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Recent problems solved by 'stanbon'
stanbon answered: 57151 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next
Polynomials-and-rational-expressions/337166: please help me solve this equation:x to the third power +4x square-3x-12
1 solutions
Answer 241667 by stanbon(57219)   on 2010-08-31 12:52:16 (Show Source):
You can put this solution on YOUR website!x to the third power +4x square-3x-12
----------------
x^3+4x^2-3x-12 = 0
---
I graphed it and found a zero at x = -4
---
Then I used synthetic division:
----
-4)....1....4....-3....-12
........1.....0....-3...|..0
Quotient: x^2-3 = 0
Factor:(x-sqrt(3))(x+sqrt(3)) = 0
-------------------------------------------
Solutions: x = -4 or x = sqrt(3) or x = -sqrt(3)
===================================================
Cheers,
Stan H.
=========
|
Linear_Equations_And_Systems_Word_Problems/337162: How do you set up this word problem using I=P*R*T?
Steve has $25,000 to invest and wishes to earn an overall annual rate of return of 8%. His financial advisor recommends that he invest some of the money in a 5-year CD paying 4% per annum and the rest in a corporate bond paying 9% per annum. How much should be placed in each investment in order for Steve to achieve his goal?
1 solutions
Answer 241664 by stanbon(57219) on 2010-08-31 12:45:31 (Show Source):
You can put this solution on YOUR website!How do you set up this word problem using I=P*R*T?
Steve has $25,000 to invest and wishes to earn an overall annual rate of return of 8%. His financial advisor recommends that he invest some of the money in a 5-year CD paying 4% per annum and the rest in a corporate bond paying 9% per annum. How much should be placed in each investment in order for Steve to achieve his goal?
-------
Interest from the CD will be P*(0.05)(5)
Interest from the bond will be p(0.09)5
Equation:
interest + interest = interest
0.05*5x + 0.09*5*(25000-x) = 0.08*5*25000
-----------------
Multiply thru by 100 to get:
5*5x + 9*5(25000-x) = 8*525000
----
25x + 45*25000- 45x = 40*25000
-20x = -5*25000
x = $6250 (amt. to invest in 5% CDs)
----
25000-x = $18750 (amt. to invest in 9% bonds
=================================================
Cheers,
Stan H.
|
Graphs/337161: I am trying to figure finding slopes, if it exists, of the line containing the pair of points.
However I do not know what the and in the equation means? for example (8,4)and(9,-9)
trying to find slope m=
Can you help explain what this is please? Thanks Mary
1 solutions
Answer 241657 by stanbon(57219) on 2010-08-31 12:33:44 (Show Source):
You can put this solution on YOUR website!(8,4)and(9,-9)
trying to find slope m=
==============
slope = (change in y)/(corresponding change in x)
----------------
m = (-9-4)/?
Notice the order in which the y-values were selected.
You MUST use the same order in selecting the x-values
m = (-9-4)/(9-8)
m = -13/1
m = -13
==============
Cheers,
Stan H.
|
Rectangles/337159: The product of two consecutive odd integers is 99. Find the two integers.
1 solutions
Answer 241653 by stanbon(57219) on 2010-08-31 12:29:44 (Show Source):
You can put this solution on YOUR website!The product of two consecutive odd integers is 99. Find the two integers.
1st = 2x-1
2nd = 2x+1
----------------
Equation:
(2x-1)(2x+1) = 99
4x^2-1 = 99
4x^2 = 100
x^2 = 25
x = 5 or -5
---
If x = 5
2x-1 = 9
2x+1 = 11
----------------
If x = -5
2x-1 = -11
2x+1 = -9
================
Cheers,
Stan H.
|
Probability-and-statistics/337022: To test the null hypothesis that the average lifetime for a particular brand of bulb is 725 hours versus the alternative that the average lifetime is different from 725 hours, a sample of 100 bulbs is used. If the standard deviation is 50 hours and α is equal to 0.01, what values for will result in rejection of the null hypothesis (show all work).
(Points :4)
A 95% confidence interval estimate for a population mean was computed to be (36.5 to 56.0). Determine the mean of the sample, which was used to determine the interval estimate (show all work).
