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Recent problems solved by 'stanbon'
stanbon answered: 57894 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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54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 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 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899, >>NextProbability-and-statistics/507430: use the given confidence interval limits to find the point estimate and the margin of error for the equation: 0.772 is less than p and p is less than 0.776
1 solutions
Answer 340648 by stanbon(57967)   on 2011-10-01 20:02:18 (Show Source):
You can put this solution on YOUR website!use the given confidence interval limits to find the point estimate and the margin of error for the equation: 0.772 is less than p and p is less than 0.776
-----------------------
The point estimate is the average of the confidence interval limits:
----
p-hat = (0.772+0.776)/2 = 0.774
------
Margin of Error = 0.776-0.774 = 0.002
===============
Cheers,
Stan H.
===============
|
Probability-and-statistics/507442: A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 15. Overall 5 students failed the test, how many students were enrolled in her course?
1 solutions
Answer 340646 by stanbon(57967) on 2011-10-01 19:57:53 (Show Source):
You can put this solution on YOUR website!A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 15. Overall 5 students failed the test, how many students were enrolled in her course?
-----
Assuming the failure cutoff is 70%,
z(70) = (70-78)/15 = -0.5333
---
P(z < -0.333) = normalcdf(-100,-0.5333) = 0.2959
---
Let x be the number students enrolled in the course:
Solve: 0.2959x = 5 students
x = 5/0.2959
x = 16.84
Round up to 17 students in the class.
========================================
Cheers,
Stan H.
=============
|
Probability-and-statistics/507513: Given the following frequency distribution, find the mean, variance, and standard deviation. Please show all of your work.
Errors Frequency
36-38 18
39-41 7
42-44 12
45-47 22
48-50 13
This is what I have so far, not sure if I'm on the right track.
Mean: 18+7+12+22+13=72/5= 14.4
Standard deviation = 3.6, -7.4, -2.4, 7.6, 1.4
Variance = I am lost now
I really some guidance here, I have been working on this for awhile can't seem to get it. Any help and explanation please
1 solutions
Answer 340641 by stanbon(57967) on 2011-10-01 19:21:12 (Show Source):
You can put this solution on YOUR website!Given the following frequency distribution, find the mean, variance, and standard deviation. Please show all of your work.
Errors Frequency
36-38 18
39-41 7
42-44 12
45-47 22
48-50 13
----
You have to use each class mark as the representative data value
for each class:
1st class mark is (38+36)/2 = 37
Do the same for each class.
---
Mean = [37*18+40*7+41*12+46*22+49*13]/[18+7+12+22+13] = 43
std = 4.7434
variance = 4.7434^2 = 22.4998
============================
Cheers,
Stan H.
|
Probability-and-statistics/507581: How many different 5-card poker hands can be made from a deck of 52 cards?
Two equal circles are cut out of a rectangle of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out?
1 solutions
Answer 340630 by stanbon(57967) on 2011-10-01 18:54:51 (Show Source):
You can put this solution on YOUR website!How many different 5-card poker hands can be made from a deck of 52 cards?
----
52C5 = 52!/[(52-5)!*5!] = [52*51*50*49*48]/[1*2*3*4*5] = 2598960
----------------------------------------
Two equal circles are cut out of a rectangle of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after the circles have been cut out?
----
Area of the rectangle: 16*8 = 128 sq units
----
Area of each circle: (pi)*4^2= 16(pi)
----
Area of remaining paper: 128-2*16(pi) = 27.47 sq units
|
Probability-and-statistics/507592: A study conducted by the research department of a pharmaceutical company claims that the annual spending (per person) for prescription drugs for allergy relief, m1, is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine, m2. A health insurance company conducted an independent study and collected data from a random sample of 205 individuals for prescription allergy relief medicine. The sample mean is found to be 17.8 dollars/year, with a sample standard deviation of 5.5 dollars/year. They have also collected data for non-prescription allergy relief medicine. An independent random sample of 235 individuals yielded a sample mean of 18.2 dollars/year, and a sample standard deviation of 4.1 dollars/year. Since the sample size is quite large, it is assumed that the population standard deviation of the sales (per person) for prescription and non-prescription allergy relief medicine can be estimated by using the sample standard deviation values given above. Is there sufficient evidence to reject the claim made by the research department of the company, at the 0.1 level of significance? Perform a one-tailed test.
null hypothesis:
alternative hypothesis:
type of test:
value of test:
pvalue:
are we able to reject the claim?
