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Recent problems solved by 'stanbon'
stanbon answered: 57260 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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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, >>Next
Square-cubic-other-roots/122780: How do you evaluate expressions involving radicals? 4,square root symbol over -20736
1 solutions
Answer 90136 by stanbon(57328)   on 2008-01-26 21:12:09 (Show Source):
You can put this solution on YOUR website!How do you evaluate expressions involving radicals? 4,square root symbol over -20736
-----------------
The 4th root of 20736 is 12
-------------------
How do you get that without a calculator?
You express 20736 as a product of primes:
20736 = 2*10368
=2*2*5184
=2*2*2*2592
=2*2*2*2*1296
=2*2*2*2*2*648
=2^5*2*324
=2^5*2*2*162
=2^7*2*81
=2^8*3^4
-------------
4th root or 2^8*3^4 = 2^2*3 = 12
====================
Cheers,
Stan H.
|
Finance/122771: I figured out the answer but I am clueless as to the equation. Can you please help???? thanks
Simple interest word problems refer to applications in which money is invested in an account paying simple interest rather than compounded. The relationship between principle (P), interest rate (r), length of time the money is invested (t), and earned interest (I) is given by the following formula:
I = Prt
An approach to solving a simple interest problem runs pretty close to how one would set up a table and from that table, formulate a single variable equation to solve the problem. As an example, consider the following simple interest problem.
Mr. Jones deposits $8000 in one simple interest account and $2000 in a second simple interest account. The interest rate on the $8000 account is 2% more than the rate on the $2000 account. If the total yearly amount of interest on the two accounts is $578, find the interest rate on each account.
Steps to solve this problem:
Step 1: Identify which column you can complete from the information given in the problem (without having to use a variable) and fill it out. In this case you can set up a table since you know the amount invested in each account.
Principle T (Time) R ( rate) = Interest
$8000 account $8000
$2000 account $2000
Step 2: Identify what you are looking for and define your variable. Here we are looking for the interest rate on each account. But since they are not the same interest rate we cannot let x represent them both. Arbitrarily I will choose the following:
Let x represent the interest rate for the $2000 account.
• Place x in the appropriate cell (interest rate of the $2000 account)
• Fill out the rest of the column using the fact that the interest rate of the $8000 account is 2% more than the interest rate (x) of the $2000 account.
Principle T (Time) R ( rate) = Interest
$8000 account $8000 x + .02
$2000 account $2000 x
Note: We want to express the interest rate as a decimal rather than a percentage. Therefore, instead of using 2% (the percent form) we use .02 (the decimal form).
Step 3: Since the money is only deposited for one year, Time = 1. Fill out the last column by using the first two columns and following the equation at the top of the chart
Prt = I
Principle T (Time) R ( rate) = Interest
$8000 account $8000 (1) x + .02 $8000 (x+.02)
$2000 account $2000 (1) x $2000 (x)
Step 4: The equation that will model this problem will now be drawn from the last column
Interest earned on the $8000 account + Interest earned on the $2000 account
= $578
8000 (x+.02) + 2000 (x) = 578
Step 5: Now solve the equation and answer the original question.
Solving, we get: x = .0418 and x + .02 = .0618
Answer to the original question: The interest rate on the $2000 account is 4.18% and the interest rate in the $8000 account is $6.18%.
Now using this example as a template, formulate the following problem in a table format and solve the following problem. Keep in mind that full credit for this project will only be awarded if your solution is correct.
Ms. Parker deposits $8000 in one simple interest account and $2000 in a second simple interest account. The interest rate on the $8000 account is 2% more than the rate on the $2000 account. If the total yearly amount of interest earned on the $8000 account is $459 more than the interest earned on the $2000 account, find the interest rate on each account. Clearly state your solution in relation to the interest rate on each account.
The interest on the $8000 account is .069834 = 6.9834%
The interest on the $2000 account is .049834 = 4.9834%
1 solutions
Answer 90127 by stanbon(57328) on 2008-01-26 20:10:58 (Show Source):
You can put this solution on YOUR website!solve the following problem. Keep in mind that full credit for this project will only be awarded if your solution is correct.
-------------------------
Ms. Parker deposits $8000 in one simple interest account and $2000 in a second simple interest account.
