x+25
1 solutions
Answer 146636 by stanbon(57377) on 2009-05-08 22:40:13 (Show Source):
You can put this solution on YOUR website!Set up a table of values (minimum 5 ordered pairs) equally arranged around the axis of symmetry x value to prepare to graph:
y=x^2-10x+25
-------------
(x-5)^2 = y-0
------------------------
Axis of symmetry: x = 5
--------------------------
Table:
If x = 3, y = 3^2-10*3+25 = 4
If x = 4, y = 4^2-10*4+25 = 1
If x = 6, y = 6^2-10*6+25 = 1
If x = 7, y = 7^2-10*7+25 = 4
==================================
Cheers,
Stan H.
|
Quadratic_Equations/195500: The equation for the axis of symmetry written as a decimal
for y=x^2-7x+12 is x= _____ .
1 solutions
Answer 146635 by stanbon(57377) on 2009-05-08 22:32:17 (Show Source):
You can put this solution on YOUR website!The equation for the axis of symmetry written as a decimal
for y=x^2-7x+12 is x= _____ .
-----------------
You have a quadratic with a = 1 ; b = -7 ; c = 12
Axis of symmetry : x = -b/(2a) = 7/2 = 3.5
=============================================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/195501: In 1995, the life expectancy of males in a certain country was 72.3 years. In 2001, it was 75.8 years. Let E represent the life expectancy in year t and let t represent the number of years since 1995.
1 solutions
Answer 146633 by stanbon(57377) on 2009-05-08 22:19:56 (Show Source):
You can put this solution on YOUR website!In 1995, the life expectancy of males in a certain country was 72.3 years. In 2001, it was 75.8 years. Let E represent the life expectancy in year t and let t represent the number of years since 1995.
------------------
t = 0 represent 1995
Then t = 6 represents 2001.
----------------------------------------
You have two points: (0,72.3) , (6,75.8)
----
slope = (75.8-72.3)/(6-0) = 7/12
intercept = (0,72.3)
-----------------------------------
Equation:
E(t) = (7/12)t + 72.3
=============================
Cheers,
Stan H.
|
Probability-and-statistics/195485: This question is from textbook
To test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is this a significant difference at α = .05? (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p-value assuming equal variances. Interpret these results. (c) Is the difference in mean scores large enough to be important? (d) Is it reasonable to assume equal variances? (e) Carry out a formal test for equal variances at α = .05, showing all steps clearly.
1 solutions
Answer 146627 by stanbon(57377) on 2009-05-08 20:35:41 (Show Source):
You can put this solution on YOUR website!To test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in.
The first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9.
Is this a significant difference at α = .05?
(a) State the hypotheses for a right-tailed test.
Ho: u(first) - u(later) = 0
H1: u(first) - u(later) > 0
-----------------------------
(b) Obtain a test statistic and p-value assuming equal variances. Interpret these results.
I ran a 2-sample t-Test and got the following:
test statistic: t = 1.2152
p-value = 0.1154:
Interp: 11.54% of test results could have provided stronger evidence for
rejecting Ho.
-----------------------------
(c) Is the difference in mean scores large enough to be important?
No ; Fail to reject Ho
-----------------------------
(d) Is it reasonable to assume equal variances?
I'll leave that to you.
-----------------------------
(e) Carry out a formal test for equal variances at α = .05, showing all steps clearly.
test statistic F = 24.9^2/19.6^2 = 1.6139
--------------
Critical value: F = 2.23
------------------------------
Conclusion: Fail to reject Ho.
===================================
Cheers,
Stan H.
|
Radicals/195488: Algebra 1 Glencoe Mathematics- workbook lesson 11-3, page 75
6 + the square root of 5r divided by 6 = -2
1 solutions
Answer 146624 by stanbon(57377) on 2009-05-08 20:13:51 (Show Source):
You can put this solution on YOUR website!6 + the square root of 5r divided by 6 = -2
-------------
(6 + sqrt(5r))/6 = -2
6 + sqrt(5r) = -12
sqrt(5r) = -18
-------------------
No solution:
No square root cannot be negative.
