Hi Amy -- start with 168 hrs per week ... an hour is 1/3 bigger than 45 min ... rescale ... boost 168 by 56 ... 224 hovercraft trips per week ... times 2.5 => double and add 1/2 ... 448 plus 112 ==> 560 mph ... Best regards, ma'am :)

word problem (answer)

Hi Amy -- start with 168 hrs per week ... an hour is 1/3 bigger than 45 min ... rescale ... boost 168 by 56 ... 224 hovercraft trips per week ... times 2.5 => double and add 1/2 ... 448 plus 112 ==> 560 mph ... Best regards, ma'am :)

how do you get the answer? (answer)

Hey Lizzy -- for small 'powers', we can just "spell it out" if we're unsure ... [xxx yyy yyy] [xxx yyy yyy] [xxx yyy yyy] = x^9 y^18 ... All the best :)

Hey Abaline -- except for H2 or He, if there's only one or two e-'s in the outer shell, those loosely-bound e-'s will "pull-off" or conduct in metallic fashion. Regards, ma'am :)

From Graphical Analysis (answer)

Hey Michaela -- in this data set, q/r is a constant [eyeballing a factor of "11"] ... the exponent "n" in this case must be "1" [n=1] ... the correlation is super-strong ... only the 280pC over 25cm is a bit off the "11" at "11...

amount of interest earned (answer)

Hi Amy -- using rough "mid-point" estimates, Bob cooks 10k for 15yrs and 20k for 5yrs ... Mary cooks 20k for 15yrs and 10k for 5yrs ... 8% for 15yrs triples the mid-point outlays ... BOB: 30k plus 21.6 ... 23.4 ... 25.4 ... 27.5 ... 30k ~ Bob 60k MARY:...

investment (answer)

Hi Amy -- here's how the cash streams look 5 yrs from now (roughly) ... 150 @6% ... 159 ... 169 ... 179 ... 190 => 5-yr sum is ~ 850 => take $900 5 yrs later 150 @14% ... 171 ... 195 ... 223 ... 254 => 5yr sum ~ 993 => take $150 each yr ... interest...

Hey Craig -- we may draw a line from each angle to the midpoint of the opposite side ... each line basically cuts the triangle's area in half -- "halve" areas from each corner ... the intersection of these three lines locates a 'centroid' of a triangle .....

Hey Raven -- an intuitive approach ... perimeter 4d must be an even # ... area d*d seems to be an odd multiple of 5 to produce an "offset" of 165 ... 5x5 too small ... try 15x15 ==> 225 minus 60 is 165 ==> d= 15cm ... Best regards :)

Hey Ako -- at 100 Hz, one cycle is 0.01s or 10ms ... 1st peak to 2nd peak => 10ms ... to 3rd peak => 20ms ... to 4th peak => 30ms ... to next trough, add 1/2 cycle => 35ms :)

Hey Shyanna -- we may "plug in" [2-3i][2-3i] minus 4[2-3i] plus 13 = 0 ... 2*2 minus 6i minus 6i plus 9i*i -8 plus 12i plus 13 ... i-terms cancel [12 less 6 less 6] ... real #'s cancel [4 and 13 -8 less 9] since i*i is -1 ... the key? "signage"...

diffusion of gasses (answer)

Hey Amy -- HCl mw is about 36 ... CH3NH2 mw is about 31 ... nearly identical masses meet "in the middle" ... Best wishes, ma'am :)

absolute value question (answer)

Hey Abaline -- the ( ) must become a "5" to shrink 9 into 4 ... when m=0 the ( ) is at it's smallest (7) ... any other m grows the ( ) > 7 ... Regards :)

story problem (answer)

Hey Michael -- key feature: "5 years from now" the 'Mom offset' is still one (-1) year ... suggests multiples of 5 ... kid 5, Mom 24 => kid 10, Mom 29 ... Best wishes, sir :)

Hey Donald -- a "verbal" reasoning approach ... 18mph downstream, 12mph upstream ... the midpoint is 15mph for rowers, with +/- 3mph on each side for the current ... Best :)

Hey Donald -- we can "rescale" the 1st buy up by 25% ... 20N + 25W is $2300 ... 2 extra N's cost 100 ... N= 50, 25W is 1300 ... 100W = 5200 ==> W= $52 ... Regards :)

Hey Donald -- another "verbal" approach ... 'brackets' can frame a reasonable answer ... 2 larges would cool in 1/2-time or 25min ... 2 smalls would cool in 37.5min ... the small takes 50% longer ... small = 2/3 large ... large + small equals 5/3 larges...

Find the rate of the jet (answer)

Hey Donald -- here's a "verbal" approach with easy 'test values' ... 7 'legs' of 180mi ... if chopper takes 1hr, then jet moves 720mph taking way less than 4hrs ... if chopper takes 2hr, then jet moves 360mph taking 3hrs ==> jet 360mph ... Regards :)

x+2y=22 x-y=-2 (answer)

Hey John -- sometimes we may "eyeball" the solution ... since "x" is the same in both ... increasing from -y to 2y raises the total from -2 to 22 ==> 3y's adds 24 ... y=8 ... for x-y to put us "2 below," x must be 6 ==> (6,8) works...

How do you find the perimeter of a rectangle/square when you have the area of circles inside of it? (answer)

Hey Emma -- circles have about 75-80% of the area of squares [d*d] ... Acirc ~ 4/5 d*d ... area of your box is about 5/4 * 4 Acirc's ... or about 5 of the circles ... Regards :)

Hi Rhonda -- looks like 100 sq.ft. with two (2) "notch-outs" of 5' X 3.75' ... subtract 37.5 sq.ft. leaving 62.5 sq.ft. ==> Buy two 60 by 60 (5'x5') to cut in half for l,l ... Buy one 60 by 30 (5'x2.5') for the crossbar "-" ... total sq.ft....

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