The interest rate on the $8000 account is 2% more than the rate on the $2000 account.
If the total yearly amount of interest earned on the $8000 account is $459 more than the interest earned on the $2000 account, find the interest rate on each account.
Clearly state your solution in relation to the interest rate on each account.
---------------------
1st Investment:
Principal = $8000
Let rate = "x"
Interest = 8000x
---------------------
2nd Investment:
Principal = #2000
Rate = "x-.02"
Interest = 2000(x-.02)
-----------------------
EQUATION:
Interest in 1st - Interest in 2nd = 459
8000x - 2000(x-0.02) = 459
6000x+40 = 459
6000x = 419
x = 0.0698 (interest on the $8000)
x-0.02 = 0.0498 (interest on $2000)
============================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/122754: Solve.
The demand equation for a certain type of printer is given by d = -200p + 35,000. The supply equation is predicted to be s = -p squared + 400p - 20,000. Find the equilibrium price.
1 solutions
Answer 90114 by stanbon(57328) on 2008-01-26 18:55:34 (Show Source):
You can put this solution on YOUR website!The demand equation for a certain type of printer is given by d = -200p + 35,000. The supply equation is predicted to be s = -p squared + 400p - 20,000. Find the equilibrium price.
------------
Equilibrium occurs when demand = supply
------------
-p^2+400p-20,000 = -200p+35000
p^2-600p+55000 = 0
p=[600 +- sqrt(600^2-4*55000)]/2
p=[600 +- sqrt(140000)]/2
p = $112.92 or p=$487.08
====================
Cheers,
Stan H.
|
Graphs/122760: Find the x-intercept of y = x squared - 3x - 10
Find the axis of symmetry of y = -x squared - 6x + 2
1 solutions
Answer 90105 by stanbon(57328) on 2008-01-26 18:18:20 (Show Source):
You can put this solution on YOUR website!Find the x-intercept of y = x squared - 3x - 10
--------
Let y = 0 and solve for "x":
x^2-3x-10 = 0
(x-5)(x+2)=0
x = 5 and x=-2 are the x-intercepts.
-------------------
Find the axis of symmetry of y = -x squared - 6x + 2
The axis occurs at x = -b/2a = 6/(2(-1)) = 3
=====================
Cheers,
Stan H.
|
Graphs/122756: I need help trying to solve this problem..you are trying to find the slope.
(1/12, 1/8) (3/7, 9/17)..THANKS!
1 solutions
Answer 90104 by stanbon(57328) on 2008-01-26 18:13:17 (Show Source):
You can put this solution on YOUR website!find the slope.
(1/12, 1/8) (3/7, 9/17)
----------
slope = [(9/17)-(1/8)]/[(3/7)-(1/12)]
= [(72-17)/136]/[(36-7)/84]
= [55/136]/[29/84]
= [55/136]
= 1155/986 or 1.1714
==============
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/122747: Please help me solve this word problem!!!
A market researcher predicted that the profit function for the first year of a new business would be P(x)=-0.3x^2+3x-15, where x is based on the number of items produced. Will it be possible for the business to break even in its first year?
1 solutions
Answer 90102 by stanbon(57328) on 2008-01-26 18:04:22 (Show Source):
You can put this solution on YOUR website!A market researcher predicted that the profit function for the first year of a new business would be P(x)=-0.3x^2+3x-15, where x is based on the number of items produced. Will it be possible for the business to break even in its first year?
-----------
No because P(x) is negative for all values of "x":
================
Cheers,
Stan H.
|
Probability-and-statistics/122733: A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans. The results are given in the following table. Does it seem that there is a relationship between the pension plan selected and the job classification of the employees? Use the .01 significance level.
Pension Plan
Job Class Plan A Plan B Plan C
supervisor 10 13 29
clerical 19 80 19
labor 81 57 22
If needed I can email this plan if it makes it easier to understand.
1 solutions
Answer 90092 by stanbon(57328) on 2008-01-26 17:02:37 (Show Source):
You can put this solution on YOUR website!A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans. The results are given in the following table. Does it seem that there is a relationship between the pension plan selected and the job classification of the employees? Use the .01 significance level.
