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stanbon answered: 57314 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, >>Next

Percentage-and-ratio-word-problems/369488: Find 175% of 24 (must write and solve an equation)
1 solutions

Answer 263308 by stanbon(57387) About Me  on 2010-11-11 09:46:06 (Show Source):
You can put this solution on YOUR website!
Find 175% of 24 (must write and solve an equation)
---
x = (175/100)*24
---
x = 175/0.24
x = 42
===========
Cheers,
Stan H.


Graphs/369358: What would the graph be for: y = x + 2?
1 solutions

Answer 263159 by stanbon(57387) About Me  on 2010-11-10 21:10:24 (Show Source):
You can put this solution on YOUR website!
What would the graph be for: y = x + 2?
----
Plot a couple of points and draw a line thru them.
If x = 0, y = 2
If x = 2, y = 4
---
Plot (0,2) and (2,4).
--------------------------
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%2B2%29
Cheers,
Stan H.


Inequalities/369337: Please show me how to solve this problem.
Nicole has less than $400 in her account, she must deposit money. If she uses $65 a week. How many weeks until she needs to deposit money?
1 solutions

Answer 263155 by stanbon(57387) About Me  on 2010-11-10 21:06:19 (Show Source):
You can put this solution on YOUR website!
Nicole has less than $400 in her account, she must deposit money.
If she uses $65 a week. How many weeks until she needs to deposit money?
--------------
Solve 65x < 400 where "x" is the number of weeks she can deposit $65
---------------
x < 6.15.. weeks
----
Ans: 6 weeks
---
Note: 6*65 = $390
===================
Cheers,
Stan H.
==========


Probability-and-statistics/369128: A clinical trial is conducted to compare an expetimental medication to placebo to reduce the symptoms of asthma. Two hundred participants are enrolled in the study and randomized to reveive either the experimental medication or placebo. The primary outcome is self-reported reduction of symptoms. Among 100 participants who received the experimental medication, 38 reported a reduction of symptoms aws compared to 21 participants of 100 assigned to placebo. Test if there is a significant difference in the proportions of participants reporting a reduction of symptoms between the wxperimental and placebo groups. Use a 5% level of significance. Run the test using the five-step approach In computing this fully discuss the hypothesis 5 step approach and any difficulties in computing it and the problems experienced.
1 solutions

Answer 263148 by stanbon(57387) About Me  on 2010-11-10 20:51:31 (Show Source):
You can put this solution on YOUR website!
A clinical trial is conducted to compare an expetimental medication to placebo to reduce the symptoms of asthma. Two hundred participants are enrolled in the study and randomized to reveive either the experimental medication or placebo. The primary outcome is self-reported reduction of symptoms.
-----------------------
Among 100 participants who received the experimental medication, 38 reported a reduction of symptoms as: p-hat(ex) = 0.38
-----------------------
21 participants of 100 assigned to placebo: p-hat(cebo) = 0.21
-----------------------
Test if there is a significant difference in the proportions of participants reporting a reduction of symptoms between the experimental and placebo groups.
-----------------------------
Ho: p(ex)-p(cebo) = 0
Ha: p(ex)- p(cebo)is not zero
---------------------------------
Use a 5% level of significance. Run the test using the five-step approach In computing this fully discuss the hypothesis 5 step approach and any difficulties in computing it and the problems experienced.
---------------------
CV: +-1.96
Test stat: z(0.38-0.21)/sqrt[(0.21*0.79/100 + 0.38*0.62/100)] = 42.34
------------------
Since the TS is in the reject interval, reject Ho.
====================================================
Cheers,
Stan H.


Probability-and-statistics/369145: A new drug can cause two unwanted sife effects: Drowsiness and headache. 6% of its users experienced drowsiness, 4% experienced headache, and 2% experienced both. What is the percentage of users who experienced neither side effect?
1 solutions

Answer 263146 by stanbon(57387) About Me  on 2010-11-10 20:32:59 (Show Source):
You can put this solution on YOUR website!
A new drug can cause two unwanted sife effects: Drowsiness and headache. 6% of its users experienced drowsiness, 4% experienced headache, and 2% experienced both. What is the percentage of users who experienced neither side effect?
-----
P(drowsy OR headache) = 6+4-2 = 8%
----
P(neither) = 100%-8% = 92%
========================
Cheers,
Stan H.


