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Recent problems solved by 'stanbon'
stanbon answered: 57151 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>NextTravel_Word_Problems/80075: I need help to solve this problem
Two ships leave port at the same time, one heading due south and the other heading due east. Several hours later, they are 170 miles apart. If the ship traveling south traveled 70 miles farther than the other ship, how many miles did they each travel?
1 solutions
Answer 57437 by stanbon(57219)   on 2007-04-30 07:32:25 (Show Source):
You can put this solution on YOUR website!Two ships leave port at the same time, one heading due south and the other heading due east. Several hours later, they are 170 miles apart. If the ship traveling south traveled 70 miles farther than the other ship, how many miles did they each travel?
--------------
Draw the picture.
You have a right triangle with the south leg being x+7 and the east leg
being x; the hypotenuse is 170.
---------
Use Pythagoras to get:
x^2+(x+70)^2= 170^2
x^2+x^2+140x+4900 = 170^2
2x%2+140x+-24000 = 0
x^2+70x-12000=0
(x+150)(x-80)=0
Positive answer is x=80 miles
x+70 = 150 miles
==============
Cheers,
Stan H.
|
Radicals/80076: What values of b in the following equations will give one or more real number solutions?
a). 3x^2+bx-3=0
b). 5x^2+bx+1=0
c). -3x^2+bx-3=0
what is a rule for judging if an equation has solutions by looking at it in standard form?
thanks!
1 solutions
Answer 57435 by stanbon(57219) on 2007-04-30 07:25:38 (Show Source):
You can put this solution on YOUR website!What values of b in the following equations will give one or more real number solutions?
Look at b^2-4ac for each equation:
a). 3x^2+bx-3=0
b^2-4ac
=b^2-4*3*-3
=b^2+36
This expression will be non-negative for all values of "b".
-----------
b). 5x^2+bx+1=0
b^2-4ac
=b^2-4*5*1
=b^2-20
This expression will be non-negative for all b>=2sqrt5 or less than -2sqrt5
---------------
c). -3x^2+bx-3=0
b^2-4ac
=b^2-4*-3*-3
=b^2-36
This expression be non-negative for all b >=6 or <= than -6
-------------
what is a rule for judging if an equation has solutions by looking at it in standard form?
b^2>=4ac
===============
Cheers,
Stan H.
|
Quadratic_Equations/80077: Can someone help me please I do not understand this any portion of it can someone help me please? identify the axis of symmetry, create a suitable table of values, and sketch the graph (including the axis of symmetry).
y=x^2-5x+3
1 solutions
Answer 57432 by stanbon(57219) on 2007-04-30 07:14:28 (Show Source):
You can put this solution on YOUR website!identify the axis of symmetry, create a suitable table of values, and sketch the graph (including the axis of symmetry).
y=x^2-5x+3
-------------
One way to accomplish this is to find the x-coordinate of the vertex:
x=-b/2a= -(-5)/2=5/2
That is the axis of symmetry.
----------
To create the "table" let x have a few values and solve for y:
If x=0, y=3
If x=1, y=-1
If x=2, y=4-10+3=-3
If x=3, y=9-15+3=-3
If x=4, y=16-20+3=-1
------------
Cheers,
Stan H.
|
absolute-value/80005: please help,
solve the following:
7|z+6|+8 is less than or equal to 57
1 solutions
Answer 57417 by stanbon(57219) on 2007-04-29 22:10:57 (Show Source):
You can put this solution on YOUR website!7|z+6|+8 <= 57
Subtract 8 from both sides:
7|z+6| <= 49
Divide both sides by 7:
|z+6| <= 7
Rewrite as:
-7 <= z+6 <= 7
Subtract 6 along the line to get:
-13 <= z <= 1
===========
Cheers,
Stan H.
|
Quadratic_Equations/80023: I need help writing a quadratic function using 3 out of these 5 points on a parabola. Can you help me please? (0,254)(4,234)(8,235)(12,239)(16,255)
Thank You
1 solutions
Answer 57414 by stanbon(57219) on 2007-04-29 22:02:34 (Show Source):
You can put this solution on YOUR website!Pick any of the three points.
