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stanbon answered: 57888 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 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899, >>Next
Quadratic_Equations/648113: A farmer has 40 metres of fencing with which he intends to make a rectangular enclosure for a few sheep and their lambs. The farmer calculates that he requires 96m²of grass in the sheep pen. By forming a quadratic equation find the dimensions of the pen
1 solutions
Answer 406555 by stanbon(57961)   on 2012-09-09 10:56:33 (Show Source):
You can put this solution on YOUR website!A farmer has 40 metres of fencing with which he intends to make a rectangular enclosure for a few sheep and their lambs. The farmer calculates that he requires 96m²of grass in the sheep pen. By forming a quadratic equation find the dimensions of the pen
-----
Perimeter = 2(L + W) = 40 metres
----
Area = L*W = 96 m^2
----
Solve the 1st equation for "L":
L + W = 20
L = 20-W
----
Sustitute into the 2nd equation and solve for "W":
(20-W)W = 96
20W-W^2 = 96
W^2 - 20W + 96 = 0
----
(W -16)(W-4) = 0
Width = 16 m or Width = 4 m
---
If W = 16, then L = 4
If W = 4, then L = 16
=========================
Cheers,
Stan H.
=========================
|
Mixture_Word_Problems/648111: Trying to help my daughter...
kali mixes together 9 gal of brand a fruit drink and 6 gal of brand b fruit drink which contains 5% fruit juice. find the percent of fruit juice in brand a if the mixture contained 11% fruit juice.
Thanks
1 solutions
Answer 406554 by stanbon(57961) on 2012-09-09 10:51:02 (Show Source):
You can put this solution on YOUR website!kali mixes together 9 gal of brand a fruit drink and 6 gal of brand b fruit drink which contains 5% fruit juice. find the percent of fruit juice in brand a if the mixture contained 11% fruit juice.
-------
Equation:
concentrate + concentrate = concentrate
Let the unkown percent in "b" be x.
-----------------------------------------
0.05*6 + x*9 = 0.11(6+9)
---
Multiply thru by 100 to get:
5*6 + 900x = 11*15
---
30 + 900x = 165
900x = 135
x = 0.15
----
Ans: Percent of fruit juice in Brand b is 15%
=================
Cheers,
Stan H.
======================
|
test/647923: |x-3| is less than or equal to k. Find a value of k
1 solutions
Answer 406475 by stanbon(57961) on 2012-09-08 20:52:59 (Show Source):
You can put this solution on YOUR website!|x-3| is less than or equal to k. Find a value of k
Let k = 5
Then |x-3| <= 5
Then -5<= x-3 <= 5
So, -2 <= x <= 8
=======================
Cheers,
Stan H.
==========================
|
Money_Word_Problems/647924: A factory increases the production of cars annually by 5%. If presently it manufactures 610, 000 cars per year, how many cars will it manufacture per year after 3 years
1 solutions
Answer 406473 by stanbon(57961) on 2012-09-08 20:49:02 (Show Source):
You can put this solution on YOUR website!A factory increases the production of cars annually by 5%. If presently it manufactures 610, 000 cars per year, how many cars will it manufacture per year after 3 years
----
start: 610,000
after 1 year: 1.05*610,000
after 2 yrs: 1.05^2*610,000
after 3 yrs: 1.05^3*610,000 = 706151.25 cars
Round down to 706,151
===============================================
Cheers,
Stan H.
==============
|
test/647925: What is the slope of a line parallel to the line through the points (8,6) and (-12,-10).
1 solutions
Answer 406471 by stanbon(57961) on 2012-09-08 20:44:52 (Show Source):
You can put this solution on YOUR website!What is the slope of a line parallel to the line through the points
(8,6) and (-12,-10).
-----
slope = (6--10)/(8--12) = 16/20 = 4/5
=========================================
Cheers,
Stan H.
=============
|
Probability-and-statistics/647783: Following are many patients' diastolic blood pressure (mm Hg) figures. The standard deviation is about 6. If you were to add 5 to all of them, what would be the new standard deviation?
