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Recent problems solved by 'stanbon'
stanbon answered: 57145 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>NextRectangles/175538: A rectangle has a width of 5 meters and an area of 40 square meters. Write and solve an equation to find the rectangle's length.
1 solutions
Answer 130619 by stanbon(57213)   on 2009-01-07 21:43:22 (Show Source):
You can put this solution on YOUR website!A rectangle has a width of 5 meters and an area of 40 square meters. Write and solve an equation to find the rectangle's length.
--------------------
Area = W*L
40 = 5*L
Length = 8 meters
=======================
Cheers,
Stan H.
|
Radicals/175540: Here is another application I am struggling with. I submitted it earlier but my computer shut down and I am unsure if it went through or not. Here it is again.
2. The equation [D=1.2 square root of h] gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.
a. Solve this equation for h.
b. Long’s Peak in the Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne, Wyoming (about 89 miles away)?
1 solutions
Answer 130615 by stanbon(57213) on 2009-01-07 21:36:38 (Show Source):
You can put this solution on YOUR website!2. The equation [D=1.2 square root of h] gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.
a. Solve this equation for h.
D = 1.2sqrt(h)
sqrt(h) = D/1.2
h = [D/1.2]^2
---------------------------------------
b. Long’s Peak in the Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long’s Peak?
D = 1.2sqrt(14255) = 143.27 miles
--------------------------------------
Can you see Cheyenne, Wyoming (about 89 miles away)?
According to the formula, Yes.
-----------------
Cheers,
Stan H.
|
Probability-and-statistics/175479: Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to gender. They collected the following responses from 100 randomly selected students: Speeds Does not speed Males 40 25 Females 10 25
1. The appropriate test to analyze the relationship between gender and education is:
A. regression analysis
B. Analysis of variance
C. Contingency table analysis
D. Goodness-of-fit
2. The null hypothesis for the analysis is:
A. There is no relationship between gender and speeding.
B. The correlation between gender and speeding is zero.
C. As gender increases, speeding increases.
D. The mean of gender equals the mean of speeding.
3. The degrees of freedom for the analysis is:
A. 1
B. 2
C. 3
D. 4
4. Using 0.05 as the significance level, what is the critical value for the test statistic?
A. 9.488
B. 5.991
C. 7.815
D. 3.841
5. What is the value of the test statistic?
A. 100
B. 9.89
C. 50
D. 4.94
6. Based on the analysis, what can be concluded?
A. Gender and speeding are correlated.
B. Gender and speeding are not related.
C. Gender and speeding are related.
D. No conclusion is possible.
1 solutions
Answer 130613 by stanbon(57213) on 2009-01-07 21:31:37 (Show Source):
You can put this solution on YOUR website!Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to gender. They collected the following responses from 100 randomly selected students: Speeds Does not speed
Males 40 25
Females 10 25
1. The appropriate test to analyze the relationship between gender and education is:
A. regression analysis
B. Analysis of variance
C. Contingency table analysis
D. Goodness-of-fit
----
Ans: B
---------------------
2. The null hypothesis for the analysis is:
A. There is no relationship between gender and speeding.
B. The correlation between gender and speeding is zero.
C. As gender increases, speeding increases.
D. The mean of gender equals the mean of speeding.
---
Ans: A
-------------------
3. The degrees of freedom for the analysis is:
A. 1
B. 2
C. 3
D. 4
---
Ans: A
---------------------
4. Using 0.05 as the significance level, what is the critical value for the test statistic?
A. 9.488
B. 5.991
C. 7.815
D. 3.841
---
Ans: D
----------------------
5. What is the value of the test statistic?
A. 100
B. 9.89
C. 50
D. 4.94
---
Ans: B
--------------------------
6. Based on the analysis, what can be concluded?
A. Gender and speeding are correlated.
B. Gender and speeding are not related.
C. Gender and speeding are related.
D. No conclusion is possible.
---
Ans: A
-----------------------------
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/175459: In numbering the pages of a book, a printer uses 522 digits. How many numbered pages does the book have?
: So this is what i tried:
Ones: 9
Tens: 90
Hundreds: 900
I just don't know what to do, please, please help!
1 solutions
Answer 130534 by stanbon(57213) on 2009-01-07 16:36:41 (Show Source):
You can put this solution on YOUR website!In numbering the pages of a book, a printer uses 522 digits. How many numbered pages does the book have?