Substitute their x,y values one at a time into the form y=ax^2+bx+c
You will get three equations with the three unknowns a,b, and c.
Solve the system of three equations for a, b, and c.
Cheers,
Stan H..
-----------
|
Rational-functions/80054: Is the relationship between te varibables in the table a direct variation an inverse or neither? if it is a direct or inverse write a functon to model it.
x= -9 -5 0 3
Y= -3 (-5/3) 0 1
(-5/3) is a fraction
1 solutions
Answer 57412 by stanbon(57219) on 2007-04-29 21:55:57 (Show Source):
You can put this solution on YOUR website!Is the relationship between te varibables in the table a direct variation an inverse or neither? if it is a direct or inverse write a functon to model it.
x= -9 -5 0 3
Y= -3 (-5/3) 0 1
-------------
y=x/3
or
y=(1/3)x
x and y have a direct relation.
That means "as x increases, y increases".
Cheers,
Stan H.
|
Equations/80053: Two chemical storage tanks hold the same amount. Tank A is 3/4 full while tank B is 2/3 full The two tanks currently have a combined total of 1700 gallons of CO2. How much do the tanks hold?
I have tried so many formulas to solve this problem and none of them work. I get about as far as x=what the tanks hold. I've tried 3/4x + 2/3x = 1700 + x.
1 solutions
Answer 57407 by stanbon(57219) on 2007-04-29 21:49:51 (Show Source):
You can put this solution on YOUR website!Two chemical storage tanks hold the same amount. Tank A is 3/4 full while tank B is 2/3 full The two tanks currently have a combined total of 1700 gallons of CO2. How much do the tanks hold?
--------
Let the amount held by each tank be "x" gallons.
Tank A has (3/4)x gallons
Tank B has (2/3)x gallons
EQUATION:
(3/4)x+(2/3)x=1700
(9/12)x+(8/12)x=1700
(17/12)x=1700
(1/12)x=100
x=1200 gallons (each tank holds 1200 gallons)
Cheers,
Stan H.
|
Rational-functions/80052: For each of the following sketch the asympyotes and graph the function
Y=( 5 divided by x-3)+1
Y= (-4x+1 divided by -x-3)
1 solutions
Answer 57405 by stanbon(57219) on 2007-04-29 21:41:56 (Show Source):
You can put this solution on YOUR website!Y=( 5 divided by x-3)+1
y=[5/(x-3)]+1
Vertical asymptote at x=3
-----------
Y= (-4x+1 divided by -x-3)
y=[(-4x+1)/(x-3)]
Vertical asymptote at x=3
==========
Cheers,
Stan H.
|
Probability-and-statistics/80042: during a difficult release move, a gymnast has fallen from the parallel bars 2 of the 12 competitions this season. the state meet is next week. what is the probability that she will successfully complete the release move?
1 solutions
Answer 57404 by stanbon(57219) on 2007-04-29 21:36:03 (Show Source):
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Angles/80049: Hi i am really hoping you can help me here, i have never uses a tutor before but i was frantically trying to find something to help me so here it goes...
if i have 3 ordered pairs (3,15) (12,13) (5,7) on a graph and are making a scalene triangle. The question is how to do make this into in the an equation of two of the perpendicular Bisectors. and then getting that information i am not sure how to solve it. i am thinking if i get it started i will be able to finish it but i have NO idea even how to start to get an equation set up.
THANK YOU SO MUCH!
1 solutions
Answer 57401 by stanbon(57219) on 2007-04-29 21:34:08 (Show Source):
You can put this solution on YOUR website!i have 3 ordered pairs (3,15) (12,13) (5,7) on a graph and are making a scalene triangle. The question is how to do make this into in the an equation of two of the perpendicular Bisectors.
