3 answers

A horticulturist working for large plant nursery is conducting experiments on the growth rate of new shrub: Based on previous

Question:

A horticulturist working for large plant nursery is conducting experiments on the growth rate of new shrub: Based on previous research; the horticulturist feels the average weekly growth rate ofthe new shrub is 3 cm per week: random sample of 45 shrubs has an average growth of Cm per week with standard deviation of cm: Is there overwhelming evidence to support the claim that the growth rate of the new shrub ess than 3 cm per week at_ 0.025 significance level? Step 2 of 3: Is there overwhelming evidence to support the claim that the growth rate of the new shrub is less than 3 cm per week ata 0.025 significance level? State your conclusion in the context of the original problem_ Answer Points Keypad Fail to reject the null hypothesis; there is sufficient evidence at the 0.025 level of significance_ to conclude that the average weekly growth rate of the new shrub is less than 3 cm: Fail to reject the null hypothesis; there not sufficient evidence at the 0.025 level of significance_ to conclude that the average weekly growth rate of the new shrub is less than 3 Cm: Reject the null hypothesis; there not sufficient evidence at the 0.025 level of significance to conclude that the average weekly growth rate of the new shrub less than cm; Reject the null hypothesis; there is sufficient evidence at the 0.025 level of significance, to conclude that the average weekly growth rate of the new shrub is less than 3 cm_


Answers

The growth of plants or animals does not follow a linear pattern. For relatively short intervals of time, however, a linear function may provide a reasonable description of the growth. Exercises 25 and 26 provide examples of this. (a) In an experiment with sunflower plants, H. S.

Reed and R. H. Holland measured the height of the plants every seven days for several months. IThe experiment is reported in Proceedings of the National Academy of Sciences, vol. $5(1919), \text { p.

} 140 .]$ The following data are from this experiment. $$\begin{array}{lll}\hline x \text { (number of days) } & 21 & 49 \\ \begin{array}{l}y \text { [average height (cm) } \\\text { of plants after x days] }\end{array} & 67.76 & 205.50 \\ \hline\end{array}$$ Find the linear function whose graph passes through the two points given in the table. (Round each number in the answer to two decimal places.) (b) Use the linear function determined in part (a) to estimate the average height of the plants after 28 days. (Round your answer to two decimal places.) (c) In the experiment, Reed and Holland found that the average height after 28 days was $98.10 \mathrm{cm} .$ Is your estimate in part (b) too high or too low? Compute the percentage error in your estimate. (d) Follow parts (b) and (c) using $x=14$ days.

For the computation of percentage error, you need to know that Reed and Holland found that the average height after 14 days was $36.36 \mathrm{cm}$ (e) As you've seen in parts (c) and (d), your estimates are quite close to the actual values obtained in the experiment. This indicates that for a relatively short interval, the growth function is nearly linear. Now repeat parts (b) and (c) using $x=84$ days, which is a longer interval of time. You'll find that the linear function does a poor job in describing the growth of the sunflower plants. To compute the percentage error, you need to know that Reed and Holland determined the average height after 84 days to be $254.50 \mathrm{cm}$.

.

Everybody. My name is Colin. And let's go ahead and jump into this problem that deals with corn and weeds and whether or not there is a potential relationship between on increase in weeds per meter and an increase or decrease in the output of corn. So part they asked us to analyze this scatter plot that we've got here and describe the relationship. There were the potential relationship between the corn yield and weeds per meter so we can see from those data points there and from that regression line that they've got drawn in there.

We've got what I would describe as a week linear relationship between the two variables. So you can see that big because there is a general downward trend down to the right negative slope. Um, we can kind of see that there is a potential relationship between these two variables. It is not super strong, but it is there, and we'll get into how strong it is later on. So let's go ahead and jump now into part B or asked to simply find ah, that regression the least squares regression line equation from that many tap output.

And so if you see my earlier videos from this chapter where we talk about how to find Ah, that regression line. You'll know that about the overall. Our general equation for your regression line is in the forum. Why equals Alfa plus Beta X? And in this case, we're looking for Alfa, which is the intercept of the regression line, and Beta, which is the slope. And so, in this case, for this problem to find that Alfa value, we're gonna go ahead and look at the Constant Row coefficient column and you'll see that that intercept is 1 66.483 and you'll see that that beta value, which is that same coefficient column but now in the weeds per meter row is negative 1.987 So from this, we get our overall general formula for the the equation of the least squares regression line as 1 66.483 minus 1.987 x.