Probability-and-statistics/369140: Min-Ki was told that his systolic blood pressure reading of 134 was in the 72nd percentile for people aged 40-49. Interpret its meaning.
1 solutions

Answer 263145 by stanbon(57387) About Me  on 2010-11-10 20:29:01 (Show Source):
You can put this solution on YOUR website!
Min-Ki was told that his systolic blood pressure reading of 134 was in the 72nd percentile for people aged 40-49. Interpret its meaning.
----
72% of people aged 40-49 have sbp lower than Min-Ki.
=====================
Cheers,
Stan H.


logarithm/369306: ln(4x+5)=4
1 solutions

Answer 263135 by stanbon(57387) About Me  on 2010-11-10 20:13:31 (Show Source):
You can put this solution on YOUR website!
ln(4x+5)=4
---
4x+5 = e^4
4x+5 = 54.5982
x = 13.6495..
Cheers,
Stan H.


Equations/369255: Hi, I have to find the vertical and horizontal asymptotes, as well as the y-intercept for the following:
y=%281+%2B+2x%29%2F%28x%2B2%29
If I'm not mistaken,
vertical asymptote = -2
horizontal asymptotes are -2 and -1%2F2
I calculated the y-intercept by plugging 0 in for x and got 1/2, but when I graph the equation it doesn't look like 1/2. I appreciate any help you can provide :)

1 solutions

Answer 263116 by stanbon(57387) About Me  on 2010-11-10 19:37:16 (Show Source):
You can put this solution on YOUR website!
find the vertical and horizontal asymptotes, as well as the y-intercept for the following:
y=(1 + 2x)/(x+2)
If I'm not mistaken,
vertical asymptote = -2
horizontal asymptote: y = 2x/x = 2
--------------------------------------------
I calculated the y-intercept by plugging 0 in for x and got 1/2, but when I graph the equation it doesn't look like 1/2.
---
x-int: Solve [(1+2x)/(x+2)] = 0
True when 1+2x = 0
2x = -1
x = -1/2
=========================
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%281%2B2x%29%2F%28x%2B2%29%29
===================================================
Cheers,
Stan H.
========


Mixture_Word_Problems/369251: Nick has two cans of white paint, one with a 2% yellow pigment and the other with a 5% yellow pigment. He wants to mix the two paints to get paint with a 4% yellow pigment. How much of the 5% yellow pigment paint should be mixed with 0.4 gallon of the 2% yellow pigment paint to get the desired paint?

1 solutions

Answer 263113 by stanbon(57387) About Me  on 2010-11-10 19:30:39 (Show Source):
You can put this solution on YOUR website!
Nick has two cans of white paint, one with a 2% yellow pigment and the other with a 5% yellow pigment. He wants to mix the two paints to get paint with a 4% yellow pigment. How much of the 5% yellow pigment paint should be mixed with 0.4 gallon of the 2% yellow pigment paint to get the desired paint?
-----------------
Equation:
yellow + yellow = yellow
0.05x + 0.02*0.4 = 0.04(x+0.4)
----
Multiply thru by 100 to get:
5x + 2*0.4 = 4x+4*0.4
x = 2*0.4
x = 0.8 gallons (amt. of 5% paint needed in the mixture)
===================================
Cheers,
Stan H.


Graphs/369252: is there an easier way to graph linear equations
1 solutions

Answer 263109 by stanbon(57387) About Me  on 2010-11-10 19:26:40 (Show Source):
You can put this solution on YOUR website!
Easier than what?
Cheers,
Stan H.


