<ol>
<li><p>The average (arith. meaning) of a set of n numbers is what percent of the sum of those numbers? ( a: 100/n)</p></li>
<li><p>How many positive interfers less than 1000 contain the digit 7? What I need for this question is the wisest and most quickly method to solve cause I write almost all of them down on paper to count...</p></li>
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<p>3.if three different circles are drawn on a piece of paper, at most how many points can be common to ll three? The aswer is 2 but I can only think of one!!</p>
<ol>
<li><p>What is the least positive interger p for which 441p is the cube of an interfer? This one kinda mixes me up cause i literally dont know where to start..</p></li>
<li><p>(Opposite to) most people know, annie, a good photographer herself, actually enjoys seeing the photographs that her friends take on their vacations. What's wrong with opposite to??</p></li>
<li><p>For reasons (know) only to themselves, neither A nor his friends in the soccerteam intend to stay on the team once the semester is over. (NE).
The answer is NE but I thought that know is supposed to be: reasons KNOWN only to ...= reasons which are known to....</p></li>
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<p>Thanks in advance!</p>
<ol>
<li><p>The arithmetic mean is 1/n times the sum of the numbers, which is 100/n percent of the sum. For example, if n = 5 and the arithmetic mean is 10, then their sum is 50. Plugging in n=5 gives 20% which is correct here.</p></li>
<li><p>The best way is to count positive #'s that do not contain a 7. There are 8<em>9</em>9 = 648 positive 3-digit integers with no 7, 89 = 72 2-digit integers with no 7, and 8 1-digit integers with no 7. 648+72+8 = 728. We subtract from 999 since there are 999 positive integers less than 1000, 999-728 = 271.</p></li>
<li><p>First draw two circles. They can intersect at at most 2 points. So the answer is at most 2. Then you can draw the third circle so that it hits those two points (e.g. a circle whose diameter is determined by those two points).</p></li>
<li><p>441p = 3^2 * 7^2 * p. You want all the exponents to be multiples of 3, so greedily select p = 37 = 21. There’s your answer.</p></li>
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<p>I’m not a grammar expert, but “opposite to what most people know” makes much more sense to me. I don’t understand 6. either since I would also use “For reasons known…”</p>
<p>For 5, I’m pretty sure “opposite” takes the preposition “of”. For 6…it almost seems like a typo to me. “For reasons know” makes no sense?</p>
<p>Everything MITer94 said was right, but just to expand, you could also solve #4 by setting up the equation 441p = p^3. Solving for p would give you 0, -21, and 21 and thus, 21 is your answer.</p>
<p>^That gets you the right answer for #4, but the solution itself is incorrect.</p>
<p>“Opposite” can take either “of” or “to” (or nothing) depending on usage.
The opposite of up is down.
My opinion is opposite to yours.
This house is opposite that house.</p>