80, 91, 81, 75, 72, 76, 84, 90, 95, 77, 79, 86, 71, 75, 89, 85, 80, 77, 74, 80, 79, 82, 90, 83, 81, 72, 82, 78, 80
1 solutions
Answer 406469 by stanbon(57961) on 2012-09-08 20:43:12 (Show Source):
You can put this solution on YOUR website!The spread will still be the same, although each number would be 5 higher.
So the standard deviation would still be 6.
Cheers,
Stan H.
|
Probability-and-statistics/647891: The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of ten 18-year-old men will be between 69 and 71 inches?
Answer
a. 0.8539
b. 0.2922
c. 0.3539
d. 0.1461
e. 0.1611
If you could please show me how to solve this problem.
1 solutions
Answer 406464 by stanbon(57961) on 2012-09-08 20:32:56 (Show Source):
You can put this solution on YOUR website!The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height of a sample of ten 18-year-old men will be between 69 and 71 inches?
-------
Note: The mean of the sample means is 68
The standard deviation of the sample means is 3/sqrt(10)
----
z(69) = (69-68)/(3/sqrt(10)) = 1.0541
z(71) = (71-68)/(3/sqrt(10)) = 3.1623
---------------------------
P(69 < x-bar < 71) = P(1.0541 < z < 3.1623) = 0.1451
===================
Cheers,
Stan H.
===================
Answer
a. 0.8539
b. 0.2922
c. 0.3539
d. 0.1461
e. 0.1611
|
Probability-and-statistics/647893: Answer the question Yes or No. Suppose x has a distribution with (a weird shaped u)= 80 and (a weird shaped o)= 12. If random samples of size n = 21 are selected, can we say that the distribution of sample means (x with a line over it) for samples of this size is approximately normal?
Answer
a. No
b. Yes
1 solutions
Answer 406459 by stanbon(57961) on 2012-09-08 20:26:15 (Show Source):
You can put this solution on YOUR website!Answer the question Yes or No. Suppose x has a distribution with (a weird shaped u)= 80 and (a weird shaped o)= 12. If random samples of size n = 21 are selected, can we say that the distribution of sample means (x with a line over it) for samples of this size is approximately normal?
------
The Central Limit Theorem says the answer is Yes.
Cheers,
Stan H.
===================
Answer
a. No
b. Yes
|
Probability-and-statistics/647894: Is the standard score positive or negative when the raw score is 6 and the mean is 4?
Answer
a. The standard score is negative.
b. The standard score is positive.
1 solutions
Answer 406455 by stanbon(57961) on 2012-09-08 20:24:19 (Show Source):
You can put this solution on YOUR website!Is the standard score positive or negative when the raw score is 6 and the mean is 4?
---
The standard score is the number of standard deviations above or
below the mean.
Since 6 is above the mean, the standard score will be positive.
=================================================
Cheers,
Stan H.
==================
Answer
a. The standard score is negative.
b. The standard score is positive.
|
Probability-and-statistics/647895: Find the area under the standard normal curve over the interval specified below.Between z = -2 and z = 0.4
Answer
a. 0.655
b. 0.477
c. 0.155
d. 0.977
e. 0.633
1 solutions
Answer 406453 by stanbon(57961) on 2012-09-08 20:22:02 (Show Source):
You can put this solution on YOUR website!Find the area under the standard normal curve over the interval specified below.Between z = -2 and z = 0.4
----
Use your z-chart or calculator to get:
P(-2 < z < 0.4) = normalcdf(-2,0.4) = 0.6327
-----------
I used a TI-84 calculator.
===================================
Cheers,
Stan H.
===================================
Answer
a. 0.655
b. 0.477
c. 0.155
d. 0.977
e. 0.633
|
Probability-and-statistics/647898: Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose that for healthy females, x has an approximately normal distribution with mean (weird looking u symbol) = 4.1 and standard deviation (weird looking o symbol) = 0.7. Convert the following z interval to an x interval.z < 2.9
Answer
a. x>6.13
b. x>-6.13
c. x<-6.13
d. x>-2.07
e. x<6.13
Could someone please show me how to solve this problem?