==================================
Cheers,
Stan H.
|
Probability-and-statistics/195259: The average commute to work(one way) is 25.5 minutes according to the 2000 census. If we assume that commuting times are normally distributed with a standard deviation of 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes a day commuting one way?
1 solutions
Answer 146623 by stanbon(57377) on 2009-05-08 20:10:50 (Show Source):
You can put this solution on YOUR website!The average commute to work(one way) is 25.5 minutes according to the 2000 census.
If we assume that commuting times are normally distributed with a standard deviation of 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes a day commuting one way
------------------------
Find the z-value of 30 minutes.
z(30) = (30-25.5)/6.1 = 0.7377
------------------------------------
P(x > 30) = P(z > 0.7377) = 0.2303
=====================================
Cheers,
Stan H.
|
Triangles/195490: Hi I have a question about how to find out if a set of three numbers can be sides of a triangle or not. I remember doing this in class, & I remember that it was really easy... I think it's something like if you get a certain number from using the Pythagorean Theorem, it's a right triangle, if you get this number, it's an acute, etc.... I just don't remember what exactly to do, although I do recall that it involves the Pythagorean Theorem, correct? I don't have the notes from this b/c I cleared out my binder. It gets too full if I keep all of the papers from the entire year, so I take old chapters out. No, I don't know any Pythagorean triplets, & no i don't think the units matter. This is all I remember.... This is the question:
Which of the following could not be the lengths of the sides of a triangle?
A: 5km, 2km, 4km
B: 3cm, 4cm, 5cm <== might be a triplet...
C:4in, 6in, 8in
D:6ft, 3ft, 9ft
Thank you in advance, I'd love your help! :D
1 solutions
Answer 146622 by stanbon(57377) on 2009-05-08 20:03:43 (Show Source):
You can put this solution on YOUR website!Which of the following could not be the lengths of the sides of a triangle?
A: 5km, 2km, 4km
B: 3cm, 4cm, 5cm <== might be a triplet...
C:4in, 6in, 8in
D:6ft, 3ft, 9ft
---------------------
This is not a Pythagorean problem.
You are not checking to see if you have a right triangle.
You want to know if the three sides could be the sides of a triangle (any
triangle).
----
Criteria: The sum of every two sides must be greater than the 3rd side.
Example: sides of 1,2, and 7 could not be a triangle.
------------
Your Problem.
6,3,9 would not form a triangle.
Try it and you'll see.
============================
Cheers,
Stan H.
|
Probability-and-statistics/195486: This question is from textbook
A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At α = .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule. (Data are from a project by statistics students Kim Dyer, Amy Pease, and Lyndsey Smith.)
1 solutions
Answer 146621 by stanbon(57377) on 2009-05-08 19:56:24 (Show Source):
You can put this solution on YOUR website!A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02.
-----------------------------------
For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14.
-------------------------------------
The means appear to be very close, but not the variances. At α = .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.
--------------
Ho: variance1 = variance 2
H1: variance 1 is not equal to variance 2
-------------
test statistic: F = 3.02^2/2.14^2 = 1.9915...
----
alpha = 5%
numerator df = 24 (not on the F chart so use df=25)
denominator df = 25
---
Use Appendix F to find the critical values: (p. 288)
Critical F value 2.23
--------------------------
Conclusion: Since the test statistic is not in the reject interval,
Fail to reject Ho.
--------------------------
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/195475: perform th eindicated operation and simplify. Assume all variable represent positive real number.
{a-little 5square root b^3}{5a+ little 3square root b}
1 solutions
Answer 146619 by stanbon(57377) on 2009-05-08 18:35:27 (Show Source):
You can put this solution on YOUR website!{a-little 5square root b^3}{5a+ little 3square root b}
-------------
((a - (b^3)^(1/5) * (5a + (b)^(1/3))
((a - (b
)^(3/5) * (5a + (b)^(1/3))
-------------------------------------------
Use FOIL:
F:a *5a = 5a^2
O: a *b^(1/3)
I: -5a * b^(3/5)
L:(-b^(3/5)*(b^(1/3) = -b^(1/3 + 3/5) = -b^(14/15)
-----------
Add the 4 terms to get the answer.
