<p>Could someone explain the following problems to me:</p>
<hr>
<p>Pg. 427, #16:</p>
<p>Set X has x members and set Y has y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k > 0). Which of the following represents the number of members in set Z?</p>
<p>A. x + y + k
B. x + y - k
C. x + y + 2k
D. x + y - 2k</p>
<h2>E. 2x + 2y + 2k</h2>
<p>Pg. 412, #18:</p>
<p>Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and average 30 miles per how many miles did Ester drive to work in the morning?</p>
<p>For this one I set it up like this: (45/X) + (30/X) = 1, where X = distance she drove. I figured that if you divide the rate by the distance you get the time, and then you could add both of those and get 1 hour. I multiplied both sides by "X" and got 75 miles, but the correct answer is 18 miles. Any ideas?</p>
<p>For number 2 remember the formula 2 (R1 * R2)/ (R1 + R2) = average rate. This helps a lot
Now plug in the two rates they give
2700/75 = 36 mp/h This is her average speed for the WHOLE thing. So divide it by 2 which = 18 m/h to get how much she would go up one way.</p>
<p>For the first one the answer is D. x+y-2k. Set X has x ( say 50) members. Set Y has y ( say 40) members. They both have common k ( say 10) members. Now Z has all the members of X n Y except k. So from X set the members in Z is x-k ( 50-10) members and from Y is y-k (40-10) members. So the total members in Z will be
(40-10)+ (50-10)=40+50-10-10= 40+50-2*10=70.
i.e. (x-k)+(y-k)= x+y-k-k= x+y-2k.</p>
<p>For the second one use the formula 2 (R1 * R2)/ (R1 + R2) = average rate. This way it wud be much easier. Your way didn’t work because rate divided by distance is not time. Distance divided by rate is time. ( r= d/t).</p>
<p>The 1 is the time (1 hour). I meant this: (X/45) + (X/35) = 1 (Time1 + Time2 = Total Time; T=D/R). Multiply both sides by 1575: 35X + 45X = 1575. Solve for X and you get 19.6875.</p>
<p>I've got some more, so it'd be nice if you guys could help me with these as well:</p>
<hr>
<p>Pg. 464, #19:</p>
<p>(Figure of a sector with a 30 degree angle)</p>
<p>In the figure above, QR is the arc of a circle with center P. If the length of arc QR is 6pi, what is the area of sector PQR?</p>
<p>A. 108pi
B. 72pi
C. 54pi
D. 36pi</p>
<h2>E. 9pi</h2>
<p>Pg. 472, #6:</p>
<p>The eggs in a certain basked are either white or brown. If the ratio of the number of white eggs to the number of brown eggs is 2/3, each of the following could be the number of egegs in the basket EXCEPT:</p>
<p>A. 10
B. 12
C. 15
D. 30
E. 60</p>
<h2>(For this one I thought it was A because you can't have 2/3's of 10 when dealing with something like eggs. With all of the other numbers you can get a nice whole number. However, the correct answer seems to be B.)</h2>
<p>Pg. 475, #11:</p>
<p>A certain triangle has two angles that have the same measure. If the lengths of two of the sides of the trangle are 50 and 30, what is the LEAST possible value for the perimeter of the triangle.</p>
<p>(For this one I made sure that the sum of any 2 sides was greater than the other. Since it's asking for the least value, I made the other side 21, giving me a perimeter of 101. The correct answer is 110 though.)</p>
<p>silly mistakes remind me of my problem. I get the hard questions right. But get nos. 9,10, etc wrong. Once I made a careless mistake in no.1. Had to do only 2*5=10. But ended up doing sumting else. Any suggestions to avoid such mistakes. They r costing me a lot.</p>
<p>for the original post:
1 is D cuz the k members r in BOTH sets n u have to subtract them twice.</p>
<p>2 is 18 because (lol i was just looking at this prob a few mins ago...):
you can use algebra formula
let x = time in hours taken for first trip.
since total time = 1, the time taken for second trip = 1 - x
and since you know the first and second trip are the same distances,
you can set up an algebraic equation:
45(x) = 30(1-x)
45x = 30-30x
75x = 30
x = 2/5, which tells us that it takes 2/5 of an hour to make first trip.
so,
45(x) = 45(2/5) = 45(0.4) = 18 qED :).</p>
<p>i think you don't need to remember the formula if u've got ure basics straight :)</p>
<p>For the First one.
The answer is A. 108pi. I don’t know if there is a easy way to do it but since it is a 19 no question, I hope it is worth this long. A central angle has the same degree as its intercepted arc. So the arc of length 6pi will also measure the same degree. The circumference of the circle will be twelve times the length of arc QR ( since 360/30= 12). The circle of circumference 72pi will have a radius of 36pi and area of 1296pi. Now use the relation Central angle/ Circle angle= sector area/ circle area. i.e. 30/360=sector area/1296pi which will give you 108pi.</p>
<p>For the second one
The answer is B. it shouldn’t be 2/3 of the numbers given. It shud be 2or 3/ 5 of the given numbers. All but 12 won’t give you the answer. The point is two parts are white and three parts are brown. </p>
<p>For the third one
Here two of the angles have equal measure. i.e the triangle is an isosceles triangle. If two of the sides are 30 and 50 then the other has to be either 50 or 30. Since we r talking abt the Least perimeter then taking two sides to be 30. the answer will be 110. This doesn’t defy the rule as well. 30+30> 50.</p>
<p>The ratio of the number of white eggs to the number of brown eggs i.e white eggs: brown eggs = 2:3. Not that 2/3 parts is white. The total number of parts is 2+3= 5. You get the number of white and brown egg by 2/5 of given nos or 3/5 of given nos. A gives 4 white(w) and 6 Brown(B). C. gives 6W n 9B. D. gives 12W n 18B and E. gives 24W n 36B. But B cannot be the number of eggs. Hence B. Hope u understood now.</p>
