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Recent problems solved by 'stanbon'
stanbon answered: 57304 problems
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53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 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, >>Next
Polynomials-and-rational-expressions/436524: Can someone please help me with this? I would appreciate it!!!
Find the exact perimeter of the rectangle. Then approximate your answer.
√18cm
√50cm
The exact perimeter of the rectangle is ? cm
Type an exact answer using radicals as needed.
Thank you
1 solutions
Answer 302009 by stanbon(57377)   on 2011-04-16 07:44:37 (Show Source):
You can put this solution on YOUR website!Find the exact perimeter of the rectangle. Then approximate your answer.
√18cm
√50cm
---
Note: I'm guessing those are the length and the width.
---
Perimeter = 2(length + width)
P = 2(sqrt(18)+sqrt(50)]
P = 2[3sqrt(2) + 5sqrt(2)]
P = 2sqrt(2)(8)
P = 16sqrt(2)
=======================
The exact perimeter of the rectangle is 16sqrt(2) cm
Type an exact answer using radicals as needed.
====================
Approximate answer is 16*1.414 = 22.6 cm
===============================================
Cheers,
Stan H.
================
|
Polynomials-and-rational-expressions/436523: Someone PLEASE help me!!!
In some other universe, K. Pack believes he has discovered a relationship between a planet’s distance D from its sun and the time T it takes to orbit its sun. This formula ∜(D⁹), where T is in earth years and D=1 corresponds to the distance between earth and our sun, or 93,000,000 miles.
(a) Planet Eta is 28 times farther from its sun than earth is to our sun. Estimate the number of earth years required for Eta to orbit its sun according to K. Pack’s formula.
(b) Write this formula with rational exponents.
I can not get this Thank you for your help.
1 solutions
Answer 302006 by stanbon(57377) on 2011-04-16 07:31:31 (Show Source):
You can put this solution on YOUR website!In some other universe, K. Pack believes he has discovered a relationship between a planet’s distance D from its sun and the time T it takes to orbit its sun. This formula T = ∜(D⁹), where T is in earth years and D=1 corresponds to the distance between earth and our sun, or 93,000,000 miles.
-----------------------------
(a) Planet Eta is 28 times farther from its sun than earth is to our sun. Estimate the number of earth years required for Eta to orbit its sun according to K. Pack’s formula.
---
T = 4th root of 28^9 = 28^(9/4) = 1803.46 years
---------------------------------------------------------
(b) Write this formula with rational exponents.
T = D^(9/4)
=======================
Cheers,
Stan H.
|
Linear-systems/436421: How do you find the slope intercept equation of a line through the given point (-5,1) and the slope of -1
1 solutions
Answer 301931 by stanbon(57377) on 2011-04-15 20:29:47 (Show Source):
You can put this solution on YOUR website!How do you find the slope intercept equation of a line through the given point (-5,1) and the slope of -1
-----------------------
Form: y = mx+b
You know y = 1 when x = -5, and you know m = -1;
So solve for "b":
--------
1 = -1*-5 + b
1 = 5+b
b = -4
-----
Equation:
y = -x-4
========================
Cheers,
Stan H.
========================
|
Angles/436416: 1.If the measure of an angle is 72 degrees what is the measure of an angle that is complementary, supplementary, and vertical?
2.In a triangle, two of the angles measure 31 degree and 71 degree. What is the measurment of the third angle?
May you also show how you got the answer so I will understand. Thank you SO MUCH!
1 solutions
Answer 301929 by stanbon(57377) on 2011-04-15 20:18:41 (Show Source):
You can put this solution on YOUR website!1.If the measure of an angle is 72 degrees what is the measure of an angle that is
complementary::90-72 = 18 degrees
---
supplementary::180-72 = 108 degrees
----
and vertical?::: 72 degrees
-----------------------------------
2.In a triangle, two of the angles measure 31 degree and 71 degree. What is the measurment of the third angle?
Ans: 180-[31+71] = 180-102 = 78 degrees
---------------------------------------------------
Cheers,
Stan H.
