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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, >>NextLinear-systems/266549: Why you are using minus(-)instead of plus(+) in substitution?
1 solutions
Answer 195836 by stanbon(57424)   on 2010-02-07 09:34:07 (Show Source):
You can put this solution on YOUR website!Use minus if it eliminates a variable.
Example:
3x +y = 7
3x -2y = 3
Subtracting will eliminate the x-terms and allow you to solve for "y":
----------------------------------------------
Use plus if it eliminates a variable.
3x + y = 7
3x - y = 3
Adding will eliminate the y-terms and allow you to solve for "x"
Subtracting would eliminate the x-terms and allow you to solve for "y".
-------------------------
It's your choice.
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/266547: The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke0.12t where k is a constant and t is the time in years. If the current population is 15,000, in how many years is the population expected to be 37,500? Round to the nearest year
51
8
5
3
1 solutions
Answer 195832 by stanbon(57424) on 2010-02-07 09:29:05 (Show Source):
You can put this solution on YOUR website!The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke^(0.12t) where k is a constant and t is the time in years. If the current population is 15,000, in how many years is the population expected to be 37,500? Round to the nearest year
---
Use current population to find "k":
15000 = 1 +k*e^(0.12*0)
15000 = 1 + k
k = 14999
----------------------------------------
Equation:
P(t) = 14999e^(0.12t)
----
in how many years is the population expected to be 37,500?
37,000 = 14999*e^(0.12t)
2.467 = e^(0.12t)
Take the natural log of both sides to get:
0.12t = ln(2.467)
t = 7.52 years
Rounded up t = 8 years.
============================
Cheers,
Stan H.
51
8
5
3
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Probability-and-statistics/266533: what is Q1 Q2 and Q3 of this set of data 43 45 53 56 56 57 57 58 66 73 74 79 80 80 81 81 81 82 82 83 83 84 88 89 91 91 92 97 99 99 100 101 102 102 103 104 107 108 109 113 114 118 121 123 126 128 137 138 139 144 156 162 174 178 179 184 191 198 211 214 243 149 329 380 403 507 510 511 514 520 521 522 530 53 533 540 541
1 solutions
Answer 195829 by stanbon(57424) on 2010-02-07 09:19:38 (Show Source):
You can put this solution on YOUR website!what is Q1 Q2 and Q3 of this set of data 43 45 53 56 56 57 57 58 66 73 74 79 80 80 81 81 81 82 82 83 83 84 88 89 91 91 92 97 99 99 100 101 102 102 103 104 107 108 109 113 114 118 121 123 126 128 137 138 139 144 156 162 174 178 179 184 191 198 211 214 243 149 329 380 403 507 510 511 514 520 521 522 530 53 533 540 541
--------
There are 77 data values arranged in ascending order.
----
Find the "locator" for Q1 = 25%ile
---
Locator = (0.25)77 = 19.25 rounded up = 20
---
Q1 is the 20th element = 83
-----------------
Do the same for Q2 = 50%ile and for Q3 = 75%ile
====================================================
Cheers,
Stan H.
|
Probability-and-statistics/266350: A couple has three children. Find each probability
A. All boys
B. All girls or all boys
C. Exactly two boys or two girls
D. At least one child of each gender
1 solutions
Answer 195817 by stanbon(57424) on 2010-02-07 08:19:09 (Show Source):
You can put this solution on YOUR website!A couple has three children. Find each probability
A. P(All boys) = (1/2)^3 = 1/8
-----------------------------------------------
B. P(All girls or all boys) = 1/8 + 1/8 = 1/4
-----------------------------------------------
C. P(Exactly two boys or two girls) = 2*3C2(1/2)^2*(1/2) = 2*3*(1/8) = 3/4
---------------------------------------
D. P(At least one child of each gender) = 1 -P(all girls or all boys)
= 1 - 1/4 = 3/4
===================
Cheers,
Stan H.
|
Probability-and-statistics/266354: Can someone please help me with answering the following question?