: So this is what i tried:
Ones: Pages:9......Digits:9
Tens: Pages:99-9= 90....Digits: 2*90 = 180
Hundreds: Digits: 522-(189) = 333; Pages = 111
--------------
Total Pages 9+99+111 = 219
===================================
Cheers,
Stan H.
|
Rational-functions/175440: times to unload a certain truck:
al,bob,chuck together t hours
al alone t+1
bob alone t+6
chuck alone 2t
find t
1 solutions
Answer 130510 by stanbon(57213) on 2009-01-07 15:00:22 (Show Source):
You can put this solution on YOUR website!times to unload a certain truck:
al,bob,chuck together t hours
al alone t+1
bob alone t+6
chuck alone 2t
find t
-----------------------
You are given the time for each person and the group.
For example Al alone takes (t+1) hr/job
Invert that to get Al's rate: 1/(t+1) job/hr
------------------------------------------------
Equation:
rate + rate + rate = together rate
1/(t+1) + 1/(t+6) + 1/2t = 1/t
Multiply thru by 2t(t+1)(t+6) to get:
2t(t+6) + 2t(t+1) + (t+1)(t+6) = 2(t+1)(t+6)
2t^2+12t + 2t^2 + 2t + t^2 + 7t + 6 = 2t^2 + 14t + 12
3t^2 + 7t -6 = 0
3t^2 + 9t - 2t-6 = 0
3t(t+3) -2(t+3) = 0
(t+3)(3t-2) = 0
Positive solution:
t = 2/3 hr
=============
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/175439: 2m^2+13m-18/2m+3
an polynomial wiz can break down why the answer is: m+5 -33/2m+3 totallu confused with this problem
1 solutions
Answer 130507 by stanbon(57213) on 2009-01-07 14:52:12 (Show Source):
You can put this solution on YOUR website!2m^2+13m-18/2m+3
----------------------
Set it up as you would a long-division problem
----
Divide 2m into 2m^2 to get m
Multiply m times 2m+3 to get 2m^2+3m
Subtract that from 2m^2 + 13m - 18 to get 10m-18
Divide the 10m by 2m to get 5
Multiply 5 times 2m+3 to get 10m+15
Subtract that from from 10m-18 to get -33
=============================
The quotient is m+5
The remainder is -33
========================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/175435: 15t^2-29t-14\ 3t-7
answer:5t+2
need a full break down of how my book got this answer i go as far as 15t\3t+5t and -14t/-7=+2 but what happened to the -29t in this equation
1 solutions
Answer 130504 by stanbon(57213) on 2009-01-07 14:31:08 (Show Source):
You can put this solution on YOUR website!15t^2-29t-14\ 3t-7
Factor to get:
(3t-7)(5t+2)/(3t-7)
= 5t+2
-------------
Proof:
(3t-7)(5t+2)
Use FOIL:
F: 3t*5t = 15t^2
O: 3t*2 = 6t
I: -7*5t = -35t
L: -7*2 = -14
------------------
Combine to get:
15t^2 -29t - 14
===================
So the -29t comes from combining the Outer and the Inner products.
====================
Cheers,
Stan H.
|
Rational-functions/175432: bob has 3000 ft of fence to build 4 adjacent pens. what is x and y? what is the maximum area he can obtain?
1 solutions
Answer 130502 by stanbon(57213) on 2009-01-07 14:25:11 (Show Source):
You can put this solution on YOUR website! bob has 3000 ft of fence to build 4 adjacent pens. what is x and y? what is the maximum area he can obtain?
------------------
Draw the adjacent pens as a rectangle with base and top of y and height of x.
Notice there are 5 vertical pieces needed to construct four pens.
-------------
Fence Equation: 5x + 2y = 3000
Area = xy
---------------
Solve 1st for y: y = (-5/2)x + 1500
Substitute into the Area Equation:
A(x) = x[(-5/2)x+1500]
A(x) = (-5/2)x^2 + 1500x
-------------------
Maximum Area occurs when x = -b/2a = -1500/(-5) = 300
If x = 300 y = (-5/2)(300) + 1500 = 750
-------------
Maximum area = xy = 300*750 = 225000 sq. ft.
=========================================
Cheers,
Stan H.
|
Probability-and-statistics/175302: In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?
1 solutions
Answer 130499 by stanbon(57213) on 2009-01-07 14:10:32 (Show Source):
You can put this solution on YOUR website! In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?
--------------------------------
Draw a normal curve with mean 36.84.
Sketch a left tail containing 10% of the population of HDTV that fail.