And just like that off the bat, we've solved parts A and B in part C just asked us to interpret what the slope and the Y intercept mean and constant in context accused me So we were given that our our slope or at beta value waas negative 1.987 And what this just means in context, uh is that we're Look, we're looking for the slope is just the change in corn yield given one additional we'd premier. So basically what? This negative number right here is telling us negative 1.987 is telling us that the corn yield decreases by 1.987 bushels given on additional we'd per meter and that Alfa value that we've got or the intercept apologize. I'll go ahead and draw better Alfa than that, Which was that 1 66 point for a three number? When we analyze that, that's just are expected corn yield when we there are zero weeds per meter. And so that just means that if there are zero weeds per meter, um, we're going to have an estimated corn yields of 1 66.483 And when you think about it, this kind of makes sense. We have, ah, high corn yield when they're zero weeds per meter.

And intuitively, we know that the addition of weeds may hinder the growth of corn and eso. You can see that the slope is negative or the amount of corn decreases as you increase the amount of weeds per meter. But now we move on the part D, which is we are asked to carry out a test at the Alfa equals 0.5 level of significance to answer this question. And so this is where we're going to now start to get into our no hypothesis test. So for part D, we're going to set up two different hypothesis.

First, we're going to have the no hypothesis on. That's just going to be, Ah, that beta, the slope of the regression line is zero on what this means is, is our We're looking at whether or not we reject this null hypothesis. So obey the equal zero. That means the slope zero and there is no relation between the corn yield and the number of weeds in a particular plot. And so then we'll be looking at that against the help.

The alternative hypothesis that beta does not equal zero r beta is less than zero. Excuse me. Um, because if you read that problem, you'll see that we're looking at, whether or not more weeds reduced corn yield on we're going to be doing this is they ask for at that Alfa off 0.5 level of significance, I'll point out that this outfit value right here is a different Alfa value than the one that we calculated. Our we looked at in the progression announced that this problem are reminded that we're now doing a hypothesis test and the number of degrees of freedom. We saw that there were 16 corn plots plan sets.

The degrees of freedom is always end minus two or the number off trials or plots minus two. We will go with a degrees of freedom here for 14 for this test. So first, we're gonna go ahead and calculate our tr critical, uh, value our T statistic on to do that. We're going to, uh, do beta. We're going to ah, subtract are no hypothesis value of beta or zero from our given beta negative 1.987 And we're going to put that all over the standard deviation from this problem or R s output from that regression analysis which is just going to give US negative 1.987 all over 0.5712 Which will see is that Sigma value? In the mini tap output, we calculate that we get a T value of negative 1.923 and now we're going to go ahead and use that to find RPI value, which is what's going to we're going to compare to Alfa to see whether or not we reject the null hypothesis.

So are inputs for that p value. We are looking at a T star R R T Value T statistic of negative 1.923 We're looking at 14 degrees of freedom and because we just need a large number, I'm going to just pick 10 million. Um, are negative 10 million any value of any large value and will work here. But I'm going to pick negative 10 million, and I'm going to go ahead and run eight a test on that you can use Excel. You can use an online TI calculator or you can use a table on.

When you do that, you get a P value of zero point are sorry 0.0.375 and So that's what we're going to compare. Teoh Alfa Value that we started with at the beginning and sends 0.375 is less than 0.5 You'll remember from the rules of these tests, you know that we can reject that. No hypothesis. And since we reject the null hypothesis and are no hypothesis was that the, uh, more weeds do not reduce cornfield or more weeds do not impact corn, yield it all. We can reject that that that idea.

There is no correlation between weeds and corn yield and say that there is, in fact, sufficient evidence to support the claim that weeds that the increase in weeds are more weeds in a certain plot do reduce the corn yield..

In this video, we're going to look at log arrhythmic transformations and the power law model. We can use a law algorithmic transformation to determine if the power law is a good power law model is actually a good fit for our data. Now, the power law formula is right here, Y equals alpha X to the beta. And in our particular example, X represents the time in microseconds and Y equals the amps built up in the circuit at time X. So here are exes and here's our why.