As part of an advertising campaign, the Dairy Council is interested in determining the daily intake of milk among adults. A random sample of 10 adults gave the following results. (Values are given in ounces.)
23.0 30.6 20.3 10.1 11.5
21.8 22.2 26.9 21.0 30.1
a. Find x-bar and s for this data set.
b. Construct a 99 percent confidence interval for the mean daily intake of milk. You may assume the daily intake amounts are normally distributed. (Note: These results could then be used in later studies to see if the ad campaign is succeeding in increasing the amount of milk adults drink.)
1 solutions
Answer 195816 by stanbon(57424) on 2010-02-07 08:08:49 (Show Source):
You can put this solution on YOUR website!As part of an advertising campaign, the Dairy Council is interested in determining the daily intake of milk among adults. A random sample of 10 adults gave the following results. (Values are given in ounces.)
23.0 30.6 20.3 10.1 11.5
21.8 22.2 26.9 21.0 30.1
a. Find x-bar and s for this data set.
xbar = 21.75 ; s = 6.8295
E = invT(0.995,9)*6.8295/sqrt(10) = 7.0186
----------------------------------------------------
b. Construct a 99 percent confidence interval for the mean daily intake of milk. You may assume the daily intake amounts are normally distributed.
----
99% CI: 21.75-7.0186 < u < 21.75+7.0186
=========================================
Cheers,
Stan H.
=========================================
|
Probability-and-statistics/266356: I need help with the following question please.
A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 90% confidence interval for the mean score of all such subjects. You may assume the scores are normally distributed.
1 solutions
Answer 195814 by stanbon(57424) on 2010-02-07 07:51:16 (Show Source):
You can put this solution on YOUR website!A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 90% confidence interval for the mean score of all such subjects. You may assume the scores are normally distributed.
-------------
sample mean = xbar = 76.2
standard error = E = zs/sqrt(n)
E = [invT(0.95,df=26)*21.4/sqrt(27) = 1.7056*21.4/sqrt(27) = 7.0245..
--------
90% CI: 76.2-7.0245 < u < 76.2+7.0245
============================================
Cheers,
Stan H.
|
Probability-and-statistics/266471: To test the null hypothesis that the average lifetime for a particular brand of bulb is 750 hours versus the alternative that the average lifetime is different from 750 hours, a sample of 75 bulbs is used. If the standard deviation is 50 hours and a is equal to 0.01, what values for will result in rejection of the null hypothesis. Remember to determine whether this is a one- or two-tailed test.
1 solutions
Answer 195813 by stanbon(57424) on 2010-02-07 07:44:18 (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 750 hours versus the alternative that the average lifetime is different from 750 hours, a sample of 75 bulbs is used.
If the standard deviation is 50 hours and a is equal to 0.01, what values for will result in rejection of the null hypothesis. Remember to determine whether this is a one- or two-tailed test.
=========
An "unequal" test is two tail.
A "less than" test is left-tail.
A "greater than" is right-tail.
-----------------
Your Problem:
Ho: u = 750
Ha: u is not equal to 750
----
critical values = ?
Find the t-values with 0.005 tails with df = 74
invT(0.005,74) = -2.6439
The CV's are -2.6439 and +2.6439
---
The rejection intervals are t< -2.6439 and t> 2.6439
=========================================================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/266451: In a math class a grade was assigned for a combination of homework and quizzes. A student had an overall homework/quiz average of 84.3. His quiz average was 78 and his homework average was 87. There were a total of 20 homework and quizzes assigned. How many were homework and how many were quizzes?
1 solutions
Answer 195776 by stanbon(57424) on 2010-02-06 21:30:26 (Show Source):
You can put this solution on YOUR website!In a math class a grade was assigned for a combination of homework and quizzes. A student had an overall homework/quiz average of 84.3. His quiz average was 78 and his homework average was 87. There were a total of 20 homework and quizzes assigned. How many were homework and how many were quizzes?
