Sunday

August 2, 2015

August 2, 2015

Total # Posts: 30,519

**Algebra**

let the border be x cm wide picture is (30-2x) by (36-2x) (30-2x)(36-2x) = 480 1080 - 132x + 4x^2 - 480 = 0 4x^2 - 132x + 600 = 0 x^2 - 33x + 150 = 0 solve using the quadratic equation,
*March 22, 2015*

**Advanced Algebra**

It would simply be 10 x 9 x 8 x 7 or 5040 ways This is the same as P(10,4) = 10!/(10-4)! = 10!/8! = 5040
*March 22, 2015*

**Math**

Set them equal or R(x) - C(x) = 0 2x + 10 = -5x^2 + 21x 5x^2 - 19x + 10 = 0 x = .6311 thousand or appr 631 or x = 3.169 thousand or appr 3169 check: if x = .6311 , R(.6311) - C(.6311) = .00053.. , not bad if x = 3.169 , ...... = .001805 both answers are valid
*March 21, 2015*

**Pre-Calculus**

It is considered "better form" to have your quadratics start with a positive x^2 term So for #2, I would write: 6x^2 - 25x + 24 = 0 , (just switch all the signs, like multiplying by -1) Each of your roots satisfy your equations, but each of your quads should have a ...
*March 21, 2015*

**algebra**

Is y = -3x^2 - 4x + 3 supposed to be your answer ? Can't be right, since (0,-4) clearly does not satisfy your equation. Method1: let the equation be ax^2 + bx+c = y for (0,-4), 0+0+c=-4 , c = -4 for (-2,-20), 4a-2b - 4 = -20 4a - 2b = -16 2a - b = -8 for (4,-20), 16a + 4b...
*March 21, 2015*

**Calculus**

V = (4/3)π r^3 dV/dt = 4π r^2 dr/dt so when r = .5, dr/dt = .01 just plug it in... dV/dt = 4π(.25)(.01) = ..... cm^3/day
*March 21, 2015*

**maths**

fourth term is 11 ---> a+3d = 11 sixth term is 17 ----> a+5d = 17 subtract them 2d = 6 d = 3 back in a+3d = 11 a + 9 = 11 a = 2 tenth term = a+9d = 2+9(3) = 29
*March 21, 2015*

**math**

sub in y = x+k x^2 + y^2 = 25 x^2 + (x+k)^2 = 25 x^2 + x^2 + 2kx + k^2 - 25 = 0 2x^2 + 2kx + (k^2-25) = 0 a = 2, b = 2k, c = k^2-25 discriminant = b^2 - 4ac = 4k^2 - 4(2)(k^2-25) = 4k^2 - 8k^2 + 100 = 100 - 4k^2 now proceed the same way as in the previous post to "Eloise&...
*March 21, 2015*

**MATH**

I will assume your "equation" is equal to zero, that is, kx - 10 - 5x^2 = 0 or 5x^2 - kx + 10 =0 your discriminant is b^2 - 4ax, or k^2 - 4(5)(10) = k^2 - 200 to have one real root: k^2 - 200 = 0 k^2 = 200 k = ±√200 or ±10√2 for 2 distinct ...
*March 21, 2015*

**math**

so you want the vertex of the parabola the x of the vertex is -b/(2a) = -50/-3.724 = 13.426.. subbing that back int gives a height of 2+50(13.426..) - 1.862(13.426..)^2 = appr 337.66 m above "ground" --> h(t) > 0 , for t ≥ 0 solve 2+50t-1.862t^2 = 0 to ...
*March 21, 2015*

**Math**

3x + 2y < 6 2y < -3x + 6 y < -(3/2)x + 3 so the slope is -3/2 and the y-intercept is 3 so start with the y-intercept of 3 , or the point (0,3) slope is rise/run = -3/2 so from (0,3) , drop down 3 , then 2 units to the right. This should bring you to the point (-3,5) ...
*March 21, 2015*

**math**

oranges --- x apples ---- x + 32 overripe oranges = (3/5)x overripe apples = (1/3)(x+32) but they are the same .... (1/3)(x+32) = (3/5)x multiply by 15 , the LCD 5(x+32) = 9x 5x + 160 = 9x 160 = 4x x = 40 overripe fruit = (1/3)(x+32) + (3/5)x = (1/3)(72) + (3/5)(40) = 48 check...
*March 21, 2015*

**Algebra**

boat's speed in still water --- x mph against the current ----- x-3 mph with the current -------- x + 3 mph time against current = 12/(x-3) time with the current = 12/(x+3) 12/(x+3) + 12/(x-3) = 3 times (x-3)(x+3) or x^2 - 9 12(x-3) + 12(x+3) = 3(x^2 - 9) 12x-36 + 12x + 36...
*February 23, 2015*