I believe my null is h0:m1>=M2
alternative is h1:m1
I also think that it needs to be a ztest, can you help?
1 solutions
Answer 340627 by stanbon(57967) on 2011-10-01 18:42:02 (Show Source):
You can put this solution on YOUR website!A study conducted by the research department of a pharmaceutical company claims that the annual spending (per person) for prescription drugs for allergy relief, m1, is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine, m2.
---
A health insurance company conducted an independent study and collected data from a random sample of 205 individuals for prescription allergy relief medicine. The sample mean is found to be 17.8 dollars/year, with a sample standard deviation of 5.5 dollars/year.
------------------------------
They have also collected data for non-prescription allergy relief medicine. An independent random sample of 235 individuals yielded a sample mean of 18.2 dollars/year, and a sample standard deviation of 4.1 dollars/year.
Since the sample size is quite large, it is assumed that the population standard deviation of the sales (per person) for prescription and non-prescription allergy relief medicine can be estimated by using the sample standard deviation values given above.
Is there sufficient evidence to reject the claim made by the research department of the company, at the 0.1 level of significance?
Perform a one-tailed test.
null hypothesis: m1pre - m2non >= 0 (claim)
alternative hypothesis: m1pre - m2non < 0
-----
type of test: 2Sample T test
value of test: t = -0.8546
pvalue: 0.1967
are we able to reject the claim?
---
Since the p-value is greater than 1%, fail to reject Ho.
The test results support the claim.
======================================
Cheers,
Stan H.
|
Travel_Word_Problems/507622: a bus traveled on level road 4h hours at average speed 20 miles per hour faster than it traveled on a winding road the time sent on the winding road was 4 hours find the average speed on level road if the entire trip was 376 miles
1 solutions
Answer 340620 by stanbon(57967) on 2011-10-01 17:52:25 (Show Source):
You can put this solution on YOUR website!a bus traveled on level road 4 hours at average speed 20 miles per hour faster
distance = r*t = 20*4 = 80 miles
----------------------------------------
than it traveled on a winding road: The time spent on the winding road was 4 hours find the average speed on level road if the entire trip was 376 miles
distance = t*r = 4r miles
----
Equation:
distance + distance = 376
80 + 4r = 376
4r = 296
rate = 72 mph (rate on the level road)
==========================================
Cheers,
Stan H.
|
Money_Word_Problems/507618: Find the simple interest on a $1200 investment made for 2 years at an interest rate of 8%/year. What is the accumulated amount? (Round your answers to the nearest cent.)
simple interest $
accumulated amount $
1 solutions
Answer 340619 by stanbon(57967) on 2011-10-01 17:44:42 (Show Source):
You can put this solution on YOUR website!Find the simple interest on a $1200 investment made for 2 years at an interest rate of 8%/year. What is the accumulated amount? (Round your answers to the nearest cent.)
---
A(t) = P(1+rt)
----------
A(2) = 1200(1 + 0.08*2)
---
A(2) = 1200 + 2400*0.08
---
A(2) = 1200 + 192
----------------------------
simple interest $192
accumulated amount $1392
==============================
Cheers,
Stan H.
|
Polygons/507483: if the sum of the interior angles of a regular polygon is 720 (degree) and the perimeter of that regular polygon is 72 feet, then what is the area (in square feet) of that polygon?
1 solutions
Answer 340485 by stanbon(57967) on 2011-10-01 09:17:18 (Show Source):
You can put this solution on YOUR website!if the sum of the interior angles of a regular polygon is 720 (degree) and the perimeter of that regular polygon is 72 feet, then what is the area (in square feet) of that polygon?
---
(n-2)180 = 720
n-2 = 4
n = 6 sides
---
72/6 = 12 feet (length of each side
--
Sum of exterior angles = 360
Each of the 6 exterior angles = 360/6 = 60
So each of the interior angles is 180-60 = 120
---
So each pie-shaped interior regular triangle is 60-60-60
---
Knowing all that you should be able to find the area
of each of the interior triangles; then multiply by
6 to get the total interior area.
