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Recent problems solved by 'stanbon'
stanbon answered: 57880 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, >>Nexttest/308644: On a spelling test, Mariah had 1/6 of her words wrong. If 15 words were wrong, how many were right?
1 solutions
Answer 220687 by stanbon(57953)   on 2010-05-26 08:46:13 (Show Source):
You can put this solution on YOUR website!On a spelling test, Mariah had 1/6 of her words wrong. If 15 words were wrong, how many were right?
---------------------
If 1/6 were wrong, 5/6 were correct.
---
Equation:
Let "x" be be the total number in the test.
(1/6)x = 15
x = 90
---
# correct = (5/6)90 = 75
================================
Cheers,
Stan H.
================================
|
Probability-and-statistics/308620: City A B C D E F G
Noon Temperature 50 33 27 t 68 44 40
F
The table above shows the noon temperatures for seven cities designated A through G. If the median noon temperature of these cities is 40oF, then the noon temperature for City D could be any of the following EXCEPT
a) 29F b) 35F c) 39F d) 40F e) 42F
1 solutions
Answer 220680 by stanbon(57953) on 2010-05-26 08:31:58 (Show Source):
You can put this solution on YOUR website!City A B C D E F G
Noon Temperature 50 33 27 t 68 44 40
F
The table above shows the noon temperatures for seven cities designated A through G. If the median noon temperature of these cities is 40oF, then the noon temperature for City D could be any of the following EXCEPT
a) 29F b) 35F c) 39F d) 40F e) 42F
-----
List the numbers in numerical order putting 40 in the middle:
27,33,t,40,44,50,68
----
t could not be 42 if 40 is the middle temperature.
====================
Cheers,
Stan H.
|
Radicals/308585: Solve.
9x^4-18x^2+5=0
Simplify your answer. Type an exact answer,using radicals as needed. Rationalize all denominators.
Thank you!
1 solutions
Answer 220649 by stanbon(57953) on 2010-05-25 23:35:49 (Show Source):
You can put this solution on YOUR website!Solve.
9x^4-18x^2+5=0
-------------------
Factor:
9x^4 - 15x^2 - 3x^2 + 5 = 0
---
3x^2(3x^2-5)-(3x^2-5) = 0
(3x^2-5)(3x^2-1) = 0
----
x = +-sqrt(5/3) or x = +- sqrt(1/3)
------
x = +-(1/3)sqrt(15) or x = +-(1/3)sqrt(3)
===============================================
Cheers,
Stan H.
===================
|
Polygons/308578: how many sides does a polygon have if it has an interior angle of 145 degrees
1 solutions
Answer 220647 by stanbon(57953) on 2010-05-25 23:29:38 (Show Source):
You can put this solution on YOUR website!how many sides does a polygon have if it has an interior angle of 145 degrees
---------------------------------------------------
The corresponding exterior angle is 180-145 = 35 degrees
-----------
The sum of all the exterior angles is 360
----
# of exterior angles = 360/35 = 10.2857
===========
Note: That answer makes no sense as it must be a whole number.
Cheers,
Stan H.
|
Probability-and-statistics/308569: Lisa has nine rings in her jewelry box. Five are gold and four are silver. If she randomly selects 3 rings to wear to a party, find each probality:
P(2 silver or 2 gold)
P(at least 2 gold)
1 solutions
Answer 220642 by stanbon(57953) on 2010-05-25 23:04:58 (Show Source):
You can put this solution on YOUR website! Lisa has nine rings in her jewelry box. Five are gold and four are silver. If she randomly selects 3 rings to wear to a party, find each probability:
-------------------------------------
P(2 silver or 2 gold) = P(2 silver) + P(2 gold) = 5C2/9C2 + 4C2/9C2
= [10+6]/36 = 4/9
-----------------------------
P(at least 2 gold) = P(2 gold) + P(3 gold) = 5C2/9C2 + 5C3/9C2
= [10+10]/36 = 5/9
=============================================================
Cheers,
Stan H.
|
Linear-equations/308536: Hello,
I am trying to solve quadratic equations by graphing, I have been looking at the example of the book and makes no sence to me.
the problem is asking me to use a graph to estimate the solutions of the equation, and to check my solutions algebraically.