Pension Plan
Job Class Plan A Plan B Plan C
supervisor 10 13 29
clerical 19 80 19
labor 81 57 22
------------------
Run a ANOVA on the Data:
Ho: rows and columns factors are independent
Ha: there is a dependency relation between row elements and column elements.
I ran a ANOVA on a TI calculator and have p-value of 0.3321
----------
Conclusion: Since p-value is greater that alpha = 1% fail to reject Ho.
The row and column factors are independent.
===================
Cheers,
Stan H.
|
Volume/122735: The thickness of a film of oil is 6x10^-9cm. what area will 150,000 cubic cm. of oil cover on the surface of a large body of water. Need the answer in scientific notation.
thank you in advance.
1 solutions
Answer 90091 by stanbon(57328) on 2008-01-26 16:51:10 (Show Source):
You can put this solution on YOUR website!The thickness of a film of oil is 6x10^-9cm. what area will 150,000 cubic cm. of oil cover on the surface of a large body of water. Need the answer in scientific notation.
------------------------------
1.5x10^5 cm cm / 6x10^-9 cm = 2.5x10^13 sq cm
==========================
Cheers,
Stan H.
|
Probability-and-statistics/122730: This is homework and again, I need help!!
A research firm wants to compare the miles per gallon of unleaded regular, mid-grade,and super premium gasolines. Because of differences in the performance of different automobiles, seven different automobiles were selected and treated as blocks. Therefore, each brand of gasoline was tested with each type of automobile. The results of the trials, in miles per gallon, are shown in the following table. At the .05 significance level, is there a difference in the gasolines and automobiles?
Automobile Reg Mid. Super
1 21 23 26
2 23 22 25
3 24 25 27
4 24 24 26
5 26 26 30
6 26 24 27
7 28 27 32
1 solutions
Answer 90090 by stanbon(57328) on 2008-01-26 16:45:35 (Show Source):
You can put this solution on YOUR website! A research firm wants to compare the miles per gallon of unleaded regular, mid-grade,and super premium gasolines. Because of differences in the performance of different automobiles, seven different automobiles were selected and treated as blocks. Therefore, each brand of gasoline was tested with each type of automobile. The results of the trials, in miles per gallon, are shown in the following table. At the .05 significance level, is there a difference in the gasolines and automobiles?
Automobile Reg Mid. Super
1 21 23 26
2 23 22 25
3 24 25 27
4 24 24 26
5 26 26 30
6 26 24 27
7 28 27 32
----------------
You need to run a ANOVA (analysis of variance) test.
Hopefully you have software or a calculator to do this.
--------------------------
Ho: The Reg, Mid, and Super results are the same
Ha: At least one of them is different.
alpha = 0.05
------------------
I ran the ANOVA function on a TI calculator and got
a p-value = 0.0251
---------
Conclusion: Since the p-value is less than alpha,
reject Ho; at least one of the car results is
significantly different than the others.
======================
Cheers,
Stan H.
|
Linear-systems/122299: At the market you purchase some apples and oranges. There were 12 items purchased. You buy twice as many apples as oranges.
a. Define the variables.
b. Write an algebraic equation using one variable for the above situation.
c. Solve this equation for the number of apples and oranges you purchase
Please, I really need help on this one!
1 solutions
Answer 90088 by stanbon(57328) on 2008-01-26 16:31:38 (Show Source):
You can put this solution on YOUR website!At the market you purchase some apples and oranges. There were 12 items purchased. You buy twice as many apples as oranges.
a. Define the variables.
Let # of oranges be "r"
Then # of apples is "2r"
---------------------------
b. Write an algebraic equation using one variable for the above situation.
r + 2r = 12
----------------
c. Solve this equation for the number of apples and oranges you purchase
3r = 12
r = 4 (# of oranges)
2r = 8 (# of apples)
=================
Cheers,
Stan H.
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Equations/122726: how would this story problem work?
Char inherited $30,000 from her great uncle. She invested it in 2 different funds. One earns 5% adn the other earns 6%. If she earned $1600 last year, how much did she invest in each fund?
1 solutions
Answer 90086 by stanbon(57328) on 2008-01-26 16:27:03 (Show Source):
You can put this solution on YOUR website!Char inherited $30,000 from her great uncle. She invested it in 2 different funds. One earns 5% adn the other earns 6%. If she earned $1600 last year, how much did she invest in each fund?
