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Recent problems solved by 'stanbon'
stanbon answered: 57288 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, >>NextTrigonometry-basics/180552: This problem came from a worksheet given to us. It says: Find 2 values of theta that satisfy cot of theta = -0.2679
1 solutions
Answer 135313 by stanbon(57361)   on 2009-02-05 21:39:35 (Show Source):
You can put this solution on YOUR website!Find 2 values of theta that satisfy cot(theta) = -0.2679
---------------------------------------------------------------
If cot(theta) = -0.2679, tan(theta) = -1/(0.2679)
----------------------
Use your calculator to find tan^-1(-1/0.2679))
I get -75 degrees.
The 2nd angle is -75-180 = -255 degrees
---------------------------------------------
The corresponding positive angles are:
-75 + 360 = 285 degrees
and
-255 + 360 = 105 degrees
===============================
Cheers,
Stan H.
|
Linear-equations/180557: someone asked for my help. they said they needed help with linear equations which i feel i can help them with but
what are recurring sequences and routines?
can you give me an example or a site that would explain it?
thanks much.
i appreciate it.
s
1 solutions
Answer 135310 by stanbon(57361) on 2009-02-05 21:28:23 (Show Source):
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Probability-and-statistics/180536: A rainstorm in Portland, Oregon, wiped out the electricity in 7% of the households in the city. Suppose that a random sample of 50 Portland households is taken after the rainstorm.
A Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.
B Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.
1 solutions
Answer 135308 by stanbon(57361) on 2009-02-05 21:24:38 (Show Source):
You can put this solution on YOUR website!A rainstorm in Portland, Oregon, wiped out the electricity in 7% of the households in the city. Suppose that a random sample of 50 Portland households is taken after the rainstorm.
-------------------------------------------------
A Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.
---
The distribution is binomial (households either do or do not lose electricity).
Mean = np = 50*0.07 = 3.5 households
--------------------------------------------------------------
B Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places
---
s = sqrt(npq) = sqrt(50*0.07*0.93) = 1.804..
-------------------------------------------------
Cheers,
Stan H.
|
Probability-and-statistics/180539: This question is from textbook Chapter 11 Skill practice
Can you explain these problem?
1.) When text messaging on a telephone, pressing a 3 types D, E, F, or 3. Pressing a 7 types P, Q, R, S, or 7. How many messages are possible by pressing a 3, a 7, and then a 3?
11.) What is the probability that a random 2-digit number is a multiple of 7?
13.) A mother is making different lunches for each of her 3 children. If each child grabs a lunch bag at random, what is the probability that all 3 children will get the correct bag?
21.) Two number cubes are rolled--one blue and one yellow. Find the probability that the yellow cube is even, and the sum is 7. Explain why the events are dependent.
Please answer me as soon as you could. Thank you for your help.
1 solutions
Answer 135300 by stanbon(57361) on 2009-02-05 20:48:31 (Show Source):
You can put this solution on YOUR website!1.) When text messaging on a telephone, pressing a 3 types D, E, F, or 3. Pressing a 7 types P, Q, R, S, or 7. How many messages are possible by pressing a 3, a 7, and then a 3?
Ans: 3*4*3 = 36
--------------------------------------
11.) What is the probability that a random 2-digit number is a multiple of 7?
Ans: There are 99 2-digit numbers if you do not include 00.
Multiples of 7 are: 7,14,21,28,35,42,49,etc, 98
So there are 14 multiples of 7 that are 2-digit numbers
Ans: Probability = 14/99
------------------------------------------
13.) A mother is making different lunches for each of her 3 children. If each child grabs a lunch bag at random, what is the probability that all 3 children will get the correct bag?
Ans: There are 3!=6 possible ways to pick the bags; only 1 is the right way.
Probability = 1/6
-----------------------------------------
21.) Two number cubes are rolled--one blue and one yellow. Find the probability that the yellow cube is even, and the sum is 7.
(yellow is even and sum is 7) = (2,5), (4,3), (6,1)-------3 elements
Total number of outcomes: 6*6 = 36
Probability(yellow even and sum is 7) = 3/36 = 1/12
----------------------------------
Explain why the events are dependent.
