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Recent problems solved by 'stanbon'
stanbon answered: 57351 problems
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2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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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, >>NextProbability-and-statistics/752301: 1. A baseball pitcher has only three pitches: a fast ball, a curve ball, and a
knuckle ball. As the pitcher warms up before an inning, she wants to throw a
fast ball 7 times, a curve ball 2 times, and a knuckle ball 3 times. How many
different ways can this be done.
2. A teacher has 7 boys and 11 girls in her class. In how many ways can she select
8 of the children to be in a play if she must select 4 boys and 4 girls.
1 solutions
Answer 457871 by stanbon(57424)   on 2013-05-25 22:17:53 (Show Source):
You can put this solution on YOUR website!1. A baseball pitcher has only three pitches: a fast ball, a curve ball, and a
knuckle ball. As the pitcher warms up before an inning, she wants to throw a
fast ball 7 times, a curve ball 2 times, and a knuckle ball 3 times. How many
different ways can this be done.
-----
Ans: 12!/(7!*2!*3!) = 7920 ways
=================================================
2. A teacher has 7 boys and 11 girls in her class. In how many ways can she select 8 of the children to be in a play if she must select 4 boys and 4 girls.
Ans: 8!/(4!*4!) = 70 ways
===============================
Cheers,
Stan H.
=================
|
Probability-and-statistics/752397: A cafeteria has 5 turkey sandwiches, 6 cheese sandwiches, and 4 tuna sandwiches. There are two students in line and each will take a sandwich. What is the probability that the first student takes a cheese sandwich and the next student takes a turkey sandwich?
a. 1/7 b. 1/14 c. 2/15 d. 2/21
1 solutions
Answer 457869 by stanbon(57424) on 2013-05-25 22:11:21 (Show Source):
You can put this solution on YOUR website!A cafeteria has 5 turkey sandwiches, 6 cheese sandwiches, and 4 tuna sandwiches. There are two students in line and each will take a sandwich. What is the probability that the first student takes a cheese sandwich and the next student takes a turkey sandwich?
Ans: (6/15)(5/14) = 30/(15*14) = 2/14 = 1/7
------------------------------------
Cheers,
Stan H.
===================================
a. 1/7 b. 1/14 c. 2/15 d. 2/21
|
Probability-and-statistics/752398: There are 3 black marbles and 4 red marbles in a bag. Trevor will take out 2 marbles without looking.
A. What is the probability that both marbles will be black?
Show your work.
B. Suppose that Trevor takes out 1 marble, replaces it in the bag, then takes out another marble. What is the probability that both marbles will be black in this situation? Show your work.
1 solutions
Answer 457868 by stanbon(57424) on 2013-05-25 22:08:38 (Show Source):
You can put this solution on YOUR website!There are 3 black marbles and 4 red marbles in a bag. Trevor will take out 2 marbles without looking.
A. What is the probability that both marbles will be black?
Show your work.
Ans: 3C2/7C2 = 3/21 = 1/7
-------------------------------
B. Suppose that Trevor takes out 1 marble, replaces it in the bag, then takes out another marble. What is the probability that both marbles will be black in this situation? Show your work.
Ans: (3/7)^2 = 9/49
=========================
Cheers,
Stan H.
|
Probability-and-statistics/752399: A builder has 8 lots available for sale.
* 6 lots are greater than one acre
* 2 lots are less than one acre
What is the probability that the next three lots sold will be greater than one acre?
a. 3/4 b. 15/28 c. 27/64 d. 5/14
1 solutions
Answer 457867 by stanbon(57424) on 2013-05-25 22:03:24 (Show Source):
You can put this solution on YOUR website!A builder has 8 lots available for sale.
* 6 lots are greater than one acre
* 2 lots are less than one acre
What is the probability that the next three lots sold will be greater than one acre?
-----
Binomial Problem with n = 3 and p(> 1 acre) = 6/8 = 3/4
-----------------------------------
P(x = 3) = (3/4)^3 = 27/64
===============================
Cheers,
Stan H.
======================
a. 3/4 b. 15/28 c. 27/64 d. 5/14
|
Probability-and-statistics/752474: please i need urgent help with finding the probability of complementary events
P(E Union M) = 0,85; P(E)= 0,65 and P(M) = 0.55
how can i find the P[M(complement) Union E) and P[M(complement) Intersection E(complement)]? it is not stated that the elements are mutually exclusive or independent. Thanks for the help.
