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# geri wants to put 6 stamps on some pages in her stamp book and 9 stamps on other pages. how could she do this with stamp set of 78 (answer)

Hey Faizi -- we could make a "set" of 6+9 ... 5 "sets" makes 75 stamps ...   for 3 more, swap a "6" for a "9" ==> 4pX6 and 6pX9 works (24 plus 54) ... Regards :)

# what is three things waves include? (answer)

Hey Jessica -- waves have three basic traits ... how big it wiggles -- "amplitude" ...   how fast it wiggles -- "frequency" ... how "delayed" it is -- "phase" lag   (cosine starts at 1, sine starts at 0 and doesn't reach 1 until 90 degrees later: phase lag of 90deg) ... Regards...

# All but 2 wore white. All but 2 wore yellow. All but 2 wore red. How many total? (answer)

Hey Linda -- that's quite a riddle for 4th grade! Rewriting in "recipe" form looks like ...   All = W plus 2 All = Y plus 2 All = R plus 2 ... totaling both sides of the recipe ...     3 "All's" = (W plus Y plus R) plus 6 = "All" plus 6 ... deduct an "All" set from each side...

# Percentage via standard deviation (answer)

Hey Jordan -- the spread between means is 4 in. or 1.33 SD ...   one SD contains about 1/3 more population than the half above 73"  for a total of ~83% ...   1.33 SD spread means about 90% of Alpines are taller than average USA men :)

# What is the value of x in 4x + 3y +15 2X - 5y+1 (answer)

Hey Joy -- we may double the 2x -5y =1 and subtract it from 4x +3y = 15 ... 13y = 13 ...   y=1, x=3 or (3,1) solves ... All the best, ma'am :)

# A theater sold a total of 240 tickets for a show, some of which were adult tickets and the rest child tickets. An adult ticket cost \$15 and a child ticket cost (answer)

Hey Roseland -- we may start "simple" ... pretend all 240 tickets sold are \$15 ...   total sales would be \$3600 -- that's \$540 too much ... "trade in" \$9 tickets for the \$15 ones ...   the \$6 difference "traded in" 90x corrects the \$540 "overshoot" ... 150A, 90C works, ma'am...

# If the probability distribution for the random variable X is given in the table, what is the expected value of X? (answer)

Hey Omar -- we may expect the sum of Xi*Pi ... 10 and 4 and 9 and 4 = 27 works, sir :)

# Find three consecutive integers whose sum is -78 (answer)

Hi Haley ... with 3 consecutive integers, the middle no. is the average ... divide by 3 ...   -78 cut in 3rds is -26 -- the middle number ... -25, -26, -27 works ... Best wishes :)

# A car needs 3 gallons of gas every 70 miles. how much gas would it need for 105 miles? (answer)

Hey Alice -- half of 70 miles is 35 ... adding half to 70 gets 105mi ...   half of 3 gal is 1.5 gal ... adding half to 3 means 4.5 gal ... Best wishes, ma'am :)

# How many mL of a 0.10 M NaOH solution are needed to neutralize 15 mL of 0.20 M H3PO4? (answer)

Hello again, B -- matching OH- with H+ ... need 3 hydroxides for each H3 ...   need 2x to match M concentrations, and need 3x to match the ions ...   need 6x 15ml or 90ml of NaOH ... All the best :)

# How many grams of Mg(OH)2 will be needed to neutralize 25 mL of stomach acid if stomach acid is 0.10 M HCl? (answer)

Hey Brieonna -- neutrailizing acid usually means making water HOH ...   each M of HCl needs a M of OH- ... Mg(OH)2 provides a PAIR ... need 0.05M of Mg ...   each M of Mg(OH)2 has about 58g/mol ... need 1/20th or about 2.9g of Mg per L ...   to counter 25ml of 0.10M HCl,...

Hey Sydney -- "noticing offsets" ... an extra x+y drops the 7 to 3 ... x+y = -4 ...   double and subtract from 2x +5y =7 ... 3y = 15 ... y=5, x= -9 ... (-9,5) solves ... Regards :)

# let A,B,C and D be the four rational zeros of the function defined by p(x)= 3x^4-8x^3-11x^2+28x-12 Compute (1+A)(1+B)(1+C)(1+D) (answer)

Hey Ariana -- roots we may try: (+/- factors of the last term) over (+/- factors of the 1st) ...   (+/- 1 thru 4, 6 or 12) over (+/- 1 or 3) ... "1" looks nice, since there's +31 and -31 ...   "-2" seems good, since -112 on the right end matches 64 and 48 on the left end ....

# The perimeter of a rectangular floor is 180 feet. Find the dimensions of the floor if the length is five times the width (answer)

Hey Kevin -- cutting the perimeter in half means one L and one W is 90ft ...   since the ratio is 5:1, W is 1/6 of 90ft or 15ft ... 75L, 15W does it ... Regards :)

# A helicopter goes 270 miles with the wind in the same time it can go 180 miles against the wind. The wind speed is 6 miles/hour. Find the speed with no wind. (answer)

Hey Tisha -- here's a verbal approach ... +6mph and -6mph creates a 90-mile spread ...   12mph means 90mi ... 180mi needs 24mph ... 270mi would need 36mph   => windless is in between at 30mph ... Best wishes, ma'am :)

# A store sells cashews for \$6.00 per pound. and peanuts for \$2.50 per pound... (answer)

Hey Kevin -- the cashew-peanut spread is \$3.50 ... we want to land 15/35ths thru that gap   to \$4 ... the 35ths are split 20:15 ==> 15lb of cashews: 20lb peanuts mix ... Regards :)

Hey Christine -- the "break-even" point is when p(x) =0 ... Set 750x^2 = (15k)x ...   Xbreak-even is 15k over 750 or 20 units. Test p(21) ... p(21) is negative, money-losing ...   x> 20 ans. "b" ... Best wishes ma'am :)

# At what time will they be together at point B for the first time? (answer)

Hey Abaline -- Tyler reaches B at 5mi, 15mi, 25mi, 35mi, 45mi ... Amanda lands on B at 10mi, 20mi, 30mi, 40mi, 50mi ...   At 3mph, T reaches B at 100min, 300min, 500min, 700min ... At 2mph, Amanda's home after 5hr or 300min==> both at B at 5pm ... Regards :)

# I need to solve for x and give an exact answer. Exponential equation (answer)

Hey Adrienne -- since 2^x is 14, then x log 2 = log 14 ... x = log 14 / log 2 ~ a bit under 4 for your answer ... All the best, ma'am :)

# Last statistics question of the semester for extra credit and I am done. Any help will be appreciated. Thank you (answer)

Hey Tito -- my apologies for the terminology in stats ... it reminds me of authorities using Latin in the Dark Ages ... "std dev" of 4.8hr from the true center means that sample aves will likely have 0.8hr s.d. from the true ave for sample sizes of 36 (4.8/sqrt 36 = 0.8).   I'm 95%...