=====================
|
Permutations/436407: The question is How many arrangements of the letters in INSTRUCTOR have all of the following properites:
a. The vowel appearing in alphabetical order,
b. At least 2 consonants between each vowel.
a.In a I understand that vowels are fixed in the alphabet as A,I,O,U abd there is only one way to put 3 vowels but I am lost after that.
b. I understand that there are two sections that appear with atleast 2 consonants in the word, but after that I do not know how to solve it.
1 solutions
Answer 301928 by stanbon(57377) on 2011-04-15 20:12:14 (Show Source):
You can put this solution on YOUR website!1)Find the measure of the complement to angle A, whose angle measures 48 degrees.
Ans: 90-48 = 42 degrees
----------------------------------------------
2)How many degrees are there in the central angles on the interior of a circle?
Ans: 360 degrees
-----------------------------------------
3)Angle RST measures 80 degrees. Ray SU bisects the angle and each of the bisected angles measures how many degrees?
----
Ans: 40 degrees each.
========================
Cheers,
Stan H.
==================================
|
Linear_Algebra/436409: need help graphing this x-y=-1 and 2y=2x+8
1 solutions
Answer 301927 by stanbon(57377) on 2011-04-15 20:05:16 (Show Source):
You can put this solution on YOUR website!need help graphing these:
x-y=-1
y = x+11
Plot (0,11), (-11,0)
Draw a line thru those two points to get:
-----
and 2y=2x+8
y = x+4
Plot (0,4)(-4,0)
Draw a line thru those two points to get:
-----
Cheers,
Stan H.
|
Probability-and-statistics/436238: Please show the formula(s) for question given.
Given a normal distribution with a mean of 85 and a sample standard deviation of 15, how much of the data should be in the interval between 55 and 115? Thank you.
1 solutions
Answer 301924 by stanbon(57377) on 2011-04-15 19:56:50 (Show Source):
You can put this solution on YOUR website!Please show the formula(s) for question given.
Given a normal distribution with a mean of 85 and a sample standard deviation of 15, how much of the data should be in the interval between 55 and 115? Thank you.
-------------------------------
z(55) = (55-85)/15 = -30/15 = -2
---
z(115) = (115-85)/15 = 30/15 = 2
----
-----
P(85< x < 115) = P(-2< z < 2) = 0.9545
=============================================
Cheers,
Stan H.
===============
|
Angles/436384: The sum of two angles is 137°. One angle is 25° less than twice the other. Find the angles.
1 solutions
Answer 301912 by stanbon(57377) on 2011-04-15 18:51:11 (Show Source):
You can put this solution on YOUR website!The sum of two angles is 137°. One angle is 25° less than twice the other. Find the angles.
--------------------
Equations:
x + y = 137
x = 2y-25
-------------
Substitute for "x" and solve for "y":
(2y-25)+y = 137
3y = 162
y = 54
--------
Solve for "x":
x = 2y-25
x = 2*54-25
x = 108-25
x = 83
=============
Solution: (83,54)
=====================
Cheers,
Stan H.
|
Probability-and-statistics/436362: Military radar and missile detection system are designed to warn a country of an enemy attack. A
reliability question is whether a detection system will be able to identify an attack and issue a warning.
Assume that a particular detection system has a .90 probability of detecting a missile attack.
a. What is the probability that single detection system will detect the attack?
b. If two detection systems are installed in the same area and operating independently, what is the
probability that at least one of the systems will detect the attack?
c. If three systems are installed, what is the probability that at least one of the systems will detect
the attack?
d. Would you recommend the multiple detection systems be used? Explain.
1 solutions
Answer 301896 by stanbon(57377) on 2011-04-15 18:03:01 (Show Source):
You can put this solution on YOUR website!Military radar and missile detection system are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning.
Assume that a particular detection system has a 0.90 probability of detecting a missile attack.
a. What is the probability that single detection system will detect the attack?Ans: 0.9
=================
b. If two detection systems are installed in the same area and operating independently, what is the probability that at least one of the systems will detect the attack?
P(at least one) = 1-P(none detect)
= 1 -0.1^2
= 1-0.01
= 0.99
-------------
c. If three systems are installed, what is the probability that at least one of the systems will detect the attack?
1-(0.01)^3 = 1- 0.000001 = 0.999999 -----------------------------------
d. Would you recommend the multiple detection systems be used? Explain
I'll leave that to you.
Cheers,
Stan H.