1 solutions
Answer 457863 by stanbon(57424) on 2013-05-25 21:55:42 (Show Source):
You can put this solution on YOUR website!P(E Union M) = 0,85;
P(E)= 0,65 ; P(E') = 0.35
P(M) = 0.55 ; P(M') = 0.45
------------------------------------
how can i find the P[M(complement) Union E)
P(M' or E) = P(M')+P(E)-P(M' and E}
= (0.45)+ (0.65)- P(M' and E)
Note: This implies that M' and E are not mutually exclusive.
-----
P[M(complement) Intersection E(complement)]
P(M' AND E') = P(M')+P(E')-P(M' or E')
= 0.45+0.35 - P(M' or E')
Note: This does not tell us wheter M' and E' are mutually exlusive.
----
Cheers,
Stan H.
===================
it is not stated that the elements are mutually exclusive or independent.
|
Mixture_Word_Problems/752567: how many gallons of 20% antifreeze should be mixed with 10 gallons of 83% antifreeze to obtain 55% antifreeze mixture?
1 solutions
Answer 457851 by stanbon(57424) on 2013-05-25 21:24:12 (Show Source):
You can put this solution on YOUR website! how many gallons of 20% antifreeze should be mixed with 10 gallons of 83% antifreeze to obtain 55% antifreeze mixture?
---------
Equation:
alcohol + alcohol = alcohol
0.20x + 0.83*10 = 0.55(x+10)
-----
20x + 83*10 = 55x + 55*10
----------
35x = 28*10
x = (2/7)28
x = 8 gallons (amt. of 20% solution needed)
==============================================
Cheers,
Stan H.
================
|
Coordinate-system/752565: Determine whether the lines 2x + 7y = 14 and y + 2/7x = 6 are parallel, perpendicular, or neither.
1 solutions
Answer 457845 by stanbon(57424) on 2013-05-25 21:13:04 (Show Source):
You can put this solution on YOUR website!Determine whether the lines
are parallel, perpendicular, or neither.
-------------------------
Compare the slopes.
2x + 7y = 14
y = (-2/7)x + 2
slope = -2/7
-------------------
y + 2/7x = 6
y = (-2/7)x + 6
slope = -2/7
====================
The slopes are the same so the lines are parallel
==============================
Cheers,
Stan H.
|
Rectangles/752562: The length of a rectangle is 6 inches more than its width. The area of the rectangle is 91 square inches.
Please tell how this is done thanks
1 solutions
Answer 457841 by stanbon(57424) on 2013-05-25 21:08:30 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is 6 inches more than its width. The area of the rectangle is 91 square inches.
-------------------
Let width be "x":
Then length will be "x+6":
---------------------
Equation:
Area = length*width
A(x) = x(x+6) = 91
x^2 + 6x - 91 = 0
----------------------
x^2 + 13x - 7x -91 = 0
x(x+13)-7(x+13) = 0
(x+13)(x-7) = 0
Positive solution:
x = 7 inches (width)
x+6 = 13 inches (length)
=================
Cheers,
Stan H.
======================
|
Coordinate-system/752560: Determine the slope and y–intercept of the line for the equation of the line x- 3y = -12
1 solutions
Answer 457838 by stanbon(57424) on 2013-05-25 21:01:57 (Show Source):
You can put this solution on YOUR website!Determine the slope and y–intercept of the line
for the equation of the line
x- 3y = -12
3y = x+12
----
y = (1/3)x + 4
-----
slope: (1/3)
intercept: 4
============
Cheers,
Stan H.
===============
|
Linear-equations/752541: Can someone help me find the slope-intercept form for the line satisfying the following conditions?
x-intercept 2, y-intercept 1/3
Thanks for anyone that can help. I don’t get this slope thing at all.
1 solutions
Answer 457811 by stanbon(57424) on 2013-05-25 18:49:01 (Show Source):
You can put this solution on YOUR website!Can someone help me find the slope-intercept form for the line satisfying the following conditions?
x-intercept 2, y-intercept 1/3
------
You have two points (2,0) and (0,1/3)
-----
Equation:
x/2 + y/(1/3) = 1
------
Modify:
x/2 + 3y = 1
---
y = (-x/6) + 1/3
=======================
Cheers,
Stan H.
=======================
|
Linear-equations/752477: please help..
In 1980, median family income was about $19,000 and in 2000 it was about $40,000. a) Find the slope of the line passing through the points (1980,19000) and (2000, 40000). b) Interpret the slope as a rate of change. c) If this trend continues, estimate the median family income in 2004.
1 solutions
Answer 457809 by stanbon(57424) on 2013-05-25 18:43:54 (Show Source):
You can put this solution on YOUR website!In 1980, median family income was about $19,000 and in 2000 it was about $40,000.
---
You have 2 points: (0,19000) and (20,40,000)
---------------------------
a) Find the slope of the line passing through the points (1980,19000) and (2000, 40000).
slope = (40000-19000)/(2000-1980) = 21000/20 = 2100/2 = 1050
---------------------------------------------------
b) Interpret the slope as a rate of change.