1 solutions
Answer 406451 by stanbon(57961) on 2012-09-08 20:18:45 (Show Source):
You can put this solution on YOUR website!Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose that for healthy females, x has an approximately normal distribution with mean (weird looking u symbol) = 4.1 and standard deviation (weird looking o symbol) = 0.7. Convert the following z interval to an x interval.z < 2.9
------
You are given u = 4.1 and s = 0.7 and z = 2.9
---
The formula that relates x and z is x = z*s + u
Substitute and solve for "x":
x = 2.9*0.7 + 4.1 = 6.13
---
Ansswer: x > 6.13
========================
Cheers,
Stan H.
========================
Answer
a. x>6.13
b. x>-6.13
c. x<-6.13
d. x>-2.07
e. x<6.13
|
Miscellaneous_Word_Problems/647907: It is an odd number.
The sum of the digits is 6.
The product of the digits is 9.
1 solutions
Answer 406448 by stanbon(57961) on 2012-09-08 20:13:33 (Show Source):
You can put this solution on YOUR website!It is an odd number.
The sum of the digits is 6.
The product of the digits is 9.
-------
I'm going to assum it is a 2-digit number:
Let the number be 10t + u
-----
Equations:
t + u = 6
tu = 9
-----
t = 6-u
---
(6-u)u = 9
6u-u^2 = 9
u^2 -6u + 9 = 0
Factor:
(u-3)(u-3) = 0
u = 3
---
Solve for "t":
t + u = 6
t + 3 = 6
t = 3
---
The number is 33
=====================
Cheers,
Stan H.
=====================
|
Polynomials-and-rational-expressions/647901: Please help me simply the expression:
(12x^2y/3z^4)(-21x^2z^3/12y^2)
I need to know the steps and answer. Please help!
1 solutions
Answer 406447 by stanbon(57961) on 2012-09-08 20:09:35 (Show Source):
You can put this solution on YOUR website!simplify the expression:
(12x^2y/3z^4)(-21x^2z^3/12y^2)
---------
1st: Simplify each fraction by canceling common factors:
---------
= (4x^2y/z^4)(-7x^2z^3/4y^2)
2nd Cancel any factor common to a numerator and a denominator:
---------
= (1*x^2*1/z)(-7*x^2*1/(1*y)
---------
= (-7x^4)/(yz)
====================
Cheers,
Stan H.
====================
|
Permutations/647857: Can you help me write the following expression without using the factorial symbol?:
(n-4)!/(n-2)!
thank you
1 solutions
Answer 406439 by stanbon(57961) on 2012-09-08 18:36:12 (Show Source):
You can put this solution on YOUR website! Can you help me write the following expression without using the factorial symbol?:
(n-4)!/(n-2)!
-----
[(n-4)(n-3)(x-2)!]/(n-2)! = (n-4)(n-3) = n^2 -7n + 12
================================
Cheers,
Stan H.
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Average/647863: Charlie must take four exams in his finite math class. His scores on his first three exams are 91, 77, and 83. What must he score on his fourth exam if he wants his overall mean to be at least 80?
1 solutions
Answer 406437 by stanbon(57961) on 2012-09-08 18:33:14 (Show Source):
You can put this solution on YOUR website!His scores on his first three exams are 91, 77, and 83. What must he score on his fourth exam if he wants his overall mean to be at least 80?
---------
Solve:
(91 + 77 + 63 + x)/4 >= 80
----
(231+x) >= 320
x >= 89
=======================
Cheers,
Stan H.
=======================
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Travel_Word_Problems/647843: The revenue and cost equations for a product are
R=x(50-0.0002x) and C=12x+150,000
where R and C are measured in dollars and x represents the number of units sold. How many units must be sold be obtain a profit of at least $1,650,000?