------------
Let amt. invested at 5% by "x"; interest on this is 0.05x dollars
--------------
Amt. invested at 6% is "30,000-x" ; int is 0.06(30000-x)=1800-0.06x dollars
---------------------
EQUATION:
interest + interest = 1600 dollars
0.05x + 1800-0.06x = 1600
-0.01x = -200
x = $20,000 (amt. invested at 5%)
------------
30,000-x = $10,000 (amt. invested at 6%)
===============
Cheers,
Stan H.
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Radicals/122713: what is the radical sign of 72 simplified???
i don`t know how to do the raical sign on the computer
so i need to know wut 72 in a radical sign is when it is simplified
1 solutions
Answer 90078 by stanbon(57328) on 2008-01-26 15:44:21 (Show Source):
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test/122714: The sum of two numbers is 240. The larger number is 6 less than twice the smaller. Find the numbers.
1 solutions
Answer 90077 by stanbon(57328) on 2008-01-26 15:41:36 (Show Source):
You can put this solution on YOUR website!The sum of two numbers is 240. The larger number is 6 less than twice the smaller. Find the numbers.
----------
Let the smaller be "x" ; Larger is "2x-6"
EQUATION:
x + 2x-6 = 240
3x= 246
x = 82 (smaller)
2x-6 = 158 (larger)
==============
Cheers,
Stan H.
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Graphs/122715: Write an equation in slope-intercept form for the line that is perpendicular to the line y = (-1/3)x + 4 that passes through the given point (-4,2). That is just one question. I have another question....
Write an equation in slope-intercept form for the line that is parallel to the line y = -4x + 5 and that passes through the given point (-8,5).
1 solutions
Answer 90076 by stanbon(57328) on 2008-01-26 15:38:19 (Show Source):
You can put this solution on YOUR website!Write an equation in slope-intercept form for the line that is perpendicular to the line y = (-1/3)x + 4 that passes through the given point (-4,2).
---------------------
The slope must be 3 if the line is to be perpendicular.
The form is y=mx+b and you know y,x, and m; solve for "b":
2 = 3*-4 + b
b = 14
EQUATION:
y = 3x+14
===================
That is just one question. I have another question....
Write an equation in slope-intercept form for the line that is parallel to the line y = -4x + 5 and that passes through the given point (-8,5).
--------------------
The slope must be -4 if the line is to be parallel.
The form is y = mx+b and you know y,x, and m; solve for "b":
5 =-4*-8+b
5 = 32+b
b = -27
EQUATION:
y = -4x-27
===================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/122712: Mercury, Venus, and Earth revolve around the sun once every 3,7, and 12 months, respectively. If the three plants are in a straight line, what is the smallest number of months that pass before they line up agian?
1 solutions
Answer 90074 by stanbon(57328) on 2008-01-26 15:20:44 (Show Source):
You can put this solution on YOUR website!Find the least common multiple of 3, 7, and 12
Write the prime-factor form of each of the nuimbers:
3 = 3
7 = 7
12 = 3*2^2
The lcm must have each factor raised to the highest power present.
----------------
lcm = 3*7*2^2 = 84 months
--------------------
Earth will make 7 revolutions, each taking 12 months.
Venus will take 12 revolutions, each taking 7 months.
Mercury will take 28 revolutions, each taking 3 months.
========================
Cheers,
Stan H.
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Quadratic_Equations/122671: My economic class is quite challenging. Here is a question regarding the CPI.
I(t) = - 0.2t2 + 3t = 200 , t = 0 and corresponds to the year of 1995 where as 0 ≤ t & ≤ 5
What would the CPI by at in 1996?
What’s the rate of change from 1995 – 96?
How’s the index changing in 1998?
Any help in answering these questions on the CPI would be greatly appreciated. Thank you so much in advance!
1 solutions
Answer 90072 by stanbon(57328) on 2008-01-26 14:06:15 (Show Source):
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Probability-and-statistics/122474: This question is from textbook Statistical Techniques in Business and Economics,
For Exercises 5–8: (a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.
5) The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is 5,000 miles. The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 59,500 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significance level?