=========================================
Cheers,
Stan H.
|
Probability-and-statistics/195262: A local medical research association proposes to sponsor a footrace. The average time it takes to run the course is 45.8 minutes with a standard deviation of 36 minutes. If the association decides to include only the top 25% of the racers, what should be the cut off time in the tryout run? Assume the variable is normally distributed. Would a person who runs the course in 40 minutes qualify?
1 solutions
Answer 146618 by stanbon(57377) on 2009-05-08 18:20:56 (Show Source):
You can put this solution on YOUR website!A local medical research association proposes to sponsor a footrace. The average time it takes to run the course is 45.8 minutes with a standard deviation of 36 minutes. If the association decides to include only the top 25% of the racers, what should be the cut off time in the tryout run? Assume the variable is normally distributed. Would a person who runs the course in 40 minutes qualify?
67
Find the z-value associated with the top 25% point.
InVNorm(0.75) = 0.6745
----------------------------
Find the corresponding raw score value.
x = zs + u
x = 0.6745*36 + 45.8
x = 70.08 minutes (cut-off time)
--------------------------------------
40 minutes? Sure
=====================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/195478: explain how you can tell whether a parabola opens upward, downward, to the left, or to the right
1 solutions
Answer 146617 by stanbon(57377) on 2009-05-08 18:11:31 (Show Source):
You can put this solution on YOUR website!explain how you can tell whether a parabola opens upward, downward, to the left, or to the right
----------------------------
The x^2 or y^2 term is the deciding element.
------------
y = x^2 opens upward
y = -x^2 opens downward
x = y^2 opens to the right
x = -y^2 opens to the left
=================================
Cheers,
Stan H.
|
Rational-functions/195457: Rewrite each function to make it easy to graph using a translation. Describe the graph.
[] means its in square root!! please help me
y=3[-27x-27]+4
y=[16x-32]
and can you tell me how many numbers did is shift right/left?? THANKS
1 solutions
Answer 146616 by stanbon(57377) on 2009-05-08 18:06:08 (Show Source):
You can put this solution on YOUR website!Rewrite each function to make it easy to graph using a translation. Describe the graph.
[] means its in square root!! please help me
y=3[-27x-27]+4
---
y = 3*sqrt(-27(x+1)) + 4
---
y = 3*3sqrt(-3(x+1)) + 4
---
y = 9*sqrt(-3(x+1)) + 4
---
The vertex is at (-1,4) ; the top half of the parabola opens to the left.
------------------------------------
y=[16x-32]
---
y = sqrt(16(x-2))
y = 4sqrt(x-2)
---
The shift is two to the right.
------
Cheers,
Stan H.
|
Equations/195456: This question is from textbook
A cell divides into two identical copies every 4 minutes. How many cells will exist after 5 hours? Here is the answer, Could you be more specific? A(0) represents the number of what at time = 0? A(300) represents the value of what after 5 hours?
Thanks
Growth Formula
A(t)=Ao(2)^(t4) where t is the number of minutes after t=0
A(300)= 1*2^(300/4)
A(300)=2^(75)
A(300)= 3.77x10^22 cells
1 solutions
Answer 146588 by stanbon(57377) on 2009-05-08 13:18:02 (Show Source):
You can put this solution on YOUR website!A cell divides into two identical copies every 4 minutes. How many cells will exist after 5 hours? Here is the answer, Could you be more specific? A(0) represents the number of what at time = 0? A(300) represents the value of what after 5 hours?
Thanks
Growth Formula
A(t)=Ao(2)^(t/4) where t is the number of minutes after t=0
A(300)= 1*2^(300/4)
A(300)=2^(75)
A(300)= 3.77x10^22 cells
--------------
A(300) is the # of cells present after 300 minutes, or 5 hours.
============================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/195415: y varies jointly as x and z and inversely as the product of w and p, and y=45/160 when x=5,z=9,w=5, and p =8
the directions are to find an equation of variation in which the following are true.
