The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can be expressed as...
Triangle ABC has ∠A=40∘, ∠B=60∘, ∠C=80∘. Points M,N trisect the side BC and points P,Q trisect the side AC. The lines AM,AN,BP,BQ intersect at the points S,T,U,V as shown in the figure below, dividing the triangle into 9 regions. Determine t...
a=54 r=1/3 Take it from there.
300 yards = 900 ft So, the bullet gets there in 0.32 seconds. How far does the bullet fall in that time? s = 1/2 at^2
.62 is 1 std away from the mean. P(Z>1) = .1587
You want the Z values containing 69%. Those are -1 <=Z <= 1 (well, 1.015, really) that is, within 1 std of the mean.
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.05 is P(Z<-1.645) That is, 18 is 1.645 std below the mean. So, the mean is 18+2*1.645 = 21.29
cosΘ < 0 in QII and QIII arccos(-1/3) = 1.91 = pi-1.23 or pi+1.23 = 4.37 So, t = (6/pi) * (1.91 or 4.37) t = 3.64 or 8.35 hours
Math For Educators
Looks pretty good to me. 144/7 = 20 R4 but it's the remainder that counts
depends on how fast he swims. If his speed is s ft/min, the depth d will be d/5s = sin 32
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