<p>I like this one from 5 SAT Math Practice Tests.</p>
<p>Max decides to carve out a cylinder in a wooden cube. The cube has a side length of 6 cm, and the cylinder has a radius of 2 cm. What is the surface area of the cube after the cylinder has been carved out?</p>
<p>A) 216 - 24π
B) 216 + 16π
C) 144 + 24π
D) 216 - 16π
E) 18π - 36</p>
<p>I don’t get this… Could you explain a bit more???</p>
<p>I believe the answer to truthdude’s question is B. </p>
<p>Think about how a cylinder cut out of a cube would look. The surface area of the cube would now include the inside of the cube where the cylinder was removed. Additionally, compared to the original surface area, it would be missing circle shaped areas on 2 sides (the ends of the cylinder). </p>
<p>To express this in numbers, we find the original cube’s surface area to be
6^2 * 6 = 216 (the area of each face * 6 sides on a cube)</p>
<p>The inside area that we must add corresponds edges of the cylinder that was touching the cube (the cylinder’s surface area minus its faces)</p>
<p>That area is the circumference of the cylinder * its length (which is given as the edge length of the cube = 6). </p>
<p>The circumference is 2<em>2</em>pi or 4pi. Multiplied by the length gives us 24pi</p>
<p>Now we subtract the 2 edges of the cylinder by calculating the area of those circles</p>
<p>pi *(2)^2 = 4pi (2 faces = 8pi)</p>
<p>To put it all together 216 +24pi - 8pi = 216 +16pi</p>
<p>Somewhat of a long explanation, but tough to do w/o drawing. Let me know if I made a dumb mistake.</p>
<p>"This passage is excerpted from a novel published in 1970. As the passage begins, four men are looking at a map in preparation for a canoe trip.</p>
<p>…</p>
<p>‘When they take another survey and rework the map,’ Lewis said, ‘all this in here will be blue. The dam at Aintry has already been started, and when it’s finished next spring the river will back up fast. This whole valley will be under water. But right now it’s wild. And I mean wild; it looks like something up in Alaska. We really ought to go up there before the real estate people get hold of it and make it over into one of their heavens.’ "</p>
<p>Lewis’ use of the word “heavens” is best described as</p>
<p>E) Ironic</p>
<p>Why??!</p>
<p>Consider sequences of positive real numbers of the form x,2000,y,…, in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x does the term 2001 appear somewhere in the sequence?</p>
<p>(A) 1 (B) 2 (C) 3 (D) 4 (E) More than 4</p>
<p>From 2008 Math SAT</p>
<p>that question was pretty hard, still got it though</p>
<p>That question can’t be from the SAT. In no way does the SAT require any lengthy calculations. The correct answer, however, is D. Compute a few terms and you notice a pattern.</p>
<p>If x and y are positive integers,
which of the following is equivalent to
(2x)^3y - (2x)^y</p>
<p>this is #19 of math section 2
<a href=“College Board - SAT, AP, College Search and Admission Tools”>College Board - SAT, AP, College Search and Admission Tools;
<p>I am really clueless x_x;
Any help is much appreciated!!!</p>
<p>You should be able to work this out if you know the law of exponents and basic algebra. All they’re asking for is an equivalent form. This does not mean reduced. If you work it out real fast, you should get down to answer choices A and C. C is the answer. They don’t ask you to actually perform any operations.</p>
<p>A) (2x)^2y. This would be the answer if they asked you to simplify (2x)^3y - (2x)^y. They didn’t, though.
B) 2^yx^3 - 2^yx^y isn’t equivalent to (2x)^3y - (2x)^y because the original broken down is 2^3yx^3y-2^yx^y.
C) is the right answer. (2x)^y[(2x)^2y -1] is in accordance. Same bases for the first one, so add the exponents and you get (2x)^3y and when you multiply the (2x)^y to the negative one, you get the same as the original. All they did was factor out a (2x)^y.
D) There’s a four. Clearly not the answer.
E) If you tried to multiply through, you would get (2x)^y+3 -(2x)^y, not (2x)^3y - (2x)^y.</p>
<p>oic, thanks a lot CalDud!!!
I saw a bunch of exponents and freaked out >.>
&& I didn’t exactly get what they were asking.
