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Recent problems solved by 'stanbon'
stanbon answered: 57222 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next
Probability-and-statistics/420721: A bag contains 8 purple marbles and 12 yellow marbles. Once a marble is drawn from the bag, it is not replaced. What is the probability of drawing a purple marble and then a blue marble?
1 solutions
Answer 293873 by stanbon(57290)   on 2011-03-10 19:58:06 (Show Source):
You can put this solution on YOUR website!A bag contains 8 purple marbles and 12 yellow marbles. Once a marble is drawn from the bag, it is not replaced. What is the probability of drawing a purple marble and then a blue marble?
-----
Ans: (8/20)(0/19) = 0
===========================
Cheers,
Stan H.
============
|
Probability-and-statistics/420712: An unprepared student randomly circles answers in a multiple choice test having 25 questions each with 5 possible answers. How many answers should he expect to get right?
1 solutions
Answer 293872 by stanbon(57290) on 2011-03-10 19:56:17 (Show Source):
You can put this solution on YOUR website!An unprepared student randomly circles answers in a multiple choice test having 25 questions each with 5 possible answers. How many answers should he expect to get right?
----
E(x) = mean = np = 25(1/5) = 5 (# he can expect to get right)
=================================================================
Cheers,
Stan H.
========
|
Radicals/420696: hello , can you please help me on this equation .
Find the perimeter and area of the rectangle with length of 8 sqrt (7) inches and width of 2 sqrt (7) - 3 sqrt(5) inches.
1 solutions
Answer 293866 by stanbon(57290) on 2011-03-10 19:42:24 (Show Source):
You can put this solution on YOUR website!Find the perimeter and area of the rectangle with
length of 8 sqrt (7) inches and
width of 2 sqrt (7) - 3 sqrt(5) inches.
-------------------------
Perimeter = 2(length + width)
P = 2(8sqrt(7) + 2sqrt(7)-3)
---
P = 2(10sqrt(7) - 3)
P = [20sqrt(7) -6] inches
=================================
Area = length * width
A = (8sqrt(7)*(2sqrt(7)-3))
---
A = 16*7 - 24sqrt(7)
---
Area = 112 - 24sqrt(7)
==========================
Cheers,
Stan H.
===========
|
Miscellaneous_Word_Problems/420682: THE SUM OF A NUMBER AND THE DIFFERENCE BETWEEN 16 AND A NUMBER PLUS 5 IS 21
1 solutions
Answer 293863 by stanbon(57290) on 2011-03-10 19:33:07 (Show Source):
You can put this solution on YOUR website!THE SUM OF A NUMBER AND THE DIFFERENCE BETWEEN 16 AND A NUMBER PLUS 5 IS 21
----------
Equation:
Let the number be "x":
x + (16-(x+5)) = 21
-------
x + 21 - x = 21
21 = 21
----
Solution: x can be any Real Number
=============================
Cheers,
Stan H.
|
Probability-and-statistics/420668: A survey of 4,581 U.S. households that owned a mobile phone found that 58 percent are satisfied with the coverage of their cellular phone provider. (a) Assuming that this was a random sample, construct a 90 percent confidence interval for the true proportion of satisfied U.S. mobile phone owners. (b) Why is the confidence interval so narrow?
1 solutions
Answer 293860 by stanbon(57290) on 2011-03-10 19:25:24 (Show Source):
You can put this solution on YOUR website!A survey of 4,581 U.S. households that owned a mobile phone found that 58 percent are satisfied with the coverage of their cellular phone provider.
----------------------------------------
(a) Assuming that this was a random sample, construct a 90 percent confidence interval for the true proportion of satisfied U.S. mobile phone owners.
---
p-hat = 0.58
ME = 1.645*sqrt[0.58*0.42/4581] = 0.0987
---
90%CI: 0.58-0.0987< p < 0.58+0.0987
---
90%CI: 0.4813 < p < 0.6787
-------------------------------
(b) Why is the confidence interval so narrow?
Its width is 2ME and ME is small because the sample size is large.
======================================================================
Cheers,
Stan H.