1 solutions
Answer 90059 by stanbon(57328) on 2008-01-26 11:30:35 (Show Source):
You can put this solution on YOUR website!5) The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is 5,000 miles. The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 59,500 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significance level
(a) State the null hypothesis and the alternate hypothesis.
Ho: mu= 60,000
Ha: mu is not equal to 60,000
--------
Two-tailed test because of the Ha statement of "not equal to".
Critical Values: z = +-1.96
-----------
Test Statistic:
z(59,500) = (59,500-60,000)/[5000/sqrt(48)] = -0.6928
p-value = P(z<-0.6928))= 0.2442
----------
Conclusion: Since 0.2442 > 0.025, fail to reject Ho.
==============
Cheers,
Stan H.
(b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.
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Probability-and-statistics/122477: This question is from textbook Statistical Techniques in Business and Economics,
Tests of Hypothesis
23) Experience raising New Jersey Red chickens revealed the mean weight of the chickens at five months is 4.35 pounds. The weights follow the normal distribution. In an effort to increase their weight, a special additive is added to the chicken feed. The subsequent weights of a sample of five-month-old chickens were (in pounds):
4.41 4.37 4.33 4.35 4.30 4.39 4.36 4.38 4.40 4.39
At the .01 level, has the special additive increased the mean weight of the chickens? Estimate the p-value
1 solutions
Answer 90055 by stanbon(57328) on 2008-01-26 11:18:42 (Show Source):
You can put this solution on YOUR website!Experience raising New Jersey Red chickens revealed the mean weight of the chickens at five months is 4.35 pounds. The weights follow the normal distribution. In an effort to increase their weight, a special additive is added to the chicken feed. The subsequent weights of a sample of five-month-old chickens were (in pounds):
4.41 4.37 4.33 4.35 4.30 4.39 4.36 4.38 4.40 4.39
At the .01 level, has the special additive increased the mean weight of the chickens? Estimate the p-value
--------------
Are you using T-tests and Z-tests for your Hypothesis testing of means?
Cheers,
Stan H.
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Linear-equations/122643: How would I write the equation of the line with slope 5 and y-intercept (0,-3)?
1 solutions
Answer 90051 by stanbon(57328) on 2008-01-26 11:06:43 (Show Source):
You can put this solution on YOUR website!How would I write the equation of the line with slope 5 and y-intercept (0,-3)?
--------------------------
Use the slope-intercept form, y = mx+b where m is the slope
and b is the y-intercept:
Your Problem:
y = 5x-3
===========
Cheers,
Stan H.
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Graphs/122639: Can you show me a graph for the slope of these lines?
(a) 1/2
(b) -2
(c) -1/2
(d) 2
1 solutions
Answer 90047 by stanbon(57328) on 2008-01-26 10:32:48 (Show Source):
You can put this solution on YOUR website!Can you show me a graph for the slope of these lines?
-----------------
slope is change in y over change in x.
------------
(a) 1/2
Put your pencil on (0,0)
Since 2 in in the denominator move your pencil 2 to the right
then, since 1 is in the numerator, move your pencil one up:
put a dot at that point. Draw a line thru (0,0) (2,1)
That is a line with slope = 1/2:
------------------------
(b) -2= -2/1
Start at (0,0); move 1 to the right; move 2 down
Draw a line thru (0,0) (1,-2)
------------------------
(c) -1/2
Start at (0,0); move 2 to the right; move 1 down
Draw a line thru (0,0) (2,-1)
--------------------------
(d) 2 = 2/1
Start at (0,0); move 1 to the right; move 2 up
Draw a line thru (0,0) (1,2)
====================
Cheers,
Stan H.
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Radicals/122614: I have three questions.
1. Simplify [√(32xy^7)/(√2xy)] I think it is 4y^3 but not sure if it is
[√ 4y^3]
2. Simplify and combine like radicals.
[5(forth root√(16x) + 5(forth root √625x]. I have 25(forth root√x) is that correct?
3. Simplify the expression by rationalizing the demoninator √[3/7]. This one I have no idea what they are talking about.
Thank you in advance for any assistance .
Gina
1 solutions
Answer 90043 by stanbon(57328) on 2008-01-26 09:30:12 (Show Source):
You can put this solution on YOUR website!1. Simplify [√(32xy^7)/(√2xy)]
= sqrt[(32xy^7)/(2xy)]
= sqrt[16y^6]
= 4y^3
You are correct
--------------
2. Simplify and combine like radicals.
[5(forth root√(16x) + 5(forth root √625x].
