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Recent problems solved by 'stanbon'
stanbon answered: 57218 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>NextQuadratic_Equations/193591: on a scatter plot of data,a trend line passes through the points (-6,7) and (-2,10). describe the correlation.
1 solutions
Answer 145306 by stanbon(57286)   on 2009-04-28 17:54:55 (Show Source):
You can put this solution on YOUR website!on a scatter plot of data,a trend line passes through the points (-6,7) and (-2,10). describe the correlation.
--------------
slope = (10-7)/(2--6) = 3/8
---------------------------------
Form: y = mx + b
You have x,y,and m ; solve for "b":
10 = (3/8)*2 + b
10 = (3/4) + b
b = 37/4
-------------------
Equation: y = (3/8)x + (37/40)
======================================
Cheers,
Stan H.
|
Quadratic_Equations/193575: I'm sorry. I know this problem is very similar to the example, but I get a very crazy answer when I've tried to do this like the example many times. I must be doing something wrong. Please help.
One leg of a right triangle is 96 inches. Find the hypotenuse and teh other leg if the length of the hypotenuse exceeds 2 and 1/2 times teh other leg by 4 inches.
1 solutions
Answer 145299 by stanbon(57286) on 2009-04-28 17:35:13 (Show Source):
You can put this solution on YOUR website!One leg of a right triangle is 96 inches. Find the hypotenuse and the
other leg if the length of the hypotenuse exceeds 2 and 1/2 times teh other leg by 4 inches.
--------------------
One leg is 96 in
Let the "other leg" be "x" inches.
hypotenuse = (5/2)x + 4
----------------------------
Equation:
h^2 = leg^2 + "otherleg"^2
[(5/2)x + 4]^2 = 96^2 + x^2
[(5x+ 8)/2^2 = 96^2 + x^2
(5x+8)^2 = 4*96^2 + 4x^2
25x^2 + 90x + 91 = 36864 + 4x^2
21x^2 + 90x - 36773 = 0
-----
Positive solution:
x = 39.76
hypotenuse = (5/2)x+4 = 103.4
====================================
Cheers,
Stan H.
|
Quadratic_Equations/193573: Please check my work:
Form each of the following:
A linear equation in one variable: X + 3 = -5
A linear equation in two variables: y = 5x - 3
A quadratic equation: 3x2 + x - 2 = 0
A polynomial of three terms: 7x2y3 + 4x − 9
An exponential function: 32 = 9
A logarithmic function: log39 = 2
1 solutions
Answer 145295 by stanbon(57286) on 2009-04-28 16:21:40 (Show Source):
You can put this solution on YOUR website!Please check my work:
Form each of the following:
A linear equation in one variable: Y + 3 = -5
A linear equation in two variables: y = 5x - 3
A quadratic equation: 3x2 + x - 2 = Y
A polynomial of three terms: 7x^2 + 4x − 9 = y
An exponential function: y = 3^x +2
A logarithmic function: y = 3 + log(x-2)
=============================================
Cheers,
Stan H.
|
Probability-and-statistics/193546: Determining null and alternative hypotheses
A presidential candidate claims that the proportion of college students who are registered to vote in the upcoming election is at least 63%. Suppose that we want to sample a number of college students and carry out a hypothesis test to see if this claim may be refuted. State the null hypothesis Ho and the alternative hypothesis H1 that we would use for this test.
Ho:
H1:
1 solutions
Answer 145290 by stanbon(57286) on 2009-04-28 15:52:43 (Show Source):
You can put this solution on YOUR website!Determining null and alternative hypotheses
A presidential candidate claims that the proportion of college students who are registered to vote in the upcoming election is at least 63%. Suppose that we want to sample a number of college students and carry out a hypothesis test to see if this claim may be refuted. State the null hypothesis Ho and the alternative hypothesis H1 that we would use for this test.
