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Recent problems solved by 'stanbon'
stanbon answered: 57911 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 , 57900..57929, >>NextProbability-and-statistics/695855: bags of mixed lollies are being made by selecting:
2 different lolly pops from a choice of 4 lollypops; 3 different caramels from a choice of 6 caramels and 5 jellybeans from 10 different flavours.
how many different types of mixed lolly bags can be made?
1 solutions
Answer 428710 by stanbon(57984)   on 2012-12-19 12:53:15 (Show Source):
You can put this solution on YOUR website! bags of mixed lollies are being made by selecting:
2 different lolly pops from a choice of 4 lollypops; 3 different caramels from a choice of 6 caramels and 5 jellybeans from 10 different flavours.
how many different types of mixed lolly bags can be made?
---
# of ways to get 2 pops from 4: 4C2 = 6
# of ways to get 3 cara from 6: 6C3 = (6*5*4)(1*2*3) = 20
# of ways to get 5 jelly from 10: 10C5 = 252
====
Total # of mixed bags: 6*20*252 = 30,240
==================
Cheers,
Stan H.
==================
|
Probability-and-statistics/695876: Ms. Swift's reading class can read an average of 170 words per minute with a standard deviation of 25 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would need to read in order to get the award? Assume the data is normally distributed.
1 solutions
Answer 428709 by stanbon(57984) on 2012-12-19 12:48:49 (Show Source):
You can put this solution on YOUR website!Ms. Swift's reading class can read an average of 170 words per minute with a standard deviation of 25 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would need to read in order to get the award? Assume the data is normally distributed.
-------------------
Find the z-value with a left-tail of 0.97.
invNorm(0.97) = 1.8808
-------
Solve for x using x = z*s + u
x = 1.8808*25 + 170
x = 217 words per minute
=========================
Cheers,
Stan H.
===============
|
Probability-and-statistics/695878: The average hourly wage of workers at a fast food restaurant is $7.75. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $7.50 per hour?
1 solutions
Answer 428706 by stanbon(57984) on 2012-12-19 12:44:44 (Show Source):
You can put this solution on YOUR website!The average hourly wage of workers at a fast food restaurant is $7.75. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $7.50 per hour?
-------
z(7.5) = (7.5-7.75)/0.45 = -0.5556
--------
P(x > 7.50) = P(z > -0.5556) = 0.7107
=======================================
Cheers,
Stan H.
|
Probability-and-statistics/695879: Of the members of a Boy scout troop, 15% have received the First Aid merit badge. If 40 Boy Scouts are selected at random, use the normal distribution as an approximation to the binomial distribution to find the probability that four or more will have the First Aid merit badge.
MULTIPLE CHOICE:
A)86.6%
B)81.3%
C)36.6%
D)31.3%
1 solutions
Answer 428704 by stanbon(57984) on 2012-12-19 12:40:57 (Show Source):
You can put this solution on YOUR website!Of the members of a Boy scout troop, 15% have received the First Aid merit badge. If 40 Boy Scouts are selected at random, use the normal distribution as an approximation to the binomial distribution to find the probability that four or more will have the First Aid merit badge.
------
u = np = 0.15*40 = 6
s = sqrt(6*0.85) = 2.258
-------------------------------
z(3.5) = (3.5-6)/[2.258] = -1.1072
-----
P(4<= x <=15) = P(-1.1072<= z <= 100) = 0.8659
-------------
Cheers,
Stan H.
===============
MULTIPLE CHOICE:
A)86.6%
B)81.3%
C)36.6%
D)31.3%
|
Probability-and-statistics/695896: In a recent survey 80% of the citizens in the community favored the building of a municipal golf course. If you ask 15 citizens about this project find the probability that
a. at least 9 favor the project
b. exactly 9 favor the project
c. less than 9 favor the project
I cannot remember how to calculate this formula or use minitab to calculate it for me. Can you help?