=============
|
Exponential-and-logarithmic-functions/420664: If Marcelle deposits $250,000 into a mutual fund which pay an annual interest rate of 5% compounded continuously. Assuming that there are no further deposits and there were no withdrawals, how long must she wait before her investment reaches $1 million?
1 solutions
Answer 293856 by stanbon(57290) on 2011-03-10 19:11:13 (Show Source):
You can put this solution on YOUR website!If Marcelle deposits $250,000 into a mutual fund which pay an annual interest rate of 5% compounded continuously. Assuming that there are no further deposits and there were no withdrawals, how long must she wait before her investment reaches $1 million?
----------------------------
A(t) = Ao*e^(rt)
1,000,000 = 250,000*e^(0.05t)
e^(0.05t) = 4
----
Take the natural log of both sides:
0.05t = 4
---
t = 80 years
=====================
Cheers,
Stan H.
===============
|
Miscellaneous_Word_Problems/420656: The product of 2 numbers is 36.
The quotient of the numbers is 1
What are the numbers
6 and 1 ?
1 solutions
Answer 293854 by stanbon(57290) on 2011-03-10 19:04:24 (Show Source):
You can put this solution on YOUR website!The product of 2 numbers is 36.
The quotient of the numbers is 1
What are the numbers
-------------------
Equations:
xy = 36
x/y = 1
----
Using the 2nd equation you get x = y
---
Substitute in the 1st equation and solve:
x^2 = 36
x = 6
---
Then y = 6
----
Solution: x = 6; y = 6
===========================
Cheers,
Stan H.
=============
|
Sequences-and-series/420655: Having just taken a year of Algebra, Algebra II and College Algebra, my Statistics class is now using Summation, which was never covered in my algebra classes. One question which I do not understand is:
Why is: Sigma x^2 different from (Sigma x^2)? given the following values for x: 1,7,0,8, -6
The answer given me was non parenthesied answer is 150, parenthesied answer is 100.
1 solutions
Answer 293853 by stanbon(57290) on 2011-03-10 18:59:57 (Show Source):
You can put this solution on YOUR website!Why is: Sigma x^2 different from (Sigma x^2)? given the following values for x: 1,7,0,8, -6
The answer given me was non parenthesied answer is 150, parenthesied answer is 100.
------
Sigma(x^2) = 1^2 + 7^2 + 0^2 + 8^2 + (-6)^2
= 1 + 49 + 0 + 64 + 36
= 50 + 100
= 150
-----
[Sigma(x)]^2 = [1 + 7 + 0 + 8 + -6]^2 = 10^2 = 100
===================
Cheers,
Stan H.
|
Expressions-with-variables/420654: solve for the variable in each equation below. show all work. check answer. if a solution is undefined, state that in answer.
3/a+1=5/a+7
please help if you can. thanks
1 solutions
Answer 293852 by stanbon(57290) on 2011-03-10 18:53:37 (Show Source):
You can put this solution on YOUR website!solve for the variable in each equation below. show all work. check answer. if a solution is undefined, state that in answer.
3/a+1=5/a+7
----
Cross-multiply:
3(a+7) = 5(a+1)
3a+21 = 5a+5
2a = 16
a = 8
===================
Cheers,
Stan H.
===============
|
Expressions-with-variables/420653: solve for the variable in each equation below. show all work. check answer. if a solution is undefined, state that in answer.
10/x-6=5
1 solutions
Answer 293851 by stanbon(57290) on 2011-03-10 18:51:33 (Show Source):
You can put this solution on YOUR website! solve for the variable in each equation below. show all work. check answer. if a solution is undefined, state that in answer.
10/x-6=5
-----
Is the denominator on the left side "x" or
is it "x-6" ?