(Points :4)
1 solutions
Answer 241615 by stanbon(57219) on 2010-08-31 09:55:13 (Show Source):
You can put this solution on YOUR website!To test the null hypothesis that the average lifetime for a particular brand of bulb is 725 hours versus the alternative that the average lifetime is different from 725 hours, a sample of 100 bulbs is used. If the standard deviation is 50 hours and α is equal to 0.01, what values for will result in rejection of the null hypothesis (show all work).
---------
2-tail Ttest with alpha = 1% and df = 99
Critical Value = +/-invT(0.005,99) = +/-2.6264
Reject intervals are (-inf,-2.6264)U(2.6264,+inf)
===========================================================
A 95% confidence interval estimate for a population mean was computed to be (36.5 to 56.0). Determine the mean of the sample, which was used to determine the interval estimate
xbar-E = 36.5
xbar+E = 56
----------------
2xbar = 92.5
xbar = 46.25
==================
Cheers,
Stan H.
==================
|
Miscellaneous_Word_Problems/337085: A marketing company uses to photocopiers to make 30,000 copies for advertising. One copier can produce 3000 copies per hour. What is the hourly rate of the second copier if together they take 4 hours to produce the advertising?
1 solutions
Answer 241596 by stanbon(57219) on 2010-08-31 09:10:05 (Show Source):
You can put this solution on YOUR website!A marketing company uses to photocopiers to make 30,000 copies for advertising. One copier can produce 3000 copies per hour. What is the hourly rate of the second copier if together they take 4 hours to produce the advertising?
----
Fact: rate *time = # produced
-----------
Equation:
3000*4 + r*4 = 30,000
---
4r = 30,000-12000
---
4r = 18,000
r = 4500 per hour (rate of the 2nd copier)
==============
Cheers,
Stan H.
|
Permutations/337091: A teacher is to be assigned to teach 5 different courses in 5 different class periods on Mondays. If exactly one course meets each period, how many different assignments of courses to these class periods are possible for Mondays?
1 solutions
Answer 241595 by stanbon(57219) on 2010-08-31 09:05:43 (Show Source):
You can put this solution on YOUR website!A teacher is to be assigned to teach 5 different courses in 5 different class periods on Mondays. If exactly one course meets each period, how many different assignments of courses to these class periods are possible for Mondays?
-------
1st period; 2nd period; 3rd period;....;5th period
----
5 course choice for 1st
4 course choice for 2nd
3 course choice for 3rd
...
1 course choice for 5th
-----------------------------
Total number of choices: 5P5 = 5! = 120
===========================================
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/337092: Hi- I teach Adult Basic Education, mostly I help students pass the GED test. I am no Mathematician, and sometimes I get a question that I can not explain the Mathematics behind solving. This is an example of one such problems.
James Torres works in an electircal equiptment factory and does the final assembly on power trasfer units. He keeps a log of the number of units he completes each day. He works five days a week. Below is his log for the week of October 2 through October 6.
Production Log
Name: James Torres
Week: 10/2-10/6
Date No. units Assembled
10/2 12
10/3 15
10/4 18
10/5 17
10/6 16
Weekly total ______
Daily average ______
Here is the question:
The total for 10/3 is how much higher than the total for 10/2?
a. 3%
b. 12.5%
c. 20%
d. 25%
The answer is d. 25%.. . but WHY? The only rational I can come up with is 3 is the difference of 15 and 12, and 3 is 25% of 12. But why do I do that to solve this problem? How do I explain this to my students? Most of my students are visual learners so anything I can do to help me understand this, will in turn help them..
Thanks so much for taking the time to explain this to me, I really appreciate it.
1 solutions
Answer 241592 by stanbon(57219) on 2010-08-31 09:00:34 (Show Source):
You can put this solution on YOUR website!10/2 12
10/3 15
10/4 18
10/5 17
10/6 16
Weekly total ______
Daily average ______
Here is the question:
The total for 10/3 is how much higher than the total for 10/2?
a. 3%
b. 12.5%
c. 20%
d. 25%
The answer is d. 25%.. . but WHY? The only rational I can come up with is 3 is the difference of 15 and 12, and 3 is 25% of 12. But why do I do that to solve this problem? How do I explain this to my students? Most of my students are visual learners so anything I can do to help me understand this, will in turn help them..