**algebra**

Let the shorter wire be x m long and let that wire be y m from the base of the pole so x^2= 576 + y^2 ----> x^2 - y^2 = 576 let the longer be x+5 and we have (x+5)^2 = 24^2 + (y+11)^2 x^2 + 10x + 25 = 576 + y^2 + 22y + 121 x^2 - y^2 = 22y - 10x + 672 22y - 10x + 672 = 576 ...
*February 23, 2015*

**Algebra**

I agree with all you answers
*February 23, 2015*

**Vectors Math**

Anwered here: http://www.jiskha.com/display.cgi?id=1424665237 take a vector (a,b,c) now do (a,b,c) x (a,b,c) to get (0,0,0) by whatever means you have learned. The steps will become your explanation.
*February 23, 2015*

**Math**

Maria, as I told you yesterday, you don't have enough information http://www.jiskha.com/display.cgi?id=1424650591
*February 23, 2015*

**Math**

amount = 3000(1.02)^8 = ... subtract $3000 from that answer and you got your interest earned.
*February 23, 2015*

**Math**

Circumference of the wheel = 1.05π number of turns = 3300/1.05π Btw, on your calculator, key in 3300 ÷ (1.05 x π) = to make sure the order of operations is correct
*February 23, 2015*

**Maths**

numbers which when divided by 5 leave a remainder of 1: 6 11 16 21 26 31 36 41 46 .. numbers which when divided by 8 leave a remainder of 1: 9 17 25 33 41 49 ... looks like 41 is the smallest common to both
*February 23, 2015*

**Vectors Math**

http://www.jiskha.com/display.cgi?id=1424665199
*February 22, 2015*

**Vectors Math**

If using whichever method you have to find the cross-product, if you take (a,b,c) x (a,b,c) you will get (0,0,0)
*February 22, 2015*

**Algebra 2**

On here, we write rational expressions this way: (6x^2 + 13x - 5)/(6x^2 -23x + 7) = (3x-1)(2x + 5)/((3x-1)(2x - 7) = (2x+5)/(2x-7) , x ≠ 1/3 (or else I divided by zero)
*February 22, 2015*

**Vectors**

I don't know what your method is but I got (59,42,-29)
*February 22, 2015*

**Vectors**

done, see your earlier post
*February 22, 2015*

**math**

To go from -5 to -1, we moved 4 to the right to go from 4 to -1, we moved 5 to the left, so (x,y) ---> (x+4, y-5) then (-4,5) ---> (0,0)
*February 22, 2015*

**Vectors Math**

the projection of vector a on vector b = (a dot b)/|b| = (5-10+9)/√(1+4+9) = 4/√14 or = 4√14 /14 = 2√14/7
*February 22, 2015*

**math**

And the question is .... ?
*February 22, 2015*

**Math**

cell1 = 50 + 40m cell2 = 0 + 50m when is 50m = 50+40m ??? (seems too easy)
*February 22, 2015*

**Algebra 2**

pr = k(1/d) when d = 2, pr = 750000 750000 = k(1/2) k = 1500000 so pr = 150000(1/d) if d = 5 pr = 150000(1/5) = $300,000
*February 22, 2015*

**Mathematics**

let f(x) = 7x^6-9x^2+2 f(0) = 2 f(1) = 7-9+2 = 0 , well , isn't that special, we accidentally found a solution So I guess there has to be at least one solution.
*February 22, 2015*

**expected value**

If you look at the outcomes, you will see that half of the sums are even, the other half are odd. So prob (even) = 1/2 prob(odd) = 1/2 expected value= (1/2)$10 + (1/2(-$25) = -7.5 Who would possible want to play this game ?
*February 22, 2015*

**math**

Not enough information, you need some angles Imagine the shape having pivots or hinges at the vertices. I can "squish" the hexagon, thus changing the area, while keeping all the sides the same.
*February 22, 2015*

**math**

prob(both red) = (3/6)(2/5) = 1/5
*February 22, 2015*

**Algebra 2**

f(x) = 5x+50 g(x) = x/5 - 10 f(g(x)) = 5(x/5-10) + 50 = x - 50 + 50 = x g(f(x) = (5x+50)/5 - 10 = x + 10 - 10 = x Yup they are check: let f(x) = 5x+50 be written as y = 5x+50 to form the inverse, interchange the x and y x = 5y + 50 now solve this for y 5y = x - 50 y = x/5 - 10...
*February 22, 2015*