----------------
Find the z-value corresponding to left-tail 10%: -1.2816
-----------------
Find the x-value corresponding to that z-value:
z(x) = (x-u)/sigma
-1.2816 = (x-36.84)/3.34
x-36.84 = -4,2804
x = 32.56 months is the upper limit of time for the warranty.
==============================
Cheers,
Stan H.
|
Trigonometry-basics/175425: find the center and radius of y^2+x^2+9y-6x-10=0
1 solutions
Answer 130494 by stanbon(57213) on 2009-01-07 14:00:02 (Show Source):
You can put this solution on YOUR website!find the center and radius of y^2+x^2+9y-6x-10=0
--------------
Complete the square on the x-terms and on the y-terms:
[x^2 - 6x + ?] + [y^2 + 9y + ?] = 10
[x^2 -6x + 9] + [y^2 + 9y + (9/2)^2] = 10 + 9 + (9/2)^2
---
(x-3)^2 + (y+(9/2))^2 = 23.5
------------------
Center: (3,(-9/2))
Radius: sqrt(23.5)
======================
Cheers,
Stan H.
|
Rational-functions/175427: a tangent to a circle is a line that touches the circle at one point and is perpendicular to a radius of the circle. a circle has center (3,1) and has point (4,5) on the circle. find the equation of the line tangent to circle at (4,5).
1 solutions
Answer 130492 by stanbon(57213) on 2009-01-07 13:54:52 (Show Source):
You can put this solution on YOUR website!a tangent to a circle is a line that touches the circle at one point and is perpendicular to a radius of the circle. a circle has center (3,1) and has point (4,5) on the circle. find the equation of the line tangent to circle at (4,5).
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The slope of the radius is (5-1)/(4-3) = 4
So the slope of the tangent is -1/4
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The intercept of the tangent: 5 = (-1/4)4 + b
b = 6
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Equation of the tangent line: y = (-1/4)x + 6
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Cheers,
Stan H.
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Travel_Word_Problems/175428: can u help me solve this problem
solve and graph on a numberline
8>=2x+4>=16
thank you
I don't know how to solve this problem on my midterm, because i was sick on that day
1 solutions
Answer 130491 by stanbon(57213) on 2009-01-07 13:51:47 (Show Source):
You can put this solution on YOUR website!solve and graph on a numberline
8>=2x+4>=16
Note: Your problem says that 8 is greater than or equal to 16.
There is no solution for that problem.
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Cheers,
Stan H.
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Travel_Word_Problems/175420: an airplane travwl 100km/h then another airplane. In 4 hours the faster airplanes travel the same distance as the slower airplane travel in 6 hours. Find the rate of the faster airplane.
1 solutions
Answer 130489 by stanbon(57213) on 2009-01-07 13:48:44 (Show Source):
You can put this solution on YOUR website!an airplane travwl 100km/h slower then another airplane. In 4 hours the faster airplanes travel the same distance as the slower airplane travel in 6 hours. Find the rate of the faster airplane.
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Slower plane DATA:
rate = x-100 km/h ; time = 6 hrs; distance = rt = 6(x-100) km
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Faster plane DATA:
rate = x km/h ; time = 4 hrs; distance = rt = 4x km
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Equation:
distance = distance
6(x-100) = 4x
2x = 600
x = 300 km/h (rate of the faster airplane)
x-100 = 200 km/h ( rate of the slower airplane)
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Cheers,
Stan H.
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Permutations/175401: Please help, I'm gettin no where with it. Car thieves steal on automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for theft insurance in the amount of $16,000 on the certain type of car?
1 solutions
Answer 130481 by stanbon(57213) on 2009-01-07 12:47:49 (Show Source):
You can put this solution on YOUR website!Car thieves steal on automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for theft insurance in the amount of $16,000 on the certain type of car?
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That is an "expected value" problem.
The random variable is "cost to the car owner".
Cost is -x if his car is not stolen or (16000-x) if it is stolen
The probability of -x is (399/400); the prob of (16000-x) is (1/400)
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The expected value is (399/400)(-x) + (1/400)(16000-x)
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For the owner to "break even" this expected value should be zero.
(399/400)(-x) + (1/400)(16000-x) = 0
-399x + 16000-x = 0
-400x = -16000
x = $40.00 (His annual cost should be $40).
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Cheers,
Stan H.
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Permutations/175406: How many arrangements of the letters in the word 'olive' can you make if each arrangement must use three letters?
1 solutions
Answer 130476 by stanbon(57213) on 2009-01-07 12:28:43 (Show Source):
You can put this solution on YOUR website!How many arrangements of the letters in the word 'olive' can you make if each arrangement must use three letters?
