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$mathrm{Um}$ is being blackmailed by numerous individuals and is having a very difficult time keeping his blackmailers from going public. He has been keeping them a...

Question

$mathrm{Um}$ is being blackmailed by numerous individuals and is having a very difficult time keeping his blackmailers from going public. He has been keeping them at bay with two kinds of payoff: gold bars from the Royal Treasury and political favors. Through bitter experience, he has learned that each payoff in gold gives him peace for an average of about 1 month, while each political favor seems to earn him about a month and a half of reprieve. To maintain his flawless reputation in the Court,

$mathrm{Um}$ is being blackmailed by numerous individuals and is having a very difficult time keeping his blackmailers from going public. He has been keeping them at bay with two kinds of payoff: gold bars from the Royal Treasury and political favors. Through bitter experience, he has learned that each payoff in gold gives him peace for an average of about 1 month, while each political favor seems to earn him about a month and a half of reprieve. To maintain his flawless reputation in the Court, he feels he cannot afford any revelations about his tainted past to come to light within the next year. Thus it is imperative that his blackmailers be kept at bay for 12 months. Furthermore, he would like to keep the number of gold payoffs at no more than one-quarter of the combined number of payoffs because the outward flow of gold bars might arouse suspicion on the part of the Royal Treasurer. The Grand Vizier feels that he can do no more than seven political favors per year without arousing undue suspicion in the Court. The gold payoffs tend to deplete his travel budget. (The treasury has been subsidizing his numerous trips to the Himalayas.) He estimates that each gold bar removed from the treasury will cost him four trips. On the other hand because the administering of political favors tends to cost him valuable travel time, he suspects that each political favor will cost him about two trips. Now, he would obviously like to keep his blackmailers silenced and lose as few trips as possible. What is he to do? How many trips will he lose in the next year?



Answers

A $siphon$ ($\textbf{Fig. P12.88}$) is a convenient device for removing liquids from containers. To
establish the flow, the tube must be initially filled with fluid. Let the fluid have density $\rho$, and let
the atmospheric pressure be $p$$_a$$_t$$_m$. Assume that the cross-sectional area of the tube is the same at all points along it. (a) If the lower end of the siphon is at a distance $h$ below the surface of the liquid in the container, what is the speed of the fluid as it flows out the lower end of the siphon? (Assume that the container has a very large diameter, and ignore any effects of viscosity.) (b) A curious feature of a siphon is that the fluid initially flows "uphill." What is the greatest height $H$ that the high point of the tube can have if flow is still to occur?
$\textbf{ELEPHANTS UNDER PRESSURE.}$ An elephant can swim or walk with its chest several meters underwater while the animal breathes through its trunk, which remains above the water surface and acts like a snorkel. The elephant’s tissues are at an increased pressure due to the surrounding water, but the lungs are at atmospheric pressure because they are connected to the air through the trunk. The figure shows the gauge pressures in an elephant's lungs and abdomen when the elephant’s chest is submerged to a particular depth in a lake. In this situation, the elephant's diaphragm, which separates the lungs from the abdomen, must sustain the difference in pressure between the lungs and the abdomen. The diaphragm of an elephant is typically 3.0 cm thick and 120 cm in diameter. (See "Why Doesn't the Elephant Have a Pleural Space?" by John B. West, $Physiology$, Vol. 17:47–50, April 1, 2002.)