1 solutions
Answer 428702 by stanbon(57984) on 2012-12-19 12:32:04 (Show Source):
You can put this solution on YOUR website!In a recent survey 80% of the citizens in the community favored the building of a municipal golf course. If you ask 15 citizens about this project find the probability that:
Binomial Problems with n = 15 ; p(favor) = 0.80
--------------------
I use a TI-84 calculator.
---------------------------------
a. at least 9 favor the project
P(9<= x <=15) = 1-P(0<= x <=8) = 1 - binomcdf(15,0.8,8) = 0.9819
------------------------------------------
b. exactly 9 favor the project
P(x = 9) = binompdf(15,0.8,9) = 0.0430
------------------------------------------
c. less than 9 favor the
P(0<= x <=8) = binomcdf(15,0.8,8) = 0.0181
===================================
Cheers,
Stan H.
===============
|
Probability-and-statistics/695916: There are 60 tables in a restaurant, with 25% of them seating 2 people. The tables remaining seat 4 people. How many seats are there in the restaurant?
1 solutions
Answer 428701 by stanbon(57984) on 2012-12-19 12:20:33 (Show Source):
You can put this solution on YOUR website!There are 60 tables in a restaurant, with 25% of them seating 2 people. The tables remaining seat 4 people. How many seats are there in the restaurant?
------
Tables Equation: t + f = 60
t = 0.25(t+f)
t = 0.25t + 0.25f
0.75t = 0.25f
t = (1/3)f
--------
Substitute for "t" and solve for "f":
(1/3)f + f = 60
(4/3)f = 60
f = 45 (# of tables that seat 4 people)
---------
Solve for "t":
t + f = 60
t + 45 = 60
t = 15 (# of tables that seat 2 people)
======================
Cheers,
Stan H.
======================
|
Trigonometry-basics/695503: A)write the equation cos(2 theta)-sin(theta)=0 in terms of sin (theta)
B) Hence solve cos(2 theta)-sin(theta)=0 for 01 solutions
Answer 428645 by stanbon(57984) on 2012-12-18 21:35:26 (Show Source):
You can put this solution on YOUR website!A)write the equation cos(2 theta)-sin(theta)=0 in terms of sin (theta)
----
cos(2x) - sin(x) = 0
---
1 - 2sin^2(x) - sin(x) = 0
----
2sin^2(x)+sin(x) -1 = 0
Factor:
(2sin(x)-1)(sin(x)+1) = 0
-----------------------
sin(x) = 1/2 or sin(x) = -1
x = 30 or 120 degrees OR x = 270 degrees
==========================================
Cheers,
Stan H.
==============
|
Trigonometry-basics/695548: How do I find the opposite sine of -pi divided by 3 without using a calculator or the opposite sine of the positive sine of 2pi divided by 3?
1 solutions
Answer 428644 by stanbon(57984) on 2012-12-18 21:17:11 (Show Source):
You can put this solution on YOUR website!How do I find the opposite sine of -pi divided by 3 without using a calculator or the opposite sine of the positive sine of 2pi divided by 3?
----------
find the opposite sine of -pi divided by 3 without using a calculator
sin(-pi/3) = -sin(pi/3) = -sin(60 degrees) = -1/sqrt(3)
----
sin((2/3)pi) = sin(120 degrees) = sin(30) = 1/2
---------------------
Cheers,
Stan H.
=====================
|
Trigonometry-basics/695750: Write down the period of the graph of y = 3/(2+cos^2 2x) (that's 2 plus cosine squared 2x in case it isn't clear) and also the coordinates of a maximum value of y.
Okay so I've always been confused about the period thing. The equation is 2pi/b, where the b value is the frequency, but I'm not sure how to use that. And also, to find the coordinates of the max, you take the derivative and set it equal to 0 and find the values that make that true and then test for if it's a minimum or maximum, correct?
1 solutions
Answer 428641 by stanbon(57984) on 2012-12-18 20:37:23 (Show Source):
You can put this solution on YOUR website!Write down the period of the graph of y = 3/(2+cos^2 2x) (that's 2 plus cosine squared 2x in case it isn't clear) and also the coordinates of a maximum value of y.