1 solutions
Answer 146554 by stanbon(57377) on 2009-05-08 07:13:08 (Show Source):
You can put this solution on YOUR website!y varies jointly as x and z and inversely as the product of w and p
---
y = k[xz/wp]
----------------------
and y=45/160 when x=5,z=9,w=5, and p =8
---
(45/160) = k[5*9/5*8]
(45/160) = k[9/8]
k = (8/9)(45/160)
k = 5/20
k = 1/4
-------------
Therefore the equation is
y = (1/4)[xz/wp]
=========================
Cheers,
Stan H.
|
Probability-and-statistics/195376: PLs hELP!!UrGENT!,,nEED youR cOOperAtion..THANK you>>
#1 problem:
A local medical research association proposes to sponsor a footrace. The average time it takes to run the course is 45.8 minutes with a standard deviation of 36 minutes. If the association decides to include only the top 25% of the racers, what should be the cut off time in the tryout run? Assume the variable is normally distributed. Would a person who runs the course in 40 minutes qualify?
#2 problems:
During october, the average temperature Whitman Lake is 53.2 and the standard deviation is 2.3. Assume the variable is normally distributed. For a randomly selected day in october, find the probability that the temperature will be as follows.
a. above 54.
b. below 60.
c. between 49 and 55.
d. if the lake temperature were above 60 would you call it very warm?
#3 problem:
The average time a person spends at the Barefoot Landing Seaquarium 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributes. if a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium.
A. at least 120 minutes
b. At most 80 minutes
c. suggest a time for a bus to return to pick up a group of tourists.
#4 problem:
The average commute to work(one way) is 25.5 minutes according to the 2000 census. If we assume that commuting times are normally distributed with a standard deviation of 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes a day commuting one way?
#5 problem:
If the average price of a new home is $145,500, find the maximum and minimum prices of the houses that a contractor will build to include the middle 80% of the market. Assume that the standard deviation of prices $1500 and the variable is normally distributed
1 solutions
Answer 146539 by stanbon(57377) on 2009-05-07 21:27:26 (Show Source):
You can put this solution on YOUR website!#1 problem:
A local medical research association proposes to sponsor a footrace. The average time it takes to run the course is 45.8 minutes with a standard deviation of 36 minutes.
If the association decides to include only the top 25% of the racers, what should be the cut off time in the tryout run?
---
The z that corresponds to the top 25% is 0.6745
Then x = z*s + u
x = 0.6745*36 + 45.8 = 70.08 minutes (cut-off time)
----------------------------------------------
Assume the variable is normally distributed.
Would a person who runs the course in 40 minutes qualify?
Ans: Absolutely
============================================
#2 problems:
During october, the average temperature Whitman Lake is 53.2 and the standard deviation is 2.3.
Assume the variable is normally distributed. For a randomly selected day in october, find the probability that the temperature will be as follows.
a. above 54.
b. below 60.
c. between 49 and 55.
d. if the lake temperature were above 60 would you call it very warm?
---
Find the z value of each of these using z = (x-u)/s
Then find the answer to the question.
Example
a. above 54
z(54) = (54-53.2)/2.3 = 0.3478
P(temperature is above 54) = P(z > 0.3478) = 0.3640
----------------------------------------------------------
#3 problem:
The average time a person spends at the Barefoot Landing Seaquarium 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributes. if a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium.
A. at least 120 minutes
b. At most 80 minutes
c. suggest a time for a bus to return to pick up a group of tourists.
Comment: Use the same procedure as in question #2
--------------------------------------------------------------
#4 problem:
The average commute to work(one way) is 25.5 minutes according to the 2000 census. If we assume that commuting times are normally distributed with a standard deviation of 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes a day commuting one way?
#5 problem:
If the average price of a new home is $145,500, find the maximum and minimum prices of the houses that a contractor will build to include the middle 80% of the market. Assume that the standard deviation of prices $1500 and the variable is normally
---
Comment:
#4 and #5 are worked the same as 1-3. Find the appropriate z score. Then
convert to an x score using x = zs + u
==============================================
Cheers,
Stan H.
|
Probability-and-statistics/195278: The information I am given is
ACT composite Scores for NVJ(a school) are normaly distrubuted with:
Population mean= 23.9422 and a population standard deviation= 4.3977
Sample Data:
26 526 28 22 31 22 26 22 28 28 28 17 16 21 29 18 35 25 25 28
Find:
Mean Median Mode Midrange Varance Standard Deviation P80 D3
i have found Mean Median Mode and Midrange but am having trouble solving for Varance Standard Deviation P80 and D3.
