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Scccer sonous fouls esuIninpenalty kick with one kicker and one defonding goalkeeper: The accompanying table summarizos rasults from 290 kicks during namos among to...

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Scccer sonous fouls esuIninpenalty kick with one kicker and one defonding goalkeeper: The accompanying table summarizos rasults from 290 kicks during namos among top Icams the tablo_ nunaic direction indicates which way the goalkeepe jumped. where the kick direction from the perspective of the goal Ikeeper: Use 0.01 gnificance level to test the claim that the direction of the kick Independent ol Ihe direction l Ihe goalkeeper Jump. Do Ihe results suppart Ine Iheory that because Ihe klcks are s0

scccer sonous fouls esuInin penalty kick with one kicker and one defonding goalkeeper: The accompanying table summarizos rasults from 290 kicks during namos among top Icams the tablo_ nunaic direction indicates which way the goalkeepe jumped. where the kick direction from the perspective of the goal Ikeeper: Use 0.01 gnificance level to test the claim that the direction of the kick Independent ol Ihe direction l Ihe goalkeeper Jump. Do Ihe results suppart Ine Iheory that because Ihe klcks are s0 (ast; goalkeepers have no Ilmie to reacl; sa Ihe directions ol Ihelr jumps Are Independent of thc directions f thc kicks? Click Ihe icon view Ine penally kick dua Determine the null and alternative hypotheses JA Hu: Jump direction dependent kick direction: H1: Jump direction independent kick direction: Pentalty Kick Data Ho ; Jump direction independent of kick direction; H1: Juma direclion dependent kick direction. Goalkeeper_Jump Left Center Right Goalkoepors do not jump in the direcion of tho kick Hq : Goalkecpers jump thc direction of the kick_ Kick to Left Kick to Center Kick Right Ho: Coalkeepers jump in the direction of the kick H1; Coalkeepers do not jump the direcion of the kick: Print Done Detormine the tost statistic: X =| (Round three decimal places as needed.) Determine Ihe P-value stalistic; P-Vale (Round four decimal Dlacee needed ) Do the Osults support thc tncory tnat bCCauSc the kicks arc so fast, goalkccpers have no timc rcaci the dircctions tclr uMpS arc pendent of thc directions of the kicks? Tnere cuccncc warantrejection of the claim that the direction of the kick independent of the direction of the 9oa Ikeeper jump. The results kicks are s0 fast, goalkeepers have no time react the theory that because the 00 nat support support



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In soccer, serious fouls in the penalty box result in a penalty kick with one kicker and one defending goalkeeper. The table below summarizes results from 286 kicks during games among top teams (based on data from "Action Bias Among Elite Soccer Goalkeepers: The Case of Penalty Kicks," by Bar-Eli et al., Journal of Economic Psychology, Vol. 28, No. 5). In the table, jump direction indicates which way the goalkeeper jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.05 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so fast, goalkeepers have no time to react, so the directions of their jumps are independent of the directions of the kicks?