Okay so I've always been confused about the period thing. The equation is 2pi/b, where the b value is the frequency, but I'm not sure how to use that. And also, to find the coordinates of the max, you take the derivative and set it equal to 0 and find the values that make that true and then test for if it's a minimum or maximum, correct?
------
The (2pi)/b for the period relates to f(x) = acos(2x+b)=c, not to
y = 3/(2+cos^2 2x).
----
What you say about the derivative to find the max or min is true.
Cheers,
Stan H.
===============
|
Mixture_Word_Problems/695706: a grocer mixed nuts worth $.80 per pound with nuts worth $.50 per pound. How many pounds of each did he use to make a mixture of 30 pounds to sell at $.75 per pound?
1 solutions
Answer 428621 by stanbon(57984) on 2012-12-18 19:02:59 (Show Source):
You can put this solution on YOUR website!a grocer mixed nuts worth $.80 per pound with nuts worth $.50 per pound. How many pounds of each did he use to make a mixture of 30 pounds to sell at $.75 per pound?
==================
Using 2 equations:
Quantity: a + b = 30 lbs
Value:::80a + 50b = 75*30
------------
Modify the equations for elimination:
8a + 8b = 8*30
8a + 5b = 3*75
------
Subtract and solve for "b":
3b = 15
b = 5 lbs (amt of 50 cent nuts)
--------
Solve for "a" using a + b = 30
a + 5 = 30
a = 25 lbs (amt. of 80 cent nuts)
==============
Cheers,
Stan H.
================
|
Exponents/695699: Multiply.
(1/5x^4y^3)(y^2z^4)(20x^2z^3)
I do not understand the steps or where to begin
1 solutions
Answer 428609 by stanbon(57984) on 2012-12-18 18:13:19 (Show Source):
You can put this solution on YOUR website!Multiply.
(1/5x^4y^3)(y^2z^4)(20x^2z^3)
----------
[(1/5)(1)(20)][x^4*1*x^2][y^3*y^2*1][1*z^4*z^3]
----------
= (4)(x^6)(y^5)(z^7)
------
= 4x^6y^5z^7
=======================
Cheers,
Stan H.
====================
|
Exponents/695698: This is what I have so far before I got confused
multiply
(2r+3s)^2
1st step: (2r+3s)(2r+3s)
2nd step: 2r^2 9s^2
this is where I got confused:
Do I multiply the 3s and 2r? If so do I get
6s^2r^2 or 5s^2r^2
1 solutions
Answer 428608 by stanbon(57984) on 2012-12-18 18:05:55 (Show Source):
|
Exponents/695689: I started this problem then I got stuck
multiply
(2r+3s)^2
1st step: (2r+3s)(2r+3s)
2nd step: 2r^2 9s^2
this is where I got confused:
Do I multiply the 3s and 2r? If so do I get
6s^2r^2 or 5s^2r^2
1 solutions
Answer 428607 by stanbon(57984) on 2012-12-18 18:03:18 (Show Source):
You can put this solution on YOUR website!multiply
(2r+3s)^2
1st step: (2r+3s)(2r+3s)
Use FOIL:
F: 2r*2r = 4r^2
O: 2r*3s = 6rs
I: 2r*3s = 6rs
L: 3s*3s = 9s^2
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Combine those products to get: 4r^2 + 12rs + 9s^2
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Cheers,
Stan H.
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Quadratic_Equations/695678: find b if you happen to know the maximum y-value of the function y= -4x^2 + bx -1 is 21.
1 solutions
Answer 428606 by stanbon(57984) on 2012-12-18 17:52:46 (Show Source):
You can put this solution on YOUR website!find b if you happen to know the maximum y-value of the function
y= -4x^2 + bx -1 is 21
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Comment:
Maximum occurs where x = -b/(2a) = -b/(-8) = b/8
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Max = f(b/8) = -4(b/8)^2 + b(b/8) -1 = 21
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-4(b^2/64) + b^2/8 = 22
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-b^2/16 +2(b^2/16) = 22
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-b^2 + 2b^2 = 16*22
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b^2 = 16*22
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b = 4*sqrt(22)
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======================
Cheers,
Stan H.