==========
Cheers,
Stan H.
|
Probability-and-statistics/507486: if x is N(0,4) Find P(1<=x<=2) and P(1<=x<=2 | x>=1)
1 solutions
Answer 340480 by stanbon(57967) on 2011-10-01 09:00:48 (Show Source):
You can put this solution on YOUR website!if x is N(0,4)
Find P(1<=x<=2)
---
z(1) = (1-0)/4 = 1/4
z(2) = (2-0)/4 = 1/2
---
P(1<= x <=2) = P(1/4 < z < 1/2) = 0.0928
------
and P(1<=x<=2 | x>=1)
= P(1<=x<=2 AND x>=1)/P(x>=1)
= P(1<= x <=2)/P(x>= 1)
---
P(x>=1) = P(z >= 1/4) = 0.4013
---
Ans: 0.0928/0.4013 = 0.2313
===========================
Cheers,
Stan H.
==========
|
Probability-and-statistics/507484: Can someone please help me here? I am so confused, I am seeing so many different formulas, I have no idea where to start.
1. A set of 50 data values has a mean of 15 and a variance of 36.
Find the standard score of a data value = 30
I'm hoping someone will help me, I've posted 7 different questions in the past week for help, and only 1 was responded to. I'm looking for help to understand, not for someone just to do my work. I want to understand this please. Please explain this step by step so I can the rest of my problems on my own. Thank you
1 solutions
Answer 340479 by stanbon(57967) on 2011-10-01 08:51:20 (Show Source):
You can put this solution on YOUR website!1. A set of 50 data values has a mean of 15 and a variance of 36.
Find the standard score of a data value = 30
----
standard deviation = sqrt(36) = 6
----
z(30) = (30-15)/6 = 15/6 = 2.5
----------------------------------
If you have problems, post them and send them
to me after you have tried your best to solve
them yourself.
--------------
Cheers,
Stan H.
stanbon@comcast.net
|
Polygons/507485: The sum of the interior angles of a polygon is 3780 degrees how many side does it have?
1 solutions
Answer 340478 by stanbon(57967) on 2011-10-01 08:47:39 (Show Source):
You can put this solution on YOUR website!The sum of the interior angles of a polygon is 3780 degrees how many side does it have?
-----
(n-2)180 = 3780
---
n-2 = 21
n = 23 sides
=================
cheers,
Stan H.
=========
|
Age_Word_Problems/507491: one half of Terri's age is the same as one fourth of Brian's. The sum of their ages is 36. how old is each?
1 solutions
Answer 340477 by stanbon(57967) on 2011-10-01 08:45:37 (Show Source):
You can put this solution on YOUR website!one half of Terri's age is the same as one fourth of Brian's. The sum of their ages is 36. how old is each?
-----
Equations:
(T/2) = B/4
T + B = 36
---
Rearrange:
T = B/2
----
Substitute for "T" and solve for "B":
B/2 + B = 36
(3/2)B = 36
B = (2/3)(36) = 24 yrs (Brian's age now)
----
solve for "T":
T = B/2
T = 12 (Terri's age now)
============================
Cheers,
Stan H.
=========
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Angles/507487: The measure of a supplement of an angle is 12 more than twice the measure of the angle. Find the measures of the angle and its supplement.
1 solutions
Answer 340476 by stanbon(57967) on 2011-10-01 08:41:24 (Show Source):
You can put this solution on YOUR website!The measure of a supplement of an angle is 12 more than twice the measure of the angle. Find the measures of the angle and its supplement.
---
angle: x
supplement: 180-x
-----------
Equation:
180-x = 2x+12
3x = 168
x = 56 degrees
180-x = 124 degrees
======================
Cheers,
Stan H.
===========
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Rational-functions/507488: If I have this function: g(x)=(8x)/(x^2+3x+4) how can I get the vertical & horizontal asymptotes?
1 solutions
Answer 340475 by stanbon(57967) on 2011-10-01 08:26:00 (Show Source):
You can put this solution on YOUR website! If I have this function: g(x)=(8x)/(x^2+3x+4) how can I get the vertical & horizontal asymptotes?