---------------------------------------------------------
Ho: p >= 0.63
H1: p < 0.63
------------------
Cheers,
Stan H.
|
Functions/193570: Can you please help me with the following problem:
Find the domain of f(g(x)). F(x)= 4/(x-2) and g(x)=3/(x-5)
I know that the domain of f(x) is (-infinity,2)U (2,infinity) and g(x) is (-infinity,5)U (5,infinity)
I know that f(x) has got to be set to the number that the domain cannot use in g(x)
So that would be 5=4/(x-2)
Then multiply each side by (x-2). (x-2)(5)=(4/(x-2))(x-2) this cancel out the denominator.
Then the problem would be 5x-10=4, subtract 10 from each side to isolate the variable. 5x-10+10=4+10 => 5x=14. Then to isolate x, x would have to be divided by 5. 5x/5=14/5 => x=14/5
So would the domain be (-infinity,2)U(2,(14/5))U((14/5),5)U(5,infinity)?
please let me know if any mistakes were made
thanks!
1 solutions
Answer 145289 by stanbon(57286) on 2009-04-28 15:48:07 (Show Source):
You can put this solution on YOUR website!Find the domain of f(g(x)). F(x)= 4/(x-2) and g(x)=3/(x-5)
f[g(x)] = f[3/(x-5)] = 5/[3/(x-5) -2] = 5/[(3-2x+10)/(x-5)]
= 5/[13-2x/(x-5)/
= [5(x-5)]/[13-2x]
-----------------------
Domain: All Real numbers except x = 13/2
==============================================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/193559: This question is from textbook algebra and trigonometry structure and method book 2
``Find the vertex, focus, directrix, and axis of symmetry of each parabola.
x^2+8y+4x-4=0
We have been using the formulas y-k=a(x-h)^2 and x-h=a(y-k)^2 I don't understand
which to use here, even after completing the square and its confusing because I
don't know which is which. please explain and be specific. thank you. We also
use the fact that the focus is F(h,k+c) when a=1/4c. Please explain in these
terms so that I can understand. thank you
1 solutions
Answer 145288 by stanbon(57286) on 2009-04-28 15:42:54 (Show Source):
You can put this solution on YOUR website!Find the vertex, focus, directrix, and axis of symmetry of each parabola.
x^2+8y+4x-4=0
We have been using the formulas y-k=a(x-h)^2 and x-h=a(y-k)^2 I don't understand which to use here, even after completing the square and its confusing because I don't know which is which. please explain and be specific. thank you. We also use the fact that the focus is F(h,k+c) when a=1/4c. Please explain in these terms so that I can understand. thank you
-------------
x^2+8y+4x-4=0
-----------------
Complete the square on the x-terms
x^2 + 4x + ? = -8y+4 + ?
x^2 + 4x + 4 = -8y + 4+4
(x+2)^2 = -8(y-1)
------------------------
Rearrange:
(x-1) = (-1/8)(y+2)^2
h = 1, k= -2, a = -1/8 = (1/4)c
c = -1/2
----------------------
Find the vertex, focus, directrix, and axis of symmetry of each parabola.
Vertex = (h,k) = (1,-2)
Focus = (h+c, k) because this parabola is opening to the left.
Focus = (1-(1/2),-2) = ((1/2),-2)
Directrix: x = h - c = 1+1/2 = 3/2
Axis of symmetry: Horizontal line passing thru the vertex:
y = -2
=================================================================
Cheers,
Stan H.
|
Geometry_Word_Problems/193565: This question is from textbook
Explain how you would find the volume of an irregular
shape.
1 solutions
Answer 145286 by stanbon(57286) on 2009-04-28 15:26:12 (Show Source):
You can put this solution on YOUR website!Explain how you would find the volume of an irregular
shape.
You would have to chop it up (actually or through measurements) into
regular 3 dimensional shapes; then measure the volume of each and add.
-------------------
You could also put the ship in a "regular" container (cube or
cylinder) and measure how much the water rises.
===================================================
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/193557: Could you please provide a detailed explanation of how to solve the following...
5^3log3(2)
1 solutions
Answer 145285 by stanbon(57286) on 2009-04-28 15:18:46 (Show Source):
You can put this solution on YOUR website!provide a detailed explanation of how to solve the following...