In this problem we are going to use um functions and the graph of functions to investigate the path of a basketball. So our equation is representing the path of our basketball where H. Is the height. So um since this is a chest X. R H is going to be the Y. Equals, so this is going to be an H. Equals and V. Is the initial velocity that the ball is shot at and X. Is the forward distance from the line. So that's going to be our X here and here. So first we're going to substitute that V. And to get our equation that will be working with and we'll have a chest X. Is equal to negative 44 X squared plus X plus six. Sorry, the negative 44 X squared is Going to have a 28 squared under it. So that's our equation that will be working with. So the first um question is, what is H when X is eight? So remember that? Um X is eight means it's shot eight distance in front of the line. So what's the height when it shot eight distance in front of the line. So we're doing a church of eight is equal to negative 44 times eight squared over 28 squared plus eight plus six. And let's grab a calculator for that one. So we have negative 44 Times eight Squares. That's 64. And let's get that in parentheses to make this accurate -44 times eight squared which is 64 Divided by 28 squared plus eight plus six. So when eight when access eight R. H. Would be About 10.4. Yeah. So if you shoot the ball eight ft in front of the line then the height of the ball would be at about 10.4 said hi. So that would be a church equals 10.4. Okay, next age of 12 HF- 12 means let's shoot that 12 ft in front of the line. I don't want to do that there. So age of 12 would be equal to negative 44 times 12 squared over 28 squared plus eight plus six plus 12 plus six. Sorry. Yeah, let's go to our calculator. I'm going to change that 64, negative 44 times 12 square 12 square would be 1 40 four plus 12 plus six. And that would be at about 9.9. Well, next we are going to take a look at what the graph of this function looks like. And we're just going to look at the first quadrant. So let's say when X zero, let's use our graphing calculator here for a table. So n R. Y equals I have um our function. And then 2nd table gives us some points on it. So it's zero. We're up at six ft. So that means this ball, somebody here was Probably 6ft tall when they shot at. That's kind of where it started in their hands or something. So some more points on that graph um Looking like up at seven 12345, We were up at 10.25. So it's gone up to here. And at where is the height of this thing? It looks like the highest it gets on just when exes nine, it's up at 10.45. So up about here and then that's going to start coming down. Let's say down at 14. Certainly It's down to nine. What we have here is the graph of a parabola and that's the path of this Fall. So our next question says at 15 We have our hoop at 15:10. So what were we talking about here in our graph? We said that at 14 we were at (912) 345 678. So let's say that We know 14 9. What about it? 15 would 1510 work. So if we shot this ball 15 ft um forward distance In front of the line, would it hit the basket? That's located at 1510? So 15 10 somewhere in here Heywood 1510 Beyond Our Graph. So let's do HF 15. Yeah. And that means um let x be 15 would have no negative 44 times 15 squared over 28 squared plus 15 plus six. Would that be 10? If it's 10 we would hit that graph. But we can see on our table here That that 15 were 8.374 and that's what we would get here. So wouldn't work. no So the next question is um at what velocity would we have to shoot the ball 15 in front to make that hoop work? So in order to do that we want to we want to um Let x be 15 And why be 10 and solve for v. That's what we're going to do. I'm gonna make some room by erasing some stuff here. We want to know How hard we need to shoot the ball 15 ft for of the distance lined To hit the basket. That's at 1510. So We're going to let y be 10. We're going to let X. B. 15. We're solving for V. Yeah not an equal sign there. There's a plus sign there. Oh yeah Okay so we have 10 equals, let's see what negative 44 times 15 square it is. It's -9900. Uh huh. Over B squared plus 21. So let's subtract 21 from both sides. 10 minus 21 is negative 11. But shoes are cross multiply idea. Again we're going to have negative 11 B squared equals negative 9900 times one. And divide everything by negative 11. And we get v squared equals 900. Take the square root of both sides. Square of 900 is 30. So V would be equal to plus or -30 and we can't use the minus because we're shooting. So instead of a velocity of 28 we just had to shoot it a little bit harder and have a velocity of 30. So think about what we just did in our table When we shot with a force of 28. We at 15 we were only 28.37. Now with our shooting a little harder, it would go in the basket at 1510. Mhm Yeah.

Okay, So, uh, so we can let Okay. See, uh, beat a point right on the end of the line. So, uh, this line segment, this is this is a point on the line such that such dad, there's line segment, right? It's perpendicular. So this is how you draw perpendicular means that it cause it at 90 degrees. Right. So this line segment a see the slide here, so they see their means that this is a and doesn't see right. It's perpendicular to, um uh, the end of the line. Right. Good. So, uh, she won see a G one of see this G one times. See here or the line G. Why do you want us? You won't see right. It has been given us 38 0.3333 going forward. Right? And we knew that t two as well. The line the length of the line G two. I see. Okay, these are two points. 1.1 point, and then think if this is you want and is a seed of whom a line. Right. And the link of the line is 38.3 with a the same being d two and C also forms alive. Right? So that one is also 15 I believe. Yep. 15 and then Ah, a c Right the line that is perpendicular it 69. So a c is, uh, 69 then BC's also 64. Good. So you have this. Okay, so you have this. And, um So what is this? No, what is a snoop off? Uh, the angle. So the slope soup of, uh, angle G one 18 to okay, she to slip of this one. It's just the difference between this off angle G one a c in Angola, G two a c rate. That is just a difference. The difference between these two. So this slope here, it's just a different the difference in this Those off this guy is that guy. Right? So what is this? Those off off those too? Well, it is just an inverse Hankins. Just use the inverse tangent. All right? Tourist agent of 38.3333 over 69. Right. So it's just in Brazilian of this over that. All right, that is gonna give us the slope. So then minus what is a slope of this one? right. So this is gonna be interesting, you know, 16 over a 69. Right? So it's just, uh, 15/69 since just the investigation of those over that. Right. So investigations 15/69. So this one is pure calculator work. So once you do that, you're gonna get a approximately 16.7 night if you put it to two decimal places. Said that is a slope off angle T one a c to you. Hey, now we want to find the snow of, uh, angle e g one BG to We got one. We got one for a want to do one for the so slope off angle she won. The key to this is gonna be the same thing is gonna follow the same principle. Why? Let it be a slope of two u one b c. My is slope of, uh, G two B c angle he to BC, Right? So that is, Is there gonna be inverse tangent off 38 0.333 3/84? Right. So there are eight inverse tangent first, uh, inverse tangent. 38.333 Hey, over 84 right and put your calculator in a degree mode, right? Not Iranians move. But if you do it in the radiance move, you're gonna get a different answer. I'm doing it in the degree mode. Right. So, uh, 15/84. Right? So when it's into green move, you can see that. Or when you get it in the radiance mode, you can actually convert it to a degree mode. Right? This is gonna be 14.4 approximately. Right? So this is the answer you're looking for, and you can see that the, uh, the kicking was not improved by penalty. Right penalty did not improve kicking. So this is this your answer for