----
Vertical asymptotes occur when the denominator is zero.
Solve x^2+3x+4 = 0
Since b^2-4ac = 9-16 < 0,
there are no Real Number solutions.
So there are no vertical asymptotes.
---
Horizontal asymptotes is the limit as x goes to +/-inf
-------------
If you know something about calculus, divide numerator
and denominator by x^2 and take the limit:
y = limit as x goes to inf [(8/x)/(1 +3/x + 4/x^2)] = 0/1 = 0
---
So horizontal asymptote at y = 0
=======
Cheers,
Stan H.
============
|
Probability-and-statistics/507246: Five balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability that two or three of the balls are white.
The "two OR three of the balls are white" is confusing me!
1 solutions
Answer 340458 by stanbon(57967) on 2011-09-30 20:50:03 (Show Source):
You can put this solution on YOUR website!Five balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability that two or three of the balls are white.
----
P(A or B) = P(A) + P(B) - P(A and B)
----
P(2 or 3 white) = P(2 white) + P(3 white) -0
-----
P(2 white and 3 blue) = [3C2*5C3]/8C5 = (3*10)/56 = 30/56
----
P(3 white and 2 blue) = [3C3*5C2]/8C5 = (1*10)/56 = 10/56
----
Ans: P(2 white or 3 white) = (30+10)/56 = 40/56
=================================================
Cheers,
Stan H.
=========
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Probability-and-statistics/507367: 7. Among companies doing highway or bridge construction, 80% test employees for substance abuse (based on data from the Construction Financial Management Association) A study involves the random selection of 12 such companies.
(a) Find the probability that exactly 7 of the 12 companies test for substance abuse.
(b) Find the probability that at least half of the companies test for substance abuse.
(c) For such group of 12 companies, find the mean and standard deviation for the number (among 12) that test for substance abuse.
(d) Using the results from part (c) and the range rule of thumb, indentify the range of usual value.
1 solutions
Answer 340446 by stanbon(57967) on 2011-09-30 19:55:43 (Show Source):
You can put this solution on YOUR website!Among companies doing highway or bridge construction, 80% test employees for substance abuse (based on data from the Construction Financial Management
Association)
--------------------------------------
A study involves the random selection of 12 such companies.
Binomial Problem with n = 12 and p = 0.8
(a) Find the probability that exactly 7 of the 12 companies test for substance abuse.
P(x = 7) = 12C7(0.8)^7*(0.2)^5 = 0.0532
-----------------------------------------
(b) Find the probability that at least half of the companies test for substance abuse.
P(7<= x <=12) = 1 - P(0<= x <=6) 1 - binomcdf(12,0.8,6) = 0.9806
-----------------------------------------
(c) For a group of 12 companies, find the mean and standard deviation for the number (among 12) that test for substance abuse.
mean = np = 12*0.8 = 7.2
std = sqrt(npq) = sqrt(7.2*0.2) = 1.2
----------------------------------------
(d) Using the results from part (c) and the range rule of thumb, indentify the range of usual value.
If the "range of usual values" is 6*std, you get 6*1.2 = 7.2
=================================================================
Cheers,
Stan H.
============
|
Angles/507369: The measure of one angle is eight times the measure of its supplement. Find the measures of the angles. Set up equation and solve.
1 solutions
Answer 340445 by stanbon(57967) on 2011-09-30 19:41:50 (Show Source):
You can put this solution on YOUR website!The measure of one angle is eight times the measure of its supplement. Find the measures of the angles.
--------------
angle : x
supplement : 180-x
----------
180-x = 8x
9x = 180
x = 20 degrees
180-x = 160 degrees
=====================
Cheers,
Stan H.
===============
|
Angles/507368: The measure of one angle is twice the measure of complement, find the measure of the angles. Set up equation and solve.
1 solutions
Answer 340443 by stanbon(57967) on 2011-09-30 19:38:17 (Show Source):
You can put this solution on YOUR website!The measure of one angle is twice the measure of complement, find the measure of the angles. Set up equation and solve.
-----
angle : x
complement : 90-x
-------
Equation:
90-x = 2x
3x = 90
x = 30 degrees
90-x = 60 degrees
=========================
Cheers,
Stan H.
|
Probability-and-statistics/507360: Among students 70% own a car, 50% own a bike and 40% own both.