5^3log3(2)
Let x = 5^3log2 (2)
--------------
log means "exponent"
log2 (2) is the exponent of 2 that gives you 2.
So, log2 (2) = 1
----------------------
x = 5^3*1
x = 5^3
x = 125
Therefore 5^(3log2 ( 2)) = 125
===============
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/193547: A Coast Gaurd Ship is rushing to the aid of a sailboat. A rescue helicopter is already hovering above the sailboat at an altitude of 125 feet. The angle of elevation from the deck of the Coast Gaurd Ship and the helicopter is 24 degrees. How far is the Coast Gaurd Ship from the sail boat?
1 solutions
Answer 145283 by stanbon(57286) on 2009-04-28 15:13:46 (Show Source):
You can put this solution on YOUR website!A Coast Gaurd Ship is rushing to the aid of a sailboat. A rescue helicopter is already hovering above the sailboat at an altitude of 125 feet. The angle of elevation from the deck of the Coast Gaurd Ship and the helicopter is 24 degrees. How far is the Coast Gaurd Ship from the sail boat?
-----------------------------------
Draw the right triangle picture.
Put the sailboat at the ri. angle vertex ; the helicopter is 125ft above it.
The 24 degree angle is opposite the 125 leg
--------------------------------------------------
Find the length of the base.
tan(24) = 125/base
base = 125/tan(24) = 280.75 ft
=====================================
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/193541: Could you please provide me with a detailed explanation on how to solve the following...
log2 (5) - log2 (15) + log2 (24)
1 solutions
Answer 145282 by stanbon(57286) on 2009-04-28 15:08:29 (Show Source):
You can put this solution on YOUR website!log2 (5) - log2 (15) + log2 (24)
-----------------
logs are exponents.
When you subtract exponents you are dividing some numbers
When you add exponents you are multiplying some numbers
----------------------
Your problem involves subtracting (divide) and adding (multiply):
= logc [5*24/15]
= log2 [8]
= 3
================
Cheers,
Stan H.
Ask, if you do not understand.
===================
|
Probability-and-statistics/193471: 2)In a group of 20 adults, 4 out of 7 women and 2out of 13 men wear glasses. What is the probability that a person chosen at random from the group is a women or someone who wear glasses.
3) A firm of charted accountants has two vacancies for trainee students. In the past , 40% of the students who were offered the training contract have not reported to join.If two students are offered training contract, what is the probability that one will join?
1 solutions
Answer 145247 by stanbon(57286) on 2009-04-28 10:43:03 (Show Source):
You can put this solution on YOUR website!In a group of 20 adults, 4 out of 7 women and 2 out of 13 men wear glasses. What is the probability that a person chosen at random from the group is a women or someone who wear glasses.
---
P(w or g) = P(w) + P(g) - P(w and g)
= 7/20 + 6/20 - 4/20
= 9/20
=============================
3) A firm of charted accountants has two vacancies for trainee students. In the past , 40% of the students who were offered the training contract have not reported to join.If two students are offered training contract, what is the probability that one will join?
P(one will join) = 1 - (P(0 join) + P(both join))
= 1 - (0.6)^2 + (0.4)^2) = 1 - 0.36 - 0.14 = 1 - 0.5 = 0.5
====================================
Cheers,
Stan H.
|
Inequalities/193460: How do I solve the inequality x^3-x^2-6x>0?
1 solutions
Answer 145242 by stanbon(57286) on 2009-04-28 08:35:05 (Show Source):
You can put this solution on YOUR website!solve the inequality x^3-x^2-6x > 0
---------
Factor to find values that x cannot have:
x(x^2-x-6) > 0
x(x-3)(x+2) > 0
x cannot be 0, 3 or -2
-------------------------------
Draw a number line and plot x = -2, 0, and 3
---------------------------------
Test a value in each of the four resulting intervals to
see where solutions are for the inequality:
Test x = -5, you get (-5)^3-(-5)^2-6(-5) > 0 which is false
Test x = -1, you get (-1)^3-(-1)^2-8(-1) > 0 which is true
Test x = 1, you get 1 -1 - 6 > 0 which is false
Test x = 5, you get (5)^3 - (5)^2 -6(5) > 0 which is true
----------------------------------
Solutions are in -2 < x < 0 and 3 < x < +inf
=========================================================
Cheers,
Stan H.