So kind of you to explain each answer choice too ^.^</p>
<p>If 6 < l x - 3 l < 7 and x < 0, what is one possible value of l x l</p>
<p>this is excerpted from #16 of section 6
<a href=“College Board - SAT, AP, College Search and Admission Tools”>College Board - SAT, AP, College Search and Admission Tools;
<p>The answer key says the answer is 3 < x < 4
but since x is in between 6 & 7, shouldn’t the answer be like 9.5 ?</p>
<p>Back to the problem posted by syn in #9. dsmo gives the correct answer in #14. However, I think the solution might have been a little too condensed to explain to syn what went wrong with his/her method. Here’s why the counting scheme that syn laid out did not work:
The counting scheme gives equal weight to the cases where a blue marble is drawn first, or a green marble is drawn first. However, there are 4 blue marbles and only 2 green. Therefore, the odds of blue or green on the first draw are different. Blue is twice as probable (2/3 vs. 1/3). To take that into account, take the probabilities that you get from each list (where you’ve specified the color of the first marble) and multiply each of those by the odds that the first marble actually had that particular color. Then you’ll have it.</p>
<p>At the heart of this issue is the question of “equal a priori probabilities.” Many of the puzzles in probability center around figuring out what outcomes ought to be weighted equally, vs. unequally (pair colors, in this case).</p>
<h1>16,</h1>
<p>That was my initial impression. However, we would essentially have 9<x<10 with values that fall between 9<x<10 being positive. This doesn’t fit the x<0 restriction. And thus, while yielding a true statement blindly ignoring the x<0, you would end up choosing the wrong values to plug in.</p>
<p>Ex.</p>
<p>6<|9.3-3|<7
6<6.1<7.</p>
<p>It says x < 0, right?</p>
<p>Sometimes, it’s good strategy to plug in a huge value less than zero. Say, -1000.</p>
<p>6 < |x-3| <7</p>
<p>6 < |-1000-3| <7</p>
<p>6 < |-1003| <7</p>
<p>6<1003<7</p>
<p>This is false bigtime. But what this told me was that oh hey, I’d have to pick a number that would fall between 6 and 7 that was negative but reasonable because taking the absolute value of that would HAVE to give me a number between 6 and 7 to make this true. Now all you have to do is prove that the absolute value of some number - 3 will be in between 6 and 7. You KNOW that the values between 6 and 7 are 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, and 6.9. So, take for instance, -3.1 as x. 6<|-3.1-3|<7 is 6<6.1<7. TRUE. So you can immediately tell that any value you pick between -3.1 and -3.9 and between is going to be an answer. The question said one possible value for |x|, so this just means that this falls between 3<x<4.</p>
<p>tx + 12y = -3</p>
<p>The equation above is the equation of a line in the xy-plane, and t is a constant.
If the slope of the line is -10, what is the value of t ?</p>
<p>am I supposed to substitute t for -10?
I’m soo confused @_@</p>
<p>& thanks CalDud for answering my prev. questions :3</p>
<p>y=mx+c</p>
<p>tx+12y=-3
12y=-tx-3
y= -t/12(x)-3/12
y=-t/12x-1/4</p>
<p>t has to make the slope -10, and -t/12 is the slope in the y=mx+c form, so t=120.</p>
<p>ohhhhhhh!
wow … I’m really dumb =.=;
never occurred to me I had to make tx to -10 xP
Thanks lauttuhella for your help!</p>
<p>:] '</p>
<p>how do i solve these problems?</p>
<p>1)the eggs in a certain basket are either white or brown. if the ratio of the number of white eggs to the number of brown egg is 2/3, each of the following could be the number of eggs in the basket except…
a)10
b)12
c)15
d)30
e)60</p>
<p>2)if x^2-y^2=77 and x+y=11, what is the value of x?</p>
<p>3)
a,3a,…
the first term in the sequence above is a, and each term after the first is 3 times the preceding term. if the sum of the first 5 terms is 605, what is the value of a?</p>
<ol>
<li>If the ratio is 2 : 3 then the total number will be a multiple of 2+3 or 5. The answer will be b)12 because that is the only choice that is not multiple of 5.</li>
</ol>