1 solutions
Answer 220610 by stanbon(57953) on 2010-05-25 21:07:06 (Show Source):
You can put this solution on YOUR website!use a graph to estimate the solutions of the equation, and to check my solutions algebraically.
-4x^2-8x=12
-----
Divide thru by -4 to simplify the equation.
---
x^2 + 2x = -3
---
Graph the two equations
y = x^2+2x
and
y = -3
-------------------
-------------------
Find the points of intersection of the two graphs.
Note: The graphs do not intersect; there is no Real
Number solutions for the problem.
================================
Solving analytically:
x^2 + 2x +3 = 0
x = [-2 +- sqrt(4 -4*3)]/2
---
x = [-2 +- sqrt(-8)]/2
x = [-2 +-2isqrt(2)]/2
---
x = [-1 +- isqrt(2)]
----
Note: These solutions are complex numbers.
==============================================
Cheers,
Stan H.
|
Equations/308529: cream has approximately 22% of butterfat.how many gallons of cream must be mixed with 2% milk to give 20 gallons of milk containing 4% of butterfat
1 solutions
Answer 220607 by stanbon(57953) on 2010-05-25 20:52:41 (Show Source):
You can put this solution on YOUR website!cream has approximately 22% of butterfat.how many gallons of cream must be mixed with 2% milk to give 20 gallons of milk containing 4% of butterfat
-------------------------
Equation:
fat + fat = fat
0.22x + 0.02(20-x) = 0.04*20
-----
Multiply thru by 100 to get:
22x + 2*20 - 2x = 4*20
20x = 2*20
x = 2 gallons (amt. of cream needed in the mixture)
=============================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/308527: divide using long division
(x^3+8x^2+x-8)/ (x+1) what do u divide the second # by?
1 solutions
Answer 220605 by stanbon(57953) on 2010-05-25 20:45:40 (Show Source):
You can put this solution on YOUR website!divide using long division
(x^3+8x^2+x-8)/ (x+1) what do u divide the second # by?
----------------------
Using Synthetic Division:
-1)....1....8....1....-8
........1....7....-6...|-2
===============================
Quotient: x^2+7x-6
Remainder: -2
================================
Cheers,
Stan H.
|
Quadratic_Equations/308520: I am trying to solve the following: x2 -4x -3 = 0. I can get as far as 4 plus or minus the sqrt of 28 over 2. I don't understand why this becomes 2 plus or minus the sqrt of 7. It seems to me that it should be 2 plus or minus the sqrt of 14.
Thanks. Marieann
1 solutions
Answer 220604 by stanbon(57953) on 2010-05-25 20:40:38 (Show Source):
You can put this solution on YOUR website!I am trying to solve the following: x^2 -4x -3 = 0. I can get as far as 4 plus or minus the sqrt of 28 over 2. I don't understand why this becomes 2 plus or minus the sqrt of 7. It seems to me that it should be 2 plus or minus the sqrt of 14.
------------------------------------------
Quadratic Formula:
x = [-b +- sqrt(b^2-4ac)]/(2a)
---
x = [4 +- sqrt(4^2 - 4*1*-3)]/(2*1)
---
x = [4 +- sqrt(28)]/2
---
x = [4 +- 2sqrt(7)]/2
---
x = [2+sqrt(7)] or x = [2-sqrt(7)]
====================================
Cheers,
Stan H.
====================================
|
Triangles/308524: IF 2 sides of a triangle measure 12cm and 7cm, which of the following CANNOT be the Perimeter of the triangle?
A. 29cm
B.34cm
C.37 cm
D. 38cm
1 solutions
Answer 220599 by stanbon(57953) on 2010-05-25 20:30:44 (Show Source):
You can put this solution on YOUR website!IF 2 sides of a triangle measure 12cm and 7cm, which of the following CANNOT be the Perimeter of the triangle?
------------------------------------
Let "x" be the 3rd side of the triangle:
12-7 < x < 12+7
5 < x < 19
--------
Perimeter = 12 + 7 + x = 19+x
x = perimeter - 19
-----
If A is true x = 29-19 = 10 which is allowable for "x".
If B is true x = 34-19 = 15 which is allowable for "x".
If C is true x = 37-19 = 18 which is allowable for "x".
If D is true x = 38-19 = 19 which is not allowable for "x".
===========================================================
Cheers,
Stan H.