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test/695652: Describe how the graph of y=2log3(x-4)+2 compare to parent graph. Tell if any changes in range, domain, or asymptotes
1 solutions
Answer 428598 by stanbon(57984) on 2012-12-18 17:27:18 (Show Source):
You can put this solution on YOUR website! Describe how the graph of y=2log3(x-4)+2 compare to parent graph.
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1st: shift 4 units to the right because of x-4
2nd: Multiply all the y values by 2
3rd: Make a vertical shift of 2
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Tell if any changes in
range::: no change
domain::: x > 4 instead of x = 0
asymptotes::: x = 4 instead of x = 0
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Cheers,
Stan H.
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Angles/695650: Angle E and angle T and supplementary. If angle E is 23 degrees more than twice the complement of T, what are the two angles?
1 solutions
Answer 428587 by stanbon(57984) on 2012-12-18 16:42:18 (Show Source):
You can put this solution on YOUR website!Angle E and angle T and supplementary.
E = 180-T
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If angle E is 23 degrees more than twice the complement of T, what are the two angles?
E = 2(90-T) + 23
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Substitute for E and solve for T:
180-T = 2(90-T)+23
180 - T = 180 - 2T + 23
T = 23 degrees
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E = 180-T = 157 degrees
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Cheers,
Stan H.
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Linear-systems/695649: I am stuck on this Linear Systems problem.
Roy and Steve have the same number of coins. Roy has only dimes and Steve has only quarters. If Steve has $1.80 more than Roy does, how many coins does each have?
Thanks in advance
1 solutions
Answer 428584 by stanbon(57984) on 2012-12-18 16:34:25 (Show Source):
You can put this solution on YOUR website!Roy and Steve have the same number of coins. Roy has only dimes and Steve has only quarters. If Steve has $1.80 more than Roy does, how many coins does each have?
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Equation:
Quantity Eq:: d = q
Value Eq:: 25q = 10d +180 cents
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Substitute for "d" and solve for "q":
25d = 10d + 180
15d = 180
d = 12 (# of dimes Roy has)
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q = 12 (# of quarters Steve has)
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Cheers,
Stan H.
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Quadratic_Equations/695644: Please help me solve by completing the squares:
1 solutions
Answer 428582 by stanbon(57984) on 2012-12-18 16:26:23 (Show Source):
You can put this solution on YOUR website!(x^2) - (6x) = (27)
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x^2 - 6x + (6/2)^2 = 27 + (6/2)^2
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x^2 -6x + 9 = 27 + 9
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(x-3)^2 = 36
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x-3 = 6 or x - 3 = -3
x = 9 or x = 0
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(2x^2) - (9x) + (9) = (0)
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2[x^2 - (9/2)x + ?] = -9 + 2?
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2[x^2 -(9/2)x + (9/4)^2] = -9 + 2(9/4)^2
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2(x-(3/2))^2 = [-9*16 + 162]/16
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2(x-(3/2))^2 = 1/2
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(x-(3/2))^2 = 1/4
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x-(3/2) = 1/2 or x-(3/2) = -1/2
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x = 2 or x = 1
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Cheers,
Stan H.
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Quadratic-relations-and-conic-sections/695641: Please graph, label the vertex, the axis of symmetry and the x and y intercepts for
G(x)=(x+6)^2-1
1 solutions
Answer 428577 by stanbon(57984) on 2012-12-18 16:12:34 (Show Source):
You can put this solution on YOUR website!Please graph, label the vertex, the axis of symmetry and the x and y intercepts for
G(x)=(x+6)^2-1
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Vertex:: (-6,-1)
Axis: x = -6
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x-int ???
Let y = 0
(x+6)^2 = 1
x+6 = 1 or x+6 = -1
x = -5 or x = -7
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y-int ???
Let x = 0
y = 6^2-1 = 35
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Cheers,
Stan H.