---------------
Choose two of the points: (3,15),(12,13)
Find the slope and midpoint of the line segment joining the two points.
slope: [13-15]/[12-3]= -2/9
mid-pt: x=(3+12)/2=15/2
........y=(13+15)/2=14
Now find the equation of the line perdicular to the line segment and
passing thru the mid-p.
The slope of the bisector is 9/2 because it must be the negative inverse
of the line segment;s slope.
---------
So, slope = 9/2 and it passes thru (15/2,14)
Form is y=mx+b
Substitute the x,y, and m values to find "b", as follows:
14=(9/2)(15/2)+b
14=135/4 + b
56/4 = 135/4+b
b=-79/4
EQUATION of one of the perpendicular bisectors: y=(9/2)x-79/4
------------
Follow the same procedure to find the 2nd perpendicular bisector.
============
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/80040: Well here it goes,
write an equation for the parabola that is obtained by shifting the graph of y=one fifth x squared exactly 4 units to the right.
thank you.
1 solutions
Answer 57399 by stanbon(57219) on 2007-04-29 21:11:36 (Show Source):
You can put this solution on YOUR website!Well here it goes,
write an equation for the parabola that is obtained by shifting the graph of y=one fifth x squared exactly 4 units to the right.
--------------------------------
Original equation: y=(1/5)x^2
Four Units to the right: y=(1/5)(x-4)^2
----------
Cheers,
Stan H.
|
Money_Word_Problems/80036: Mr.Harvey invested a sum of money at 4%.He invested a second sum at 3%.If the annual income from the first investment is equal to the annual income from the second investment,and if the investments total $7000,how much did he invest at each rate?
1 solutions
Answer 57395 by stanbon(57219) on 2007-04-29 20:59:51 (Show Source):
You can put this solution on YOUR website!Mr.Harvey invested a sum of money at 4%.He invested a second sum at 3%.If the annual income from the first investment is equal to the annual income from the second investment,and if the investments total $7000,how much did he invest at each rate?
-------------
Let "x" be amt invested at 4%; Interest on this is 0.04x dollars
Then "7000-x" is amt invested at 3%; Interest on this is 0.03(7000-x)
= 210-0.03x dollars
EQUATION:
1st interest = 2nd interest
0.04x=210-0.03x
0.07x=210
x=3000 (amount invested at 4%)
7000-x=4000 (amount invested at 3%)
Cheers,
Stan H.
|
Functions/80037: 1.) Which of the following are FALSE:
a.) (a + 2)^3 = (a)^3 + (2)^3 = a^3 - 8
b.) If -a >2, then -2 < a
1 solutions
Answer 57386 by stanbon(57219) on 2007-04-29 20:40:40 (Show Source):
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Functions/80024: I have 20 of these questions to do, so once I get help with this first one, I beleive I shall be able to get the other 19 out. Thank you so much if you can help me. (My email is sasha_mahabir@hotmail.com)
HERE IS THE QUESTION:
1.) Write an algebraic function for each of the following. Use 'y' as the dependant variable and 'x' as the independant varaiable. Then evaluate the functions for the input values 9, 16.37, 0, and -10.
a.) The output is the opposite of the input.
b.) The output is the product of five and the sum of the input and six.
c.) The input is the sum of five and the product of the input and six.
d.) The output is always 100.
e.) The output is the square of the product of 3 and the input.
f.) The output is the product of three and the square of the input.
1 solutions
Answer 57384 by stanbon(57219) on 2007-04-29 20:32:29 (Show Source):
You can put this solution on YOUR website!1.) Write an algebraic function for each of the following. Use 'y' as the dependant variable and 'x' as the independant varaiable. Then evaluate the functions for the input values 9, 16.37, 0, and -10.
a.) The output is the opposite of the input.
y=-x
If x=9, y=-9
If x=16, y=-16
etc.
b.) The output is the product of five and the sum of the input and six.
y=5(x+6)
i x=9, y=5(9+6), y=5*15, y=75
etc.
c.) The output is the sum of five and the product of the input and six.
y=5+6x
If x=0 y=5+6*9, y=5+54, y=59
etc.
d.) The output is always 100.
y=100
If x=9, y=100
etc.
e.) The output is the square of the product of 3 and the input.
y=(3x)^2
If x=9, y=(3*9)^2, y= 27^2, y= 729
etc.
f.) The output is the product of three and the square of the input.
y=3x^2
If x=9,y=3*9^2, y=3*81, y=243
etc.