(a) Find a probability that a randomly chosen student own a least one of the above vehicles.
(b) What is a probability that a randomly chosen student does not own a bike?
1 solutions
Answer 340442 by stanbon(57967) on 2011-09-30 19:35:19 (Show Source):
You can put this solution on YOUR website!Among students 70% own a car, 50% own a bike and 40% own both.
(a) Find a probability that a randomly chosen student owns at least one of the above vehicles.
P(car) = 0.7 ; P(bike) = 0.5 ; p(car and bike) = 0.4
---
P(car OR bike) = 0.7 + 0.5 - 0.4 = 0.8
----
(b) What is a probability that a randomly chosen student does not own a bike?
P(not bike) = 0.5
========================
Cheers,
Stan H.
|
Probability-and-statistics/507215: when the mean is 300 and the standard deviation is 20 can the z score be a negative number? thank you
1 solutions
Answer 340441 by stanbon(57967) on 2011-09-30 19:28:47 (Show Source):
You can put this solution on YOUR website!when the mean is 300 and the standard deviation is 20 can the z score be a negative number? thank you
----
All data elements less than 300 will have a negative z-score.
The negative simply means the data value is less than the mean.
-----------------
Cheers,
Stan H.
-----------------
|
Probability-and-statistics/507366: 4. A division has 12 employees, 8 males and 4 females.
(a) How many ways can a committee of 6 members can be selected from out of these 12?
(b) Find the probability that the committee contains all males?
(c) How many ways can they choose a President of the committee, if the President has to be a female and the other officers must be males?
1 solutions
Answer 340439 by stanbon(57967) on 2011-09-30 19:26:03 (Show Source):
You can put this solution on YOUR website!A division has 12 employees, 8 males and 4 females.
(a) How many ways can a committee of 6 members can be selected from out of these 12?
Ans: 12C6 = 924 ways
-------------------------------
(b) Find the probability that the committee contains all males?
Ans: P(6 males) = 8C6/12C6 = 28/924
-------------------------------
(c) How many ways can they choose a President of the committee, if the President has to be a female and the other officers must be males?
Ans: Ways to choose a female president: 8
Question: How many other officers are there?
-------------
Cheers,
Stan H.
=============
|
Travel_Word_Problems/507362: Mr. Smith forgot his suitcase at home in his rush to leave on a business trip. His wife found the suitcase an hour later and decided to catch up to him to save him time. She knew he drives at an average speed of 55 mph. If Mrs. Smith leaves right away, travelling at 65 mph, how long will it take her to catch up?
1 solutions
Answer 340438 by stanbon(57967) on 2011-09-30 19:21:33 (Show Source):
You can put this solution on YOUR website!Mr. Smith forgot his suitcase at home in his rush to leave on a business trip. His wife found the suitcase an hour later and decided to catch up to him to save him time. She knew he drives at an average speed of 55 mph. If Mrs. Smith leaves right away, travelling at 65 mph, how long will it take her to catch up?
-------------
Mr DATA:
rate = 55 mph ; time = t hrs ; distance = 55t miles
-----
Mrs DATA:
rate = 65 mph ; time = (t-1)hrs ; distance = 65t-65 miles
-----
Equation:
distance = distance
55t = 65t - 65
10t = 65
t = 6.5 hrs (time the Mrs. will take to catch up)
==========================
Cheers,
Stan H.
=============
|
Geometry_Word_Problems/507358: A small business has an initial investment of
$8176. The unit cost of the product is $11,
and the selling price is $22.
How many units must be sold to break
even?
Answer in units of units
1 solutions
Answer 340436 by stanbon(57967) on 2011-09-30 19:16:09 (Show Source):
You can put this solution on YOUR website!A small business has an initial investment of
$8176. The unit cost of the product is $11,
and the selling price is $22.
How many units must be sold to break even?
Answer in units
---
Each unit sold yields (22-11) = $11 profit.
---
Break even occurs when x = 8176/11 = 743.27 units are sold.
---
Round up to 744 units.
