2010 AMC 10B
1 任性什么意思. What is ?
Solution
We first expand the first term, simplify, and then compute to get an answer of .
2 、Makarla attended two meetings during her -hour work day. The first meeting took minutes and the cond meeting took twice as long. What percent of her work day was spent attending meetings?
Solution 可爱的小猫作文
The percentage of her time spent in meetings is the total amount of time spent in meetings divided by the length of her workday.
The total time spent in meetings is
Therefore, the percentage is
宗旨意识不强3、A drawer contains red, green, blue, and white socks with at least 2 of each color. What is the minimum number of socks that must be pulled from the drawer to guarantee a matching pair?
Solution
After you draw socks, you can have one of each color, so (according to the pigeonhole principle), if you pull then you will be guaranteed a matching pair.
4 、For a real number , define to be the average of and . What is ?
Solution
The average of two numbers, and , is defined as . Thus the average of and would be . With that said, we need to find the sum when we plug, , and into that equation. So:
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5 、A month with days has the same number of Mondays and Wednesdays.How many of the ven days of the week could be the first day of this month?
自由们
Solution
（B）. 3
6 、A circle is centered at , is a diameter and is a point on the circle with . What is the degree measure of ?
Solution
Assuming the reader is not readily capable to understand how will always be right, the I will continue with an easily understandable solution. Since 无心法师剧情介绍is the center, are all radii, they are congruent. Thus, and are isosceles triangles. Also, note that and are supplementary, then . Since is isosceles, then . They also sum to , so each angle is .
7 、A triangle has side lengths , , and . A rectangle has width and area equal to the area of the rectangle. What is the perimeter of this rectangle?
Solution
The triangle is isosceles. The height of the triangle is therefore given by
Now, the area of the triangle is
We have that the area of the rectangle is the same as the area of the triangle, namely 48. We also have the width of the rectangle: 4.
The length of the rectangle therefor is:
The perimeter of the rectangle then becomes:
The answer is:
8 、A ticket to a school play cost dollars, where is a whole number. A group of 9th graders buys tickets costing a total of $, and a group of 10th graders buys tickets costing a total of $. How many values for are possible?
Solution
We e how many common integer factors 48 and 64 share. Of the factors of 48 - 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48; only 1, 2, 4, 8, and 16 are factors of 64. So there are possibilities for the ticket price.
9 、Lucky Larry's teacher asked him to substitute numbers for , , , , and in the expression and evaluate the result. Larry ignored the parenthe but added and subtracted correctly and obtained the correct result by coincidence. The number Larry sustitued for , , , and were , , , and , respectively. What number did Larry substitude for ?
Solution
Simplify the expression . I recommend to start with the innermost parenthesis and work your way out.
So you get: Henry substituted with respectively.
We have to find the value of , such that (the same expression without parenthesis).
Substituting and simplifying we get:
So Henry must have ud the value for .
Our answer is:
10、Shelby drives her scooter at a speed of miles per hour if it is not raining, and miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of miles in minutes. How many minutes did she drive in the rain?
Solution
We know that
守护的近义词
Since we know that she drove both when it was raining and when it was not and that her total distance traveled is miles.
We also know that she drove a total of minutes which is of an hour.
We get the following system of equations, where is the time traveled when it was not raining and is the time traveled when it was raining:
Solving the above equations by multiplying the cond equation by 30 and subtracting the cond equation from the first we get:
We know now that the time traveled in rain was of an hour, which is minutes
So, our answer is:
11 、A shopper plans to purcha an item that has a listed price greater than $ and can u any one of the three coupns. Coupon A gives off the listed price, Coupon B gives $ off the listed price, and Coupon C gives off the amount by which the listed price exceeds $.
Let and be the smallest and largest prices, respectively, for which Coupon A saves at least as many dollars as Coupon B or C. What is − ?