First thing we're asked to do is we're asked to find ex prime and why prime these are transformations. So ex prime will be log of X and Y. Prime will be log of Y. And then we're asked to graph. Actually we're asked to find the regression model for the graph of ex prime Y.

Prime. So I would find a log of two. This would be my first ex and then I'm going to round it, so Log of two again on the calculator log too. And then I would also need to find log 1.81 and I can do that for each of my values. And then I would graph that information.

But there's actually a faster way to do it. So I'll go back to my calculator but this time I'm going to go to my lists. So stat number one. Edit notice I already have the information in L. One and L.

Two. What I'm gonna do on L. three and L four is figure out the logs of those values. So I'm going to type log to so log of my original X. Value and press enter and you can see this automatically calculates it for me.

So I don't have to go through and do it all by hand, log for log six, log eight, log 10. Remember the log of 10 is one because those are in verses. All right. I'm going to pause the video and then I'm going to enter in the logs of the Y. Values.

And when I come back or in a second you will see the results of that. So, now I have the log of my Y. Each Y value entered into al. For so to find the regression model, select stat cursor over to couch, choose number eight. The linear regression model in the form of A plus B.

X. But I don't want L one, L two. I want L. Three and L. Four.

So second three will put L. Three under my ex list. Second four puts L four under my wild list, cursor down to calculate and now I have the X. Value or the A. Value, the B.

Value. And my correlation coefficient so is 0.128 B is 0.492 depending again on how you need around. And rs 0.987 So my model will be Why prime is approximately 0.128 plus 0.492 Ex prime. So there's my linear regression model. So that is part B.

So part C. Then is to find my model the my power model. And I can do that algebraic lee by using this Y. Prime equation. But we're actually just going to use our calculator.

And then if you'd like to see how you find the model drive it from the linear regression model you can but I figured most of you will just want the answer. So we'll go through and I go back to my calculator stat calc But this time I want to calculate power regression. If you cursor down you'll see here that it is at letter A. When I select it. I don't want L.

Three and L. four because remember those weren't my original Values. So I'm gonna do l. 1 2nd 1 second to. So all one L two years might already be default to L.

One L. Two, Calculate enter and you can see now I have alpha or in this case a 1.34 37 Or 1.3438 And then .4919. Now this will depend on again how how your instructor wants you around or how the textbook wants you around it. So it may be a little bit different. Okay so there is your power model and again rounding some texts might have it like this.

There would be another model again rounded differently. Okay so if you're done, pause the video. If you want to find out how we take our linear regression model and make it into a power model, then stick around. So recall that the UAE prime and the ex prime are actually logs of those values. Now I'm gonna exponentially eight both sides.

Bye. 10 And 10 log of Y will become why. And now I need to remember some of my exponential rules or exponents rules. So when I'm adding exponents, that means in my original equation I was multiplying like bases. So this actually will end up being our alpha and then this one I have to do a little more work.

I have to rearrange it a little bit more. So I'm going to rearrange it because remember with our power roll you copy down the base and you multiply the exponents. So I'm going to reverse the power rule. Can remember this is multiplication. So 10 log of x becomes x.

So this will be alpha, here's beta and when I use my calculator, second quit. So 10 carrot .128 for at the decimal point, You can see there's our 1.343 When we round it or 1.34-7. So again, it's a little different from when we use our calculator. And again, that has to do with how we end up a rounding our information..