==============================
Cheers,
Stan H.
|
Rational-functions/79970: Identify the horizontal asymptotes. please pick a right chioce
f(x)=x^2+1/x-2
a.x=1
b.y=1
c.x=2
d.y=2
1 solutions
Answer 57372 by stanbon(57219) on 2007-04-29 17:42:40 (Show Source):
You can put this solution on YOUR website!As x gets increasingly large, the numberator gets increasingly large,
and f(x) gets increasingly large. Therefore there are no horizontal
asymptotes.
If you are studying calculus this means "the limit of f(x) as x goes
to infinity, is infinity".
The same is true as x goes to negative infinity: no horizontal asymptotes.
==============
Cheers,
Stan H.
|
Linear-equations/79724: Here is my problem. I have state the problem, as it has been put to us and just below it, I have shown what I have done to this point. I'm not sure I can get any more of it and make any sense with it. Can you help? Thanks in advance.
When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )
• Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation.
• Search the Library and Internet. In the real world, where might these imaginary numbers be used?
ax2 + BX + C = 0
Move terms containing A to the left and the others to the right.
ax2 = - BX - C
ax2 = - (-XB+C)
Here Divide by X to isolate A.
-
A = + - (-XB+C)
2
X
ax2 + BX + C = 0
Solution
A = +- (-XB+C) ____
2
X
1 solutions
Answer 57203 by stanbon(57219) on 2007-04-26 22:31:44 (Show Source):
You can put this solution on YOUR website!• Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation.
---------
Do that:
y=2x^2+3x+0 will pass thru the x axis twice because b^2-4ac>0
y=2x^2+3x+7 will not touch the x axis because b^2-4ac<0
y=x^2+4x+4 will touch but not pass thru the x axis because b^2-4ac=0
-------------------
• Search the Library and Internet. In the real world, where might these imaginary numbers be used?
Use Google: Imaginary numbers are used in modeling electricity, for example.
--------
Cheers,
Stan H.
|
Probability-and-statistics/79661: Can someone solve these problems step by step for me. I got them wrong on my last test. ThanYou It will be greatly appreciated.
Question 1 : Confidence Intervals for the Mean
A random sample of 17 students were tested on the SAT english exam. If the mean score was 653.4 with a standard deviation of 135.457, find the 90% confidence interval for the popultation mean. Assume that the population standard deviation in unknown. Assume the scores are approximately normally distributed. Choose the appropriate distribution and state the reason(s) for your choice.Round off your answer to 1 decimal place.
Question 2 : Confidence Interval for a Population Proportion
In a random sample of 50 students enrolled in remedial math courses 21 passed the MAT test by the end of the semester.
A. Calculate the confidence interval for the population percentage of all students in remedial math courses who passed the MAT exam by the end of the semester. Use a 90% level of significance. Round off your final answer to 1 decimal place in percent.
B. If the margin of error is changed to 13.50% and the confidence level remains the same as in Part a, what is the minimum sample size required to estimate the population proportion of students who passed the MAT test? Use the proportions from Part a. Round up the sample size.
Question 3: Hypothesis Testing for the Mean
A sociologist wants to determine if the number of individuals per family unit the national average of 2.9. She interviews 31 randomly selected families in a large apartment complex and obtains a mean of 3.1 individuals per family unit with a standard deviation of 0.80. Test the claim that the mean number of individuals per family unit is less than 2.9. Use a significance level of 0.05. Assume that the population has a normal distribution and that the population standard deviation is unknown. You must decide whether to use the z-test or t-test. If you use the z-test use the P-value method.