The family income increases by $1000 each year from 1980 to 2000
---------------------------------------------------
c) If this trend continues, estimate the median family income in 2004.
f(24) = 1000*24+ 19000 = 24000 + 19000 = $43,000
---------------------------------
Cheers,
Stan H.
=================
|
Linear-equations/752531: help please..
An investor invested a total of $2200 in two mutual funds. One fund earned 5% profit while the other earned a 2% profit. If the investor's total profit was $68, how much was invested in each mutual fund?
The amount invested in the mutual fund that earned 5% was?
The amount invested in the mutual fund that earned 2% was?
1 solutions
Answer 457795 by stanbon(57424) on 2013-05-25 17:12:22 (Show Source):
You can put this solution on YOUR website!An investor invested a total of $2200 in two mutual funds. One fund earned 5% profit while the other earned a 2% profit. If the investor's total profit was $68, how much was invested in each mutual fund?
----------------
Quantity Equation: x + y = 2200
Interest Equation:5x +2y = 6800
-----------------------------------
Modify for elimination:
2x + 2y = 4400
5x + 2y = 6800
----
Subtract and solve for "x":
3x = 2400
x = $800 (amt. invested at 2%)
----
Solve for "y":
x + y = 2200
800 + y = 2200
y = $1400 (amt. invested at 5%
==================================
Cheers,
Stan H.
===============
The amount invested in the mutual fund that earned 5% was?
The amount invested in the mutual fund that earned 2% was?
|
Linear-equations/752533: Given the equation 5x + 2y = 7, answer the following questions.
(a) Is the slope of the line described by this equation positive or negative?
(b) As x increases in value, does y increase or decrease?
(c) If x decreases by 2 units, what is the corresponding change in y?
units
1 solutions
Answer 457792 by stanbon(57424) on 2013-05-25 17:06:33 (Show Source):
You can put this solution on YOUR website!Given the equation 5x + 2y = 7, answer the following questions.
y = (-5/2)x + (7/2
---------------------------
(a) Is the slope of the line described by this equation positive or negative?
slope = -5/2
-------------------
(b) As x increases in value, does y increase or decrease?
It decreases
----------------------
(c) If x decreases by 2 units, what is the corresponding change in y?
y increases by 5
---------------------------------
Cheers,
Stan H.
======================
|
pythagorean/752519: how do I work this problem? a nurse studied PSA readings and found the data set to be normally distributed with a mean of 50 and a standard deviation of 7.25, what is the median of this distribution.
1 solutions
Answer 457773 by stanbon(57424) on 2013-05-25 15:06:27 (Show Source):
You can put this solution on YOUR website!A rock is thrown up from the ground at a velocity of 84 feet per second. The formula h = –16t^2 + 84t gives the rock’s height in feet after t seconds. What is the maximum height of the rock?
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median is the middle score.
In your case the median is the mean
Median = 50
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Cheers,
Stan H.
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Quadratic_Equations/752508: A rock is thrown up from the ground at a velocity of 84 feet per second. The formula h = –16t^2 + 84t gives the rock’s height in feet after t seconds. What is the maximum height of the rock?
1 solutions
Answer 457772 by stanbon(57424) on 2013-05-25 15:04:45 (Show Source):
You can put this solution on YOUR website!A rock is thrown up from the ground at a velocity of 84 feet per second. The formula h = –16t^2 + 84t gives the rock’s height in feet after t seconds. What is the maximum height of the rock?
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max occurs when x = -b/(2a) = -84/(2*-16) = 2.6250 seconds
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f(2.6250) = -16(2.6250^2) + 84(2.6250) = 110.25 ft
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Cheers,
Stan H.
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Equations/752511: 1. Solve for x
a) (x-1) / (x+2) + (x+7) / (x-40) = 0
Can you please help me out? Thanks so much in advance:)
Can you please show the steps it would really help me understand:)
1 solutions
Answer 457770 by stanbon(57424) on 2013-05-25 14:57:20 (Show Source):
You can put this solution on YOUR website!(x-1) / (x+2) + (x+7) / (x-40) = 0
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Multiply thru by (x+2)(x-40) to get:
(x-1)(x-40)+(x+7)(x+2) = 0
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x^2-4x+40 + x^2+9x+14 = 0
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2x^2 + 5x + 54 = 0
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Use the Quadratic Formula.
No Real Number solutions
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Cheers,
Stan H.