Mixture_Word_Problems/369250: According to Wikipedia, the best-selling album in 2005 was Mariah Carey’s The Emancipation of Mimi. The best-selling album in 2004 was the album Confession by Usher. Confession sold 0.94 million copies less than twice the amount The Emancipation of Mimi sold. The sum of these two albums was 13.97 million copies. Determine the sales of both albums
1 solutions

Answer 263106 by stanbon(57387) About Me  on 2010-11-10 19:24:38 (Show Source):
You can put this solution on YOUR website!
The best-selling album in 2004 was the album Confession by Usher.
Confession sold 0.94 million copies less than twice the amount The Emancipation of Mimi sold.
The sum of these two albums was 13.97 million copies.
Determine the sales of both albums.
-----
Equations:
c + e = 13.97 million
c = 2e-0.94
----
Substitute for "c" and solve for "e":
2e-0.94 + e = 13.97
3e = 14.91
e = 4.97 million (# of "Emancipation" sold)
---
Since c = 2e-0.94 = 9 million (# of "Confession" sold)
=======================================================
Cheers,
Stan H.


Quadratic_Equations/369244: Graph the quadratic function f(x)=7(x+1)^2+4: state the ordeed pairs representing the x-intercept and y-intercept (if any) and the vertex or the parabola.
1 solutions

Answer 263104 by stanbon(57387) About Me  on 2010-11-10 19:17:20 (Show Source):
You can put this solution on YOUR website!
Graph the quadratic function f(x)=7(x+1)^2+4:
state the ordeed pairs representing the x-intercept and y-intercept (if any) and the vertex or the parabola.
----
Vertex: (-1,4)
y-int: (0,11)
x-int: none
-------
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C7%28x%2B1%29%5E2%2B4%29
=====
Cheers,
Stan H.



Linear_Algebra/368956: (x + 6) divided by the fraction x^2 + 5x - 6 / x^2 + 7x - 8 please find the quotient


1 solutions

Answer 262903 by stanbon(57387) About Me  on 2010-11-10 08:18:19 (Show Source):
You can put this solution on YOUR website!
(x + 6) divided by the fraction x^2 + 5x - 6 / x^2 + 7x - 8
please find the quotient
-----------------------
(x+6)/[(x+6)(x-1)/(x+8)(x-1)]
----
Invert the denominator and multiply:
----
(x+6)
----
Cancel the (x+6) and (x-1) factors to get:
----
= (x+8)/(x+6)
=================
Cheers,
Stan H.


Trigonometry-basics/368957: Ok I'm having trouble proving these harder identities.
The homework says prove that each of the following identities is true
(2sec^2)x-(2sec^2)x(sin^2)x-(sin^2)x-(cos^2)x=1
It's w/o the parenthesis in the homework, I just didn't know how to seperate the squares for the x's.
I tried multiplying by (2cos^2)x to get rid of the sec's but I'm getting nowhere with it. Here's what I did even though I know it's wrong:
*-1 then (2cos^2)x
=-(2cos^4)x+(4cos^2)x(sin^2)x=0
/(2cos^2)x
=(-cos^2)x+(2cos^2)x(sin^2)x=0
Then I don't see anywhere to go!

1 solutions

Answer 262900 by stanbon(57387) About Me  on 2010-11-10 08:13:04 (Show Source):
You can put this solution on YOUR website!
(2sec^2)x-(2sec^2)x(sin^2)x-(sin^2)x-(cos^2)x=1
-------------------------------------------------
2sec^2 - 2sec^2*sin^2 -[sin^2+cos^2] = 1
----
2sec^2[1-sin^2] - 1 = 1
----
2sec^2[cos^2] = 2
---
2(1) = 2
2 = 2
==========
Cheers,
Stan H.


Linear-systems/368958: Find the consecutive even numbers whose sum is 108.





1 solutions

Answer 262897 by stanbon(57387) About Me  on 2010-11-10 08:08:55 (Show Source):
You can put this solution on YOUR website!
Find the consecutive even numbers whose sum is 108.
-----
1st: 2x
2nd: 2x+2
-----
Equation:
2x + 2x+2 = 108
4x = 106
x = 26.5
----
1st: 2x = 53
2nd: 2x+2 = 55
-----
There are no two consecutive EVEN numbers whose sum is 108.
=============
Cheers,
Stan H.