---------------
Let h = # of homeworks ; Let q be # of quizzes
Quantity Equation: h + q = 20
Points Equation: 87h + 78q = 84.3*20
-------------------------------------------
Multiply thru 1st equation by 87 to get:
87h + 87q = 87*20
87h + 78q = 84.3*20
----------------------
Subtract 2nd from 1st and solve for "q":
9q = 2.7*20
q = 6 (# of quizzes)
-----
Since h_+ q = 20, h = 14 (# of homeworks)
===========================================
Cheers,
Stan H.
|
Probability-and-statistics/266358: Rural speed limits for all 50 states are indicated below:
60 mph: 1
65 mph: 18
70 mph: 18
75 mph: 13
Choose one state at random. Find the probability that its speed limit is:
a. 60 or 70 mph
b. greater than 65 mph
c. 70 miles per hour or less
Thanks for your help!
1 solutions
Answer 195772 by stanbon(57424) on 2010-02-06 21:19:44 (Show Source):
You can put this solution on YOUR website!Rural speed limits for all 50 states are indicated below:
60 mph: 1
65 mph: 18
70 mph: 18
75 mph: 13
Choose one state at random. Find the probability that its speed limit is:
a. 60 or 70 mph
Prob = (# of ways to succeed)/(# of possible choices) = (1+18)/50
-----
b. greater than 65 mph
Prob = (18+13)/50 = 31/50
--------------------
c. 70 miles per hour or less
Prob = (18 + 18 + 1) = 37/50
==================================
Cheers,
Stan H.
|
Travel_Word_Problems/266452: In a pen at Old MacDonald's farm there are some sheep and some geese. There is a total of 115 animals and there are 424 legs. How many sheep and how many geese are there?
1 solutions
Answer 195769 by stanbon(57424) on 2010-02-06 21:14:38 (Show Source):
You can put this solution on YOUR website!In a pen at Old MacDonald's farm there are some sheep and some geese. There is a total of 115 animals and there are 424 legs. How many sheep and how many geese are there?
---------------------------------
Quantity: s + g = 115
Legs:::: 4s +2g = 424
---------------------------
Multiply thru Quantity by 2 to get:
2s + 2g = 230
4s + 2g = 424
--------------------
Subtract 1st from 2nd to get:
2s = 194
s = 97 (# of sheep)
-----
Since s+g = 115, g = 115-97 = 18 (# of geese)
==================================
Cheers,
Stan H.
|
Probability-and-statistics/266359: A recent study of 300 patients found that of 100 alcoholic patients, 87 had elevated cholesterol levels, and of 200 nonalcoholic patients, 43 had elevated cholesterol levels. If a patient is selected at random, find the probability that the patient is the following:
a. An alcoholic with elevated cholesterol
b. A nonalcoholic
c. A nonalcoholic with nonelevated cholesterol level.
Thanks!
1 solutions
Answer 195764 by stanbon(57424) on 2010-02-06 20:58:27 (Show Source):
You can put this solution on YOUR website!A recent study of 300 patients found that of 100 alcoholic patients, 87 had elevated cholesterol levels, and of 200 nonalcoholic patients, 43 had elevated cholesterol levels. If a patient is selected at random, find the probability that the patient is the following:
----
Procedure:
1st: I sketched a contingency table with 2 rows(alc and non-alc) and
2 columns (high choles and low choles)
---
2nd: I put the given numbers into the contingency table and filled
in the missing numbers.
-------
Find the probability that the patient is the following:
a. An alcoholic with elevated cholesterol: 87/300
b. A nonalcoholic: 200/300
c. A nonalcoholic with nonelevated cholesterol level: 43/300
================================================================
Cheers,
Stan H.
|
Age_Word_Problems/266447: Jennifer is twice as old as Ramon. The sum of their ages 7 years ago was 13. How old are they now?
1 solutions
Answer 195759 by stanbon(57424) on 2010-02-06 20:47:10 (Show Source):
You can put this solution on YOUR website! Jennifer is twice as old as Ramon. The sum of their ages 7 years ago was 13. How old are they now?