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Functions/695639: The Output of a function is 7 more than 3 times the input. Find the input when the output is -8
1 solutions
Answer 428575 by stanbon(57984) on 2012-12-18 16:08:37 (Show Source):
You can put this solution on YOUR website!The Output of a function is 7 more than 3 times the input. Find the input when the output is -8
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Equation:
y = 3x+7
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Solve: -8 = 3x+7
3x = -15
x = -5 (that's the input)
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Cheers,
Stan H.
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Triangles/695634: The distance betweenn Atlanta and Cleveland is about 554 miles. The distance between Cleveland and New York City is about 399 miles. Use the Triangle Inequality Theorem to find the possible values of the distance between New York and Atlanta.
1 solutions
Answer 428572 by stanbon(57984) on 2012-12-18 16:05:06 (Show Source):
You can put this solution on YOUR website!the longest side is always shorter than the sum of the other two.
---------------------The distance betweenn Atlanta and Cleveland is about 554 miles. The distance between Cleveland and New York City is about 399 miles. Use the Triangle Inequality Theorem to find the possible values of the distance between New York and Atlanta.
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That distance is < 554+399 = 953 miles
That distance is > 554-399 = 155 miles
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Cheers,
Stan H.
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Travel_Word_Problems/695613: I need the equation and step by step directions to solve this word problem.
Two cars leave a garage traveling in opposite directions. One car leaves at 8am and averages 60mph. The other car leaves at 9am and averages 50mph. At what time will they be 225 miles apart?
1 solutions
Answer 428560 by stanbon(57984) on 2012-12-18 14:53:34 (Show Source):
You can put this solution on YOUR website!Two cars leave a garage traveling in opposite directions. One car leaves at 8am and averages 60mph. The other car leaves at 9am and averages 50mph. At what time will they be 225 miles apart?
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Early car DATA:
rate = 60 mph ; time = x hrs ; distance = 60x miles
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Later car DATA:
rate = 50 mph ; time = x-1 hrs ; distance = 50(x-1) miles
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Equation:
distance + distance = 225 miles
60x + 50(x-1) = 225
110x = 275
x = 2.5 hrs
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Ans: 8:00 AM + 2.5 hrs = 10:30 AM
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Cheers,
Stan H.
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Numeric_Fractions/695495: how do i convert 2 6/17, -5 3/4, 8 2/6, 5 3/9, 12 49/50, -7 2/8,into an improper fraction, and reduce the final answer if necessary.
1 solutions
Answer 428539 by stanbon(57984) on 2012-12-18 09:31:00 (Show Source):
You can put this solution on YOUR website! convert 2 6/17, -5 3/4, 8 2/6, 5 3/9, 12 49/50, -7 2/8,into an improper fraction, and reduce the final answer if necessary.
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2 6/17 = (2*17+6)/17 = 40/16
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-5 3/4 = -(5*4+3)/4 = -23/4
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8 2/6 = 8 1/3 = (8*3+1)/3 = 25/3
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5 3/9 = 5 1/3 = (5*3+1)/3 = 16/3
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etc.
Cheers,
Stan H.
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Permutations/695160: Count the number of possible 4-letter arrangements that can be formed using the letters in the word 'Butterworth'
1 solutions
Answer 428535 by stanbon(57984) on 2012-12-18 09:21:35 (Show Source):
You can put this solution on YOUR website! Count the number of possible 4-letter arrangements that can be formed using the letters in the word 'Butterworth'
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There are 9 different letters.
Ans: 9P4 = 9!/(9-4)! = 9*8*7*6 = 3024
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Cheers,
Stan H.
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Permutations/695170: Determine the number of ways to form 4-digit numbers by using the digits 1,2,3,4,5,6, and 7 if repetitions of digits are allowed.
1 solutions
Answer 428531 by stanbon(57984) on 2012-12-18 09:13:12 (Show Source):
You can put this solution on YOUR website!Determine the number of ways to form 4-digit numbers by using the digits 1,2,3,4,5,6, and 7 if repetitions of digits are allowed.
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Ans: 7*7*7*7 = 7^4 = 2401 numbers
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Cheers,
Stan H.
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