= 5*2*4th rt of x + 5*5*4th rt of x
=(10+25)*4th rt of x
=35*4th rt of x
You are correct
-------------------
3. Simplify the expression by rationalizing the demoninator √[3/7].
= sqrt(3/7)
Multiply numerator and denominator by 7 to get:
= sqrt(21/49)
= [sqrt(21)]/[sqrt(49)]
= [sqrt(21)]/7
= (1/7)sqrt(21)
===================
Cheers,
Stan H.
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Graphs/122613: Solve the following system of linear inequalities by graphing. 3x – y < 2
x + y > 2 please show me how to do this
1 solutions
Answer 90042 by stanbon(57328) on 2008-01-26 09:20:11 (Show Source):
You can put this solution on YOUR website!Solve the following system of linear inequalities by graphing. 3x – y < 2
x + y > 2
---------
Solve each for "Y":
y>3x-2
y>-x+2
------------
Graph the boundaries as dashed lines:
y=3x-2
y=-x+2
-----------------
Shade the iINTERSECTION of the half-plane above y=3x-2 and above y=-x+2
--------
Comment: That intersection is the solution set for your set of inequalities.
I cannot show you the intersection with the limited graphing capabilities of this site.
=================
Cheers,
Stan H.
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percentage/122538: Student x and student y took different sections of an economics class and each section had a different final exam, student x scored 83 out of 100 and had a percentile rank in his class of 72, student y scored 85 out of 100 and his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class?
1 solutions
Answer 90026 by stanbon(57328) on 2008-01-25 23:19:22 (Show Source):
You can put this solution on YOUR website!different final exam, student x scored 83 out of 100 and had a percentile rank in his class of 72, student y scored 85 out of 100 and his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class?
---------------------
Compare the % rank for each student:
student x had rank 72
student y had rank 70
----------------------------
student x performed better wrt the rest of the students in his class
===============
Cheers,
Stan H.
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Equations/122559: Find and simplify f(a+h)-f(a)/h (that is all over h by the way not just f(a) but the f(a+h) part too. (h cannot be 0) for the function f(x)=2-8x^2
thank you so much!
1 solutions
Answer 90025 by stanbon(57328) on 2008-01-25 23:10:31 (Show Source):
You can put this solution on YOUR website!Find and simplify f(a+h)-f(a)/h (that is all over h by the way not just f(a) but the f(a+h) part too. (h cannot be 0) for the function f(x)=2-8x^2
---------
f(a+h) = 2 - 8(a+h)^2 = 2-8(a^2+2ah++h^2)
= 2 -8a^2 -16ah -9h^2
-------------
f(a) = 2 -8a^2
----------------
Subtracting f(a) from f(a+h) you get;
-16ah - h^2
-----------------
Dividing that result by h you get:
-16a -h
==========================
Cheers,
StanH.
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Equations/122560: find function f such that g(x)= 1/x-5
h=g o f, and h(x)=1/(x^2-5)
Thank you!
1 solutions
Answer 90023 by stanbon(57328) on 2008-01-25 23:05:26 (Show Source):
You can put this solution on YOUR website!find function f such that g(x)= 1/x-5
h=g o f, and h(x)=1/(x^2-5)
------------------------------
h(x) = gof(x) = g[f(x)] = 1/[f(x)-5)]
----
But h(x) = 1/(x^2-5)
----------
1/[f(x)-5] = 1/[x^2-5]
f(x)-5 = x^2-5
f(x) = x^2
================
Cheers,
Stan H.
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Square-cubic-other-roots/122582: I do not understand this at all. I am to evaluate this problem but I am just confused.
5 sqrt2 - 3 sqrt 5
1 solutions
Answer 90017 by stanbon(57328) on 2008-01-25 22:51:25 (Show Source):
You can put this solution on YOUR website!5 sqrt2 - 3 sqrt 5
--------
There is nothing special you can do with
that expression except approximate its
value using a calculator:
=4(1.414...) - 3(2.2361...
= -1.0513...
Cheers,
Stan H.
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