1 solutions
Answer 406435 by stanbon(57961) on 2012-09-08 18:29:09 (Show Source):
You can put this solution on YOUR website!The revenue and cost equations for a product are
R=x(50-0.0002x) and C=12x+150,000
where R and C are measured in dollars and x represents the number of units sold. How many units must be sold be obtain a profit of at least $1,650,000?
---------------------
Profit = Revenue - Cost
P = x(50-0.0002x)-(12x+150,000)
----
P = 50x - 0.0002x^2 - 12x - 150000
-----
P(x) = -0.0002x^2 + 38x -150000
----
Solve: -0.0002x^2 + 38x -150000 >= 1650000
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etc.
===============
Cheers,
Stan H.
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Miscellaneous_Word_Problems/647822: Hello. I would like to ask you two questions... What percent of 23 is 14? And, I would also like to ask you to find a number so that 2% of it is 128. Answer ASAP! Thank you!
1 solutions
Answer 406425 by stanbon(57961) on 2012-09-08 17:59:34 (Show Source):
You can put this solution on YOUR website!What percent of 23 is 14? And, I would also like to ask you to find a number so that 2% of it is 128.
---------------------------
x/100 = 14/23
----
x = 100(14/23)
---
x = 60.87
---
Answer: 60.87%
=======================
Find a number so that 2% of it is 128.
Let the number be "x":
0.02x = 128
---
x = 128/0.02
----
x = 6400
==================
Cheers,
Stan H.
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Equations/647819: please please help me do this last problem using a tree diagram
You have two spinners,each with black, white and gray sections. The gray section is twice as large as the black or white section. If you spin them both,what is the chance that one will come up black and one gray?Show your work by drawing a tree diagram,then indicating which ones satify the experimental conditions. Please help
1 solutions
Answer 406405 by stanbon(57961) on 2012-09-08 17:05:05 (Show Source):
You can put this solution on YOUR website! You have two spinners,each with black, white and gray sections. The gray section is twice as large as the black or white section.
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For each spinner: p(gray) = 1/2 ; P(white) = 1/4 ; P(black) = 1/4
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If you spin them both,what is the chance that one will come up black and one gray?
P(black on one and gray on other) = (1/4)(1/2) = 1/8
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Show your work by drawing a tree diagram,then indicating which ones satify the experimental conditions.
------------------------------
Tree diagram:
1st column: gray ; black ; white ; gray
---
2nd column to the right of each of the four 1st column elements,
list the 4 elements gray/glack/white/gray
To get the probability of black/gray notice that you have 2 (black,gray)
pairs out of a total of 16 pairs.
So Probability of black/gray = 2/16 = 1/8
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Cheers,
Stan H.
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Numeric_Fractions/647820: A.berto rode 5/8 of the water rides at a water park. His sister rode half of the rides that Alberto rode. What fraction of water rides did she not ride?
1 solutions
Answer 406400 by stanbon(57961) on 2012-09-08 16:53:06 (Show Source):
You can put this solution on YOUR website!A.berto rode 5/8 of the water rides at a water park. His sister rode half of the rides that Alberto rode. What fraction of water rides did she not ride?
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Ans: (1/2)(5/8) = 5/16
========================
Cheers,
Stan H.
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Probability-and-statistics/647788: An executive at Hughes drives from his home to work every day. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes.
a. In what percent of the days will it take him 30 or fewer minutes to reach his office?
b. What percent of the days will it take between 40 and 50 minutes?
c. What percent of days will it take him between 30 and 45 minutes?
d. How long will the longest 10% of the trips take?
1 solutions
Answer 406399 by stanbon(57961) on 2012-09-08 16:50:53 (Show Source):
You can put this solution on YOUR website!An executive at Hughes drives from his home to work every day. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes.
a. In what percent of the days will it take him 30 or fewer minutes to reach his office?
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z(30) = (30-35)/8 = -5/8
P(x <= 30) = P(z <= -5/8) = normalcdf(-100,-5/8) = 0.2660 = 26.60%
==================
b. What percent of the days will it take between 40 and 50 minutes?