Thanks so much for taking the time to explain this to me, I really appreciate it.
-------------
Right.
The quantitative gain from 10/2 to 10/3 is 15-12.
That is a gain of 3 from a base of 12
So the percent gain is figured from a base of 12.
You could set up an equation to figure the percent (per one-hundred)
gain as follows:
x/100 = 3/12
x = 100(3/12)
x = 100(1/4)
x = 25
The percent gain is 25%.
============================
Visualizing this gain with blocks might also be a help.
Compare 12 blocks to 15 blocks to see the gain.
---
Keep duplicating the 12 to 15 picture till you have x to 100
The x will be seen to be 25.
=====================
Cheers,
Stan H.
|
Linear-equations/337093: In the xy-coordinate plane, the graph of x = y^2 - 4 intersects line l at
(0, p) and (5, t). What is the greatest possible value of the slope of l?
1 solutions
Answer 241588 by stanbon(57219) on 2010-08-31 08:50:37 (Show Source):
You can put this solution on YOUR website!In the xy-coordinate plane, the graph of x = y^2 - 4 intersects line l at
(0, p) and (5, t). What is the greatest possible value of the slope of l?
-----------------------
Substitute each point into the equation to get two equations in p and t.
---------------
p = 0^2-4
t = 5^2-4
---
p = -4
t = 21
-------
You now have two points: (0,-4) and 5,21)
slope of line L = (21--4)/(-4-0) = 25/-4 = -4/25
----------------
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/337086: Lori and Jason are gleaning (or collecting) avocados from a grove. Jason can glean 350 avocados per hour. Lori can glean 400 avocados per hour. If they start at the same time how long will it take both of them to collect a total of 10,500 avocados. Thank you!!
1 solutions
Answer 241587 by stanbon(57219) on 2010-08-31 08:45:25 (Show Source):
You can put this solution on YOUR website!Jason can glean 350 avocados per hour. Lori can glean 400 avocados per hour. If they start at the same time how long will it take both of them to collect a total of 10,500 avocados.
----
Each hour they are gleaning (350+400) = 750 avocados.
----
time to glean 10,500 = 10500/750 = 14 hrs.
==============================================
Cheers,
Stan H.
============
|
Equations/337090: how do i solve (r+6)/(5)=(r+8)/(7)
1 solutions
Answer 241586 by stanbon(57219) on 2010-08-31 08:41:47 (Show Source):
You can put this solution on YOUR website!solve (r+6)/(5)=(r+8)/(7)
-------
Multiply both sides by 35 to get:
7(r+6) = 5(r+8)
---
7r+42 = 5r+40
Subtract 5r from both sides.
Subtract 42 from both sides.
2r = -2
r = -1
===================
Cheers,
Stan H.
|
Probability-and-statistics/336916: 10. Which of the following statements is correct?
a. For a given level of significance, the critical value of Student's t increases as n increases.
b. A test statistic of t = 2.131 with d.f. = 15 leads to a clear-cut decision in a two-tailed test where α = .05
c. It is harder to reject the null hypothesis when conducting a two-tailed test rather than a one-tailed test.
If we desire α = 0.10 then a p-value of 0.13 would lead us to reject the null hypothesis.
1 solutions
Answer 241541 by stanbon(57219) on 2010-08-30 22:12:28 (Show Source):
You can put this solution on YOUR website!Which of the following statements is correct?
a. For a given level of significance, the critical value of Student's t increases as n increases.
It increases for a left-tail test; It decreases for a right-tail test.
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b. A test statistic of t = 2.131 with d.f. = 15 leads to a clear-cut decision in a two-tailed test where α = .05
2*tcdf(2.131,1000,15) = 5%
Not a clear-cut decision
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c. It is harder to reject the null hypothesis when conducting a two-tailed test rather than a one-tailed test.
The procedure is similar.
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If we desire α = 0.10 then a p-value of 0.13 would lead us to reject the null hypothesis.
No; since the p-value is greater that 10% you would fail to reject Ho.
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Cheers,
Stan H.
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Probability-and-statistics/336924: In testing the hypothesis,Ho:u >41 with line under it and Ho:u <41 , using the p-value approach, a p-value of 0.0359 was obtained. If σ = 9.2, find a sample mean which produced this p-value given that the sample of size n = 45 was randomly selected (show all work).