The part of a ball is model by the equation. X. If X is equal toe minus 44 x squared, divided by the square plus X plus, it's where X is the former distance. These initial velocity with which the ball is strong on edge is the height above the ground reached by the ball. So for the first case, if the initial velocity is dream the age feet but second, then firstly, we need to calculate what is the height off the ball going to be when it is traveling eight feet in the front so we calculate edge effects as equal toe minus 44 multiplied it. Eight whole square, divided by 28 hold square plus eight plus six, which will give us the vertical height reached is equal toe minus three point 591 plus 14 which will be equal to 10.409 feet. Next, we need to find the height the ball reaches. Bring the franche distance traveled by the bullets trail feet so we'll put Drev in place off X. In the given equation. On 20 age and place of being the given equations, we get minus 44 multiplied. The 12 Waas whole squared, divided by 28 hold square plus safe plus six. So that will become minus it 0.81 plus 18. That will be equal to 9.919 feet. Next, we need to plot a graph for the given function. So to do that, let's take a few values off X and rejects when x zero, then edge effects is six. When existent than edge off excess day 0.387 when X is 20 then enter Fix is 3.551 when x is 30 then edge effects is minus 14.510 on when exes footy been better fixes minus 43.795 Now let's plot the graph and see. Now we are given that the hope is at the height off 10 feet. So we need to find that if the ball is being thrown with an initial velocity of 28 feet per second village, make it to the hole. So to do that, let us calculate etch at 15 so that people toe minus 44 multiplied with 15 whole square divided by 28 hold square plus 15 plus six, which will be equal toe eight point 373 Freed, which is definitely lesser than 10 feet. So therefore it cannot make to the hope, so it will not reach the who. So we need to find the velocity with which it will reach the hoop. So for that, we need to put edge off. 15 is equal to 10 on death. Make the calculations. So for that we are going to get there is equal tool minus 44 multiplied with 15 whole square divided by the square plus 15 plus six that IHS, these quick will be equal to 900 so we'll get the initial velocity as equal toe 30 feet per second. So it is when the ball has been thrown with the initial velocity of 30 feet per second that it will actually cross the hope.

All right. We got free throw shots. Uh A physicist Peter friend Casio. Sorry for slaughtering that name. Um But peter he's he determined this equation for it. Um this shoots at a free throw with a 45° angle Um 6ft off the ground. Um So H. Is the height. These the initial velocity exceeds the forward position and four. Um For calculations were going to suppose that the person shoots with the velocity of 28. So then R. A. Says well yeah what's the height after heat uh feet forward? Well we can plug that in a password over 28 squared plus eight plus six. Uh huh. H. Of eight is equal to If I type that in. I got 10.4 ft. Okay. And part B. What about 12 ft away? Where is that? Well let's type that in And when I type that in my calculator I got 9.9 ft. Excellent. Now part C. Hurt. She says let's scrap this. So I pulled out my favorite graphing device and We can take this and transfer it over to this part on the screen. So negative 44 over 28 square tens X squared plus X plus six. So I'm gonna put these points on to my graph. So but something like that. So I could get from Dismas that. That was zero comma six. I also got that that was 8.9 comma 10.5. And then Over here we got 22.6 comma zero. Uh It's going to play at this point and that point so eight comma 10.4 and 12 comma 9.9. Yeah. No I. D. S. Does that go through the basket? Does that go through the hoop or where is the coop in relation to my drawing? Well it's that 15 lateral feet and 10 vertical feet. So that might be somewhere here. 15 Kama 10. And so we say no, doesn't go through. Uh huh mm. So then what do we need in order for it to go through the hoop with this equation? Well Not 10 is equal to negative 44 and it needs to go 15 ft. The squared plus 15 plus six. So that's 10 equals negative 9900 over weeks squared plus 21. Subtract 21 subtract 21 negative 11 equals negative 9900 over. Re sprayed. Let's zoom in on this. Multiply by the screwed Divide by -11. So the squared equals -9900 divided by -11. All the negatives will cancel. Which is a good thing because if I wanna square root I need a real number And I got philosophy equals 30. So if we're using This equation here, their initial velocity needs to be 30. In order for this to go through this hoop right here.


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