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Recent problems solved by 'stanbon'
stanbon answered: 57314 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, >>NextEquations/672503: It says to simplify the Alegebric equations....
Divide: (2x^3 - x^2 + 3x -1) ÷ (x + 2)
1 solutions
Answer 418140 by stanbon(57387)   on 2012-10-27 09:26:36 (Show Source):
You can put this solution on YOUR website!Divide: (2x^3 - x^2 + 3x -1) ÷ (x + 2)
----
Using synthetic division:
-2)....2....-1....3....-1
.......2....-5....13...|..-27
Quotient: 2x^2 - 5x + 13
Remainder: -27
=======================
Cheers,
Stan H.
|
Triangles/672507: the lengths of 2 sides of a triangle are 9 and 5. suppose the length of the 3rd side is an integer. Give all the possible lengths for the 3rd side.
thanks! :)
1 solutions
Answer 418138 by stanbon(57387) on 2012-10-27 09:22:42 (Show Source):
You can put this solution on YOUR website!the lengths of 2 sides of a triangle are 9 and 5. suppose the length of the 3rd side is an integer. Give all the possible lengths for the 3rd side.
----------
Let the possible length be "x":
9-5 < x < 9+5
4 < x < 14
------------------
Try drawing the triangle with 3rd side = 15 or 3rd side = 3
and you will see why you cannot.
--------------------------------------
Cheers,
Stan H.
|
Travel_Word_Problems/672529: Sue runs 8 kilometers in 45 minutes. At the same rate, how many kilometers would she run in 18 minutes.
1 solutions
Answer 418133 by stanbon(57387) on 2012-10-27 09:09:28 (Show Source):
You can put this solution on YOUR website!Sue runs 8 kilometers in 45 minutes. At the same rate, how many kilometers would she run in 18 minutes.
-------
Use a proportion:
x/18 = 8/45
x = 18(8/45)
---
x = 2(8/5) = 16/5 = 3 1/5 km
==================
Cheers,
Stan H.
|
Equations/672512: What is the general term of sequence 2, 7, 14, 23
How to derive the solution in every steps, thanks.
1 solutions
Answer 418131 by stanbon(57387) on 2012-10-27 09:04:29 (Show Source):
You can put this solution on YOUR website!What is the general term of sequence 2, 7, 14, 23
How to derive the solution in every steps,
----
Notice 2 = 2^2-2
7 = 3^2-2
14 = 4^2-2
23 = 5^2-2
---------
General Form: (n+1)^2-2 or n^2+2n-1
-------------
Cheers,
Stan H.
|
Probability-and-statistics/672487: At your university, 30% of the undergraudates are from out of state. If you randomly select 8 of the undergraduates, what is the probability that all are from out of state?
1 solutions
Answer 418127 by stanbon(57387) on 2012-10-27 08:47:29 (Show Source):
You can put this solution on YOUR website!At your university, 30% of the undergraudates are from out of state. If you randomly select 8 of the undergraduates, what is the probability that all are from out of state?
-------------
Ans: 0.30^8 = 0.00006461...
Cheers,
Stan H.
===========
|
Probability-and-statistics/672523: A landscaper wishes to use several different types of plants. The categories include color
(red, yellow, and green), type (flowers and shrubs), and height (tall, medium and short).
How many different combinations can he/she use if she selects one color, one type, and
one height?
1 solutions
Answer 418126 by stanbon(57387) on 2012-10-27 08:44:02 (Show Source):
You can put this solution on YOUR website!A landscaper wishes to use several different types of plants. The categories include color
(red, yellow, and green), type (flowers and shrubs), and height (tall, medium and short).
How many different combinations can he/she use if she selects one color, one type, and one height?
-------
Ans: 3*2*3 = 18 combinations
================================
Cheers,
Stan H.
|
Linear-equations/672526: Write an equation for the line that is parallel to y = 10x + 16 and that passes through the point (-2,5).
1 solutions
Answer 418113 by stanbon(57387) on 2012-10-27 08:20:07 (Show Source):
You can put this solution on YOUR website!Write an equation for the line that is parallel to y = 10x + 16 and that passes through the point (-2,5).
------
Form: y = mx + b
--
y = 5 when x = -2, and slope must be 10
------
5 = 10*-2 + b
b = 25
-----
Equation:
y = 10x + 25
===============
cheers,
Stan H.