===========================================================
A. 29cm
B.34cm
C.37 cm
D. 38cm
|
Numeric_Fractions/308443: Could you please help me with these 2 question.
1. When MUST we have a proper or an improper fraction? for addition, subtraction, multiplication, or division?
2. Translate in to an algebra equation: 5 less than two thirds of a number is three.
1 solutions
Answer 220524 by stanbon(57953) on 2010-05-25 16:38:07 (Show Source):
You can put this solution on YOUR website!1. When MUST we have a proper or an improper fraction? for addition, subtraction, multiplication, or division?
addition can be done with either
subtraction can be done with either
Multiplication can be done with either
division can be done with either
--------------------------------------------------------------
2. Translate into an algebraic equation: 5 less than two thirds of a number is three.
Equation:
(2/3)x-5 = 3
========================
Cheers,
Stan H.
|
Radicals/308442: four times the square root of the quantity of 3a+4 equals a+13. I know the answers are 7 and 15 but cannot figure out how to get them algebraically
1 solutions
Answer 220519 by stanbon(57953) on 2010-05-25 16:29:07 (Show Source):
You can put this solution on YOUR website! four times the square root of the quantity of 3a+4 equals a+13. I know the answers are 7 and 15 but cannot figure out how to get them algebraically
--------------------
4(sqrt(3a+4)) = a+13
--------
Square both sides to get:
16(3a+4) = a^2+26a+169
---
48a+64 = a^2+26a+169
---
a^2 - 22a + 105 = 0
---
(a-15)(a-7) = 0
---
a = 15 or a = 7
===================
Cheers,
Stan H.
|
Functions/308441: Please help me to figure this one out and more importantly understand it in laymens terms. Let f(x)=x to the second power + [x] Evaluate f(2), f(-2) I used substitution but this does not seem right.
1 solutions
Answer 220516 by stanbon(57953) on 2010-05-25 16:23:05 (Show Source):
You can put this solution on YOUR website!Please help me to figure this one out and more importantly understand it in laymens terms. Let f(x)=x^2 + [x]
-----
Evaluate f(2), f(-2) I used substitution but this does not seem right.
f(2) = 2^2+2 = 4+2 = 6
---
f(-2) = (-2)^2+(-2) = 4-2 = 2
=================================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/308435: how do I complete the square on this problem?
4x^2+2y^2-8x+4y-2=0
1 solutions
Answer 220515 by stanbon(57953) on 2010-05-25 16:19:51 (Show Source):
You can put this solution on YOUR website!complete the square on this problem?
4x^2+2y^2-8x+4y-2=0
---
Simplify by dividing thru by 2 to get:
2x^2 - 4x + y^2 + 2y = 1
----
2(x^2-2x+?) + y^2+2y + 1 = 1 + 2? + ?
---
2(x^2-2x+1) + y^2+2y+1 = 1 + 2*1 + 1
---
2(x-1)^2 + (y+1)^2 = 4
Divide thru by 4 to get:
----
(x-1)^2/2 + (y+1)/4 = 1
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Cheers,
Stan H.
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Expressions-with-variables/308429: Please help me solve the following equation....I'm beginning to think the solution in the answer book is wrong:
x/x-1 minus 1/x = 3/2.....solve for x.
Thanks in advance
1 solutions
Answer 220512 by stanbon(57953) on 2010-05-25 16:11:39 (Show Source):
You can put this solution on YOUR website!Please help me solve the following equation....I'm beginning to think the solution in the answer book is wrong:
x/(x-1) minus 1/x = 3/2.....solve for x.
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Multiply both sides by 2x(x-1) to get:
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2x^2 - 2(x-1) = 3x(x-1)
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2x^2 -2x + 2 = 3x^2 - 3x
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x^2 - x - 2 = 0
---
(x-2)(x+1) = 0
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Potential answers:
x = -1 or x = 2
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Checking you will find that both are answers.
===========================
Cheers,
Stan H.
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Average/306689: The average age of five boys is 15 years. A six boys joins them, making the average age 15 years and 6 months. What is the age of this sixth boy ?
A 15 B 16 C 18 D 17 E 14
1 solutions
Answer 219437 by stanbon(57953) on 2010-05-20 05:58:33 (Show Source):
You can put this solution on YOUR website!The average age of five boys is 15 years.
The sum of their ages is 5*15 = 75 yrs.