Can you please help me?
1 solutions
Answer 146537 by stanbon(57377) on 2009-05-07 21:11:04 (Show Source):
You can put this solution on YOUR website!Population mean= 23.9422 and a population standard deviation= 4.3977
Sample Data:
26 26 28 22 31 22 26 22 28 28 28 17 16 21 29 18 35 25 25 28
Find:
Mean Median Mode Midrange Varance Standard Deviation P80 D3
i have found Mean Median Mode and Midrange but am having trouble solving for V
Standard Deviation = 0.3233...
Variance = 0,3233^2 = 0.1045
P80 = ?
Locator : 0.8*20 = 16th number ; that data element is 28
D3= = P30
Locator : 0.3*20 = 6th number ; tat data element is 22
Can you please help me?
================================================
Cheers,
Stan H.
|
logarithm/195268: This question is from textbook
STANBON You helped me with this problem:
The level of thorium in a sample decreases by a factor of one-half every 2 million years. A meteorite is discovered to have only 8.6% of its original thorium remaining. How old is the meteorite? I already have the answer, but need to know
What does Ao represent? Do you know what the value of Ao? What does t represent? What are the units of t? Thanks!
-----------
A(t) = Ao*(1/2)^(t/2*10^6)
-----------------------
0.086Ao = Ao*(1/2)^(t/(2 million))
(1/2)^(t/2 million) = 0.086
Take the log to get:
(t/2 million) = log(0.086)/log(1/2) = 3.53951953
t = (2 million)*(3.53951953)
t = 7,079,039.06
1 solutions
Answer 146460 by stanbon(57377) on 2009-05-07 09:20:13 (Show Source):
You can put this solution on YOUR website!You helped me with this problem:
The level of thorium in a sample decreases by a factor of one-half every 2 million years. A meteorite is discovered to have only 8.6% of its original thorium remaining. How old is the meteorite? I already have the answer, but need to know
What does Ao represent? Do you know what the value of Ao? What does t represent? What are the units of t? Thanks!
-----------
A(t) = Ao*(1/2)^(t/2*10^6)
A(t) is the amount of material you have at time "t".
Ao is the amount of material you have in the beginning: at time t=0
In your problem you do not know the amount at time t=0, so you
do not know Ao. But since you have it on both sides of the equation,
it cancels out.
In your problem t represets the number of years the thorium has
been around (presumably in the meteorite).
-----------------------
0.086Ao = Ao*(1/2)^(t/(2 million))
(1/2)^(t/2 million) = 0.086
Take the log to get:
(t/2 million) = log(0.086)/log(1/2) = 3.53951953
t = (2 million)*(3.53951953)
t = 7,079,039.06 years
==============================
Cheers,
Stan H.
|
Probability-and-statistics/195264: The average charitable contribution itemized per income tax return in Pennsylvania is $792. Suppose that the distribution is normal with a standard deviation of $103. Find the limits for the middle 50% of contributions.
1 solutions
Answer 146458 by stanbon(57377) on 2009-05-07 09:08:07 (Show Source):
|
logarithm/195269: This question is from textbook
A cell divides into two identical copies every 4 minutes. How many cells will exist after 5 hours? Here is the answer, I was told I have a typo in it, cannot find it.
Growth Formula
A(t)=Ao(2)^(t4) where t is the number of minutes after t=0
A(300)= 1*2^(300/4)
A(300)=2^(75)
A(300)= 3.77x10^22 cells
Thanks
1 solutions
Answer 146457 by stanbon(57377) on 2009-05-07 09:06:23 (Show Source):
|
Probability-and-statistics/195265: If the average price of a new home is $145,500, find the maximum and minimum prices of the houses that a contractor will build to include the middle 80% of the market. Assume that the standard deviation of prices $1500 and the variable is normally distributed.
1 solutions
Answer 146456 by stanbon(57377) on 2009-05-07 09:04:25 (Show Source):
You can put this solution on YOUR website!If the average price of a new home is $145,500, find the maximum and minimum prices of the houses that a contractor will build to include the middle 80% of the market. Assume that the standard deviation of prices $1500 and the variable is normally distributed.