================
|
Polynomials-and-rational-expressions/672522: I need help solving this problem:
Divide. Write the answer in lowest terms.
6z-y/3x / 5y-30z/3x-27
1 solutions
Answer 418112 by stanbon(57387) on 2012-10-27 08:17:54 (Show Source):
You can put this solution on YOUR website![6z-y/3x] / [5y-30z/3x-27]
----------
Invert the bottom fraction and multiply:
[6z-y/3x] * [(3(x-9))/(5(y-6z))]
----------
Cancel the common "3" and "6z-y" factors in the numerator and the denominator:
= [1/x] * [((x-9))/(5(-1))]
= (1/x)(x-9)/(-5)
----
= (x-9)/(-5x)
====================
Cheers,
Stan H.
==============
|
Money_Word_Problems/672524: Felipe deposited $4000 into an account with 4.1% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 3 years?
1 solutions
Answer 418108 by stanbon(57387) on 2012-10-27 08:09:08 (Show Source):
You can put this solution on YOUR website! Felipe deposited $4000 into an account with 4.1% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 3 years?
------
A(t) = P(1+(r/n))^(nt)
----
A(3) = 4000(1+(0.041/2))^(2*3)
---------
A(3) = $4517.91
==================
Cheers,
Stan H.
===========
|
logarithm/672519: please help me on evaluating this(it is log question)
16.4*9814
1 solutions
Answer 418107 by stanbon(57387) on 2012-10-27 08:06:01 (Show Source):
You can put this solution on YOUR website!16.4*9814
------
log[16.4*9814] = log(16.4)+log(9814)
= 1.2148 + 3.9918
---
= 5.2067
------
So, 16.4*9814 = 10^ 5.2067 is approximately 160,953.34
=============
Cheers,
Stan H.
|
Probability-and-statistics/672426: The daily demand for gas at Good’s Gas station is normally distributed with a mean of 1812 gallons and a standard deviation of 254 gallons.
(a) What is the probability that the demand for gas will exceed 2000 gallons on any day?
(b) What is the probability that the demand for gas in a day will be between 1500 and 2000 gallons?
(c) What is the probability that the demand for gas will exceed 1500 gallons on any day?
(d) how much gasoline should the station have on hand at the beginning of the day so that the probability of running out of gas that day is only 1%?
1 solutions
Answer 418035 by stanbon(57387) on 2012-10-26 20:20:41 (Show Source):
You can put this solution on YOUR website!The daily demand for gas at Good’s Gas station is normally distributed with a mean of 1812 gallons and a standard deviation of 254 gallons.
(a) What is the probability that the demand for gas will exceed 2000 gallons on any day?
z(2000) = (2000-1812)/254 = 0.7402
P(x > 2000) = P(z > 0.7402) = normalcdf(0.7402,100) = 0.2296
-----------------------------------------------------------------------
(b) What is the probability that the demand for gas in a day will be between 1500 and 2000 gallons?
z(1500) = (1500-1812)/254 = -1.2283
----
P(1500<= x <=2000) = P(-1.2283<= z <=0.2296) = 0.4811
---------------------------------------
(c) What is the probability that the demand for gas will exceed 1500 gallons on any day?
Ans: P(-1.2283,100) = 0.8903
---------------------------------------
(d) how much gasoline should the station have on hand at the beginning of the day so that the probability of running out of gas that day is only 1%?
Find the z-value with a right tail of 1%.
invNorm(0.99) = 2.3263
---
Find the corresponding gas value using x = z*s+u
x = 2.3263*254+1812 = 2402.89 gallons
========================================
Cheers,
Stan H.
===============
|
Equations/672432: 12(2k+11)=12(2k+12)
1 solutions
Answer 418030 by stanbon(57387) on 2012-10-26 20:06:13 (Show Source):
You can put this solution on YOUR website!12(2k+11)=12(2k+12)
----
Divide both sides by 12 to get:
2k + 11 = 2k + 12
-----
Subtract 2k from both sides:
11 = 12
----
That contradiction implies the original equation
is a contradiction. There are no solutions.
====================
Cheers,
Stan H.
==============
|
Coordinate-system/672429: I need to set up a system of equations that represents the situations below.