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Arrangements are permutations.
You want 5P3 = 5!/(5-3)! = 5*4*3 = 60
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Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/175416: 23.5x^2+3.25x+15.6=0
1 solutions
Answer 130475 by stanbon(57213) on 2009-01-07 12:25:20 (Show Source):
You can put this solution on YOUR website!23.5x^2+3.25x+15.6=0
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There are two ways to attack messy quadratics like this.
1st; graph it and find the x-intercepts using a calculator.
Checking b^2-4ac you find there are no Real Number intercepts.
or
2nd; use the quadratic formula:
x = [-3.25 +- sqrt(3.25^2 - 4*23.5*15.6)]/[2*23.5]
x = [-3.25 +- 38.16i]/[47]
Cheers,
Stan H.
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Polygons/175245: The interior angles of a polygon have measures 170 degrees, 160 degrees, 150 degrees, 140 degrees... down to some smallest angle. The numbers 170 degrees, 160 degrees, 150 degrees, 140 degrees are members of an Arithmetic Progression. Find the number of sides of the polygon.
1 solutions
Answer 130333 by stanbon(57213) on 2009-01-06 17:12:51 (Show Source):
You can put this solution on YOUR website!The interior angles of a polygon have measures 170 degrees, 160 degrees, 150 degrees, 140 degrees... down to some smallest angle. The numbers 170 degrees, 160 degrees, 150 degrees, 140 degrees are members of an Arithmetic Progression. Find the number of sides of the polygon.
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The sum of the exterior angles is 360.
Each exterior angle is the supplement of an interior angle.
The angles exterior to the listed interior angles are:
10,20,30,40, etc.
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Equation:
10 + 20 + 30 + 40 + x = 360
x = 260
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Find the arithmetic sequence 50+60+70+80 = 260
Since there are 8 exterior angles, there are 8 sides.
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Cheers,
Stan H.
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Linear_Algebra/175247: It says classify each system and give the # of solutions but i cant get it. The problem is 3x=-y-2 and 2y+4=-6x. It is solving special Systems
1 solutions
Answer 130329 by stanbon(57213) on 2009-01-06 16:55:17 (Show Source):
You can put this solution on YOUR website!It says classify each system and give the # of solutions but i cant get it. The problem is 3x=-y-2 and 2y+4=-6x
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Put each equation in slope-intercept form.
y = 3x-2
y = -3x -2
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The slopes are 3 and -3. Since they a different the
lines must intersect at a single point.
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The system is said to be consistent and it has one
Real.
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Note:
If the slopes are the same and the intercepts are the
same, the system is dependent and has an infinite number
of solutions.
If the slopes are the same and the intercepts are different,
the system is inconsistent and has no solution.
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Cheers,
Stan H.
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Geometry_Word_Problems/175194: The lengthsof the sides of a triangle are consecutive even integers.find the length of the longest side if it is 22 units shorter than the perimeter
1 solutions
Answer 130277 by stanbon(57213) on 2009-01-06 09:38:49 (Show Source):
You can put this solution on YOUR website!The lengths of the sides of a triangle are consecutive even integers.find the length of the longest side if it is 22 units shorter than the perimeter
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1st 2x
2nd 2x+2
3rd 2x+4
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Equation:
2x+4 = (2x + 2x+2 + 2x + 4) -22
2x+4 = 6x + 6 -22
4x = 20
x = 5
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2x = 10
2x+2 = 12
2x+4 = 14
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Cheers,
Stan H.
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Expressions-with-variables/175202: Given that (x+3) and (x-1) are both factors of the same expression x^3+ax^2-bx-a,find the values of the constants a and b.
Determine the third factor or the expression.
1 solutions
Answer 130276 by stanbon(57213) on 2009-01-06 09:13:28 (Show Source):
You can put this solution on YOUR website!Given that (x+3) and (x-1) are both factors of the same expression x^3+ax^2-bx-a,find the values of the constants a and b.
Determine the third factor or the expression.
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If x-1 is a factor, f(1) = 0
f(1) = 1^3 + a(1^2) - b(1) -a = 1 + a -b -a = 1-b = 0
Therefore b = 1
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If x+3 is a factor, f(-3) = 0
f(-3) = (-3)^3 + a(-3)^2 - b(-3) -a = 0
-27 + 9a +3b -a = 0
Substitute b=1 and get
-27 +8a + 3 = 0
8a = 24
a = 3
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f(x) = x^3+ax^2-bx-a
f(x) = x^3 + 3x^2 -x - 3
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Use synthetic division to find the 3rd factor:
1)....1....3....-1....-3
.......1......4...3...|..0
-3).....1......1..|..0
3rd factor: x + 1
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Cheers,
Stan H.