Similar Solved Questions

1 answer
Add the following rational expressions. b2 - 6b - 16 b+2 b+2 b2-6b - 16 (Simplify...
Add the following rational expressions. b2 - 6b - 16 b+2 b+2 b2-6b - 16 (Simplify your answer.) b+2 b+2...
1 answer
Use the information below, answer the next 2 questions: Suppose that the distance of fly balls...
Use the information below, answer the next 2 questions: Suppose that the distance of fly balls hit to the outfield (in basebal) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. (a) What is the probability that the 49 balls traveled...
5 answers
The total revenue (in hundreds of dollars_ from the sale of x spas and solar heaters is approximated by R(x,y) = 13 272x 304y - 6x2 9y2 1Oxy. Find the number of each that should be sold to produce maximum revenue_ Find the maximum revenueFind the derivatives Rxx' Ryy ' and Rxy:RxxRyyRxy
The total revenue (in hundreds of dollars_ from the sale of x spas and solar heaters is approximated by R(x,y) = 13 272x 304y - 6x2 9y2 1Oxy. Find the number of each that should be sold to produce maximum revenue_ Find the maximum revenue Find the derivatives Rxx' Ryy ' and Rxy: Rxx Ryy Rx...
1 answer
Which is the limiting reactant when 5.00 g of H2 and 10.0 g of O2 react...
Which is the limiting reactant when 5.00 g of H2 and 10.0 g of O2 react and form water? How many grams of water are formed and what mass of excess reagent remains?...
5 answers
0 1 { VJ 1 5 2 2 2 2 [ ~Ia ~Ia ~IA ~Ia 1 L 11 1 :
0 1 { VJ 1 5 2 2 2 2 [ ~Ia ~Ia ~IA ~Ia 1 L 1 1 1 :...
1 answer
For high technological industries, you evaluate metals and ceramics beyond the Fe-C alloys to more costly applications. A. Select three alloying components for Ti alloys to give alpa+beta phases f...
For high technological industries, you evaluate metals and ceramics beyond the Fe-C alloys to more costly applications. A. Select three alloying components for Ti alloys to give alpa+beta phases from simple solidification or peritectic reaction and beta+gamma phases from a eutectic reaction. B. What...
5 answers
Fino (C €qualioncne UnlDCst Tic RCCd(eastdecimalsDarametercqualionInterpret the slope conter .Aan should erdect 0. 0334 brightness level pe houg Tlan thoulo cxpcrt 0384 hours per brightness level.What dots tht equation predict for the number hours the phone will lastbrightness levelhounsWhat the residual for the point (35,6.1)nourtQuestion Help:Vidco
Fino (C €qualion cne Unl DCst Tic RCCd (east decimals Darameter cqualion Interpret the slope conter . Aan should erdect 0. 0334 brightness level pe houg Tlan thoulo cxpcrt 0384 hours per brightness level. What dots tht equation predict for the number hours the phone will last brightness level ...
1 answer
HW3 - Calculate the number of moles of magnesium, chlorine, and oxygen atoms in 6.90 moles...
HW3 - Calculate the number of moles of magnesium, chlorine, and oxygen atoms in 6.90 moles of magnesium perchlorate, Mg(ClO4)2Mg(ClO4)2. Express the number of moles of MgMg, ClCl, and OO atoms numerically, separated by commas. --- A sample of propane, C3H8C3H8, contains 10.3 molesmoles of carbon ato...
5 answers
0w kour Voa UJ ould aachian u S2 Grignad Cor to Pound s Rrepore +h & Also Show &f-lkxin= 04 Srinard ?rogeat; howo V 0d r Pk& oH
0w kour Voa UJ ould aachian u S2 Grignad Cor to Pound s Rrepore +h & Also Show &f-lkxin= 04 Srinard ?rogeat; howo V 0d r Pk& oH...
1 answer
Problem 5 [15pt] Using the pure A-calculus, we can encode a pair of A-terms as where...
Problem 5 [15pt] Using the pure A-calculus, we can encode a pair of A-terms as where a term PAIR takes three A-terms a, b, p and applies p to a and b. That is, we can define PAIR as a bp. pab). a) (5pt) Based on this definition, we can encode function RIGHT as RIGHT under such encoding, RIGHT (PAIR ...
1 answer
The ginalaE i equal to fi lt multipl caed times (s r) The alions e2 theinverse ourier transo aw),...