(Points :4)
1 solutions
Answer 241537 by stanbon(57219) on 2010-08-30 21:58:10 (Show Source):
You can put this solution on YOUR website!In testing the hypothesis,
Ho:u >= 41
Ha:u < 41
Using the p-value approach, a p-value of 0.0359 was obtained.
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If σ = 9.2, find a sample mean which produced this p-value given that the sample of size n = 45 was randomly selected .
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Left-tail test with alpha = 9.2 and df = 44 implies the test
statistic was invT(0.0369 with df = 44) = -1.8315
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Using x-bar = zs+u, solve for x-bar.
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x-bar = -1.8315*9.2 + 41
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x-bar = 24.15
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Cheers,
Stan H.
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Probability-and-statistics/336921: there are a total of 5 angles 3 acute 1 right and 1 obtuse. one angle is selected at random and then replaced. a second angle is rendomly selected ( thus making it possible for the same angle to be selected twice). What is the probability that both angles selected are acute
1 solutions
Answer 241535 by stanbon(57219) on 2010-08-30 21:48:05 (Show Source):
You can put this solution on YOUR website!there are a total of 5 angles 3 acute 1 right and 1 obtuse.
one angle is selected at random and then replaced.
a second angle is rendomly selected ( thus making it possible for the same angle to be selected twice).
What is the probability that both angles selected are acute?
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P(select acute angle) = 3/5
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Replacement makes the selections independent.
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P(2 acute) = (3/5)(3/5) = 9/25
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Cheers,
Stan H.
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Probability-and-statistics/336942: A bag contains 5 green, 3 red, 2 orange and 6 yellow skittles. How many green skittles must be added to the bag so that the probability of ramdonly picking a green skittle is 2/3?
1 solutions
Answer 241534 by stanbon(57219) on 2010-08-30 21:44:18 (Show Source):
You can put this solution on YOUR website!A bag contains
5 green skittles
3 red skittles
2 orange skittles
6 yellow skittles
how many green skittles must be added to the bag so that the probability of randomly picking a green skittle is 2/3? explain.
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Let the number to add be "x":
(5 + x)/(16 + x) = 2/3
Cross multiply to get:
15+3x = 32 + 2x
x = 17
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Cheers,
Stan H.
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Travel_Word_Problems/336970: how do you solve: for her workout, Sarah walks north at the rate of 3mph and returns at the rate of 4mph. how many miles did she walk if the round trip took 3.5hours?
1 solutions
Answer 241516 by stanbon(57219) on 2010-08-30 20:43:56 (Show Source):
You can put this solution on YOUR website!Sarah walks north at the rate of 3mph and returns at the rate of 4mph. how many miles did she walk if the round trip took 3.5hours?
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North DATA:
rate = 3 mph ; time = x hrs ; distance = rt = 3x miles
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Return DATA:
rate = 4 mph ; time = 3.5-x hrs ; distance = rt = 4(3.5-x) miles
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Equation:
distance = distance
3x = 4(3.5-x)
3x = 14-4x
7x = 14
x = 2 hrs (North time)
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North distance = 3x = 3*2 = 6 miles
Return distance = 4(3.5-2) = 6 miles
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Round-trip = 6 miles
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Cheers,
Stan H.
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Travel_Word_Problems/336967: Please help show me how to answer this word problem:
You ride your bike up a steep mountain road at 5 miles per hour. How far do you go in 3 hours?
1 solutions
Answer 241511 by stanbon(57219) on 2010-08-30 20:35:46 (Show Source):
You can put this solution on YOUR website!You ride your bike up a steep mountain road at 5 miles per hour. How far do you go in 3 hours?
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distance = rate*time
distance = 5mph*3 hrs
distance = 15 miles
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Cheers,
Stan H.
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Linear-equations/336959: find an equation through each given pair of points. Write the answer in standard from using only integers. (-1,1) (1,-1)
1 solutions
Answer 241509 by stanbon(57219) on 2010-08-30 20:33:54 (Show Source):
You can put this solution on YOUR website!find an equation through each given pair of points. Write the answer in standard from using only integers. (-1,1) (1,-1)
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slope = (-1-1)/(1--1) = -2/2 = -1
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Form: y = mx + b
Using m = -1 and point (-1,1), solve for "b":
1 = -1*-1 + b
b = 0
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Equation: y = -x
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Cheers,
Stan H.