I'll leave that to you.
==============================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/180527: ((x^3-x^2-x+1)/(x^3-x^2+x-1))= 0 Hello, I am trying to solve this for x. I started by graphing the formula making 0 = y and the answer came out to be 1. I then plugged 1 in for x and the answer didn't match up. So i stated to factor and got the top half the equation (x^3-x^2-x+1) to factor into (x-1)(x+1)(x-1) and the bottom half (x^3-x^2+x-1) to factor into (x^2+ 1)(x-1) from there i couldn't make anythign of it. I think i'm on the right track but not sure. Thanks for your help
1 solutions
Answer 135290 by stanbon(57361) on 2009-02-05 20:26:33 (Show Source):
You can put this solution on YOUR website!((x^3-x^2-x+1)/(x^3-x^2+x-1))= 0 Hello, I am trying to solve this for x. I started by graphing the formula making 0 = y and the answer came out to be 1. I then plugged 1 in for x and the answer didn't match up. So i started to factor and got the top half the equation (x^3-x^2-x+1) to factor into (x-1)(x+1)(x-1) and the bottom half (x^3-x^2+x-1) to factor into (x^2+ 1)(x-1) from there i couldn't make anythign of it. I think i'm on the right track but not sure. Thanks for your help
------------------------------
[(x-1)(x+1)(x-1)]/[(x^2+1)(x-1)] = 0
Cancel the common factor of x-1 but keep in mind that x cannot be 1.
------------------------------------
[(x-1)(x+1)]/[(x^2+1)] = 0
Multiply both sides by (x^2+1) to get:
[(x-1)(x+1)] = 0
Then x = 1 or x = -1
But x cannot be 1
So the only solution is x = -1
===================================
cheers,
Stan H.
|
Probability-and-statistics/180515: Suppose that 53% of the women who gave birth at a certain hospital last year were over 30 years old, and that 30% were unmarried. If 28% of the women were both unmarried and over 30, what is the probability that a woman who gave birth at the hospital was over 30 or unmarried (or both)?
1 solutions
Answer 135281 by stanbon(57361) on 2009-02-05 20:12:23 (Show Source):
You can put this solution on YOUR website!Suppose that 53% of the women who gave birth at a certain hospital last year were over 30 years old, and that 30% were unmarried. If 28% of the women were both unmarried and over 30, what is the probability that a woman who gave birth at the hospital was over 30 or unmarried (or both)?
-----------------------
General Formula: P(A or B) = P(A) + P(B) - P(A and B)
--------------------------------------------------------
P(>30 or unmarried) = P(>30) + P(unmarried) - P(>30 and unmarried)
P(>30 or unmarried) = 0.53 + 0.30 - 0.28 = 0.55
================================================
Cheers,
Stan H.
|
percentage/180523: This question is from textbook Algebra 1:An Incremental Development
the weight of the elephant was 1040 percent of the weight of the bear. If the elephant weighed 20,800 pounds, what did the bear weigh? draw a diagram as an aid in solving the problem.
1 solutions
Answer 135273 by stanbon(57361) on 2009-02-05 20:00:42 (Show Source):
You can put this solution on YOUR website!the weight of the elephant was 1040 percent of the weight of the bear. If the elephant weighed 20,800 pounds, what did the bear weigh?
----------------
Let the bear weight "x" lbs.
-----------------------------
Equation:
elephant weighs (1040/100)x
20,800 = (1040/100)x
x = (100/1040)*20,800
x = 2000 lbs. (weight of the bear)
=====================================
Cheers,
Stan H.
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Equations/180522: Hello.
Can I have help in finding the equation of the line passing through (1,1) and (4,6) and putting answer in slope-intercept form.
thanks
Haley
1 solutions
Answer 135270 by stanbon(57361) on 2009-02-05 19:55:47 (Show Source):
You can put this solution on YOUR website!finding the equation of the line passing through (1,1) and (4,6) and putting answer in slope-intercept
------------------------------------
slope = (6-1)/(4-1) = 5/3
-------------------------------
intercept:
1 = (5/3)*1 = b
b = -2/3
==============
Equation:
y = (5/3)x - (2/3)
======================
Cheers,
Stan H.
|
Equations/180520: Hello.