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Numeric_Fractions/193432: i dont now how to resolve algebra fractions
x4-6
_____
5Y_7
1 solutions
Answer 145241 by stanbon(57286) on 2009-04-28 08:19:30 (Show Source):
You can put this solution on YOUR website!x4-6
_____
5Y_7
--------------------------
[x^4/5y] - [6/7]
least common divisor = 35y
---
Rewrite each fraction with the lcd as its denominator:
= [7x^4/lcd] - [5y*7/lcd]
---
Combine the numerators over the lcd:
= [x^4 - 35y]/lcd
= [x^4- 35y]/35y
=====================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/193469: Add -5 to both sides of the inequality 7 > 1. Then divide both sides of the inequality -25 > -30 by -6. Explain what happens in both examples and when the direction of the inequality symbol is reversed.
1 solutions
Answer 145239 by stanbon(57286) on 2009-04-28 07:44:23 (Show Source):
You can put this solution on YOUR website!Add -5 to both sides of the inequality 7 > 1.
You get 2 > -4 which is true
Notice that the order of the inequality has not been affected.
--------------------------------------
Then divide both sides of the inequality -25 > -30 by -6.
You get 25/6 < 5 if you do it correctly
Notice that when you divide an inequality by a negative
the order of the inequality is reversed.
------------------------------------------------
Explain what happens in both examples and when the direction of the inequality symbol is reversed.
==============================
Cheers,
Stan H.
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Probability-and-statistics/193470: 1) A Class contains 10 men and 20 women of which half of the men and half of the women have brown eyes. Find the probability that a person chosen at random is a man or has brown eyes.
1 solutions
Answer 145238 by stanbon(57286) on 2009-04-28 07:38:11 (Show Source):
You can put this solution on YOUR website!A Class contains 10 men and 20 women of which half of the men and half of the women have brown eyes. Find the probability that a person chosen at random is a man or has brown eyes.
--------
P(A or B) = P(A) + P(B) - P(A and B)
--------------
P(man or brown eyes) = P(man) + P(brown eyes) - P(man and brown eyes)
P(m or be) = (10/20) + (10/20) - (5/30)
= 1- (5/30) = 25/30 = 5/6
==============================
Cheers,
Stan H.
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Average/193466: if f(x) = 4/(x+6)`
(a) State the vertical asymptote(s).
Should be -6 right?
(b) State the horizontal asymptote.
0?
(c) Find the inverse function of f.
f(x)=4/(x+6)
y=4/(x+6)
x= 4/(y+6)
x=4(y+6)
x=4y+24
are a, b and c correct?
1 solutions
Answer 145237 by stanbon(57286) on 2009-04-28 07:33:24 (Show Source):
You can put this solution on YOUR website!if f(x) = 4/(x+6)`
(a) State the vertical asymptote(s).
Should be -6 right?
(b) State the horizontal asymptote.
0?
(c) Find the inverse function of f.
f(x)=4/(x+6)
y=4/(x+6)
x= 4/(y+6)
y+6 = 4/x
y = (4/x)-6
------------------
are a, b and c correct?
---------------
a and b are correct
I have corrected "c".
============================
Cheers,
Stan H.
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Quadratic-relations-and-conic-sections/193437: what do they mean by find the exact solutions of each system of equations: x^2+y^2=100 and y=2-x?
1 solutions
Answer 145217 by stanbon(57286) on 2009-04-27 20:57:59 (Show Source):
You can put this solution on YOUR website!what do they mean by find the exact solutions of each system of equations: x^2+y^2=100 and y=2-x?
----------------------------
They mean for you to find x/y pairs that make both equations true.