---
Equations:
J = 2R
(J-7)+(R-7) = 13
-------
Substitute for "J" and solve for "R":
2R-7 + R-7 = 13
3R - 14 = 13
3R = 27
R = 9 (Ramon's age now)
------
J = 2R = 18 (Jennifer's age now)
===================================
Cheers,
Stan H.
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Probability-and-statistics/266372: A company manufactures calculators in batches of 45 and claims that the rate of defects is 4%. Find the probability of getting exactly 2 defects in a batch of 45 if the rate of defects is 4%. If a store receives a batch of 45 calculators and finds that there are 2 defective calculators, do they have any reason to doubt the company's claimed rate of defects?
Possible answers:
a. 0.263; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators.
b. 0.548; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators.
c. 0.0166; Yes. If the rate of defects is really 4%, the probability of finding 2 defects in a batch of 45 calculators is very small.
d. 0.274; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators.
1 solutions
Answer 195756 by stanbon(57424) on 2010-02-06 20:39:28 (Show Source):
You can put this solution on YOUR website!A company manufactures calculators in batches of 45 and claims that the rate of defects is 4%. Find the probability of getting exactly 2 defects in a batch of 45 if the rate of defects is 4%.
Binomial Problem:
n = 45 ; p = 0.04 ; x=2
P(x=2) = 45C2(0.4)^2(0.96)^43 = 0.2738
-----------------------------------------
Ans: d
-----------
If a store receives a batch of 45 calculators and finds that there are 2 defective calculators, do they have any reason to doubt the company's claimed rate of defects?
No, the probability is better than 27% that 2 defects would be found in
a batch of 45.
==========================================================================
Cheers,
Stan H.
==========================================================================
Possible answers:
a. 0.263; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators.
b. 0.548; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators.
c. 0.0166; Yes. If the rate of defects is really 4%, the probability of finding 2 defects in a batch of 45 calculators is very small.
d. 0.274; No. If the rate of defects is really 4%, it is not so unlikely to find 2 defects in a batch of 45 calculators.
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Polynomials-and-rational-expressions/266446: The following problem is from my college algebra class using the book "Introduction to Algebra."
A polynomial in x has a degree 3. The coefficient of x squared is 3 less than the coefficient of x to the 3rd.? The coefficient of x is three times the coefficient of x squared. The remaining coefficient is 2 more than the coefficient of x to the third. The sum of the coefficients is -4. What is the polynomial?
I honestly don't even know where to begin, I started by using simple guesses and it got me nowhere. They assign us the most difficult question in the exercise set even though the text in no way prepares us for the answer. Please help!
1 solutions
Answer 195751 by stanbon(57424) on 2010-02-06 20:27:46 (Show Source):
You can put this solution on YOUR website!A polynomial in x has a degree 3.
The coefficient of x squared is 3 less than the coefficient of x to the 3rd. The coefficient of x is three times the coefficient of x squared.
The remaining coefficient is 2 more than the coefficient of x to the third. The sum of the coefficients is -4. What is the polynomial?
-------------
y = kx^3 + (k-3)x^2 + (3k-9)x +(k+2)
----------------------------------------
Equation:
k + (k-3) + 3k-9 + k+2 = -4
6k -10 = -4
6k = 6
k = 1
----
Polynomial:
y = x^3 - 2x^2 -6x + 3
=============================
Cheers,
Stan H.
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Probability-and-statistics/266373: Use the Poisson Distribution to find the indicated probability.
The town of Fastville has been experiencing a mean of 68.7 car accidents per year. Find the probability that on a given day the number of car accidents in Fastville is 3. (Assume 365 days in a year.)
Possible answers:
a. 0.000921
b. 0.000801
c. 0.00103
d. 0.000120
1 solutions
Answer 195746 by stanbon(57424) on 2010-02-06 20:20:26 (Show Source):
You can put this solution on YOUR website!The town of Fastville has been experiencing a mean of 68.7 car accidents per year. Find the probability that on a given day the number of car accidents in Fastville is 3. (Assume 365 days in a year.)