Can I have some help in finding the equation of the line perpendicular to the x-axis passing through the origin?
thanks.
Haley
1 solutions
Answer 135266 by stanbon(57361) on 2009-02-05 19:44:55 (Show Source):
You can put this solution on YOUR website!
finding the equation of the line perpendicular to the x-axis passing through the origin?
--------------------------
Draw the picture of that line.
Do you see that it passes thru all the points where x = 0.
It's equation is x = 0
=================================
Cheers,
Stan H.
|
Quadratic_Equations/180502: Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle
1 solutions
Answer 135258 by stanbon(57361) on 2009-02-05 19:16:02 (Show Source):
You can put this solution on YOUR website!Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle
---------------------------
Steve DATA:
distance = 150 miles ; rate = x mph ; time = d/r = 150/x hrs
-----------------------------------------------
Improved Steve DATA:
distance = 150 miles : rate = x+20 ph ; time = d/r = 150/(x+2) hrs
---------------------------------
Equations:
Old Steve time - Improved Steve time = 2 hrs
150/x - 150/(x+2) = 2
150(x+2) - 150x = 2x(x+2)
300 = 2(x^2+2x)
x^2 + 2x - 150 = 0
x = [-2 +- sqrt(4 - 4*1*-150)]/2
x = [-2 +- sqrt(604)]/2
Positive solution:
x = 11.29 mph (Old rate)
================
Cheers,
Stan H.
|
Systems-of-equations/180503: Hello I need help on showing my work for a word problem.
Here is an example
The measures of complimentary angles have a sum of 90 degrees. Angle A and B are complimentary, and their measures have a difference of 20 degrees. What are the measures of the angles.
I know the answers (35, and 55) but don't know how to set up the equations according to the question.
So please help.
1 solutions
Answer 135253 by stanbon(57361) on 2009-02-05 18:55:12 (Show Source):
You can put this solution on YOUR website!The measures of complimentary angles have a sum of 90 degrees. Angle A and B are complimentary, and their measures have a difference of 20 degrees. What are the measures of the angles.
-----------------------------------------
A + B = 90 degrees
A - B = 20
---------------
Add the equations to get: 2A = 110
A = 55 degrees
-------------------
Substitute into A+B = 90 to solve for B:
55 + B = 90
B = 35 degrees
=======================
Cheers
Stan H.
|
Linear-equations/180499: There is a flat fee x plus y dollers for every hour
A person used 4 hours and had a fee of 63
another person used it for 6 hours and had a fee of 87
What is the value of the flat fee (x) and additional fee (y)
Please explain steps
1 solutions
Answer 135251 by stanbon(57361) on 2009-02-05 18:50:29 (Show Source):
You can put this solution on YOUR website!There is a flat fee x plus y dollers for every hour
A person used 4 hours and had a fee of 63
another person used it for 6 hours and had a fee of 87
What is the value of the flat fee (x) and additional fee (y)
-----------------------------------------------------------------
Points:
(4,63) and (6,87)
----------
slope = (87-63)/(6-4) = 24/2 = 12
----------
intercept:
63 = 12*4 + b
b = 63-48
b = 15
----------
Equation:
y = 12x + 15
---
Flat fee = $15
Additional fee = $12 per hour
===================================
Cheers,
Stan H.
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Probability-and-statistics/180480: The data in the table that follows was collected by a large car manufacturer concerning a new prototype car called the CIELO. Thirty carefully selected respondents were shown the car and fully briefed about its capabilities. Here is the data, which includes age (intervally scaled), sex (nominal), social status (interval scale ranging from 10, low status, to 30, high status), attitude toward CIELO (interval scale ranging from 6, negative attitude, to 30, positive attitude) and intention to purchase CIELO (nominal, yes or no).
Is there any difference in male and female attitude scores toward the CIELO? Is there anything unusual about this data? Please note that we have to setup a hypothesis test of the difference in two population (female respondents and male respondents) means (attitude scores).