------------------
Cheers,
Stan H.
|
Linear-systems/420648: 3x - 4y = 4
x + 2y = 8
(Solve using any method, and please name the method as well)
1 solutions
Answer 293850 by stanbon(57290) on 2011-03-10 18:49:12 (Show Source):
You can put this solution on YOUR website!3x - 4y = 4
x + 2y = 8
-----
Method: elimination
Multiply thru the 2nd equation by 2:
3x - 4y = 4
2x + 4y = 16
----
Add and solve for "x":
5x = 20
x = 4
---
Solve for "y":
x + 2y = 8
4 + 2y = 8
2y = 4
y = 2
----
Solution: (4,2)
====================
Cheers,
Stan H.
===========
|
Geometric_formulas/420631: What is the geometric mean of: a and 4a?
What is the geometric mean of: 2a and 4a?
1 solutions
Answer 293849 by stanbon(57290) on 2011-03-10 18:45:47 (Show Source):
You can put this solution on YOUR website!What is the geometric mean of: a and 4a?
----
Solve for "x":
a/x = x/4a
---
x^2 = 4a^2
x = 2a
--------------------
What is the geometric mean of: 2a and 4a?
Solve for "x":
2a/x = x/4a
x^2 = 8a^2
x = 2a*sqrt(2)
-----------------------
Cheers,
Stan H.
============
|
Systems-of-equations/420621: f(x) = 3 - 1/2x^2
a)state the degree and the leading coefficient of f
b)state the end behavior of the graph of f.
1 solutions
Answer 293845 by stanbon(57290) on 2011-03-10 18:24:46 (Show Source):
You can put this solution on YOUR website!f(x) = 3 - 1/2x^2
a)state the degree: 2
and the leading coefficient of f: 1/2
-------------------------------
b)state the end behavior of the graph of f.
----
As x goes to -inf, f(x) goes to -inf
---
As x goes to +inf, f(x) goes to +inf
======================================
Cheers,
Stan H.
=======
|
Systems-of-equations/420620: I need help with this please :)
equation is f(x)= x^2 - 4x - 3
a)Graph y=f(x) in the standard viewing rectangle.
b)approximate the coordinates of each turning point.
c)estimate any local extrema.
1 solutions
Answer 293844 by stanbon(57290) on 2011-03-10 18:13:45 (Show Source):
You can put this solution on YOUR website!f(x)= x^2 - 4x - 3
a)Graph y=f(x) in the standard viewing rectangle.
--------------------------------
b)approximate the coordinates of each turning point.
The minimum occurs where x = -b/(2a) = 4/2 = 2
f(2) = 2^2-4*2-3 = -8
minimum at (2,-8)
--------------------------
c)estimate any local extrema.
(2,-8)
=================
Cheers,
Stan H.
|
Numbers_Word_Problems/420614: 1.) Mary Anne Young has enough grass sees to cover 400 square feet. She wishes to grow grass on a rectangular area that is 9 feet longer than it is wide. What dimensions should the area have?
2.) Paul and Joan Rice wish to buy floor covering that covers 150 square feet for their large recreation room. They wish to cover a rectangle that is 5 feet longer than it is wide. How wide should the rectangle be?
1 solutions
Answer 293843 by stanbon(57290) on 2011-03-10 18:07:58 (Show Source):
You can put this solution on YOUR website!1.) Mary Anne Young has enough grass seeds to cover 400 square feet.
She wishes to grow grass on a rectangular area that is 9 feet longer than it is wide. What dimensions should the area have?
----
width = x
length = x+9
---
Area = x(x+9)
400 = x^2+9x
---
Solve for "x":
x^2+9x-400 = 0
(x+25)(x-16) = 0
Positive solution:
x = 16 ft. (width)
x+9 = 25 ft. (length)
==========================
2.) Paul and Joan Rice wish to buy floor covering that covers 150 square feet for their large recreation room. They wish to cover a rectangle that is 5 feet longer than it is wide. How wide should the rectangle be?
---
Same procedure as used on problem #1.
Cheers,
Stan H.
|
Equations/420611: Does a positive plus a positive equal a positive or does it equal a negative? Also does a negative plus a negative equal a positive or does it equal a negative? Does a positive plus a negative equal a positive or a negative?
1 solutions
Answer 293841 by stanbon(57290) on 2011-03-10 17:58:06 (Show Source):
You can put this solution on YOUR website!Does a positive plus a positive equal a positive or does it equal a negative?
