<p>Was solving some real exams got these 4 questions wrong.</p>
<p>Family - Number of Consecutive Nights</p>
<p>Jackson 10
Callan 5
Epstein 8
Liu 6
Benton 8</p>
<p>8) The table above shows the number of consectuvie nights that each of five families stayed at a certain hotel during a 14-night period. If the Lie family's stay did not overlap with the Benton Family's stay, which of the following could be a night on which only one of the five families stayed at the hotel?</p>
<p>14)How many different ordered pairs (x,y) are there such that x is an even integer, where 4<= x <= 10, and y is an integer , where 4 < y < 10
1)8
2)12
3)20
4)30
5)36</p>
<p>A sphere of radius r inside a cube touches each one of the six sides of the cube. what is the volume of the cube, in terms of r?</p>
<p>1) Because you know Benton and Liu do not overlap, spread them out like:</p>
<p>B B B B B B B B L L L L L L</p>
<p>Then you know someone has 10 days and the middles are not an option since Jackson overlaps in the middle so…</p>
<p>B B B B B B B B L L L L L L
J J J J J J J J J J<br>
or…</p>
<p>B B B B B B B B L L L L L L
J J J J J J J J J J</p>
<p>So possible days can be 11, 12, 13, 14 and 1, 2, 3, 4. Answer is 1).</p>
<p>2). 4 even integers between 4<=x<=10 X 5 integers between 4<y<10 = 20. Answer is 3).</p>
<p>3) Because r is still the radius. Formula stays the same. 4/3πr^3</p>
<p>4) Visually, if you split the square in half, you see that you also split the circle in half. Anser is 5). Or, you know the arc rules and know that a triangle inscribed in a semicircle has a right angle. Angle x 2 because it lies along the circumference is 180.</p>
<p>Formula for cube volume v=L<em>W</em>H or (L/W/H)^3. The length/width/height is 2r if the sphere is touching the cubes side. So 2r is considered the L/W/H. The appropriate formula would then be v=(2r)^3, or 8r^3.</p>
<p>For the square in circle question, imagine a square with the 4 vertices touching the circle’s border. So the arcs will be 4 even sizes. 360/4 =90.</p>