RESPONDENT #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
AGE
20
19
34
23
42
55
24
26
35
41
43
51
56
62
43
51
28
19
24
26
28
35
38
23
42
41
30
29
19
26
SEX
M
F
M
M
M
F
F
M
F
M
F
M
M
F
F
F
M
M
M
F
F
M
F
M
F
F
F
M
M
F
SOCIAL STATUS
15.6
17.5
28.2
24.6
16.5
12.2
12.5
29.6
27.6
23.2
21.2
20.2
19.4
18.6
10.2
14.3
12.6
14.8
29.6
26.5
23.2
17.9
19.9
20.1
18.6
18.6
24.6
26.6
14.5
12.9
ATTITUDE SCORE
16
15
14
6
28
24
19
14
23
16
26
28
14
12
11
10
22
24
19
18
20
23
23
25
17
17
16
13
22
21
INTENTION TO PURCHASE
Y
Y
N
N
Y
N
Y
N
N
N
Y
N
N
Y
Y
N
Y
N
N
Y
N
N
N
Y
N
N
Y
N
Y
N
My question: Am I on the right track and/or if not can you please show me how to set up the hypothesis test and solve for it?
I got this:
Female: 272/15 = 18.133
Male: 284/15 = 18.933
H0: (Mu) less than or equal to 18
H1: (Mu) greater than 18
Small Sample
18.133 – 18.933/Sqrt 30(squared)*(1 over 15 + 1 over 15) = (0.8) / 900 * 2 over 15 = 120
(-0.8)/Sqrt 120 = (-0.8) / 10.954 = 0.073
Large Sample
18.133 – 18.933/Sqrt 30(squared) / 30(squared)over 15 / 30 (squared) over 15
= (0.8)/900 over 15 + 900 over 15
= (0.8)/ 60+60 = (0.8) / 120 = 0.006
Q: I am not sure if these are the right samples to use or if I should use a paired “t” sample? (below)
15
30 / sqrt (?)
Thank you
1 solutions
Answer 135249 by stanbon(57361) on 2009-02-05 18:37:17 (Show Source):
You can put this solution on YOUR website!My question: Am I on the right track and/or if not can you please show me how to set up the hypothesis test and solve for it?
I got this:
Female: 272/15 = 18.133
Male: 284/15 = 18.933
-------
Comment: I'm going to assume your mean calculations are correct.
-----------------------------------------------------------------
You need a 2-Sample Z-test addessing the question of difference between
the attitude of the sexes.
---------------------------------------------------------
H0: u(men)-u(women) = 0
H1: u(men)-u(women) is not 0
---------------------------------
Assuming alpha = 5% the Rule for the 2-Sample test is "Reject Ho if
test statistic is Less than -1.96 or greater than +1.96.
----------------------------------------------------------
Small Sample
Test statistic: (18.133 – 18.933)/Sqrt [30(squared)*(1 over 15 + 1 over 15) = (0.8) / 900 * 2 over 15 = 120
(-0.8)/Sqrt 120 = (-0.8) / 10.954 = 0.073
---
Comment: I can't follow you here:
I got the following:
t.s. = (difference of sample means)/sqrt[(s(men))^2/15 + (s(women))^2/15]
I ran it on a TI-calculator and got z = -0.073..
-----------
If that is right, since t.s. is not in the reject interval, Fail to reject
Ho. There is no statistical difference in attitude toward CIELO by the
sexes.
Large Sample
18.133 – 18.933/Sqrt 30(squared) / 30(squared)over 15 / 30 (squared) over 15
= (0.8)/900 over 15 + 900 over 15
= (0.8)/ 60+60 = (0.8) / 120 = 0.006
Q: I am not sure if these are the right samples to use or if I should use a paired “t” sample? (below)
Whether you use "t" or "z" depends on your textbook requirements or your
professor's directions. By the way, what is the textbook and what is the
chapter and problem number?
==============================
Comment: I would appreciate your feedback on these comments. Do they
help? Are they confusing or contradictory?
====================================
Cheers,
Stan H.
15
30 / sqrt (?)