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Functions/752512: write the function whose graph is the graph of y=(x+4)^2 but is reflected about the y-axis
y=____
1 solutions
Answer 457769 by stanbon(57424) on 2013-05-25 14:52:37 (Show Source):
You can put this solution on YOUR website!write the function whose graph is the graph of y=(x+4)^2 but is reflected about the y-axis
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f(-x) = (-x+4)^2
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Cheers,
Stan H.
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Money_Word_Problems/752517: The Booster Club raised $30,000 for a sports fund. No more money will be placed into the fund. Each year the fund will decrease by 5%. Determine the amount of money, to the nearest cent, that will be left in the sports fund after 4 years.
1 solutions
Answer 457767 by stanbon(57424) on 2013-05-25 14:47:01 (Show Source):
You can put this solution on YOUR website!The Booster Club raised $30,000 for a sports fund. No more money will be placed into the fund. Each year the fund will decrease by 5%. Determine the amount of money, to the nearest cent, that will be left in the sports fund after 4 years.
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Start: 30,000
after one year: 30000*0.95
after one more: 30000*(0.95)*0.95
after one more: 30,000*(0.95)^3
after 4 yrs:::: 30,000(0.95)^4 = $24,435.19
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Cheers,
Stan H.
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Equations/752513: 1. Solve for x
a) √(x+1) + √(2x-5) = 3
Can you please help me out? Thanks so much in advance:)
Can you please show the steps it would really help me understand:)
1 solutions
Answer 457763 by stanbon(57424) on 2013-05-25 14:14:28 (Show Source):
You can put this solution on YOUR website!√(x+1) + √(2x-5) = 3
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Square both sides to get:
(x+1) + (2x-5) + 2*sqrt[(x+1)(2x-5)] = 9
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2sqrt[2x^2 -3x -5] = 13 - 3x
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Square both sides again:
4[2x^2-3x-5] = 169-78x+9x^2
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8x^2 - 12x -20 = 169 - 78x + 9x^2
x^2 - 66x +189 = 0
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(x-3)(x+63) = 0
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Positive solution:
x = 3
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Check the answer in the original equation.
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Cheers,
Stan H.
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Functions/752514: Find the domain of the function
f(x)= sqrt25-x
Write the function whose graph is the graph of y=(x+2)^2 but is reflected the x-axis
y=____
1 solutions
Answer 457762 by stanbon(57424) on 2013-05-25 14:05:19 (Show Source):
You can put this solution on YOUR website!Find the domain of the function
f(x)= sqrt(25-x)
25-x has to be >= 0
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Solve: 25-x >= 0
x <= 25
x <= 5
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Write the function whose graph is the graph of
y=(x+2)^2 but is reflected the x-axis
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Ans: y = -(x+2)^2
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Cheers,
Stan H.
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y=____
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Radicals/752500: All the scene of a accident police can estimate the speed a car had been travelling by the length of the skid mark . One formula used for this purpose is V = -7 + 8.2 √(d) where v is the speed in the kilometers per hour and d is the length of the skid mark in metres.
a) Solve the formula for d
b) how long would the skid mark of the car breaking from 60 kilometre per hour?
c) What was the speed of the car if the length of the skid mark is 50 metres?
Can you please help me out? Thanks so much in advance:)
Can you please show the steps it would really help me understand:)
1 solutions
Answer 457761 by stanbon(57424) on 2013-05-25 13:59:46 (Show Source):
You can put this solution on YOUR website!All the scene of a accident police can estimate the speed a car had been travelling by the length of the skid mark .
One formula used for this purpose is V = -7 + 8.2 √(d) where v is the speed in the kilometers per hour and d is the length of the skid mark in metres.
a) Solve the formula for d
8.2*sqrt(d) = V+7
sqrt(d) = (V+7)/8.2
d = [(V+7)/8.2]^2
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b) how long would the skid mark of the car breaking from 60 kilometre per hour?
d = [(60+7)/8.2]^2 = 66.76 meters
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c) What was the speed of the car if the length of the skid mark is 50 metres?
V = -7 + 8.2sqrt(d)
V = -7 + 8.2*sqrt(50)
V = -7+ 57.98
Velocity = 50.98 km/hr
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Cheers,
Stan H.
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Polygons/752463: How to solve this question?
Each interior angle of a Regular polygon is 170 Degrees. Calculate the number of sides in the polygon.
1 solutions
Answer 457748 by stanbon(57424) on 2013-05-25 12:03:50 (Show Source):
You can put this solution on YOUR website!How to solve this question?
Each interior angle of a Regular polygon is 170 Degrees. Calculate the number of sides in the polygon.
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The corresponding exterior angles are each 180-170 = 10 degrees.
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Sum of the exterior angles is always 360.
# of sides = # of exterior angles = 360/10 = 36
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Cheers,
Stan H.
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