----------------------------
Substitute y = 2-x in the other equation to solve for "x":
x^2 + (2-x)^2 = 100
x^2 + 4 -4x + x^2 = 100
2x^2-4x-96 = 0
x^2 -2x-48 = 0
(x-8)(x+6) = 0
x = 8 or x = -6
------------------
If x = 8, y = 2-x = 6 giving you point (8,6)
If x = -6, y = 2-x = 9 giving you point (-6,8)
====================================================
Cheers,
Stan H.
|
Rational-functions/193433: FIND ALL ROOTS
List all possible rational zeroes of the function--- 5x^7-7x^3+12x-4
I don't know where to start.
1 solutions
Answer 145216 by stanbon(57286) on 2009-04-27 20:32:13 (Show Source):
You can put this solution on YOUR website!FIND ALL ROOTS
List all possible rational zeroes of the function--- 5x^7-7x^3+12x-4
--------------------------------------------------------------------
If p/q is a rational root of the polynomial,
p is a factor of -4 such as +/-1, +/-2, +/-4
and q is a factor of 5 such as +/-1, +/-5
-------------------------------------------------
So check out +/-1. +/-2, +/-4, +/-1/5, +/-2/5, +/-4/5
--------------------
If none of these is a root, there are no rational roots.
-------------------------------
I do not find any rational roots.
I do find a root around x = 0.36028589....
===============================
Cheers,
Stan H.
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Linear-equations/193431: This question is from textbook
You must state your answer in words. You must set up a system of two equations in two variables.
You must state what the variables represent.
You must show all the steps in solving the system of equations.
Heather made an extra $12,000 last year from a part-time job. She invested part of the money at 7% and the rest at 9%. She made a total of $970 in interest. How much was invested at 7%? Thank You!
1 solutions
Answer 145215 by stanbon(57286) on 2009-04-27 20:11:42 (Show Source):
You can put this solution on YOUR website!Heather made an extra $12,000 last year from a part-time job. She invested part of the money at 7% and the rest at 9%. She made a total of $970 in interest. How much was invested at 7%?
-----
Equations:
Quantity Eq: S + N = 12000
Interest Eq:0.07S + 0.09N = 970
----------------------
Multiply thru the 1st equation by 0.07
0.07S + 0.07N = 0.07*12000
0.07S + 0.09N = 970
----------------------------
Subtract to solve for "N":
0.02N = 970 - 0.07*12000
N = $6500
----
S = 12000 - 6500 = $5500 (amt. invested at 7%
================================================
Cheers,
Stan H.
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Equations/193416: Anna's recipe for apple fritters makes eighteen fritters using two-thirds cup of milk. Anna wants to make six fritters how much milk will she need?
1 solutions
Answer 145211 by stanbon(57286) on 2009-04-27 19:42:42 (Show Source):
You can put this solution on YOUR website!Anna's recipe for apple fritters makes eighteen fritters using two-thirds cup of milk. Anna wants to make six fritters how much milk will she need?
--------------------------------
x/6 = (2/3)/18
x = 4/18
x = 2-9th cup of milk
==========================
Cheers,
Stan H.
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Sequences-and-series/193422: This question is from textbook Algebra and Trignometry
the problem that i need help on states: Sebastian has a test that has 20 questions on it. The first question is worth one point, and each question after the first is worth four points more than the question before it. What is the maximum score Sebastian can obtain? Please help asap!
1 solutions
Answer 145208 by stanbon(57286) on 2009-04-27 19:22:00 (Show Source):
You can put this solution on YOUR website!Sebastian has a test that has 20 questions on it. The first question is worth one point, and each question after the first is worth four points more than the question before it. What is the maximum score
------------------
It is an arithmetic series:
Formulas
S(n) = (n/2)(a+l) ; a is the 1st term and l is the last
a(n) = a(1) + (n-1)d
a(20) = 1 + 19*4 = 77
-------------
S(20) = (20/2)(1 + 77) = 10*78 = 780
------------
Cheers,
Stan H.
|
Equations/193406: I am having a problem solving the following equation in terms of logarithms. Could someone please help?
Problem :
2^2x-4= 3^x-21
1 solutions
Answer 145206 by stanbon(57286) on 2009-04-27 19:07:25 (Show Source):
You can put this solution on YOUR website!I am having a problem solving the following equation in terms of logarithms. Could someone please help?