Thank you
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Probability-and-statistics/180477: The manufacturer of Winston Tire Company claims its new tires last for an average 40,000 miles. An independent testing agency road-tested 20 tires to substantiate the claim made by the Winston Tire Company. The sample mean was 39,000 miles with a sample standard deviation of 5,000 miles. Using the .05 level of significance and the five-step hypothesis testing procedure, determine if there is reason to reject the claim made by Winston Tire Company and conclude that tires last for less than 40,000 miles.
My question: Am I on the right track and/or if not, what are the steps and formulas to use to solve for this?
I came up with:
H0: (Mu) = 40,000
H1: (Mu) not equal to 40,000
Z = 39,000 – 40,000/5,000/ sqrt 20 = - 4
I would say:
Reject the null in favor of the alternative, since – 4 falls in the rejection region.
Thank you
1 solutions
Answer 135248 by stanbon(57361) on 2009-02-05 17:58:06 (Show Source):
You can put this solution on YOUR website!The manufacturer of Winston Tire Company claims its new tires last for an average 40,000 miles. An independent testing agency road-tested 20 tires to substantiate the claim made by the Winston Tire Company. The sample mean was 39,000 miles with a sample standard deviation of 5,000 miles. Using the .05 level of significance and the five-step hypothesis testing procedure, determine if there is reason to reject the claim made by Winston Tire Company and conclude that tires last for less than 40,000 miles.
My question: Am I on the right track and/or if not, what are the steps and formulas to use to solve for this?
I came up with:
H0: (Mu) = 40,000
H1: (Mu) < 40,000
----
Note: I changed to a left-tail test because of the words "..conclude that
tires last for LESS than 40,000 miles".
--------------
Critical Value for a left-tail test with alpha=5% is -1.645
Rule: Reject Ho if test statistic is < -1.645
Z = (39,000 – 40,000)/[5,000/ sqrt 20] = -0.8944.
p-value: P(z < -0.8944) = 0.186 = 18.6%
---
Note: I changed your test statistic result.
------------
I would say:
Reject the null in favor of the alternative, since – 4 falls in the rejection region.
-----------
Coclusion should be: Since the test statistic is not in the rejection interval,
Fail to reject Ho.
You could also say: Since p-value is greater than 5% Fail to reject Ho.
-----------------
Interpretatation of the p-value: 18.6% of test result could have provided
stronger evidence for rejecting Ho.
-----------------------------------
Cheers,
Stan H.
P.S. Please let me know if this answer is any help to you. I see quite
a few Stat questions but get little feedback from the questioners.
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Polynomials-and-rational-expressions/180463: This question is from textbook
Find the product of (x^2+7x-2 with the quotient of (16x^5+8x^4+24x^3)divided by
4x^3
Familiarize, Translate, Carry Out, Check and State to solve. I am sooo lost here. Thanks
1 solutions
Answer 135237 by stanbon(57361) on 2009-02-05 16:20:46 (Show Source):
You can put this solution on YOUR website!Find the product of (x^2+7x-2 with the quotient of (16x^5+8x^4+24x^3)divided by
4x^3
----------------------
(x^2+7x-2) * [(16x^5+8x^4+24x^3)/(4x^3)]
= (x^2+7x-2) * [4x^2+2x+6]
= 4x^4 + 2x^3 + 6x^2 + 28x^3 + 14x^2 + 42x - 8x^2 -4x -12
= 4x^4 + 30x^3 + 6x^2 + 12x^2 -4x -12
===============================================
Cheers,
Stan H.
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Money_Word_Problems/180461: limits are needed on payday-lending businesses, according to an article in the Feb. 14, 2007 issue of the Columbian. Interest rates on payday loans are so outrageous that the payday-lending industry only has itself to blame for states moving to rein them in. A typical $100 loan is payable in TWO WEEKS at $115. What is the percent interest paid on this loan? Do not round the denominator before dividing.
1 solutions
Answer 135235 by stanbon(57361) on 2009-02-05 16:09:45 (Show Source):
You can put this solution on YOUR website!A typical $100 loan is payable in TWO WEEKS at $115. What is the percent interest paid on this loan?