---------------------
Determine the z-values associated with the middle 80% of a normally-
distributed population.
Draw the picture of a normal curve.
Sketch what appears to be the middle 80% portion.
The top limit has 40% to the right of the mean.
The bottom limit has 40% to the left of the mean
The upper z limit is InverseNorm(0.90) = 1.2816
The lower z limit is InverseNOrm(0.10) = -1.2816
----------------
Now convert these z-scores to raw scores using x = z*sigma + mean
x = 1.2816*1500 + 145,500 = $147,422.33 ( max price )
x = -1.2816*1500 + 145,500 = $143,577.67 (min price )
=========================================
Cheers,
Stan H.
|
percentage/195256: Jess invested $30 more at 6% than at 5%. If the total annual interest is $100, how much is invested at each rate?
I've tried working this out but to know avail. I'm helping my son and I'm lost. Thanks
1 solutions
Answer 146454 by stanbon(57377) on 2009-05-07 06:42:28 (Show Source):
You can put this solution on YOUR website!Jess invested $30 more at 6% than at 5%. If the total annual interest is $100, how much is invested at each rate?
----------------------------
Equations:
Quantity Eq. : x = y + 30
Interest Eq. :0.06x + 0.05y = 100
------------------------------------------
Substitute:
0.06(y+30) + 0.05y = 100
Multiply thru by 100 to get:
6(y+30) + 5y = 10000
6y + 180 + 5y = 10000
11y = 9820
y = $892.73 (amount invested at 5%)
x = y + 30 = 892.73 + 30 = $922.73 (amount invested at 6%)
=============================================================
Cheers,
Stan H.
|
Probability-and-statistics/194853: The last 50 violent crimes committed in Maryville were 9 homicides, 24 robberies, and 17 assaults. What is the empirical probability that the next violent crime committed in Maryville will be an assault?
_________________
One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is not a red card.
_________________
The odds against Lightning winning the third race are 9:4. If Sally places an $8 bet on Lightning to win and Lightning wins, find Sally’s net winnings
A) $2.25 B) $36 C) $18.00 D) $9.00 E) $72
_________________
1000 raffle tickets are sold at $3 each. One grand prize of $100 and two consolation prizes of $75 will be awarded. Find Jake’s expectation if he purchases one ticket.
A) -$2.75 B) -$3.00 C) $0.24 D) $2.75 E) $3.00
______________
An independent television station airs a movie-of-the-day every Tuesday and Thursday. Their market research shows that their suspense movies are viewed by an average of 3500 people, their comedies are viewed by 4500 people, and their dramas are viewed by 6000 people. The station buys a package of 100 movies, consisting of 15 suspense movies, 40 comedies, and 45 dramas. The movies will be shown two per week for 50 weeks. Find the expected number of viewers on a given movie.
A. 4667 B. 479 C. 140 D. 5025 D. 1400
____________
How many different three-digit numbers can be formed from the digits 0 through 9 if the first digit must be odd and the last digit must be even?
____________
A box of chocolates contains 20 identically shaped chocolates. Four of them are filled with jelly, seven are filled with caramel, and nine are filled with nuts. What is the probability that one chocolate chosen at random is filled with caramel or nuts?
__________
A couple plan to have exactly four children.
(a) Construct a tree diagram and list the sample space.
(b) Find the probability that the family has at least three boys.
________
A card is selected from a deck of 52 playing cards. Find the probability of selecting
a) a seven given the card is a not a face card. (An ace is not a face card.)
b) a spade given the card is red.
1 solutions
Answer 146453 by stanbon(57377) on 2009-05-07 06:34:36 (Show Source):
You can put this solution on YOUR website!The last 50 violent crimes committed in Maryville were 9 homicides, 24 robberies, and 17 assaults. What is the empirical probability that the next violent crime committed in Maryville will be an assault?
Ans: 17/50
_________________
One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is not a red card.