---
+3 + +5 = +8
====================
Also does a negative plus a negative equal a positive or does it equal a negative?
----
-3 + -5 = -8
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Does a positive plus a negative equal a positive or a negative?
Sometime positive and sometives negative:
+3 + -5 = -2
+5 + -3 = +2
====================
It may help you to thing of this in terms of money.
+3 is a gain
-3 is a loss
-------------------
Cheers,
Stan H.
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Probability-and-statistics/420535: a card is drawn at random from a 52 card deck. tell whether event A and B are inclusive or mutually exclusive. Then find p(A or B). please
1.A; The card is a number less than 5.
B; The card is a jack, king or queen.
2.A; the card is black
B; the card is a number greater then 4
3.A; The card is red
B; The card is the ace of spades.
4.A;The card is a 2 or 3
B;The card is not a heart.
5.A; The card is a diamond
B; the card is a spade.???
1 solutions
Answer 293839 by stanbon(57290) on 2011-03-10 17:51:23 (Show Source):
You can put this solution on YOUR website!a card is drawn at random from a 52 card deck.
tell whether event A and B are inclusive or mutually exclusive.
Then find p(A or B). please
1.A; The card is a number less than 5.
B; The card is a jack, king or queen.
---
Mutually Exclusive
P(A or B) = P(A)+P(B)= P(2,3,4)+P(j,k,q) = [12/52]+[12/52] = 24/52
-----------------------
2.A; the card is black
B; the card is a number greater then 4
Inclusive:
P(A or B) = P(A)+P(B)-P(AUB) = [26+40-20]/52 = 46/52
-----------------------
Cheers,
Stan H.
==========
Can you handle the rest?
----
3.A; The card is red
B; The card is the ace of spades.
4.A;The card is a 2 or 3
B;The card is not a heart.
5.A; The card is a diamond
B; the card is a spade.???
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Probability-and-statistics/420541: 1. In a certain large college course, past records show that grades A,B,C,D, and F are equally likely. If 1 student is chosen at random, find the following probabilities:
a. P(C)
b. P(A or B)
c. P(a grade higher than D)
d. P(A,B,C,D,or F)
e. P(B and D)
f. P(E)
g. P(not-A)
h. P(not-A and not-F)
2. A pharmacist has filled a box with six different kinds of antibiotic capsules. There are a total of 300 capsules, which are distributed as follows: tetracycline(15), penicillin(30), minocycline(45), Bactrim(60), streptomycin(70), and Zithromax(80). She asks her assistant to mix the pills thoroughly and to withdra a single capsule from the box. What is the probability that the capsule selected is:
a. either penicillin or streptomycin
b. neither Zithromax nor tetracycline
c. Bactrim
d. not penicillin
e. either minocycline, Batrim, or tetracycline?
1 solutions
Answer 293837 by stanbon(57290) on 2011-03-10 17:23:10 (Show Source):
You can put this solution on YOUR website!In a certain large college course, past records show that grades A,B,C,D, and F are equally likely. If 1 student is chosen at random, find the following probabilities:
a. P(C) = 1/5
--------------------
b. P(A or B) = 2/5
--------------------
c. P(a grade higher than D) = 3/5
--------------------
d. P(A,B,C,D,or F) = 1
--------------------
e. P(B and D) = 0
-----------------------
f. P(E) = 0
---------------------
g. P(not-A) = 4/5
---------------------
h. P(not-A and not-F) = P(B,C,D,) = 3/5
-------------------------------------------
---------------------------------
2. A pharmacist has filled a box with six different kinds of antibiotic capsules.
There are a total of 300 capsules, which are distributed as follows: tetracycline(15), penicillin(30), minocycline(45), Bactrim(60), streptomycin(70), and Zithromax(80).