Hello, France. This is the problem based on but the activity here to events are given Event one on even to which we're discussing. We have to events well, even to burn. Um, when the rear bumper clear. Stop front door at this event. Like the time with zero for both Carmen. And good argument. A C one is called toe to Z one both Toby zero four and the event occurs. Yeah. Then position off Carmen and go argument Euro No event toe. Yeah, when the front bumper reaches the back toe Mm hmm. Mhm. Mhm Good. Yeah. Yeah. And register. Uh huh. Back door, part A. The Carmen drives the line with the speed up 0.998 Jiro See, Therefore related toe guard came in the length off. The name seems to be sorted. The new length is given by my Elsie upon Gamma. Here Gamma is Lauren factor which having the value one minus. We try square so elders she will be equal to lent. I'll see upon mine minus b Times Square Here, Vita having the value be upon. See, that is 19980 So and let's see, you will get 30.5 m. It is given in the problem burn minus point 9980 square. So on solving it it is one point 9 to 8 m. Not be, but according toe, the garage the X s x g Excellent please It fixed. Which means X g toe equals toe length off girls So XY two to equal toe, 6 m see part that time interval can be given it l g minus and let's see upon it's speak six minus 1.928 upon 0.99 to 8 in two. Three into 10 to the power eight. So it is to be 1.36 into 10 to the par minus eight seconds deeper. That time for which the limo trapped inside the Garry's is that time New York take to clear the Garis. So it is to be equal toe 1.36 in tow, 10 to the power minutes eight seconds. Eat According toe Carmen, the Gary's looks shorter than yeah, proponent, which is given by substitute. So it is to be 0.379 m. Yeah, according toe limo, the access exit is fixed. Bitch meets acsi Tau equals toe length off the limo. So exito equal toe 30.5 m deep. The length off limo, according to Carmen, is the proper length of the car. Wow. Length off level. According toe. Carmen is proponent off God on the length of the garage a relative toe car made. It's less than the proper length. That means limo traveled the distance. I'll see minus elders G so time will be equal to and C minus LDS g upon me. Substitute the value 30 point five minus 50.379 upon 1998 and 23 and to 10 to the power eight. So it is Toby equal toe 1.0 six into 10 to the power. My necessary seconds. The time off. Even toe T C two is called toe piece. Even minus delta T, that is zero minus point 1.6 and tow 10 to the power minus seven. So it is minus 1.6 into 10 to the power minutes. Seven seconds. Yeah, According toe. Carmen, the LeBeau never encourage in the garage. Bit both doors is certain. So answer is No. No. All right? Based on the result based on a result in part G, he went toe, of course, first before first event. I think you know Gina for even toe. Doug Garrett seems to be very short at which limo cannot be inside the Garretts. Oh, with both the doors close. No. Yeah. For event one, the carriage seems to be very sort at which Nemo cannot be inside the gheris with both the doors. All right, Closed J k. The limo cannot for you be in Greece, Bit both the doors closed. I, the car meant should lose the bet. Sit up. Since the current since the car cannot be encourage, cannot be encouraged. Bit. Who bought the doors close, That's what. Thanks for watching it.

Hello. Welcome to the video. And today we're to be talking about offices, tests and specifically how to know when our evidence does or does not sufficiently support our plane. So in this problem, it sze worded really strangely. It's written like a Shakespeare script, but basically we have Hamlet, who's trying to figure out how many of his classmates believe in ghosts. So it is proposed that the proportion of the students who believe in ghosts is, um, at least 75% so we can translate this into a no hypothesis here by saying that ex, which is just what we're gonna call the proportion of students who believe in ghosts is greater than or equal to, which is the same thing as at least 0.75 The proposed proportion here and is suspected that this number is not accurate. That is too high. So we can create a a alternative hypothesis from that by saying that exes instead less than the proposed value of 0.75 So if we look at this, if we imagine this visually, we have ah distribution over here with a peak value at the proposed uh X value of 0.75 And it is being claimed that the true value of X is either at 0.75 or it could be somewhere over here. But we hope to find evidence of during our hypothesis tests that shows the true value. It might actually be somewhere over here, and this would show that 0.75 might not be the best representation of what ex truly equals. So we'll be testing these hypotheses at a 5% confidence level here, and we, uh so in the problem, they take a sample to find a proportion. And out of 63 Um, yeah, Out of 63 people surveyed, it is found that 41 of them do believe in ghosts. So this is our sample of proportion. And keep in mind that our sample size was 63. And with this information that we have, um, the proposed value amount of people who said yes, the total amount of people surveyed and we're looking for a value that is less than the proposed value. If we give it all of this information, here we go to our calculator. I'm using ah t I 84 plus and we go to the one proportions. Easy test function. Um, and we give it, Yeah, all this information here and we press Inger, it will give us a Z score, a test statistic of negative 1.82 And this has a corresponding P value of 0.3 And although this is close, this is technically less than 0.5 though not by much. And therefore we can say that we do have sufficient evidence to sufficiently claim or argue in support of our alternate hypothesis is here. And because P is less than Alfa, we should say where we say that we should reject the null hypothesis here. So in the context of the problem, Um, based off what we found, 75% seems to be a little too high for the actual proportion of students.

For the first part, it's asking, Could there be a connection between the two deficits, the fiscal or budget deficit and the current account deficit? And the answer is, it's possible. But the data seems to be very unclear on this. It's possible that a budget deficit because it has so many effects ranging from affecting the important export market and affecting interest rates and affecting the relative value of currencies. It's possible, at least in theory, that this could cause what we call twin deficits, meaning the budget deficit causes a current account deficit. But again, the data is very mixed as to whether or not this effect actually takes place. For the second part, though, on investment we know that investment, whether it's foreign or domestic, usually leads to increased economic growth and that increased economic growth is going to mean greater production in that country and greater incomes. This overtime should reduce the current account deficit now in the final part. It's somewhat unclear what is meant by risky and volatile flows, but it's possible that it's talking about unstable export market, so an unstable export market would be one that rises and falls much more than the economy as a whole during the regular business cycle. So during an expansion it grows much more than the regular economy, and then during a contraction or a recession, it really collapses. So if that's the case than a recession could possibly cause tremendous damage to the nation's economy because of this highly unstable export market.


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