Question 4: Confidence intervals for Variance and Standard Deviation
Suppose you are given a sample set of data consisting of 17 body temperatures, with s=1.02. Assume that body temperatures are normally distributed . Find the 95% confidence interval for the population variance 0^2. Round off to 2 decimal places.
1 solutions
Answer 57197 by stanbon(57219) on 2007-04-26 22:09:10 (Show Source):
You can put this solution on YOUR website!Question 1 : Confidence Intervals for the Mean
A random sample of 17 students were tested on the SAT english exam. If the mean score was 653.4 with a standard deviation of 135.457, find the 90% confidence interval for the popultation mean. Assume that the population standard deviation in unknown. Assume the scores are approximately normally distributed. Choose the appropriate distribution and state the reason(s) for your choice.Round off your answer to 1 decimal place.
---------------------
E=z
E=1.645[32.853]=54.04
CI=(653.4-54.04,653.4+54.04)
CI=(599.36,707.44)
---------
Question 2 : Confidence Interval for a Population Proportion
In a random sample of 50 students enrolled in remedial math courses 21 passed the MAT test by the end of the semester.
A. Calculate the confidence interval for the population percentage of all students in remedial math courses who passed the MAT exam by the end of the semester. Use a 90% level of significance. Round off your final answer to 1 decimal place in percent.
E=1.645sqrt[(21/50)(19/50)]/sqrt50
E=0.093
CI=[(21/50)-0.093,(21/50)+0.093]
CI=(0.327,0.513)
=============
B. If the margin of error is changed to 13.50% and the confidence level remains the same as in Part a, what is the minimum sample size required to estimate the population proportion of students who passed the MAT test? Use the proportions from Part a. Round up the sample size.
E = z
sqrt(n)=z/E
sqrt(n)=1.645sqrt[(21/50)(19/50)]/0.135
sqrt(n)=6.014...
n=36.17
n=36 when rounded
=============
Question 3: Hypothesis Testing for the Mean
A sociologist wants to determine if the number of individuals per family unit the national average of 2.9. She interviews 31 randomly selected families in a large apartment complex and obtains a mean of 3.1 individuals per family unit with a standard deviation of 0.80. Test the claim that the mean number of individuals per family unit is less than 2.9. Use a significance level of 0.05. Assume that the population has a normal distribution and that the population standard deviation is unknown. You must decide whether to use the z-test or t-test. If you use the z-test use the P-value method.
--------
Using the z-test or the t-test pretty much depends on what text you are
using. You will have to make that decision; there is no universal agreement
on this.
---------------------------
Question 4: Confidence intervals for Variance and Standard Deviation
Suppose you are given a sample set of data consisting of 17 body temperatures, with s=1.02. Assume that body temperatures are normally distributed . Find the 95% confidence interval for the population variance 0^2. Round off to 2 decimal places.
Check this in your text book. I don't have these formulas handy.
==============
Cheers,
Stan H.
|
Points-lines-and-rays/79657: This question is from textbook geometrry reasoning
A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower to the fire is 12 degrees.
a. Draw a diagram to represent this situation.
b. To the nearest foot, how far is the fire from the base of the tower? Show the steps you use to find the solution.
1 solutions
Answer 57195 by stanbon(57219) on 2007-04-26 21:39:39 (Show Source):
You can put this solution on YOUR website!A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower to the fire is 12 degrees.
-----------------
Draw the picture.
The angle of depression looking from the tower is the same as the angle
of elevation looking at the top of the tower from the spot of the fire.
----------
So, tan(12 degrees)= 21/distance between tower and fire
distance = 21/tan(12) = 98.8 ft
=================
Cheers,
Stan H.
|
Pythagorean-theorem/79632: 1. How do you figure the Horizontal and Virtual Velocity in m/s form if the resultant m/s is 30.4 and the angle degree is 38.5?
1 solutions
Answer 57188 by stanbon(57219) on 2007-04-26 20:44:14 (Show Source):
You can put this solution on YOUR website!How do you figure the Horizontal and Virtual Velocity in m/s form if the resultant m/s is 30.4 and the angle degree is 38.5?