Expressions-with-variables/368955: 1. a electrician requires 65 min to install a ceiling fan. The electrican and an apprentice working together take 40 min to install the fan. How long would it take the apprentice working alone to install the ceiling fan?
2. 3 - x2 + x . 2x2 + x - 3
________ ___________ ____________
x-2 2x3+3x2 x2 + 3x +2

1 solutions

Answer 262891 by stanbon(57387) About Me  on 2010-11-10 08:05:07 (Show Source):
You can put this solution on YOUR website!
an electrician requires 65 min to install a ceiling fan. The electrican and an apprentice working together take 40 min to install the fan. How long would it take the apprentice working alone to install the ceiling fan?
----
Electrician rate: 1/65 job/min
Together rate:::: 1/40 job/min
Aprentice rate::: 1/x job/min
-----------------------------------
Equation:
rate + rate = together rate
1/65 + 1/x = 1/40
Multiply thru by 40*65x to get:
---
40x + 40*65 = 65x
25x = 40*65
25x = 2600
x = 2600/25
x = 104 minutes (time the apprentice would need)
==================
Cheers,
Stan H.


Linear-systems/368947: eight years ago, the sum of Peter's age and Carlo's age is at least 26. Peter is 4 years older than Carlo. At least how old is Carlo now ?
1 solutions

Answer 262889 by stanbon(57387) About Me  on 2010-11-10 08:00:48 (Show Source):
You can put this solution on YOUR website!
Eight years ago, the sum of Peter's age and Carlo's age is at least 26.
Peter is 4 years older than Carlo. At least how old is Carlo now ?
----------------
Equations:
(P-8+C-8)>=26
P = C+4
-----
Substitute and solve for "C":
(C+4+C-16) >= 26
2C-12 >= 26
2C >=38
C >= 19 (Carlo's age now)
===================
Cheers,
Stan H.


Linear_Equations_And_Systems_Word_Problems/368857: Alex stocks up for winter He buys 36 cans of vegetables he payes 80 cents per can for tomatoes and 40 cents per can for corn for a total cost of 20.80.
how many cans of corn does he buy?
1 solutions

Answer 262794 by stanbon(57387) About Me  on 2010-11-09 22:00:10 (Show Source):
You can put this solution on YOUR website!
Alex stocks up for winter.
He buys 36 cans of vegetables he payes 80 cents per can for tomatoes and 40 cents per can for corn for a total cost of 20.80.
how many cans of corn does he buy?
-----
Quantity Eq:: t + c = 36
Value Eq::: 80t +40c = 2080 cents
------------------------------------------
Multiply thru by 80 to get:
80t + 80c = 80*36
---
Subtract that from the Value Eq and solve for "c":
-40c = -800
c = 20 (# of can of corn bought)
=====================================
Cheers,
Stan H.
==============


logarithm/368853: solve the equation: log base 7 n = 2/3log base 7 8
1 solutions

Answer 262788 by stanbon(57387) About Me  on 2010-11-09 21:52:37 (Show Source):
You can put this solution on YOUR website!
solve the equation:
log base 7 n = 2/3log base 7 8
log7(n) = (2/3)log7(8)
-------
log7(n) = log7(8^(2/3))
-----
n = 8^(2/3)
---
n = 2^2
n = 4
======================
Cheers,
Stan H.


logarithm/368856: what is the solution for log of x-7 base 5= -2 solving for x?
1 solutions

Answer 262785 by stanbon(57387) About Me  on 2010-11-09 21:49:19 (Show Source):
You can put this solution on YOUR website!
what is the solution for log of x-7 base 5= -2 solving for x?
-------------
log5(x-7) = -2
----
(x-7) = 5^(-2)
------
x-7 = 1/25
---
x = 7 1/25
=====================
Cheers,
Stan H.