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A sixth boys joins them, making the average age 15 years and 6 months.
The sum of their ages is now 6*15.5 = 93
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What is the age of this sixth boy ?
He is 93-75 = 18
=========================
Cheers,
Stan H.
=========================
A 15 B 16 C 18 D 17 E 14
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Graphs/306684: Ok I need another intersection again.
For graph the inequalities 9x+8y<72 ans -7x-44<=28
I need to know what their intersection numbers are on the graph! I cannot figure it out!
Help Please!
1 solutions
Answer 219435 by stanbon(57953) on 2010-05-20 05:55:02 (Show Source):
You can put this solution on YOUR website!Ok I need another intersection again.
For graph the inequalities 9x+8y<72 ans -7x-44<=28
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Graph 9x+8y<72
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Graph -7x-44<= 28
Note: Your post did not contain a "y" so you get a one-dimensional graph:
x >= (-44/7)-4
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Cheers,
Stan H.
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Probability-and-statistics/306681: Only 1% of all American households do not have a color television set. A television marketing analyst randomly selects 160 American households.
How many households would he expect to not have a television set?What is the probability that 8 or more households do not have a television set?What is the probability than between 2 and 6 households (inclusive) do not have a color television set?
thank you!
1 solutions
Answer 219433 by stanbon(57953) on 2010-05-20 05:47:09 (Show Source):
You can put this solution on YOUR website!Only 1% of all American households do not have a color television set. A television marketing analyst randomly selects 160 American households.
How many households would he expect to not have a television set?
---
E(x) = np = 160*0.01 = 1.6
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What is the probability that 8 or more households do not have a television set?
Binomial problem with n = 160; p = 0.01
P(8 <= x <= 160) = 1 - P(0<= x <= 7) = 0.000232..
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What is the probability than between 2 and 6 households (inclusive) do not have a color television set?
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P(2<= x <= 6) = binomcdf(160,0.01,6)-binomcdf(160,0.01,1) = 0.4748
===========================
Cheers,
Stan H.
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Probability-and-statistics/306576: There are 10 marbles in a bag, there are 2 times as many green marbles at there are yellow.How many green marbles and how many yellow marbles.
1 solutions
Answer 219403 by stanbon(57953) on 2010-05-19 22:31:47 (Show Source):
You can put this solution on YOUR website!There are 10 marbles in a bag, there are 2 times as many green marbles at there are yellow.How many green marbles and how many yellow marbles.
----------------------
Equations:
g + y = 10 marbles
g = 2y
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Substitute for "g" and solve for "y":
2y + y = 10
3y = 10
y = 3 1/3 (# of yellow marbles)
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Comment: The answer does not make much sense
as you cannot have 1/3 of a yellow marble.
==============================
Cheers,
Stan H.
==============================
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Probability-and-statistics/306569: The graduate selection committee wants to select the top10% of applicants on standardize test with a mean of 500 and a standard deviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that the standardize test is normally distributed?
1 solutions
Answer 219401 by stanbon(57953) on 2010-05-19 22:24:54 (Show Source):
You can put this solution on YOUR website!The graduate selection committee wants to select the top10% of applicants on standardize test with a mean of 500 and a standard deviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that the standardize test is normally distributed?
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Find the z-value that has a right tail of 10%.
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Ans: z = 1.282
--------------------------------
Find the corresponding x-value:
x = zs+u
x = 1.282*100+500
x = 628.2
----------------------
Cheers,
Stan H.
======================
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Probability-and-statistics/306594: Bob takes an online IQ test and finds that his IQ according to the test is 134. Assuming that the mean IQ is 100, the standard deviation is 15, and the distribution of IQ scores is normal, what proportion of the population would score tigher than Bob? Lower than Bob?
1 solutions
Answer 219400 by stanbon(57953) on 2010-05-19 22:18:50 (Show Source):
You can put this solution on YOUR website!Bob takes an online IQ test and finds that his IQ according to the test is 134. Assuming that the mean IQ is 100, the standard deviation is 15, and the distribution of IQ scores is normal, what proportion of the population would score tigher than Bob? Lower than Bob?
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z(134) = (134-100)/15 = 34/15
----
P(x > 134) = P(z > 34/15) = 0.0117
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P(x < 134) = P(z < 34/15) = 0.9883
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Cheers,
Stan H.