-----------
I don't know what you mean by "Virtual Velocity" but it sounds like like
you are trying to find the horizontal and the vertical componets of
a vector of length 30.4 at an angle of 38.5.
-----------
The general form for these is:
Horizontal component: x = rcos(theta)
Vertical component : y = r(sin(theta)
---------------
Assuming your 38.5 means radians your components would be:
x=30.4cos(38.5)= 21.1605...
y=30.4sin(38.5)=21.8264...
=========
Cheers,
Stan H.
|
Trigonometry-basics/79675: How do I convert sin theta = (1/3) into degrees
please help I am not the best at math.
1 solutions
Answer 57185 by stanbon(57219) on 2007-04-26 20:35:35 (Show Source):
You can put this solution on YOUR website!How do I convert sin theta = (1/3) into degrees.
Degrees refers to the measure of an angle; it may be measured in degrees or
in radians.
To say sin(theta)=1/3 does not imply that theta (which is the angle being
described) is stated in degrees or is stated in radians. It is up the the
person determining theta whether he/she writes the answer in degrees or
in radians.
------------
For your problem theta happens to be 19.47 degrees
If I wanted to change that to radians I would multiply 19.47
by (pi)/180 to get 0.3398 radians.
===========
Hope this helps.
Cheers,
Stan H.
|
Travel_Word_Problems/79682: The Rope Around the Earth Puzzle: Imagine a rope tied around the Earth’s equator like a ring on a person’s finger. Now imagine lifting off this very long rope, cutting it somewhere so as to stitch into it exactly one meter of extra rope. Then imagine placing this longer rope back around the Earth at the equator. Since it is longer than the original rope by just one meter, a gap between the rope and the Earth’s surface will form all the way around. How large is the gap that is formed?
1 solutions
Answer 57182 by stanbon(57219) on 2007-04-26 20:26:46 (Show Source):
You can put this solution on YOUR website!The Rope Around the Earth Puzzle: Imagine a rope tied around the Earth’s equator like a ring on a person’s finger. Now imagine lifting off this very long rope, cutting it somewhere so as to stitch into it exactly one meter of extra rope. Then imagine placing this longer rope back around the Earth at the equator. Since it is longer than the original rope by just one meter, a gap between the rope and the Earth’s surface will form all the way around. How large is the gap that is formed?
-----------
The 1st rope has circumference C=(pi)d
So d = C/pi
-------------
After adding a meter you
C+1 = (pi)d+1
C+1 = pi[d+1/pi]
So the diameter of the new rope is [d+1/pi] meters
This new diameter is 1/pi m longer
So the new radius is 1/2pi m longer
So the gap is 1/2pi meter
=========
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/79685: angelica and her brother, morton, had a total fo $100 they earned washing walls. they heard about a fantastic garage sale and went to see what they could find. when they saw the prices for paperback books, jeans, and winter jackets, they decided to buy 100 items for their $100. if hte jackets were $9 each, the jeans $3 a pair, and the books 5 for $1, how many of each did they buy?
1 solutions
Answer 57181 by stanbon(57219) on 2007-04-26 20:14:06 (Show Source):
You can put this solution on YOUR website!they decided to buy 100 items for their $100. if hte jackets were $9 each, the jeans $3 a pair, and the books 5 for $1, how many of each did they buy?
----------------
Let # of jackets be "k" ; Value of those jackets is 900k cents
Let # of jeans be "n" ; value of those jeans is 300n cents
Let # of books be "b" ; value of those books is 20n cents
-------------
EQUATIONS:
k + n + b = 100
900k + 300n + 20b = 10000 cents
--------
k + n + b = 100
45k + 15n +b = 500
---------
Subtract 1st from 2nd to get:
44k + 13n = 400
---------------
Make a list of the multiples of 44 and another list of the multiples
of 13. Try to find a sum that equals 400. That should tell you
what k and n are. Using that information you can find b.
It can be done because k and n must be Natural or Counting numbers.