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Rectangles/336964: length of a rectangle is 3cm greater then its width. the perimeter is 24 cm. what is the dimensions of the rectangle
1 solutions
Answer 241504 by stanbon(57219) on 2010-08-30 20:31:04 (Show Source):
You can put this solution on YOUR website!length of a rectangle is 3cm greater then its width. the perimeter is 24 cm. what is the dimensions of the rectangle
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Let width = W
length = W+3
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Perimeter = 2(width + length)
24 = 2(W + W+3))
12 = 2W + 3
2W = 9
W = 4.5 cm
length = W+3 = 7.5 cm
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Cheers,
Stan H.
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Polygons/336962: the measure of each interior angle of a regular polygon is 14 times the measure of an exterior angle. how many sides does the polygon have?
1 solutions
Answer 241502 by stanbon(57219) on 2010-08-30 20:27:56 (Show Source):
You can put this solution on YOUR website!the measure of each interior angle of a regular polygon is 14 times the measure of an exterior angle. how many sides does the polygon have?
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The interior and its corresponding exterior angle are supplementary.
x + 14x = 180
15x = 180
x = 12 degrees (the exterior angle)
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Fact: The sum of the exterior angles is 360 degrees
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# of exterior angles = 360/12 = 30
---
# of sides = # of exterior angles = 30
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/336963: Find all points having an y-coordinate of -3 whose distance from the point (1,2) is 13.
1 solutions
Answer 241500 by stanbon(57219) on 2010-08-30 20:24:32 (Show Source):
You can put this solution on YOUR website!Find all points having an y-coordinate of -3 whose distance from the point (1,2) is 13.
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That would be a circle.
Draw the picture; put the center at (1,2) and let the radius be 13.
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Pick any point on the circle and label it (x,y)
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Equation:
distance from center to (x,y) = 13
d^2 = (x-1)^2+(y-2)^2
d = sqrt[(x-1)^2+(y-2)^2]
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Cheers,
Stan H.
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Rate-of-work-word-problems/336947: A window washer can wash the windows on one side of a building in 72 working hours. With an assistant he can do the job in 40 hours. How many hours would the assistant take to do the job working alone?
1 solutions
Answer 241499 by stanbon(57219) on 2010-08-30 20:18:48 (Show Source):
You can put this solution on YOUR website!A window washer can wash the windows on one side of a building in 72 working hours.
W W DATA:
time = 72 hrs/job
rate = 1/72 job/hr
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With an assistant he can do the job in 40 hours.
Together DATA:
time = 40 hrs/job
rate = 1/40 job/hr
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Assistant DATA:
time = x hrs/job
rate = 1/x job/hr
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How many hours would the assistant take to do the job working alone?
Equation:
rate + rate = together rate
1/72 + 1/x = 1/40
----
Multiply thru by 40*72x to get:
40x + 40*72 = 72x
32x = 40*72
x = 90 hrs (time the assistant would need to do the job alone)
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Cheers,
Stan H.
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Angles/336828: If a supplement of an angle has a measure 78 less than the measure of the angle, what are the measures of the angles?
1 solutions
Answer 241438 by stanbon(57219) on 2010-08-30 17:58:21 (Show Source):
You can put this solution on YOUR website!If a supplement of an angle has a measure 78 less than the measure of the angle, what are the measures of the angles?
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Equation:
Let the angle be "x":
180-x = x-78
2x = 180+78
2x = 258
x = 129 degrees
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180-x = 51 degrees
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Cheers,
Stan H.
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Angles/336819: the supplement of an angle is 20 less than three times the angle. find both angles.
1 solutions
Answer 241428 by stanbon(57219) on 2010-08-30 17:48:15 (Show Source):
You can put this solution on YOUR website!the supplement of an angle is 20 less than three times the angle.
find both angles.
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Let the angle be "x".
Then the supplement is "180-x".
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Equation:
180-x = 3x-20
4x = 200
x = 50 degrees (the angle)
180-x = 130 (the supplement)
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Cheers,
Stan H.
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