vgp

1 yard = 36 inches (found in internet) Area of center piece = 108 * 180 inches^2 Area of tile= 6 inches^2 Pieces of tiles needed = 108 * 180 inches^2 / 6 inches ^2 = 108 * 30 = 3,240 pieces

M-milk, T-total substance, C-constant (liters drawn out) We should assume that milk and water are “perfectly mixed” and milk/total substance (M/T) ratio will vary (as shown below) depending on dilution. Period 1: Milk left = M - M/T * C Period 2: Milk left = (M-M/T * C) – (M-M/T * C)/T * C We can derive the formula now: (M - M/T * C) – (M - M/T * C) / T * C = ( M - M/T * C)(1 – C / T) = M (1 – C / T)(1 – C / T)=M (1 – C / T )^2 We can generalize: Milk left = M (1 – C / T ) ^ n where n = number of periods

If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be A) 6x B) 4x c) 5x/3 d) 3x/2 e) 3x/5 The answers provided in various forums are not explained properly, moreover, in some cases they are misleading. I'll provide my explanation soon...

Answer should be A

I dare to disagree with the explanation and the OA. Reasoning: · Let’s first find out the conditions when the distance between any 2 of 3 points is less than r. · Critical value of maximum distance between any 2 of 3 points is r. · Take a look at the second picture of Lav’s post, the third point can be at any place on the arc between point 1 and point 2 (in order to get the distance between any 2 of 3 points is less than r). We have an equilateral triangle and the arc length (where the points must be placed in order to get the distance between any 2 of 3 points less than r) = 2pr*60/360 Circumference = 2pr Thus the approximate probability that none of the three points lies more than a straight-line distance of r away from any other of the three points= 1-((2pr*60/360)/2pr)=1-1/6=5/6

0! = 1 because it is defined to fit the combination and permutation formula: e.g. How many ways can five students be chosen from the group of five? answer: 5!/(5-5)!*5!=1/0! we know that answer is 1 (there is one way 5 people can be chosen from group of five: all of them must be chosen), 1/0! equals 1 when the denominator equals 1, thus 0! must equal 1. That's my modest suggestion, for more detailed information you can use various mathematical websites or books.

Using distance formula we know that the given 2 points are equidistant from the origin when : sqrt (a^2+b^2)=sqrt (c^2+d^2). (Note that change in Xs and Ys for both points are actually the Xs and Ys of those points due to the fact that the question asks distance from “the origin”). 1/5=2/10 but if we square them we’ll get different answer. On the other hand 1/5= -1/-5 and these points are equidistant from the origin. INS. By simplifying the equation we get: a+b=c+d, 2+4=1+5 but if we square each term then we see that 20 doesn’t equal 26. On the other hand 2+4=4+2 and the sum of their squares are equal. INS. For both statements let’s take poor mathematical approach, just for fun: Question: a^2+b^2= c^2+d^2 if ad=bc and a+b=c+d? a=c+d-b ((c+d)-b)^2+b^2= c^2+d^2 (c+d )^2-2b(c+d)+b^2+b^2= c^2+d^2 c^2+2cd+d^2-2bc-2bd+2b^2=c^2+d^2 2cd-2bc-2bd+2b^2=0 cd-bc-bd+b^2=0 -bc+b^2= bd- cd b(b-c)=d(b-c) b=d If b=d we know that a=c (statement 2 (we cannot use statement 1 for that conclusion> if b and d equal 0 then a and c can equal any number)) and if two coordinates are equal it means that the points share the same coordinates and they are equidistant from the origin. SUFF C

(A) where the household incomes of 49 percent of them are (totally ambiguous constraction) (B) where they have 49 percent of the household incomes (Who they?) © where 49 percent of the household incomes are (D) which has 49 percent of the household incomes (community-where)

please post the different questions in separate posts

Good question

One of the sides of the triangle is radius = 1. Lets take the radius as the basis. We have to maximize the height in order to get the maximum area Area of triangle=1/2 base*height Maximum height will be obtained with 90 degree angle with the base, which gives the height of 1. Area=1*1/2=1/2 B

Please post the original question

(7c2*3c1)/10c3=21/40

The product of the slopes is negative, if one line is slanted “downwards” and the other one “upwards”. Insufficient, try 1 and 6 (negative and positive slopes) and then try 6 and 6 (negative slopes) , 2 and 2 (positive slopes) , -5 and -2 (positive slopes). Insufficient, try 1 and -1 (positive slopes), 4 and -6 (positive and negative slopes). Both: The line which has negative y intercept, and one of its points lie in the first quadrant, must have positive x intercept and a positive slope . The line which has positive y intercept and positive x intercept must have negative slope. Thus the product of the slopes is negative. Suff. C

4c1*6c2+4c2*6c1+4c3=60+36+4=100