Problem :
2^(2x-4) = 3^(x-21)
Take the log of both sides:
(2x-4)log2 = (x-21)log3
2xlog2 - 4log2 = xlog3 - 21*log3
----
(2log2-log3)x = 4log(2) - 21*log(3)
0.12494x = -8.81543
x = -70.557281
Cheers,
Stan H.
|
Probability-and-statistics/192692: The mean weight of adult mountain lions is 150lbs with a standard deviation of 8 lbs. A random sample of 50 mountain lions is selected.
a) What is the probability that the mean weight of the sample is less that 150 lbs?
b) What is the probability that the mean weight of the sample is between 149 and 151 lbs?
c) What is the probability that the mean weight of the sample is more than 153lbs?
What is the standard deviation of the sampling distribution?
1 solutions
Answer 145167 by stanbon(57286) on 2009-04-27 15:41:25 (Show Source):
You can put this solution on YOUR website!The mean weight of adult mountain lions is 150lbs with a standard deviation of 8 lbs. A random sample of 50 mountain lions is selected.
a) What is the probability that the mean weight of the sample is less that 150 lbs? Ans: 0.5000
----------------------------
b) What is the probability that the mean weight of the sample is between 149 and 151 lbs? Ans: 0.09948...
-------------------------------------------
c) What is the probability that the mean weight of the sample is more than 153lbs? 0.35393..
-------------------------------------------
What is the standard deviation of the sampling distribution?
Ans: 8/sqrt(50) = 1.13137..
================================
Cheers,
Stan H.
|
Probability-and-statistics/193283: This question is from textbook Elementary Statistics
19.) A biologist knows that the average length of a leaf of a certain full-grown plat is 4 inches. The standard deviation of the population is 0.6 inch. A sample of 20 leaves of that type of plant given a new type of plant food had an average lenght of 4.2 inches. Is there reason to believe that the new food is responsible for a change in the growth of the leaves? use α=0.01. Find the 99% confidence interval of the mean. DO the results occur? Explain. Assume that the variable is approximately normally distributed.
My answer, Ho:µ = 4 and H1:µ ≠4: C.V.= ±2.58
z=1.49; 3.85<µ<4.55; do not reject. There is not enough evidence to support the cail that the growth has change. Is this correct?
10.) The tennis Industry Association reported that 14% of tennis fans were female. If, in a sample of 30 tennis fans, 15 were female, do the results suggest that the percetage may have changed? use α = 0.02.
Please help me with this problems. Thanks.
1 solutions
Answer 145165 by stanbon(57286) on 2009-04-27 15:26:23 (Show Source):
You can put this solution on YOUR website!A biologist knows that the average length of a leaf of a certain full-grown plat is 4 inches. The standard deviation of the population is 0.6 inch. A sample of 20 leaves of that type of plant given a new type of plant food had an average lenght of 4.2 inches. Is there reason to believe that the new food is responsible for a change in the growth of the leaves? use α=0.01. Find the 99% confidence interval of the mean. DO the results occur? Explain. Assume that the variable is approximately normally distributed.
My answer, Ho:µ = 4 and H1:µ ≠4: C.V.= ±2.58
z=1.49; 3.85<µ<4.55; do not reject. There is not enough evidence to support the cail that the growth has change. Is this correct?
-------
Yes, if you are allowed to use a-scores for mean problems.
Most texts require that you use t-scores.
-----------------------------------------------------------
10.) The tennis Industry Association reported that 14% of tennis fans were female. If, in a sample of 30 tennis fans, 15 were female, do the results suggest that the percentage may have changed? use α = 0.02.
Please help me with this problems. Thanks.
Ho: p = 0.14
H1: p is not equal to 0.14
----------------
test statistic: z(15/30) = ((0.5)-0.14)/sqrt[0.14*0.86/30] = 5.6826
Critical value for 2-tail test with alpha = 0.02 : z= +/-2.326
p-value: 2P(z > 5.6826) = 0.00000000665
-------------
Conclusion: since the test stat. is in the reject interval, reject Ho.