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Complex_Numbers/175161: how do I determine whether(y-3) is a factor of (y^4+2y^2-4) using the remainder and factor theorem?
1 solutions
Answer 130255 by stanbon(57213) on 2009-01-05 23:22:15 (Show Source):
You can put this solution on YOUR website!determine whether(y-3) is a factor of (y^4+2y^2-4) using the remainder and factor theorem?
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3)....1....0....2....0....-4
.......1....3....11...33..|..95
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Since the remainder is 95, and not zero, y-3 is not a factor of y^4 + 2y^2 -4.
Cheers,
Stan H.
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Polynomials-and-rational-expressions/175166: Would you please help me with these problems?
1). Area of a Parallelogram: Find a trinomial A(x) that represents the area of a parallelogram whose base is 3x+2 meters and whose height is 2x+3 meters.
Find A(3).
2. Compound Semiannually: P dollars is invested at an annual interst rate r for 1 year. If the interest is compounded semiannually, then the polynomial
P(1+r/2)² represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the Polynomial is P=$200 and r=10%.
3. Perimeter of a Rectangle: The peremeter of a rectanglar backyard is 6x+6 yards. If the width is x yards, find a binomial that represents the length.
4. Selling Shirts: If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000-100p shirts at a tournament.
Thank you so much!
1 solutions
Answer 130254 by stanbon(57213) on 2009-01-05 23:04:03 (Show Source):
You can put this solution on YOUR website!1). Area of a Parallelogram: Find a trinomial A(x) that represents the area of a parallelogram whose base is 3x+2 meters and whose height is 2x+3 meters
A(x) = (3x+2)(2x+3) = 6x^2+13x+6.
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Find A(3) = 6(3^2) + 13*3 + 6 = 54+39+6 = 99
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.
2. Compound Semiannually: P dollars is invested at an annual interst rate r for 1 year. If the interest is compounded semiannually, then the polynomial
P(1+(r/2))^2 represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the Polynomial if P=$200 and r=10%.
A(t) = P[1 + r + (r/2)^2]
A(t) = 200[1 + 0.1 + (0.05)^2] = 200[1.1025] = $220.50
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3. Perimeter of a Rectangle: The peremeter of a rectanglar backyard is 6x+6 yards. If the width is x yards, find a binomial that represents the length.
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perimeter = 6x+6
2(L+W) = 6x+6
L+W = 3x+3
L + x = 3x+3
L = 2x+3
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4. Selling Shirts: If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000-100p shirts at a tournament.
---
What is the question?
=================================
Cheers,
Stan H.
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Complex_Numbers/175170: what is the remainder when d^4+2d^2+5d-10 is divided by d+4?
1 solutions
Answer 130253 by stanbon(57213) on 2009-01-05 22:48:06 (Show Source):
You can put this solution on YOUR website!what is the remainder when d^4+2d^2+5d-10 is divided by d+4?
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Find f(-4) or use synthetic division to find the remainder.
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-4)....1....0....2....5....-10
........1....-4...18...-67...|..258
Remainder: 258
======================================================
Cheers,
Stan H.
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Average/175173: I am in desperate need of understanding Algebra. Would you please help me!?
1). Factor Out the GCF in this expression:
〖15x〗^2 y^2-〖9xy〗^2+〖6x〗^2 y
2). Use grouping to factor each Polynomial completely:
x^3+ax+3a+〖3a〗^2
3). Factor this polinomial. If it is prime, please tell me.
18z + 45 + z^2
the same with the next one:
4). 〖3x〗^3 y^2-〖3x〗^2 y^2+〖3xy〗^2
Thank you so much!
1 solutions
Answer 130251 by stanbon(57213) on 2009-01-05 22:40:08 (Show Source):
You can put this solution on YOUR website!1). Factor Out the GCF in this expression:
〖15x〗^2 y^2-〖9xy〗^2+〖6x〗^2 y
2). Use grouping to factor each Polynomial completely:
x^3+ax+3a+〖3a〗^2
3). Factor this polinomial. If it is prime, please tell me.
18z + 45 + z^2
the same with the next one:
4). 〖3x〗^3 y^2-〖3x〗^2 y^2+〖3xy〗^2
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your posting is very confusing.
Cheers,
Stan H.
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