-----
Using a TI84 I get poissonpdf(68.7/365,3) = 0.000921...
Cheers,
Stan H.
Possible answers:
a. 0.000921
b. 0.000801
c. 0.00103
d. 0.000120
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Probability-and-statistics/266375: Use the Poisson Distribution to find the indicated probability.
The number of calls received by a car towing service averages 19.2 per day (per 24-hour period). After finding the mean number of calls per hour, find the probability that in a randomly selected hour the number of calls is 2.
a. 0.15816
b. 0.14379
c. 0.11503
d. 0.17973
1 solutions
Answer 195744 by stanbon(57424) on 2010-02-06 20:15:52 (Show Source):
You can put this solution on YOUR website!Use the Poisson Distribution to find the indicated probability.
The number of calls received by a car towing service averages 19.2 per day (per 24-hour period). After finding the mean number of calls per hour, find the probability that in a randomly selected hour the number of calls is 2.
-----
I used the poissonpdf((19.2/24),2) function on a TI-84 and
got 0.14379
==================
Cheers,
Stan H.
==================
a. 0.15816
b. 0.14379
c. 0.11503
d. 0.17973
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Roman-numerals/266348: Three-quarters of a certain number exceeds two-thirds of it by 3.Find the number
1 solutions
Answer 195689 by stanbon(57424) on 2010-02-06 14:35:26 (Show Source):
You can put this solution on YOUR website!Three-quarters of a certain number exceeds two-thirds of it by 3.Find the number
----------------------
Let the number be "x":
Equation:
(3/4)x = (2/3)x + 3
---
[(3/4)-(2/3)]x = 3
(1/12)x = 3
x = 36
-------------
Cheers,
Stan H.
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Probability-and-statistics/266344: Student has 10 question test with 5 choices for each answer. He needs to answer 60% or > to pass. If he randomly guesses, what is the % probability he will pass? thank you
Choices are: 0.006 0.377 0.060
1 solutions
Answer 195686 by stanbon(57424) on 2010-02-06 14:29:31 (Show Source):
You can put this solution on YOUR website!Student has 10 question test with 5 choices for each answer. He needs to answer 60% or > to pass. If he randomly guesses, what is the % probability he will pass? thank you
Choices are: 0.006 0.377 0.060
----
Binomial Problem:
n = 10, p(correct) = 1/5, q(wrong) = 4/5
---
Find P(6 <= x <=10) = 1 - binomcdf(10,1/5,5) = 0.0064
=============
Cheers,
Stan H.
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Linear-equations/266334: Please explain this problem step by step
Solve each system of inequalities by graphing:
2x+y<(less than or equal to) 4
y+1>(greater than or equal to) -2x
1 solutions
Answer 195683 by stanbon(57424) on 2010-02-06 14:19:22 (Show Source):
You can put this solution on YOUR website!Solve each system of inequalities by graphing:
2x+y<(less than or equal to) 4
y+1>(greater than or equal to) -2x
--------------------------------------------
ALWAYS graph the boudary of the inequality first:
Graph y = -2x+4 with a solid line because = is included in your equation.
Then shade the area BELOW the boundary because you want y LESS than -2x+4
------------------------
Graph y = -2x-1 with a solid line.
Then shade the half-plane ABOVE the boundary because you want y GREATER
than -2x-1
------------------------
The solution set is the intersection of the two graphs.
=========================================================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/266340: a trucker drove for 4 hours before he encountered icy road condition. He reduced his speed by 20 mph and continued driving for 3 more hours. Find his average speed during the first part of the trip if the entire trip was 325 miles.
1 solutions
Answer 195682 by stanbon(57424) on 2010-02-06 14:02:50 (Show Source):
You can put this solution on YOUR website!a trucker drove for 4 hours before he encountered icy road condition. He reduced his speed by 20 mph and continued driving for 3 more hours. Find his average speed during the first part of the trip if the entire trip was 325 miles.