--------
She asks her assistant to mix the pills thoroughly and to withdraw a single capsule from the box. What is the probability that the capsule selected is:
a. either penicillin or streptomycin: (30+70)/300 = 1/3
--------------------------
b. neither Zithromax nor tetracycline: 1 - (80+15)/300 = 205/300
---------
c. Bactrim: 60/300 = 1/5
--------------
d. not penicillin = 270/300 = 9/10
-------------------
e. either minocycline, Batrim, or tetracycline?
Leave that to you.
=========================
Cheers,
Stan H.
==========
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Probability-and-statistics/420520: A machine is used to fill plastic soda bottles. The amount of soda dispensed into each bottle varies slightly. Suppose the amount of soda dispensed into the bottle is normally distributed. If at least 99% of the bottle must have between 585 and 595 milliliters of soda, find the greatest standard deviation, to the nearest hundredth, than can be allowed.
1 solutions
Answer 293828 by stanbon(57290) on 2011-03-10 16:26:21 (Show Source):
You can put this solution on YOUR website!A machine is used to fill plastic soda bottles. The amount of soda dispensed into each bottle varies slightly. Suppose the amount of soda dispensed into the bottle is normally distributed. If at least 99% of the bottles must have between 585 and 595 milliliters of soda, find the greatest standard deviation, to the nearest hundredth, than can be allowed.
------------------
Draw the picture.
The center of the interval [585,595] is 590
That is the mean
----
The area to the left of 585 is 0.005
Find the z-value with a left tail of 0.005
invNorm(0.005) = -2.5758
----
Find s if x = zs+u
585 = -2.5758s + 590
-2.5758s = -5
s = 1.9411
===================
Cheers,
Stan H.
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Probability-and-statistics/420515: Some one please explain!!!
Assume that the population of heights of female college students is approximately normally distributed with mean of 68 inches and standard deviation of 2.75 inches. Show all work.
(A) Find the proportion of female college students whose height is greater than 69 inches.
(B) Find the proportion of female college students whose height is no more than 69 inches.
1 solutions
Answer 293827 by stanbon(57290) on 2011-03-10 16:19:16 (Show Source):
You can put this solution on YOUR website!Assume that the population of heights of female college students is approximately normally distributed with mean of 68 inches and standard deviation of 2.75 inches. Show all work.
(A) Find the proportion of female college students whose height is greater than 69 inches.
---
z(69) = (69-68)/2.75 = 0.3640
P(x > 69) = P(z > 0.3640) = 0.3581
---------
(B) Find the proportion of female college students whose height is no more than 69 inches.
Ans: 1-0.3581 = 0.6419
===========================
Cheers,
Stan H.
=========
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Triangles/420505: How do i find the degree measurement of an acute angle?
short leg=5
long leg=20
hypotenuse=x
1 solutions
Answer 293824 by stanbon(57290) on 2011-03-10 16:13:15 (Show Source):
You can put this solution on YOUR website!find the degree measurement of an acute angle?
short leg=5
long leg=20
hypotenuse=x
----
x^2 = 5^2 + 20^2 = 425
---
x = 5sqrt(17)
------
Let A be angle opposite short leg
Let B be angle opposite long leg
Let C = 90 degrees
----
tan(A) = 5/20 = 1/4
A = tan^-1(1/4) = 14.036 degrees
---
B = 90 - 14.036 = 75.964 degrees
=====================================
Cheers,
Stan H.
============
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Evaluation_Word_Problems/420501: Suppose that $11,000 is investted at an interest rate of 5.9% per year, compounded continuously. What is the doubling time?
1 solutions
Answer 293823 by stanbon(57290) on 2011-03-10 16:07:21 (Show Source):
You can put this solution on YOUR website!Suppose that $11,000 is investted at an interest rate of 5.9% per year, compounded continuously. What is the doubling time?
-----------
A(t) = Ao*e^(rt)
----
2Ao = Ao*e^(0.059t)
e^(0.059t) = 2
---
Take the ln of both sides to get:
0.059t = ln2
t = 11.75 years
======================
Cheers,
Stan H.
=============
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Probability-and-statistics/420498: The diameters of oranges in a certain orchard are normally distributed with a mean of 5.30 inches and a standard deviation of 0.40 inches. Show all work.