The ginalaE i equal to fi lt multipl caed times (s r) The alions e2 theinverse ourier transo aw), that is choun re he exponen iaou Series o thesnalE) ) The mathennathica aquation of the aurier transfor e mathemathico thical equa tton of the sianal t) c) tve spekel graph (Erequeoty graph tytw) of the...
1 answer
0.27 m0.24 m0.06 m Q3. The assembly in the figure is composed of three homogeneous bodies: the 10-kg cylinder, the...
0.27 m0.24 m0.06 m Q3. The assembly in the figure is composed of three homogeneous bodies: the 10-kg cylinder, the 2-kg slender rod and the 4-kg sphere. For this assembly, calculate (a) , the mass moment of inertia about the x-axis and (b) I, and k, the mass moment of inertia and the radius of gyrat...
1 answer
Use the grammar $G=(N, T, P, \sigma),$ where $N=\{A, \sigma\}, T=\{\mathrm{a}, \mathrm{b}\},$ and $P=\{\sigma \rightarrow \mathbf{a} \sigma, \sigma \rightarrow \mathbf{a} \mathbf{A}, \mathbf{A} \rightarrow \mathbf{b}\}.$ Draw a derivation tree for each word in $L(G).$ ab
Use the grammar $G=(N, T, P, \sigma),$ where $N=\{A, \sigma\}, T=\{\mathrm{a}, \mathrm{b}\},$ and $P=\{\sigma \rightarrow \mathbf{a} \sigma, \sigma \rightarrow \mathbf{a} \mathbf{A}, \mathbf{A} \rightarrow \mathbf{b}\}.$ Draw a derivation tree for each word in $L(G).$ ab...
1 answer
Describe how different depreciation methods of manufacturing equipment and plant affect the cost of the product....
Describe how different depreciation methods of manufacturing equipment and plant affect the cost of the product. Why would some companies favor the double-declining-balance method? Explain the different income tax consequences of the straight-line method versus the double-declining-balance method wi...
4 answers
The rotor blades of helicopter are 18 ft long and are rotating at 150 rpm (a) Find the angular speed, W, of the rotorrad/min(b) Find the linear speed, V, of point on the tip of blade_ftfmin
The rotor blades of helicopter are 18 ft long and are rotating at 150 rpm (a) Find the angular speed, W, of the rotor rad/min (b) Find the linear speed, V, of point on the tip of blade_ ftfmin...
5 answers
Jb Ark Pc bakltz 0.L $ 0,7 5 0,852 -?7 - 42 -(41 -(4WlaF442 robb"ttz Lhal 44< jo b fiisned 1-I4 152
Jb Ark Pc bakltz 0.L $ 0,7 5 0,85 2 -? 7 - 4 2 -(4 1 -(4 WlaF 442 robb"ttz Lhal 44< jo b fiisned 1-I4 152...
5 answers
Hiershow ime Remaining Part 1 of 45Question 1 of 45 1.0 Points 4x + 3 Find the range of f(z) I +20A (To,0)OIB: (To, and (2,+o) 3 c (-0,54 and +0) D. (Jx,-2 ) and (_2,+oo) E. 0,4 ) and (4,+o)Reset Selection0 Mark for Review_Whats_Ihisz
Hiershow ime Remaining Part 1 of 45 Question 1 of 45 1.0 Points 4x + 3 Find the range of f(z) I +2 0A (To,0) OIB: (To, and (2,+o) 3 c (-0,54 and +0) D. (Jx,-2 ) and (_2,+oo) E. 0,4 ) and (4,+o) Reset Selection 0 Mark for Review_Whats_Ihisz...
1 answer
Given the following​ after-tax cash flow on a new toy for​ Tyler's Toys, find the​ project's...
Given the following​ after-tax cash flow on a new toy for​ Tyler's Toys, find the​ project's payback​ period, NPV, and IRR. The appropriate discount rate for the project is 9​%. If the cutoff period is 6 years for major​ projects, determine whether managem...
1 answer
Tabulate the nmr data and provide a concise explanation for the assignment of the nmr data....
tabulate the nmr data and provide a concise explanation for the assignment of the nmr data. give its chemical shift, multiplicity, coupling constant, assignment of peaks. molecule is [(C5H5N)2I]Br te 8.24 1.46 2.00 1.54 200 824mwweemamn 14 12 10 PPM USER:DATE: 1106 18 (11:28) PTS1d: 8192 89.983 OFI:...
5 answers
Point) Find the equation of the tangent line Ihe curve9ze' at the point (0,0) . The equation of this tangent line can be written the form y InIFind in and
point) Find the equation of the tangent line Ihe curve 9ze' at the point (0,0) . The equation of this tangent line can be written the form y InI Find in and...
5 answers
Sample 1 - Lays ClassicSampleDoritosMass of chips2.0432.269Mass of beaker (and boiling stones) Mass of beaker (and boiling stones)loz, 480l03.662loz. 780Ioz 840Mass of fat0,2000,162Percent fat in chips