Find the z-scores.
Find the percentage between those z-scores.
================================================
c. What percent of days will it take him between 30 and 45 minutes?
Same procedure as on "b".
============================
d. How long will the longest 10% of the trips take?
Find the z-value with a left tail of 0.90
invNorm(0.9) = 1.2815
------
x = zs + u
x = 1.2815*8+35 = 45.25
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Cheers,
Stan H.
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Evaluation_Word_Problems/647807: Water covers 70.8%, or about 365×106 km2, of the earth's surface. Approximate the total surface area of the earth. (Round your answer to the nearest million.)
1 solutions
Answer 406392 by stanbon(57961) on 2012-09-08 16:21:53 (Show Source):
You can put this solution on YOUR website!Water covers 70.8%, or about 365×106 km2, of the earth's surface. Approximate the total surface area of the earth. (Round your answer to the nearest million.)
----
Let x be the total surface of the earth.
----
Equation:
0.708x = 365x10^6
x = 5.155x10^8
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Cheers,
Stan H.
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Age_Word_Problems/647801: a mother is presently 5 years older than twice her daughter's sge. 10 years ago the product of the mother and daughter's age was equal to 125.What is the mom's age?
1 solutions
Answer 406390 by stanbon(57961) on 2012-09-08 16:15:02 (Show Source):
You can put this solution on YOUR website!a mother is presently 5 years older than twice her daughter's sge. 10 years ago the product of the mother and daughter's age was equal to 125.What is the mom's age?
-----------
Equations:
m = 2d + 5
(m-10)(d-10) = 125
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Substitute for "m" and solve for "d:
(2d+5-10)(d-10) = 125
--------------
(2d-5)(d-10) = 125
2d^2-25d+50-125 = 0
---
2d^2 - 25d -75 = 0
-----
(d-15)(2d+5) = 0
d = 15 (daughter's age)
---
m = 2d+5 = 35 (mom's age)
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Cheers,
Stan H.
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Probability-and-statistics/647523: The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the height of an 18-year-old man selected at random is between 64 inches and 66 inches.
a. .1597
b. .2017
c. .3677
d. .8403
e. .3403
If possible please show me how the problem is solved so maybe I can figure out as well
1 solutions
Answer 406272 by stanbon(57961) on 2012-09-07 19:55:06 (Show Source):
You can put this solution on YOUR website!The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the height of an 18-year-old man selected at random is between 64 inches and 66 inches.
---
When you need to measure propability or percentage, you need to use
the z-scale.
---
z(64) = (64-68)/3 = -1.3333
z(66) = (66-68)/3 = -0.6667
----
P(64 <= x <= 66) = P(-1.33 <= z <= -0.67)
= normalcdf(-1.3333,-0.6667) = 0.1613
============================
Cheers,
Stan H.
==============================
a. .1597
b. .2017
c. .3677
d. .8403
e. .3403
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Probability-and-statistics/647522: A psychologist studied self-esteem scores and found the sample data set to be normally distributed with a mean of 50 and a standard deviation of 5.
Part A**What raw score cuts off the bottom 10.03% of this distribution?
Steps:
What is the z-score that cuts off the bottom 10.03% of this distribution?
What is the raw score that cuts off the bottom 10.03% of this distribution?
Part B**What percentage of the scores is between 57.5 and 65?
Steps:
What is the z-score that corresponds to the raw score of 57.5?
What is the z-score that corresponds to the raw score of 65?
What percentage of the scores is between 57.5 and 65?
Part C:**A raw score of 35 is associated with what percentile?
Steps:
What is the z-score associated with a raw score of 35?
A raw score of 35 is associated with what percentile?
Part D:**What raw scores mark the middle 34% of this distribution?
Steps:
What are the z-scores that mark the middle 34% of this distribution? The z-score below the mean is The z-score above the mean is
What is the raw score below the mean?