---
1st segment DATA:
time = 4 hrs. ; rate = x mph ; distance = rt = 4x miles
------------------
2nd segment DATA:
time = 3 hrs. ; rate = x-20 mph ; distance = rt = 3x-60 miles
---------------------
Equation:
distance + distance = 325 miles
4x + 3x-60 = 325 miles
7x = 385
x = 55 mph (rate during 1st segment)
=============================
Cheers,
Stan H.
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Probability-and-statistics/266302: I am having a hard time figuring this out.
The null and alternative hypotheses are:
HO: The cell categories are equal.
H1: The cell categories are not equal.
The significance level is 0.05.
Category fo
A 10
B 20
C 30
D 20
Compute the value of chi-square.
1 solutions
Answer 195680 by stanbon(57424) on 2010-02-06 13:57:56 (Show Source):
You can put this solution on YOUR website!I am having a hard time figuring this out.
The null and alternative hypotheses are:
HO: The cell categories are equal.
H1: The cell categories are not equal.
The significance level is 0.05.
Category fo
A 10
B 20
C 30
D 20
Compute the value of chi-square.
-----------------
The numbers you have for A,B,C etc. are the "observed" data values.
The "expected" data values would be 20,20,20,20 since there are
80 data points and four categories.
---
List the "observed" values in one set.
List the expected values in another set.
Run a Chi-Sq Goodness-of-Fit test on the two sets.
---
I did and got:
Chi-Sq = 10
p-value = 0.1886
---
Conclusion: Since the p-value is greater than 5%
fail to reject Ho.
==========================
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/266276: I need to write a linear inequality for:
A company manufactures and sells personalized stationery. The weekly fixed cost is $3000 and it costs $3.00 to produce each package of stationery. The selling price is $5.50 per package. How many packages of stationery must be produced and sold each week for the company to have a profit?
I am not sure where to start. I was thinking N=300x + 3000 and N=550x+3000 but I don't believe that is correct. Help?
1 solutions
Answer 195662 by stanbon(57424) on 2010-02-06 09:18:41 (Show Source):
You can put this solution on YOUR website!I need to write a linear inequality for:
A company manufactures and sells personalized stationery.
The weekly fixed cost is $3000 and it costs $3.00 to produce each package of stationery.
The selling price is $5.50 per package.
How many packages of stationery must be produced and sold each week for the company to have a profit?
---
Let the number of packs sold be "x".
Revenue = 5.50x dollars
Overhead = 3000 + 3.00x
---------------
Inequality:
Profit means Revenue > Overhead
Solve 5.50x > 3000+3.00x for "x":
2.50x > 3000
x > 1200 (# of packs they need to sell to make a profit)
=====================================
Cheers,
Stan H.
=====================================
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Miscellaneous_Word_Problems/266267: An escalator moves up at a rate of x steps per second. Walter walks up the
escalator at the rate of one step per second and reaches the top in twenty seconds.The next day Walter’s rate was two steps per second, and he reached the top in sixteen seconds. How many steps does the escalator have?
(A) 40 (B) 50 (C) 60
(D) 80 (E) none of these
1 solutions
Answer 195659 by stanbon(57424) on 2010-02-06 09:12:27 (Show Source):
You can put this solution on YOUR website!An escalator moves up at a rate of x steps per second.
Walter walks up the escalator at the rate of one step per second and reaches the top in twenty seconds.
The next day Walter’s rate was two steps per second, and he reached the top in sixteen seconds.
How many steps does the escalator have?
======
Assume the escalator has "s" steps
---------
The escalator rate = x steps per second
Walter's rate = 1 step per second
---
In the 20 seconds it takes Walter from bottom to top at one step per second,
the escalator has gone up 20x steps. Also Walter has gone up 20 steps.
So 20x + 20 = s
---
In the 16 seconds it takes Walter from bottom to top at 2x steps per second,
the escalator has gone up 16x steps. Also Walter has gone up 2(16) steps.