===========================
Cheers,
Stan H.
|
Trigonometry-basics/507339: Evaluate the following expressions. The answer must be given as a fraction, NO DECIMALS. If the answer involves a square root it should be entered as sqrt.
If tan(theta)=4/3 and sin(theta)<0, then find:
a)sin(theta)
b)cos(theta)
c)sec(theta)
d)csc(theta)
e)cot(theta)
1 solutions
Answer 340428 by stanbon(57967) on 2011-09-30 18:00:47 (Show Source):
You can put this solution on YOUR website!Evaluate the following expressions. The answer must be given as a fraction, NO DECIMALS. If the answer involves a square root it should be entered as sqrt.
If tan(theta)=4/3 and sin(theta)<0, then find:
----
tan(theta) = y/x = 4/3
So, y = 4 and x = 3
-----
Since tan is positive and sin in negative, theta is in the 3rd Quadrant
where x and y are negative.
-----------------------------------
Find "r":
r = sqrt[3^2+4^2] = 5
--------
sin = y/r = -4/5
cos = x/r = -3/5
tan = y/x = 4/3
----
csc = r/y = -5/4
sec = r/x = -5/3
ctn = x/y = 3/4
========================
Cheers,
Stan H,
============
a)sin(theta)
b)cos(theta)
c)sec(theta)
d)csc(theta)
e)cot(theta)
|
Trigonometry-basics/507337: if theta =(7pi)/6, then find exact value for the following:
sec(theta)=
1 solutions
Answer 340427 by stanbon(57967) on 2011-09-30 17:49:58 (Show Source):
You can put this solution on YOUR website!if theta =(7pi)/6, then find exact value for the following:
sec(theta)= ?
------
The reference angle is (1/6)pi.
---
sec is negative in the 3rd Quadrant
---
sec[(7/6)pi] = -sec[(1/6)pi] = -2/sqrt(3)
==============================================
Cheers,
Stan H.
============
|
Polynomials-and-rational-expressions/507336: Please help me with this. I'm suppose to simplify and answer with only positive exponents (3/2)^8 (3/2)^-5 (3/2)^-4 I'm not sure what to do with the 3/2 am I raising to the power and then multipling them. I do know that with the (3/2) that have the negative exponents I flip them to (2/3) but I'm just not sure what to do with all of it together. Thank you for any help you can give.
1 solutions
Answer 340425 by stanbon(57967) on 2011-09-30 17:44:01 (Show Source):
You can put this solution on YOUR website!simplify and answer with only positive exponents
(3/2)^8 (3/2)^-5 (3/2)^-4
----
= (3/2)^(8-5-4)
---
= (3/2)^(-1)
----
= 2/3
============
Cheers,
Stan H.
|
Mixture_Word_Problems/507316: how many liters should be drained and replaced with pure antifreeze from a radiator containing 12 liters of 40 percent antifreeze to increase the concentration to 50 percent antifreeze.
1 solutions
Answer 340423 by stanbon(57967) on 2011-09-30 16:26:45 (Show Source):
You can put this solution on YOUR website!how many liters should be drained and replaced with pure antifreeze from a radiator containing 12 liters of 40 percent antifreeze to increase the concentration to 50 percent antifreeze.
----
alcohol - alcohol + alcohol = alcohol
0.40*12 - 0.40x + 1.0x = 0.50*12
-----
Multiply thru by 100 to get:
40*12 - 40x + 100x = 50*12
60x = 10*12
x = 2 liters (amt. to be replaced by pure antifreeze)
==============
Cheers,
Stan H.
|
Mixture_Word_Problems/507315: How many quarts of water [0% alcohol] need to be added to 50 quarts of 80% alcohol to obtain a 10% alcohol solution?
1 solutions
Answer 340421 by stanbon(57967) on 2011-09-30 16:23:25 (Show Source):
You can put this solution on YOUR website!How many quarts of water [0% alcohol] need to be added to 50 quarts of 80% alcohol to obtain a 10% alcohol solution?
----
Equation:
water + water = water
x + 0.20*50 = 0.90(x+50)
---
Multiply thru by 100 to get:
100x + 20*50 = 90x + 90*50
---
10x = 70*50
x = 350 quarts (amt. of water needed)
========================================
Cheers,
Stan H.
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