Sample 1 - Lays Classic Sample Doritos Mass of chips 2.043 2.269 Mass of beaker (and boiling stones) Mass of beaker (and boiling stones) loz, 480 l03.662 loz. 780 Ioz 840 Mass of fat 0,200 0,162 Percent fat in chips...
5 answers
Nitrogen and hydrogen combine high temperature Uhc prescnce f catalyst; produce ammoniaN,(g) + 3H,(g)2NH,(g)Assume 0.250 mol Nz and 0.818 mol H, are present initially:After complete reaction. how' Iary moles of amronia arc prxluced?NH,:How many moles of H; rqtitin ?How Iany moles olN, remaln ?What [s Ihc Iumniting rcJetunt /ullorcn
Nitrogen and hydrogen combine high temperature Uhc prescnce f catalyst; produce ammonia N,(g) + 3H,(g) 2NH,(g) Assume 0.250 mol Nz and 0.818 mol H, are present initially: After complete reaction. how' Iary moles of amronia arc prxluced? NH,: How many moles of H; rqtitin ? How Iany moles olN, re...
1 answer
Evaluate the piecewise-defined function for the given values. f(x) = 4x for x 20 - 4x...
Evaluate the piecewise-defined function for the given values. f(x) = 4x for x 20 - 4x for x < 0 Find f(1), f(2), f(-1), and f(-2). f(1) f(2) f(-1) = f(-2) =...
1 answer
An advantage of a file allocation table (FAT) file structure over a simple linked file structure...
An advantage of a file allocation table (FAT) file structure over a simple linked file structure is A. The file allocation table uses much less disk space than the linked structure. B. The simple linked structure uses much less disk space than the file allocation table method. C. The ...
5 answers
Question 3Find the volume of the region under the surface and € + 2y = 8cy? and above the area bounded by € y"
Question 3 Find the volume of the region under the surface and € + 2y = 8 cy? and above the area bounded by € y"...
5 answers
Applcations; Anterest and RAKL_ Ertd Certary Lesson; 8 5questlon 7 of 7stepCorrcclratlon Make standard 35 % protein Farmar wants t0 mix u 75 proteln supplemnent d.y Howa tany pounds aach should he use? protein ration HOD poundz of & high-grodeKeypadWalnk e renteryour answerpound: , 0f 75 %pounds 0f 35 %
Applcations; Anterest and RAKL_ Ertd Certary Lesson; 8 5 questlon 7 of 7step Corrccl ratlon Make standard 35 % protein Farmar wants t0 mix u 75 proteln supplemnent d.y Howa tany pounds aach should he use? protein ration HOD poundz of & high-grode Keypad Walnk e renteryour answer pound: , 0f 75 %...
5 answers
Find the shortest distance from the polnt (2, 1,3) to the cone (You may round (0 thc nearest hundredth )Vz? +v}
Find the shortest distance from the polnt (2, 1,3) to the cone (You may round (0 thc nearest hundredth ) Vz? +v}...
4 answers
Conduct Pareto Analysis for following dataPROBLEMAREA OCcURRENCES PERCENT OF TOTAL CUMULATIVE PERCENT
Conduct Pareto Analysis for following data PROBLEMAREA OCcURRENCES PERCENT OF TOTAL CUMULATIVE PERCENT...
5 answers
Civen thatare all positive numbers, sketch the graph of cach of the following functions:f(I) = +c T+b9(r) T ( I_6h(r) (t+b:7h(4){{#)The rational function f(z) below' is transformation of Using what you know about the transformation of rational functions, find the equation of the function f(*) graphed below. Show wurk
Civen that are all positive numbers, sketch the graph of cach of the following functions: f(I) = +c T+b 9(r) T ( I_6 h(r) (t+b: 7h(4) {{#) The rational function f(z) below' is transformation of Using what you know about the transformation of rational functions, find the equation of the function...
5 answers
For each ellipse and graph2Sx"+9y' = 225 1)
For each ellipse and graph 2Sx"+9y' = 225 1)...
1 answer
Problem 30.36 Constants| Periodic Table Part A A damped LC circuit loses 7.7% of its electromagnetic...
Problem 30.36 Constants| Periodic Table Part A A damped LC circuit loses 7.7% of its electromagnetic energy per cycle to thermal energy If L :45 mH and C : 900 μ.what is the value of R? Express your answer to two significant figures and include the appropriate units. Value Units Submit Request An...

-- 0.029966--