The BETA club is selling tote bags to raise money for their trip. It cost the club $10.00 to purchase the large bags and $7.00 to purchase the small bags. They sold the large bags for $20.00 and the small bags for $10.00. The club paid $600.00 to purchase the bags and raised 1000.00 from selling the bags.
1 solutions
Answer 418029 by stanbon(57387) on 2012-10-26 20:03:50 (Show Source):
You can put this solution on YOUR website!I need to set up a system of equations that represents the situations below.
The BETA club is selling tote bags to raise money for their trip. It cost the club $10.00 to purchase the large bags and $7.00 to purchase the small bags. They sold the large bags for $20.00 and the small bags for $10.00. The club paid $600.00 to purchase the bags and raised 1000.00 from selling the bags.
----------------------
Purchase Cost equation: 10L + 7S = 600
Revenue equation::::::: 20L + 10S = 1000
----------------------------------------------
Cheers,
Stan H.
============
|
Quadratic_Equations/672423: Answer the questions below about the quadratic function.
f(x)= 3x^2 +24x + 51
Does the function have a minimum or maximum value?
What is the functions of the minimum or maximum value?
Where does the minimum or maximum value occur? x= ?
1 solutions
Answer 418024 by stanbon(57387) on 2012-10-26 19:43:07 (Show Source):
You can put this solution on YOUR website!Answer the questions below about the quadratic function.
f(x)= 3x^2 +24x + 51
Does the function have a minimum or maximum value?:::Minimum because
the coefficient of x^2 is positive.
-------------------------------------------
What is the function of the minimum or maximum value?:: It is the
vertex of the parabola.
-------------------------------------------
Where does the minimum or maximum value occur? x = -b/(2a) = -24/(6) = -4
f(-4) = 3(-4)^2 + 24(-4) + 51 = 48-96+51 = 3
----
Min:: (-4,3)
================
Cheers,
Stan H.
================
|
Probability-and-statistics/672336: A modified roulette wheel has 44 slots.One slot is 0, another is 00, the others are numbered 1 trough 42 respectively.You are placing a bet that an outcome is an odd number (neither 0 or 00 are even or odd).
a. What is your probability of winning?
b. What are the actual odds against winning?
c. The payoff odds are 1:1. How much profit do you make if you bet $14 and win?
d. How much profit should you make on a $14 bet if the payoff odds are the same as the actual odds against winning?
1 solutions
Answer 418022 by stanbon(57387) on 2012-10-26 19:37:29 (Show Source):
You can put this solution on YOUR website!A modified roulette wheel has 44 slots.One slot is 0, another is 00, the others are numbered 1 trough 42 respectively.You are placing a bet that an outcome is an odd number (neither 0 or 00 are even or odd).
a. What is your probability of winning?
P(win) = 21/44 = 0.48
------------------------------
b. What are the actual odds against winning?
odds against = # of ways to lose: # of ways to win = 23:21
------------------------------
c. The payoff odds are 1:1. How much profit do you make if you bet $14 and win?
---------------------------
d. How much profit should you make on a $14 bet if the payoff odds are the same as the actual odds against winning?
----------
Comment: I'm not up on gambling odds and their payoff.
===============
Cheers,
Stan H.
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Probability-and-statistics/672422: if a person takes a 5 problem true or false test, what is probability that he scores 100 if he guesses on every problem? (Express your answer as a reduced fraction)
1 solutions
Answer 418020 by stanbon(57387) on 2012-10-26 19:25:17 (Show Source):
You can put this solution on YOUR website!if a person takes a 5 problem true or false test, what is probability that he scores 100 if he guesses on every problem?
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Binomial Problem with n = 5 and p(correct) = 1/2
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P(x = 5) = (1/2)^5 = 1/32 = 0.03125
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Cheers,
Stan H.
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Numeric_Fractions/672421: If there are 150 questions on a test and you get 83% for a score. How many did you get wrong?
1 solutions
Answer 418019 by stanbon(57387) on 2012-10-26 19:22:20 (Show Source):
You can put this solution on YOUR website!If there are 150 questions on a test and you get 83% for a score. How many did you get wrong?
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150-0.87*150 = 0.13*150 = 19.5
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Cheers,
Stan H.
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Probability-and-statistics/672420: A die is rolled 15 times. What is the probability of at least two 2's appearing? (Round your answer to four decimal places.)