----------------------------------------
I = Prt
15 = 100*r*(2/52)
0.15 = r(1/26)
r = 3.9 or 390%
======================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/180466: Trinidadhas $2.35 in nickels and dimes. if she has 33 coins in all , find the number of nickels and dimes.
1 solutions
Answer 135233 by stanbon(57361) on 2009-02-05 16:04:20 (Show Source):
You can put this solution on YOUR website!Trinidad has $2.35 in nickels and dimes. if she has 33 coins in all , find the number of nickels and dimes.
--------------------------------------------------------
Quantity Equation: n + d = 33
Value Equaltion..:5n +10d = 235 cents
---------------------------------------
Modify:
5n + 5d = 165
5n + 10d = 235
---------------------
Subtract 1st from 2nd to solve for "d":
5d = 70
d = 14 (# of dimes)
-----------------
Substiute into n+d = 33 to solve for "n":
n + 14 = 33
n = 19 (# of nickels)
==========================
Cheers,
Stan H.
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Graphs/180464: over the years from 1997 when it was $1.26, to 2006 when it was $2,31,gas prices have gone up. Using the coordinates (1997, 1.26) & (2006, 2.31) to find the slope (or rate of change) between the two points. I know that slope or m = y2 - y1 divided by x2 - x1. pls solve and describe how you arrived at answer
1 solutions
Answer 135232 by stanbon(57361) on 2009-02-05 15:57:06 (Show Source):
You can put this solution on YOUR website!over the years from 1997 when it was $1.26, to 2006 when it was $2,31,gas prices have gone up. Using the coordinates (1997, 1.26) & (2006, 2.31) to find the slope (or rate of change) between the two points. I know that slope or m = y2 - y1 divided by x2 - x1. pls solve and describe how you arrived at answer
-----------------------------------
m = (2.31-1.26)/(2006-1997) = 1.05/9 = 0.1167
=================================================
Cheers,
Stan H.
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Probability-and-statistics/180363: Ron has a 53% chance of receiving an A grade in geology, a 43% chance of receiving an A grade in mathematics, and a 76% chance of receiving an A grade in geology or mathematics (or both). Find the probability that he receives A grades in both geology and mathematics.
1 solutions
Answer 135231 by stanbon(57361) on 2009-02-05 15:52:53 (Show Source):
You can put this solution on YOUR website!Ron has a 53% chance of receiving an A grade in geology, a 43% chance of receiving an A grade in mathematics, and a 76% chance of receiving an A grade in geology or mathematics (or both). Find the probability that he receives A grades in both geology and mathematics
--------------------------------------------
P(geo and math) = P(geo) + P(math) - P(geo or math)
= 0.53 + 0.43 - 0.76
= 0.96 = 0.76
= 0.20
===============================
Cheers,
Stan H.
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Expressions-with-variables/180348: This question is from textbook algebra structure and method
can you please help me solve the following: (((How many x-intercepts the parabola has and wheather its vertex lies above or below or on the x-axis, y=-x^2+2x-1)))
1 solutions
Answer 135178 by stanbon(57361) on 2009-02-05 10:33:39 (Show Source):
You can put this solution on YOUR website!can you please help me solve the following: How many x-intercepts the parabola has and wheather its vertex lies above or below or on the x-axis, y=-x^2+2x-1
-----------------
Discriminant: b^2-4ac
D = 2^2 - 4*-1*-1 = 4 - 4 = 0
--------------
Since D = 0 there are two x-intercepts, but they are both the same.
-----------------
Since a < 0 the parabola opens down.
The vertex is on the x-axis:
------------------------------------------------
Cheers,
Stan H.
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Expressions-with-variables/180349: This question is from textbook algbra structure and method
can you please help me answer the following: (((The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet? )))
1 solutions
Answer 135177 by stanbon(57361) on 2009-02-05 10:27:03 (Show Source):
You can put this solution on YOUR website!The distance an object falls is directly proportional to the square of the time it has been falling.
---
d = k(t^2)
---------------------
After 6 seconds it has fallen 1296 feet.