--------------
Cheers,
Stan H.
|
Systems-of-equations/79690: Sometimes both equations will need to be multiplied to obtain opposite coefficients
EXAMPLE
3X + 5Y =6
-4X + 2Y =5
1 solutions
Answer 57179 by stanbon(57219) on 2007-04-26 19:59:20 (Show Source):
You can put this solution on YOUR website!3X + 5Y =6
-4X + 2Y =5
-------------
Let's say you want to get rid of the X-terms:
Multiply 1st equation by 4 so you get a 12X term:
Multiply 2nd equation by 3 so you get a -12x term:
----------
12x + 20y = 24
-12x+ 6y = 15
-----------
Now, add the two equations to get:
26y=39
y=39/26
-----------
Substitute that value of y into one of the equations so you can solve for x:
3x +5(39/26) = 6
x+5(13/26) = 2
x+5/2 = 2
x= -1/2
===========
Cheers,
Stan H.
|
Probability-and-statistics/79663: Please show me step by step answers on how to solve the 4 problems. Thankyou. It will be greatly appreciated.
Question 1
A researcher wants to estimate the proportion of students at York College who will choose Computer Science as their major in Spring 2008. She wants to be within 5.3% of the actual popultaion proportion and have a 95% level of significance. In a preliminary survey of 42 students 29 said they wanted to take Computer Science in 2008. What is the minimum sample size that she will require? Round final answer up to the next whole number.
Question 2
A fast food restaurant claims that the mean waiting time is not equal to 3 minutes. A random sample of 45 customers revealed a mean waiting time of 3.3 minutes with a standard deviation of 0.7 minutes. Test the restaurants claim at a, a=0.05 level of significance. Assume that the population is normally distributed, and the population standard deviation is 0.7. Use the P-value method.
Question 3: Hypothesis Testing for Proportions.
A researcher at York claims that for Mathematics courses the proportion of grades B or higher was more than 33.0%. In a random sample of 100 grades issued in the year 2006 there were 27 F's, 15 D's, 22 C's, 14 B's, 22 A's. At a=0.10 test the researcher's claim.
Use "rejestion region" claim.
Question 4: Determining sample size
A. A large public university wants to estimate the average(mean) teaching experience of it's faculty. A preliminary random sample of 20 faculty yields a standard deviation of s=2.5 years.
The dean wants to be 95% confident that the sample mean does not have a maximum error of estimate of more than 1.6 years. (Hint: this is maximum error of estimate E). How large of a sample should she use? Use the preliminary sample sample standard deviation as an approximation of the population standard deviation. ROund up to the next whole number.
B. If she decides on a maximum error of estimate of 1.8years. and a level of significance of 95% how large of a sample should she use? Round up to next whole number.
1 solutions
Answer 57169 by stanbon(57219) on 2007-04-26 16:35:14 (Show Source):
You can put this solution on YOUR website!A researcher wants to estimate the proportion of students at York College who will choose Computer Science as their major in Spring 2008. She wants to be within 5.3% of the actual popultaion proportion and have a 95% level of significance. In a preliminary survey of 42 students 29 said they wanted to take Computer Science in 2008. What is the minimum sample size that she will require? Round final answer up to the next whole number.
-----------
margin of error formula:
E=z*sqrt[pq/n]
sqrt(n) = z*sqrt(pq)/E
sqrt(n) = 1.96sqrt([29/42][13/42])/0.053
sqrt(n) = 17.096
n=292 (this is the required sample size)
------------
Can't do any more now; have to run. Mail me back if
you need help with the other probs.
Cheers,
Stan H.
|
Rational-functions/79274: Identify all asymptotes and hole in the graph of each rational function:
b(x)=x+6/2x-1
your help would be greatly appreciated
1 solutions
Answer 57144 by stanbon(57219) on 2007-04-26 09:24:12 (Show Source):
You can put this solution on YOUR website!Identify all asymptotes and hole in the graph of each rational function:
b(x)=x+6/2x-1
--------
Asymptote where the the denominator is zero.