==============
|
Inequalities/436360: I need help with this absolute value rational inequality:
|(2/3)x -1| - 2 >1/3
The solution should be:
(-infinity, -2) U (5,infinity)
I a getting 5 right but I cant figute out how to get -2.
Thank you!
1 solutions
Answer 301891 by stanbon(57377) on 2011-04-15 17:40:17 (Show Source):
You can put this solution on YOUR website!|(2/3)x -1| - 2 >1/3
The solution should be:
(-infinity, -2) U (5,infinity)
I a getting 5 right but I cant figute out how to get -2.
----------------------------------
|(2/3)x -1| - 2 >1/3
---
Add 2 to both sides to get:
---
|(2/3)x -1| > 2 + 1/3
------
|(2/3)x -1| > 7/3
---------------------------
(2/3)x-1<-7/3 or (2/3)x-1>7/3
----
(2/3)x < -4/3 or (2/3)x > 10/3
---
x < -2 or x > 5
----
Solution:
(-inf,-2)U(5,+inf)
===========================
Cheers,
Stan H.
============
|
Evaluation_Word_Problems/436339: find the equation of the line that passes through (-3.5) and perpendincular to a line 3x-6y-7 = 0 (p.s put this line in the form of y=mx+c)
1 solutions
Answer 301879 by stanbon(57377) on 2011-04-15 16:42:08 (Show Source):
You can put this solution on YOUR website!find the equation of the line that passes through (-3.5) and perpendincular to a line 3x-6y-7 = 0 (p.s put this line in the form of y=mx+c)
-----------------------------
If 3x-6y-7 = 0
6y = 3x-7
y = (1/2)x-(7/6)
Slope = 1/2
--------
Any line perpendicular to the given line must
have slope = -2
-----------------------
Find equation of line thru (-3,5) with slope = -2.
Form: y = mx+b
5 = -2*-3+b
b = -1
----
Equation:
y = (1/2)x-1
==================
Cheers,
Stan H.
================
|
logarithm/436308: I have a formula that has 20*log(10) in it and I am confused as to what log would be in this formula. Can you please help me with this?
1 solutions
Answer 301875 by stanbon(57377) on 2011-04-15 16:20:35 (Show Source):
You can put this solution on YOUR website! I have a formula that has 20*log(10) in it and I am confused as to what log would be in this formula.
------
What does 20*log(10) mean?
----
log(10) = 1
So 20*log(10) = 20*1 = 20
=============================
Hope that helps you.
Cheers,
Stan H.
============
|
Probability-and-statistics/436310: A battery operated digital pressure monitor is being developed for use in calibrating pneumatic pressure gauges in the field. It is thought that 95% of the readings it gives lie within 0.01 lb/in^2 of the true reading. In a series of 100 tests, the gauge is subjected to a pressure of 10,000 lb/in^2. A test is considered to be a success if the reading lies withing 10,000 +/- lb/in^2. We want to tst Ho: p=.95 H1: p does not equal .95 at the alpha = .05 level.
A. What are the critical points for the test?
B. When the data are gathered, it is found that 98 of the 100 readings were successful. Can Ho be rejected at the alpha =.05 level? To what type error are you now subject?
THANK YOU in advance.
1 solutions
Answer 301874 by stanbon(57377) on 2011-04-15 16:17:34 (Show Source):
You can put this solution on YOUR website!A battery operated digital pressure monitor is being developed for use in calibrating pneumatic pressure gauges in the field.
It is thought that 95% of the readings it gives lie within 0.01 lb/in^2 of the true reading.
In a series of 100 tests, the gauge is subjected to a pressure of 10,000 lb/in^2. A test is considered to be a success if the reading lies withing 10,000 +/- (?)lb/in^2. We want to test
Ho: p=.95
H1: p does not equal .95
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at the alpha = .05 level.
A. What are the critical points for the test?
z = +/-1.96
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B. When the data are gathered, it is found that 98 of the 100 readings were successful. Can Ho be rejected at the alpha =.05 level?
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z(0.98) = (0.98-0.95)/sqrt[0.95*0.05/100] = 1.3765
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Since the test stat is not in the reject interval,
fail to reject Ho.