1 solutions
Answer 418018 by stanbon(57387) on 2012-10-26 19:08:11 (Show Source):
You can put this solution on YOUR website!A die is rolled 15 times. What is the probability of at least two 2's appearing? (Round your answer to four decimal places.)
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Binomial Problem with n = 15 and p(2) = 1/6
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P(2<= x <=15) = 1 - P(0<= x <=1) = 1-binomcdf(15,1/6,1) = 0.7404
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Cheers,
Stan H.
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Quadratic_Equations/672418: find the equation of a parabola with a vertex (2,-12) that passes through the point (0,0)
1 solutions
Answer 418017 by stanbon(57387) on 2012-10-26 19:04:35 (Show Source):
You can put this solution on YOUR website!find the equation of a parabola with a vertex (2,-12) that passes through the point (0,0)
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Plotting the vertex and the point (2,-12), the parabola
must open down or to the right.
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y = a(x-h)^2 + k with a < 0
Using (2,-12) and (0,0)
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-12 = a(2-0)^2 + 0
4a = -12
a = -3
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Equation:
y = -3(x-2)^2
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/672409: If the square of a positive number is increased by 3 times the number,the result is 54.Find the number.
1 solutions
Answer 418015 by stanbon(57387) on 2012-10-26 18:36:53 (Show Source):
You can put this solution on YOUR website!If the square of a positive number is increased by 3 times the number,the result is 54.Find the number.
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Let the number be "x":
Equation:
x^2 + 3x = 54
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x^2 + 3x - 54 = 0
(x+9)(x-6) = 0
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x = -9 or x = 6
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Cheers,
Stan H.
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Graphs/672413: a.)write an equation for a line that is parrel to the x-axis____________
b.)what is the y intercept for the line whose equation you wrote in a?________
c.) what is the x interept for the line whose equation you wrote in a?__________
Please help me-I just do not get it!!!
1 solutions
Answer 418010 by stanbon(57387) on 2012-10-26 18:22:56 (Show Source):
You can put this solution on YOUR website!a.)write an equation for a line that is parallel to the x-axis:: y = 8
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b.)what is the y intercept for the line whose equation you wrote in a?:: (0,8)________
c.) what is the x intercept for the line whose equation you wrote in a?::: there is no x-intercept. The line is parallel to the x-axis.
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Cheers,
Stan H.
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Signed-numbers/672360: Jenna is now x years old and Amy is 3 years younger than Jenna. In terms of x, how old will Amy be in 4 years?
1 solutions
Answer 417989 by stanbon(57387) on 2012-10-26 17:20:38 (Show Source):
You can put this solution on YOUR website!Jenna is now x years old
Amy is 3 years younger than Jenna::: x-3
In terms of x, how old will Amy be in 4 years?
Ans: x-3+4 = x+1
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Cheers,
Stan H.
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Age_Word_Problems/672389: I am 12 years old and my brother is 5 years old. In how many years will I be twice as old as my brother?
1 solutions
Answer 417980 by stanbon(57387) on 2012-10-26 17:09:25 (Show Source):
You can put this solution on YOUR website! I am 12 years old and my brother is 5 years old. In how many years will I be twice as old as my brother?
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Let that number of years be "x":
Equation:
12+x = 2(5+x)
12+x = 10+2x
x = 2 years
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In 2 years you will be 14 and your brother will be 7.
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Cheers,
Stan H.
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Quadratic_Equations/672364: y=-(1/4)(2)^(x-4)+5
Sketch the above equation by first including a table describing its major features.
Can someone explain me how to make the table that discribes thhe major features?
1 solutions
Answer 417976 by stanbon(57387) on 2012-10-26 17:06:15 (Show Source):
You can put this solution on YOUR website!y=-(1/4)(2)^(x-4)+5
Sketch the above equation by first including a table describing its major features.
Can someone explain me how to make the table that discribes thhe major features?
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y = 2^x is a groth curve asymptotic to y = 0 and passing thru (0,1)
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y = 2^(x-4) moves all the points 4 to the right.
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y = (1/4)2^(x-4) brings all the y-values down by a factor of 1/4
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y = (1/4)2^(x-4) +5 raises all the points by 5
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Cheers,
Stan H.
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