Ans: 26/52 = 1/2
_________________
The odds against Lightning winning the third race are 9:4. If Sally places an $8 bet on Lightning to win and Lightning wins, find Sally’s net winnings
A) $2.25 B) $36 C) $18.00 D) $9.00 E) $72
Ans: 18
_________________
1000 raffle tickets are sold at $3 each. One grand prize of $100 and two consolation prizes of $75 will be awarded. Find Jake’s expectation if he purchases one ticket.
A) -$2.75 B) -$3.00 C) $0.24 D) $2.75 E) $3.00
Answered yesterday: -$2.75
______________
An independent television station airs a movie-of-the-day every Tuesday and Thursday. Their market research shows that their suspense movies are viewed by an average of 3500 people, their comedies are viewed by 4500 people, and their dramas are viewed by 6000 people. The station buys a package of 100 movies, consisting of 15 suspense movies, 40 comedies, and 45 dramas. The movies will be shown two per week for 50 weeks. Find the expected number of viewers on a given movie.
A. 4667 B. 479 C. 140 D. 5025 D. 1400
Answered yesterday
____________
How many different three-digit numbers can be formed from the digits 0 through 9 if the first digit must be odd and the last digit must be even?
Answered yesterday
____________
A box of chocolates contains 20 identically shaped chocolates. Four of them are filled with jelly, seven are filled with caramel, and nine are filled with nuts. What is the probability that one chocolate chosen at random is filled with caramel or nuts?
Answered yesterday
__________
A couple plan to have exactly four children.
(a) Construct a tree diagram and list the sample space.
(b) Find the probability that the family has at least three boys.
Ans: 5/16
________
A card is selected from a deck of 52 playing cards. Find the probability of selecting
a) a seven given the card is a not a face card. (An ace is not a face card.)
b) a spade given the card is red.
Answered today
======================
Cheers,
Stan H.
|
Probability-and-statistics/195141: A box contains three blue balls and three white balls. if two balls are drawn one at a time, find the probability that both balls are blue if the draws are made as follows:
a). with replacement
b.) without replacement
1 solutions
Answer 146452 by stanbon(57377) on 2009-05-07 06:25:50 (Show Source):
You can put this solution on YOUR website!A box contains three blue balls and three white balls. if two balls are drawn one at a time, find the probability that both balls are blue if the draws are made as follows:
a). with replacement
1st draw : P(blue) = 3/6 = 1/2
2nd draw : P(blue) = 3/6 = 1/2
P(2 blue in two draws = (1/2)^2 = 1/4
---------------------------------------------
b.) without replacement
1st draw : P(blue) = 3/6 = 1/2
2nd draw : P blue) = 2/5
P(2 blue in two draws) = (1/2)(2/5) = 1/5
=============================================
Cheers,
Stan H.
|
Probability-and-statistics/195217: A card is selected from a deck of 52 playing cards. Find the probability of selecting
a) a seven given the card is a not a face card. (An ace is not a face card.)
b) a spade given the card is red.
1 solutions
Answer 146451 by stanbon(57377) on 2009-05-07 06:15:11 (Show Source):
You can put this solution on YOUR website!A card is selected from a deck of 52 playing cards. Find the probability of selecting
a) a seven given the card is a not a face card. (An ace is not a face card.)
# of face cards = 12
# of not face = 40
# of 7's = 4
# of 7's that are not face cards 4
P(7 | not face) = 4/40 = 1/10
------------------------------------------
b) a spade given the card is red.
# of red cards = 26
# of spades = 13
# of spades that are red = 0
P(spade | red) = 0/26 = 0
====================================
Cheers,
Stan H.
|
Probability-and-statistics/195225: I need help i am really stumped. I appreciate anyone who can help. Thank you
How many different three-digit numbers can be formed from the digits 0 through 9 if the first digit must be odd and the last digit must be even?
1 solutions
Answer 146423 by stanbon(57377) on 2009-05-06 22:44:17 (Show Source):
You can put this solution on YOUR website!How many different three-digit numbers can be formed from the digits 0 through 9 if the first digit must be odd and the last digit must be even?
-----------------
# of ways to choose the 1st digit: 5
# of ways to choose the 2nd digit: 10
# of ways to choose the 3rd digit: 5
------------------------------------------
Total number of digits: 5*10*5 = 250
=======================================================
Cheers,
Stan H.
|
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