Rate-of-work-word-problems/368805: I need help solving this problem.
There is a table given that says weight in pounds, x: 5,10,15
then cost to mail, y: $7, $11, $15
then it asks..
How much does it cost per pound to mail a package?
Then.. What would a 16 pound package cost to mail?
Thanks for the help!
1 solutions

Answer 262750 by stanbon(57387) About Me  on 2010-11-09 21:16:01 (Show Source):
You can put this solution on YOUR website!
There is a table given that says
weight in pounds, x: 5, 10, 15
then cost to mail, y: $7, $11, $15
then it asks..
How much does it cost per pound to mail a package?
Then.. ----
slope = (11-7)/(10-5) = 4/5 = 80 cents per pound
-----
Equation:
y = mx+b
7 = (4/5)5 + b
b = 3
---
Equation:
c(x) = (4/5)x + 3
What would a 16 pound package cost to mail?
c(16) = (4/5)*16 + 3
c(16) = 64/5+3 = $15.80
==========================
Cheers,
Stan H.
==========================



Equations/368806: john has 3 pairs of pants, 4 shirts and 2 belts. how many combinations can he wear? can you tell me a formula for this, i can do it manually but would like a formula, thx mike
1 solutions

Answer 262742 by stanbon(57387) About Me  on 2010-11-09 21:06:59 (Show Source):
You can put this solution on YOUR website!
john has 3 pairs of pants, 4 shirts and 2 belts. how many combinations can he wear? can you tell me a formula for this, i can do it manually but would like a formula,
-----
Counting Principle:
If step one of a process can be done in n1 ways
and step k can be done in nk ways,
the process can be done in n1*n2*n3*...*nk ways
-------------------------------------
Your problem
# of combinations is 3*4*2 = 24 ways
=======================================
Cheers,
Stan H.


test/368803: Multiply and simplify
(9a^2)/(5a^2-30a+45)*(5a-15)/(3a)
1 solutions

Answer 262734 by stanbon(57387) About Me  on 2010-11-09 20:54:36 (Show Source):
You can put this solution on YOUR website!
Multiply and simplify
(9a^2)/(5a^2-30a+45)*(5a-15)/(3a)
-------
(9a^2)/(5(a^2-6a+9)*(5(a-3))/(3a)
---
Cancel factors common to a numerator and a denominator,
such as 3a,5,(a-3), to get:
------
= (3a)/(a-3)
------
Cheers,
Stan H.


test/368802: factor completely
150r^2+360rg+216g^2
1 solutions

Answer 262728 by stanbon(57387) About Me  on 2010-11-09 20:49:20 (Show Source):
You can put this solution on YOUR website!
factor completely
150r^2+360rg+216g^2
-------
= 2[75r^2 + 180rg + 108q^2]
----
= 2*3[25r^2 + 60rg + 36]
----
= 6(5r+6)(5r+6)
==================
Cheers,
Stan H.
==================


Probability-and-statistics/368750: In the department of education at UR university, student records suggest that the population of students spends an average of 5.5 hrs per week playing organized sports. The population's standard deviation is 2.2 hrs per week. Based on a sample of 121 students, healthy lifestyles Inc. (HLI) would like to apply the central limit theorem to make various estimates.
Compute the standard error of the sample mean
what is the chance HLI will find a sample mean between 5 and 6 hrs?
calculate the probability that the sample mean will be between 5.3 and 5.7 hrs
how strange would it be to obtain a sample mean greater than 6.5 hrs?
1 solutions

Answer 262708 by stanbon(57387) About Me  on 2010-11-09 20:13:48 (Show Source):
You can put this solution on YOUR website!
In the department of education at UR university, student records suggest that the population of students spends an average of 5.5 hrs per week playing organized sports. The population's standard deviation is 2.2 hrs per week.
-----------------------
Based on a sample of 121 students, healthy lifestyles Inc.
(HLI) would like to apply the central limit theorem to make various estimates.
-----------------------
Compute the standard error of the sample mean?
Ans: 2.2/sqrt(121) = 0.2
-------------------------------
What is the chance HLI will find a sample mean between 5 and 6 hrs?
t(5) = (5-5.5)/0.2 = -2.5
t(6) = (6-5.5)/0.2 = +2.5
P(5< x-bar <6) = P(-2.5< t < 2.5 when df=120) = 0.9862
-------------------------------
Calculate the probability that the sample mean will be between 5.3 and 5.7 hrs
how strange would it be to obtain a sample mean greater than 6.5 hrs?
---
Find the t-values; then find the probabilities.
=================
Cheers,
Stan H.