=========================
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Probability-and-statistics/306628: Can you please explain the meaning and usage of Σ (upper case “sigma”)
and Π (upper case “pi”) in statistic.
Also, what are the equations written above and below the symbols mean?
:)
1 solutions
Answer 219399 by stanbon(57953) on 2010-05-19 22:13:47 (Show Source):
You can put this solution on YOUR website!I believe that if you Google "sigma notation"
the meaning of that notation will be explained
and you will see examples.
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Cheers,
Stan H.
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Probability-and-statistics/306605:
Nine percent of men and .25 % of women cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals. If 6 men are randomly selected for a study of traffic signal perceptions, find the probability that exactly 2 of them cannot distinguish between red and green.
1 solutions
Answer 219398 by stanbon(57953) on 2010-05-19 22:09:29 (Show Source):
You can put this solution on YOUR website!Nine percent of men and .25 % of women cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals.
If 6 men are randomly selected for a study of traffic signal perceptions, find the probability that exactly 2 of them cannot distinguish between red and green.
---------------
Binomial Problem with n = 6 ; p = 0.09 ; x = 2
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P(x=2) = 6C2*0.09^2*0.91^4 = 0.0833
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Cheers,
Stan H.
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Geometric_formulas/306617: Sorry for the lact of picture...I don't know how to post it. I do know that it is an oblique triangle where a is the bottom (width) and b and c are on the left and right side, respectively. a = 5, b = 6, and angle between a and b = 1/3pi. Find c. Thank you in advance.
1 solutions
Answer 219397 by stanbon(57953) on 2010-05-19 22:00:09 (Show Source):
You can put this solution on YOUR website!Sorry for the lact of picture...I don't know how to post it. I do know that it is an oblique triangle where a is the bottom (width) and b and c are on the left and right side, respectively. a = 5, b = 6, and angle between a and b = 1/3pi. Find c.
-------------------
Use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cos(pi/3)
---
c^2 = 25 + 36 - 2*5*6*(1/2)
---
c^2 = 61 - 30
---
c = sqrt(31)
==================
Cheers,
Stan H.
==================
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Probability-and-statistics/306615: For μ = 60 and σ = 7
1. z score of 78
2. z score of 45
3. probability of 59
4. probability of 62
5. score at z = 1.64
6. score at z = –1.96
7. percent less than 73
8. proportion between 45 and 78
1 solutions
Answer 219394 by stanbon(57953) on 2010-05-19 21:50:53 (Show Source):
You can put this solution on YOUR website!For μ = 60 and σ = 7
1. z score of 78 = (78-60)/8 = 18/8
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2. z score of 45 = (45-60)/8 = -15/8
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3. probability of 59 = 0
------------------------------------
4. probability of 62 = 0
------------------------------------
5. score at z = 1.64
x = 1.64*8+60 = 75.12
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6. score at z = –1.96
x = -1.96*8+60 = 44.32
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7. percent less than 73
z(73) = (73-60)/8 = 13/8
Percent < 73 = P(z < 13/8) = normalcdf(-100,13/8) = 0.9479
--------------------------------------------------------
8. proportion between 45 and 78
z(45) = (45-60)/8 = -15/8
z(78) = (78-60)/8 = 18/8
--
P(45 < x < 78) = P(-15/8 < z < 18/8) = 0.9574
=======================================================
Cheers,
Stan H.
======================================
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Probability-and-statistics/306608: Suppose there are 10 balls in an urn, 4 blue,4 red , 2 green. The balls are also numbered 1 to 10. How many ways are there to select an ordered sample of 4 balls without replacement such that there are 2 blue balls and 2 red balls in the sample?
1 solutions
Answer 219393 by stanbon(57953) on 2010-05-19 21:40:32 (Show Source):
You can put this solution on YOUR website!Suppose there are 10 balls in an urn, 4 blue,4 red , 2 green. The balls are also numbered 1 to 10. How many ways are there to select an ordered sample of 4 balls without replacement such that there are 2 blue balls and 2 red balls in the sample?
---
# of ways to select 2 blue balls: 4C2 = 6
# of ways to select 2 red balls:: 4C2 = 6
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# of ways to select 4 random balls from 10 : 10C4 = 210
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P(2 blue and 2 red) = (6*6)/210 = 36/210 = 0.17
====================================================
Cheers,
Stan H.
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