Solve for "k":
1296 = k(6^2)
k = 36
So the equation for this situation is d = 36t^2
------------------------------------------------------
How long will it take to fall 2304 feet?
2304 = 36t^2
t^2 = 64
t = 8 seconds
====================
Cheers,
Stan H.
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Expressions-with-variables/180350: This question is from textbook algebra structure and method
can you please help me solve the following: (((x varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and t are doubled?)))
1 solutions
Answer 135176 by stanbon(57361) on 2009-02-05 10:22:22 (Show Source):
You can put this solution on YOUR website!x varies directly as the square of s and inversely as t.
---
x = k[s^2/t]
--------------------
How does x change when s is doubled?
Change from s to 2s to get:
x = k[(2s)^2/t] = k[4s^2/t] = 4[k[s^2/t]]
From this you can see that the value of x is multiplied by 4.
--------------------------------------------------------------------
When both s and t are doubled?)))
Change s to 2s and change t to 2t to get:
x = k[(2s)^2/(2t)] = k[4s^2/2t] = k[2s^2/t] = 2[k[s^2/t]]
From this you can see that the value of x is multiplied by 2.
=========================================
Cheers,
Stan H.
----------------------
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Finance/180308: This question is from textbook Foundations Of Finance
Please help with the formula use to solve the following problem:
A company is considering borrowing $5000 for a 90 day period. The firm will repay the $5000 principle amount plus $150 in interest. What is the effective annual rate of interest? Use a 360-day year.
1 solutions
Answer 135171 by stanbon(57361) on 2009-02-05 07:15:07 (Show Source):
You can put this solution on YOUR website!Please help with the formula use to solve the following problem:
A company is considering borrowing $5000 for a 90 day period. The firm will repay the $5000 principle amount plus $150 in interest. What is the effective annual rate of interest? Use a 360-day year.
--------------------
Interest = Prt
150 = 5000*r*(90/360)
150 = 5000r*(1/4)
600 = 5000r
r = 0.12 = 12%
====================
Cheers,
Stan H.
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Money_Word_Problems/180329: Mike invested a total of $14,600, part at 9% simple interest and Part 6% interest for one year. If the interest in the 9% account was $300 greater than the interest in the 6% account, how much was invested in the 9% account?
1 solutions
Answer 135170 by stanbon(57361) on 2009-02-05 07:11:35 (Show Source):
You can put this solution on YOUR website!Mike invested a total of $14,600, part at 9% simple interest and Part 6% interest for one year. If the interest in the 9% account was $300 greater than the interest in the 6% account, how much was invested in the 9% account?
------------------------------
Equation:
9% int = 6%int + 300
0.09x = 0.06(14000-x) + 300
Multiply both sides by 100 to get:
9x = 6(14000)-6x + 30000
15x = 30000 + 84000
x = $7600 (amt. invested at 9%)
===================================
Cheers,
Stan H.
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Rational-functions/180333: This question is from textbook Algebra & Trigonometry
Determine Algebraically weather the function is even, odd, or neither.
h(x)= x / (x^2-1) or x over x squared minus one
My understanding>> I know you can fill in h(-x) at which point if the answer comes out to be h(-x) then it is odd, or h(x)then it is even. If the answer is neither then it is (well) neither.
Where I get confused is >> When I fill in negative x to the denominator I then have a negative numerator and a negative denominator which in turn becomes positive (right?). Then, when my fraction becomes positive- do I change the (-1) to a (+1) [second position of the denominator]?
Afterwards, should I cross multiply (assuming the value of h(-x) can be placed over one.. OR should I multiply both sides by my denominator and work from there?
Please help.
1 solutions
Answer 135169 by stanbon(57361) on 2009-02-05 07:05:28 (Show Source):
You can put this solution on YOUR website!Determine Algebraically weather the function is even, odd, or neither.
h(x)= x / (x^2-1)
---
h(-x) = (-x)/[(-x)^2-1] = -x/(x^2-1
-------------------------------------
-(h(-x)) = x/(x^2-1)
-------------------------
Since h(x) = -h(-x) the function is symmetric to the origin.
------------------------------
------------------------------
Cheers,
Stan H.
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