So 16x + 32 = s
----
Solve 20x+20 = 16x +32 for "x".
4x = 12
x = 3 steps per second
---
Then s = 20x + 20 = 20*3 +20 = 80 (# of steps is 80)
=========================================================
Cheers,
Stan H.
(A) 40 (B) 50 (C) 60
(D) 80 (E) none of these
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Numbers_Word_Problems/266270: Michelle receives a 10 percent raise every year. Her salary after four such raises
has gone up by what percent?
(A) between 30 and 35 percent (B) between 35 and 40 percent
(C) between 40 and 45 percent (D) between 45 and 50 percent
(E) none of these
1 solutions
Answer 195654 by stanbon(57424) on 2010-02-06 08:23:59 (Show Source):
You can put this solution on YOUR website! Michelle receives a 10 percent raise every year.
Her salary after four such raises has gone up by what percent?
----
If she starts at salary = x
1st raise she has x + 0.1x = (1.1)x
2nd raise she has (1.1)x + 0.1(1.1x) = (1.1)x(1.1) = (1.1)^2 x
3rd raise she has (1.1)^3 x
4th raise she has (1.1)^4x
----
1.1^4 = 1.4641
1.4641x = x + 0.4641x
% increase = 46.41%
===========================
Cheers,
Stan H.
(A) between 30 and 35 percent (B) between 35 and 40 percent
(C) between 40 and 45 percent (D) between 45 and 50 percent
(E) none of these
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Numbers_Word_Problems/266272: The sum of three consecutive integers starting with x is 24
Write down and solve an equation to find the three integers.
1 solutions
Answer 195653 by stanbon(57424) on 2010-02-06 08:18:29 (Show Source):
You can put this solution on YOUR website!The sum of three consecutive integers starting with x is 24
Write down and solve an equation to find the three integers.
---
1st: x
2nd: x+1
3rd: x+2
----------
Equation:
3x + 3 = 24
x+1 = 8
x = 7
---
1st: 7
2nd: 8
3rd: 9
==============
Cheers,
Stan H.
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Numbers_Word_Problems/266269: The sum of the square of 22 and the square of 19 equals the sum of the squares
of two other two-digit numbers. Give the sum of four digits of the other two-digit
numbers.
(A) 11 (B) 12 (C) 18 (D) 21 (E) none of these
1 solutions
Answer 195652 by stanbon(57424) on 2010-02-06 08:16:17 (Show Source):
You can put this solution on YOUR website!The sum of the square of 22 and the square of 19 equals the sum of the squares
of two other two-digit numbers. Give the sum of four digits of the other two-digit numbers.
---
22^2 + 19^2 = x^2 + y^2
845 = x^2 + y^2
---
845 = 169 + 676
845 = 13^2 + 26^2
---
Sum of digits = 1+3+2+6 = 12
===================================
Cheers,
Stan H.
===================================
(A) 11 (B) 12 (C) 18 (D) 21 (E) none of these
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Geometry_Word_Problems/266265: Two opposite sides of a square are increased by twenty-five percent while the other two are decreased by forty percent. Find the percent of decrease in the area of the square.
(A) 15% (B) 25% (C) 30% (D) 32.5% (E) none of these
1 solutions
Answer 195650 by stanbon(57424) on 2010-02-06 08:05:43 (Show Source):
You can put this solution on YOUR website! Two opposite sides of a square are increased by twenty-five percent while the other two are decreased by forty percent. Find the percent of decrease in the area of the square.
Area of original square: s^2 where s is the length of a side
Area of new rectangle:
((5/4)s)((6/10)s) = (3/4)s^2
Quantity of decrease = s^2 - (3/4)s^2 = (1/4) s^2
% of decrease = [(1/4)s^2]/s^2 = 1/4 = 25%
=================
Cheers,
Stan H.
(A) 15% (B) 25% (C) 30% (D) 32.5% (E) none of these
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