===========================================================
Cheers,
Stan H.
|
Probability-and-statistics/193297: 2) A bag contains 9 white and 12 black balls. Find the probability of drawing 5 black balls.
3)A bag contains 2 red, 3 green, 5 blue, and 2 yellow balls. Find the probability that balls of all the colours are represented in a sample if four balls are selected at random.
1 solutions
Answer 145162 by stanbon(57286) on 2009-04-27 15:12:47 (Show Source):
You can put this solution on YOUR website!A bag contains 9 white and 12 black balls. Find the probability of drawing 5 black balls.
# of ways to draw the 5 black balls : 12C5 = 792
# of ways to draw 5 balls without restriction: 21C5 = 20349
Ans: 12C5/21C5 = 0.03892
----------------------------------------
3)A bag contains 2 red, 3 green, 5 blue, and 2 yellow balls. Find the probability that balls of all the colors are represented in a sample if four balls are selected at random.
# of ways to succeed: 2*3*5*2 = 60
# of 4-ball groups in 12: 12C4 = 495
Probability: 60/495 = 0.1212..
==========================================
cheers,
stan H.
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Probability-and-statistics/193344: In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s
employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a twotailed
test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your
conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify
that F = t2 for the slope. (f) In your own words, describe the fit of this regression.
R2 0.202
Std. Error 6.816
n 35
ANOVA table
Source SS df MS F p-value
Regression 387.6959 1 387.6959 8.35 .0068
Residual 1,533.0614 33 46.4564
Total 1,920.7573 34
Regression output confidence interval
variables coefficients std. error t (df = 33) p-value 95% lower 95% upper
Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331
Slope 0.0343 0.0119 2.889 .0068 0.0101 0.0584
1 solutions
Answer 145159 by stanbon(57286) on 2009-04-27 15:02:56 (Show Source):
You can put this solution on YOUR website!In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees.
(a) Write the fitted regression equation. Y 0.0343X + 30.7963
---------------------------
(b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at α = .05.
df = 34 ; I don't have your D-chart.
(c) What is your conclusion about the slope?
Since the p-value is greater than 5% the slope fail to reject Ho: rho = 0
(d) Interpret the 95 percent confidence limits for the slope.
We are 95% confident the slope is between 17.7595 and 43.8331
(e) Verify that F = t2 for the slope. 8.35 = 2.89^2
(f) In your own words, describe the fit of this regression.
It is not very good as seen in R^2 = 0.202. Only 20% of the
variation in Y is explained by the regression equation.
Cheers,
Stan H.
===============================================================
R2 0.202 ; Std. Error 6.816 ; n 35
ANOVA table
Source....... SS... df... MS... F... p-value
Regression 387.6959 1 387.6959 8.35 .0068
Residual 1,533.0614 33 46.4564
Total... 1,920.7573 34
------------------------------------------------
Regression output confidence interval
variables coefficients std. error t (df = 33) p-value 95% lower 95% upper
Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331
Slope .....0.0343 0.0119 2.889 .0068 0.0101.. 0.0584
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Linear-equations/193355: You must state your answer in words. You must set up a system of two equations in two variables.
You must state what the variables represent.
You must show all the steps in solving the system of equations.
An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it. Find the speed of each train.
Thank You!
1 solutions
Answer 145155 by stanbon(57286) on 2009-04-27 14:35:16 (Show Source):
You can put this solution on YOUR website!An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it. Find the speed of each train.
--------------------------
Express DATA:
distance = 60 miles ; rate = E mph ; time = 60/E hrs
-------------------
Local DATA:
distance = 60 miles ; rate = L mph ; time = 60/L hrs
--------------------
Equations:
E = 2L
60/L - 60/E = 2
------------------
Substitute to solve for L:
60/L - 60/2L = 2
Multiply thru by 2L to get:
120 - 60 = 4L
60 = 4L
L = 15 mph (speed of the local train)
E = 2L = 30 mph (speed of the express train)
================================================
Cheers,
Stan H.
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