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By the way, the p-value = 2*P(z> 1.3765) = 2*0.0843 = 0.1686
Since the p-value is greater than 5% fail to reject Ho.
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To what type error are you now subject?
Ans: You have not reject Ho. You are subject
to a Type II error.
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Cheers,
Stan H.
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Pythagorean-theorem/436335: In trigonometry, how do i know if i use sine, cosine, or tangent with a triangle?
1 solutions
Answer 301871 by stanbon(57377) on 2011-04-15 16:07:51 (Show Source):
You can put this solution on YOUR website!In trigonometry, how do i know if i use
sine,
cosine,
or tangent
with a triangle?
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Since sine = y/r you need information about 2 of those
components to find the 3rd.
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Since cosine = x/r you need info about 2 of those
components to find the 3rd.
---
Since tangent = y/x you need info about 2 of those
components to find the 3rd.
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/436336: Factoring out the opposite of the GCF
Factor each polynomial twice. First factor out the greatest common factor, and then factor out the opposite of the GCF.
Factor: 12u^5v^6 + 18u^2v^3 - 15u^4v^5
1 solutions
Answer 301869 by stanbon(57377) on 2011-04-15 16:03:55 (Show Source):
You can put this solution on YOUR website!First factor out the greatest common factor, and then factor out the opposite of the GCF.
Factor: 12u^5v^6 + 18u^2v^3 - 15u^4v^5
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GCF: 3u^2v^3
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Factored form:
3u^2v^3[4u^3v^3 + 6 - 5u^2v^2]
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Cheers,
Stan H.
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Probability-and-statistics/436313: Find the probability of choosing each type of card combination at random from a standard deck of 52 cards if you replace the first card.
at least one of the two cards is a red face card
1 solutions
Answer 301868 by stanbon(57377) on 2011-04-15 16:01:13 (Show Source):
You can put this solution on YOUR website! Find the probability of choosing each type of card combination at random from a standard deck of 52 cards if you replace the first card.
at least one of the two cards is a red face card
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P(red card) = 1/2
P(not red) = 1/2
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P(at least one of two is red) = 1 - p(neither is red)
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= 1-(1/2)^2
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= 1 - 1/4
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= 3/4
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Cheers,
Stan H.
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Linear-systems/436331: I need help understanding this problem.
x+3y=15
-8x+3y=-12
So far I have done it 3 times ive got the (3,_) but cant understand how to get 4 using process of elimination
1 solutions
Answer 301866 by stanbon(57377) on 2011-04-15 15:54:44 (Show Source):
You can put this solution on YOUR website!x+3y=15
-8x+3y=-12
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Subtract and solve for "x":
9x = 27
x = 3
---
Solve for "y":
x + 3y = 15
3 + 3y = 15
3y = 12
y = 4
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Solution: (3,4)
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/436332: Soybean is 18% protein
Cornmeal is 9% protein
How many lbs of each should be mixed together to get 360-lb mixture that is 12% protein?
1 solutions
Answer 301865 by stanbon(57377) on 2011-04-15 15:52:33 (Show Source):
You can put this solution on YOUR website!Soybean is 18% protein
Cornmeal is 9% protein
How many lbs of each should be mixed together to get 360-lb mixture that is 12% protein?
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Equations:
Quantity Eq: s + c = 360 lb
Protein Eq:0.18s+0.09c = 0.12(360)
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Multiply thru the 1st by 18
Multiply thru the 2nd by 100
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18s + 18c = 18*360
18x + 9c = 12*360
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Subtract and solve for "c":
9c = 6*360
c = (2/3)360
c = 240 lb. (amt. of cornmeal needed)
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Solve for "s":
s + c = 360
s + 240 = 360
s = 120 lb (amt of soybean needed)
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Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/436324: will you show me how to construct a truth table for (p^q)<-->~p thanks Cathy
1 solutions
Answer 301864 by stanbon(57377) on 2011-04-15 15:47:40 (Show Source):
You can put this solution on YOUR website!will you show me how to construct a truth table for (p^q)<-->~p thanks Cathy
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I would be happy to do that but they get very
messed up when posted on this site. Please
use Google to search for "constructing truth tables".
There you will see the tables and examples of how
to apply them to compound statements.
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Cheers,
Stan H.
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