1 solutions
Answer 406270 by stanbon(57961) on 2012-09-07 19:46:28 (Show Source):
You can put this solution on YOUR website!A psychologist studied self-esteem scores and found the sample data set to be normally distributed with a mean of 50 and a standard deviation of 5.
Part A**What raw score cuts off the bottom 10.03% of this distribution?
Steps:
What is the z-score that cuts off the bottom 10.03% of this distribution?
z = invNorm(0.1003) = -1.280
What is the raw score that cuts off the bottom 10.03% of this distribution?
x = zs + u
x = -1.280*5 + 50 = 43.6
========================================
Part B**What percentage of the scores is between 57.5 and 65?
Steps:
What is the z-score that corresponds to the raw score of 57.5?
z(57.5) = (57.5-50)/5 = 1.5
---------------------------------
What is the z-score that corresponds to the raw score of 65?
z(65) = (65-50)/5 = 3
---
What percentage of the scores is between 57.5 and 65?
P(57.5<= x <=65) = P(1.5<= z <=3) = 0.0655 = 6.55%
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Part C:**A raw score of 35 is associated with what percentile?
Steps:
What is the z-score associated with a raw score of 35?
z(35) = (35-50)/5 = -15/5 = -3
-------------------------------------
A raw score of 35 is associated with what percentile?
P(z < -3) = normalcdf(-100,-3) = 0.0013 = 0.13%
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Part D:**What raw scores mark the middle 34% of this distribution?
Steps:
What are the z-scores that mark the middle 34% of this distribution?
The z-score below the mean is
z = invNorm(.50-0.17) = -0.44
----
The z-score above the mean is +0.44
---
What is the raw score below the mean?
x = -0.44*5+50 = 47.8
===========================
Cheers,
Stan H.
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Human-and-algebraic-language/647517: kaari is taller than elane the difference between the height is 20 cn . kaari's height times 8 is equal to 9 times elane's height. What are their heights
1 solutions
Answer 406267 by stanbon(57961) on 2012-09-07 19:29:28 (Show Source):
You can put this solution on YOUR website!kaari is taller than elane the difference between the height is 20 cn . kaari's height times 8 is equal to 9 times elane's height. What are their heights
----
Equations:
k - e = 20 cm
8k = 9e
----
Substitute for "k" and solve for "e":
k = 20+e
---
8(20+e) = 9e
160 + 8e = 9e
e = 160 cm (Elane's height)
-----
Solve for "k":
k = 20 + e
k = 180 cm (Kaari's height)
=================
Cheers,
Stan H.
==============
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Human-and-algebraic-language/647519: a t shirt and a pair of socks cost 12.70$ if 2 pairs of socks cost 1.45$ less than one t shirt. how much does the t shirt cost
1 solutions
Answer 406264 by stanbon(57961) on 2012-09-07 19:25:42 (Show Source):
You can put this solution on YOUR website!a t shirt and a pair of socks cost 12.70$ if 2 pairs of socks cost 1.45$ less than one t shirt. how much does the t shirt cost
----
Equations:
t + s = 12.70
2s = t-1.45
------
Rearrange:
t + s = 12.70
t - 2s = 1.45
------------------
Subtract and solve for "s":
3s = 11.25
-----
s = $3.75 (price of a pair of socks)
-----
Solve for "t":
t + s = 12.70
t + 3.75 = 12.70
t = 8.95 (price of one t-shirt)
===================
Cheers,
Stan H.
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Reduction-of-unit-multipliers/647406: A hose fills a hot tub at a rate of 3.2 gallons per minute. How many hours will it take to fill a 300-gallon hot tub?
1 solutions
Answer 406177 by stanbon(57961) on 2012-09-07 14:14:51 (Show Source):
You can put this solution on YOUR website!A hose fills a hot tub at a rate of 3.2 gallons per minute. How many hours will it take to fill a 300-gallon hot tub?
-------
Equation:
hours/gallons = hours/gallons
x/300 = (1/60)/3.2
----
x = 5/3.2
---
x = 1.56 hours = 1 hr 33 min 36 seconds
=======================
Cheers,
Stan H.
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