2x-1=0
x=1/2 (therefore asymptote at x=1/2)
=========
Cheers,
Stan H.
|
Rational-functions/79627: really need this answer
1)Graph f(x)=(x^2 - 4)/(x - 2) using a graphing calculator. Using a standard window with the trace feature, trace the graph to x=2. What happens?
2. Why is there a "break" in the line at x=2? Why is the graph a line without a vertical asymptote at x=2? If x is "close to" 2, what is the y value "close to"?
Create a function that has either a hole, a break, or an asymptote in the graph.
1 solutions
Answer 57143 by stanbon(57219) on 2007-04-26 09:21:06 (Show Source):
You can put this solution on YOUR website!1)Graph f(x)=(x^2 - 4)/(x - 2) using a graphing calculator. Using a standard window with the trace feature, trace the graph to x=2. What happens?
At x=2 you get an ERROR.
2. Why is there a "break" in the line at x=2?
The denominator cannot be zero; Because there is also a factor of
(x-2) in the numerator you get a "hole" in the graph.
----------
Why is the graph a line without a vertical asymptote at x=2?
If you cancel the (x-2) factor that is common to numerator and denominator
you get the function y=x+2 which graphs as a line.
-----------
If x is "close to" 2, what is the y value "close to"?
y=4
----------
Create a function that has either a hole, a break, or an asymptote in the graph.
Asymptote: y=x/(x-2) will have a vertical asymptote at x=2.
Hole: y=[x^2-3x]/[x-3] will have a hole at x=3
=============
Cheers,
Stan H.
|
Linear-equations/79607: Does anyone have any idea what this problem means? Any help would be appreciated!
Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a) What is the function that describes this problem?
Answer:
b) The ball will be how high above the ground after 1 second?
Answer:
c) How long will it take to hit the ground?
Answer:
d) What is the maximum height of the ball?
Answer:
Show work in this space.
1 solutions
Answer 57131 by stanbon(57219) on 2007-04-25 22:47:22 (Show Source):
You can put this solution on YOUR website!Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents ½g, the gravitational pull due to gravity (measured in feet per second 2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a) What is the function that describes this problem?
Answer:
Vo=32 ; So=0 because the ball started at a height of zero.
EQUATIOn:
h(t)=-16t^2+32t+0
--------------
b) The ball will be how high above the ground after 1 second?
Answer:
h(1)=-16+32 = 16 ft (that is how high the ball will be after one second)
------------------------
c) How long will it take to hit the ground?
Answer:
The height of the ball will be zero when it is back on the ground:
0 = -16t^2+32t
-16t(t-2)=0
t=0 or t=2
The ball started on the ground and will be back at the end of 2 seconds.
------------------
d) What is the maximum height of the ball?
Answer:
Show work in this space.
Max height occurs when t=-b/2a = -32/2*(-16) = 1
Max height occurs at the end of 1 second.
===========
Cheers,
Stan H.
|
Distributive-associative-commutative-properties/79608: 1 pipe will fill a container in 20 minutes, the second pipe will fill the container in 30 minutes, how long will it take to fill the conatiner with both pipes?
1 solutions
Answer 57130 by stanbon(57219) on 2007-04-25 22:33:52 (Show Source):
You can put this solution on YOUR website!1 pipe will fill a container in 20 minutes, the second pipe will fill the container in 30 minutes, how long will it take to fill the conatiner with both pipes?
-----------------------
First pipe DATA:
Time = 20 min/job : Rate = 1/20 job/min
------------------
Second pipe DATA:
Time = 30 min/job ; Rate = 1/30 job/min
---------------
Together DATA:
Time = x min/job ; Rate = 1/x job/min
============
EQUATION:
1st pipe rate + 2nd pipe rate = together rate
1/20 + 1/30 = 1/x
Multiply thru by 60x to get:
3x + 2x = 60
5x = 60
x= 12 min/job (time required for pipes working together to do the job)
===================
Cheers,
Stan H.
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