Exponential-and-logarithmic-functions/368745: Does following represent a function? Explain.
X's: 3,4,5,-1,-2,-2
Y's: 5,9,12,3,0,-4
1 solutions

Answer 262704 by stanbon(57387) About Me  on 2010-11-09 20:00:45 (Show Source):
You can put this solution on YOUR website!
Does following represent a function? Explain.
X's: 3,4,5,-1,-2,-2
Y's: 5,9,12,3,0,-4
----
Not a function, because -2 is associated with 0
and -2 is associated with -4.
============================
Cheers,
Stan H.


Quadratic_Equations/368747: Divide
3 over 3+i
1 solutions

Answer 262701 by stanbon(57387) About Me  on 2010-11-09 19:58:17 (Show Source):
You can put this solution on YOUR website!
Divide
3 over 3+i
------
3/(3+i)
Multiply numerator and denominator by 3-i to get:
----
[3(3-i)]/[(3+i)(3-i)]
----
= [3(3-i)]/10
------------------------
===========================
Cheers,
Stan H.


Coordinate-system/368742: How do I find the range of a function with a given domain such as x is less than or equal to 0?
1 solutions

Answer 262700 by stanbon(57387) About Me  on 2010-11-09 19:55:32 (Show Source):
You can put this solution on YOUR website!
How do I find the range of a function with a given domain such as x is less than or equal to 0?
---------------------------
That depends on the equation (rule) that defines the function.
Cheers,
Stan H.


Probability-and-statistics/368708: A bag contains green and yellow color tiles. You pick two tiles at random with out replacing the first one. The probability that the first tile is yellow is 3 to 5. The probability of drawing two yellow tiles is 12 to 35. Find the probability that the second tile you pick is yellow.
1 solutions

Answer 262694 by stanbon(57387) About Me  on 2010-11-09 19:24:22 (Show Source):
You can put this solution on YOUR website!
A bag contains green and yellow color tiles. You pick two tiles at random with out replacing the first one.
The probability that the first tile is yellow is 3/5.
------
The probability of drawing two yellow tiles is 12 to 35.
P(yellow and yellow) = P(y)*P(y|y)
12/35 = (3/5)*P(y|y)
P(y|y) = 12/21 = 4/7
------
Find the probability that the second tile you pick is yellow.
P(y|y) = 4/7
=================
Cheers,
Stan H.
=================


Quadratic_Equations/368684: Car speed. On a sales trip, Mark drives the 600 mi to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 mph slower. Total time for the round trip is 22 hr. Find Mark’s average speed on each part of the trip.
1 solutions

Answer 262691 by stanbon(57387) About Me  on 2010-11-09 19:13:03 (Show Source):
You can put this solution on YOUR website!
Car speed. On a sales trip, Mark drives the 600 mi to Richmond averaging a certain speed. The return trip is made at an average speed that is 10 mph slower. Total time for the round trip is 22 hr. Find Mark’s average speed on each part of the trip.
------------------------------
To Richmond DATA:
distance = 600 miles ; rate = x mph ; time = 600/x hrs
-----------------------
From Richmond DATA:
distance = 600 miles ; rate = x-10 mph ; time = 600/(x-10) hrs.
-------------------------
Equation:
time + time = 22 hrs
600/x + 600/(x-10) = 22
----
600(x-10) + 600x = 22x(x-10)
-----
1200x - 6000 = 22x^2-220x
-----
22x^2 - 1420x + 6000 = 0
11x^2 - 710x + 3000 = 0
-----
Positive solution:
x = 60 mph (rate to Richmond)
x-10 = 50 mph (rate from Richmond)
===============================
Cheers,
Stan H.


Polynomials-and-rational-expressions/368670: please help me factor this trinomial 8y^2-6y-9
1 solutions

Answer 262685 by stanbon(57387) About Me  on 2010-11-09 18:43:05 (Show Source):
You can put this solution on YOUR website!
please help me factor this trinomial
8y^2-6y-9
----
8y^2-12y + 6y-9
----
4y(2y-3) + 3(2y-3)
----
(2y-3)(4y+3)
----
Cheers,
Stan H.