(A) What percentage of the oranges in this orchard have diameters less than 4.7 inches?
(B) What percentage of the oranges in this orchard are larger than 5.10 inches?
1 solutions
Answer 293822 by stanbon(57290) on 2011-03-10 16:04:03 (Show Source):
You can put this solution on YOUR website!The diameters of oranges in a certain orchard are normally distributed with a mean of 5.30 inches and a standard deviation of 0.40 inches. Show all work.
(A) What percentage of the oranges in this orchard have diameters less than 4.7 inches?
Find the z of 4.7:
z(4.7) = (4.7-5.3)/0.4 = -1.5
P(x < 4.7) = P(z < -1.5) = 6.68%
------------------------------------
(B) What percentage of the oranges in this orchard are larger than 5.10 inches?
z(5.10) = (5.10-5.3)/0.4 = -0.2/0.4 = -1/2
P(x > 5.10) = P(z > -1/2) = 69.15%
=============================================
Cheers,
Stan H.
============
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Probability-and-statistics/420418: Hello, I have a question that I could use some assistance on.
Raffle tickets. 1,000 raffle tickets are sold for $1.00 each. One prize of $800.00 is to be awarded.
a) Reng Condos purchases one ticket. Determine her expected value.
b) Determine the fair price of a ticket.
Thank you so much for your help!!!
1 solutions
Answer 293798 by stanbon(57290) on 2011-03-10 14:33:01 (Show Source):
You can put this solution on YOUR website!Raffle tickets. 1,000 raffle tickets are sold for $1.00 each.
One prize of $800.00 is to be awarded.
a) Reng Condos purchases one ticket. Determine her expected value.
Random gain values: 799, -1
Corresponding Probs: 1/1000, 999/1000
-------
E(x) = (1/1000)799 -1(999/1000) = (799-999)/1000 = -200/1000 = -20 cents
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b) Determine the fair price of a ticket.
Let the cost to play be "x".
----
Random gain values: 800-x and -x
Corresponding Probs 1/1000 , 999/1000
-----
Note: A fair price means E(x) = 0
---------------------------------------
Solve:
(800-x)/1000-999x/(1000) = 0
---
800-x-999x = 0
800-1000x = 0
x = 8/10 = $0.8 = 80 cents
==============================
Cheers,
Stan H.
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Probability-and-statistics/420459: a random sample of 100 babies is obtained and the mean head circumference is found to be 4.06cm.Assuming that the population standard deviation is known to be 1.6cm, use 0.05 significance level to test the claim that the mean head circumference of all two-month old babies is equal to 40.0cm
1 solutions
Answer 293793 by stanbon(57290) on 2011-03-10 14:23:06 (Show Source):
You can put this solution on YOUR website!A random sample of 100 babies is obtained and the mean head circumference is found to be 4.06cm.
-----------------------------
Assuming that the population standard deviation is known to be 1.6cm, use 0.05 significance level to test the claim that the mean head circumference of all two-month old babies is equal to 40.0cm
------------
Ho: u = 4.0 cm
Ha: u is not equal to 4.0 cm
-----------------
t(4.0) = (4.06-4)/[1.6/sqrt(100)] = 0.06/0.16 = 0.375
----------------
p-value = 2*P(0.375< t < 100, when df = 99) = 2*0.3542 = 0.7085
---
Conclusion: Since the p-value is greater tan 5%, fail to reject Ho.
=========================
Cheers,
Stan H.
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Probability-and-statistics/420429: when rolling a pair of dice, p(sum of 8) > p(sum of 2)
true or false and why?
1 solutions
Answer 293789 by stanbon(57290) on 2011-03-10 14:12:05 (Show Source):
You can put this solution on YOUR website!when rolling a pair of dice, p(sum of 8) > p(sum of 2)
true or false and why?
-----------
True
---
Sum of 8: 6/2,5/3,4/4,3/5,2/6
P(sum of 8) = 5/36
---
Sum of 2: 1/1
P(sum of 2) = 1/36
========================
3/36 > 1/36
===================
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