**Math Help!**

#6 Let the three consecutive odd numbers be n, n+2, n+4 their sum = 3n + 6 = 3(n+2) so the sum is a multiple of 3. but 29 does not divide evenly by 3, so it cannot be 29
*February 22, 2015*

**Math Help!**

#5. visualize the number or write them out 123456789101112131415161718192021222324252627282930313233 Now circle all the 3's. By the time you reach 33, you will have counted 8 3's. So to write from 1 to 10 took 11 digits so we have 11 12 ... 33, which is 23 double ...
*February 22, 2015*

**Math Help!**

#1. so you have x + (x+2) + (x+4) + .. + (x+18) = 200 ( explanation for term(10) = a+9d = x + 9(2) = x+18) sum(10) = 5(first + last) 5(x + x+18) = 200 2x + 18 = 40 2x = 22 x =11
*February 22, 2015*

**Trigonometry (Logarithmic Function)**

or 15 = (10x3÷2) take log of both sides log 15 = log (10x3÷2) = log10 + log3 - log2 = 1 + y - x
*February 22, 2015*

**Math**

To obtain the product ab, you are simply choosing pairs of numbers form the 6 different numbers. e.g. (3,-5), (1,-1) etc that would be 6x5 or 30 but isn't (5,3) the same product as (3,5), and don't we have a double choice for each pair like that ? so the number of ...
*February 22, 2015*

**Math**

based on the theorem that the area of similar figures is proportional to the square of their corresponding sides, thus also their perimeters. so (p1)^2 : (p2)^2 = 1 : 4 p1 : p2 = √1 : √4 = 1 : 2
*February 22, 2015*

**AP CALC**

I agree with Steve, it is 97/3
*February 21, 2015*

**math**

the arithmetic looks good. I would insist on an equal sign in front of each new line commission = 100000(.024) + 0.015(280000 - 100000) = 2400 + 2700 = 5100
*February 21, 2015*

**math**

what you have is 1+2+3+...+n let S(n) = 1+2+3+...+ (n-2) + (n-1) + n writing this in reverse order S(n) = n + (n-1) + (n-2)+ ... + 3+2+1 add them 2S(n) = (1+n) + (2+n-1) + (3+n-2) +...+(3+n-2) + (2+n-1) + (n+1) = (n/2)(n+1) or = n(n+1)/2 , as required
*February 21, 2015*

**Math**

2x-3y ≤ 6 -3y ≤ -2x + 6 y ≥ (2/3)x - 2 so shade in everything above and including the line y = (2/3)x - 2 4x + 4y ≤ 8 x + y ≤ 2 y ≤ -x + 2 now shade in everything below and including the line y = -x + 2 the solution is all the shaded region ...
*February 21, 2015*

**Math**

You have to consider the speed of the plane without wind and the speed of the wind itself Let the speed of the plane in still air be x km/h le the speed of the wind be y km/h so going with the wind -- speed is x+y mph going against the wind -- speed is x - y mph 2 equations: 4...
*February 21, 2015*

**maths**

I did this last Wednesday http://www.jiskha.com/display.cgi?id=1424295544
*February 21, 2015*

**Math**

Clearly, since 3 does not divide evenly into 25, you cannot do this without some marbles left over.
*February 21, 2015*

**Math**

∛64 = 64^(1/3) = 4 = 2^2 243^1/5 = 3 so 6 log2 ∛64 +10log3 (243)^1/5) = 6log2 (2^2) + 10 log3 (3) = 6(2 log2 2) + 10 log3 3 = 12 (1) + 10(1) = 22
*February 21, 2015*

**Math**

I like Steve's thinking, but sometimes I like to take a hammer to a thumbtack.
*February 21, 2015*

**Math**

Yes, you are adding 5+10+15+...+45+50 here a=5 and d = 5 How many terms are there? term(n) = a+(n-1)d 50 = 5 + (n-1)(5) 45 = 5n - 5 50 = 5n n = 10 so we want the sum of 10 terms sum = (10/2)(first + last) = 5(5+ 50) = 275
*February 21, 2015*

**math**

Meg's age --- x Jill's age ----- x-2 Beth's age --- x/2 or (1/2)x Of course we could have started by defining: Beth's age --- y Meg's age --- 2y Jill's age -----2y - 2 or , starting with Jill's age ----- z Meg's age ---- z+2 Beth's age...
*February 21, 2015*

**math**

If we consider 2004 to be represented by 0, then 2009 would correspond with 5 and we have two ordered pairs (0,14.54) and (5,15.37) slope = (15.37-14.54)/(5-0) = .83 N = .83t + c at (0,14.54) 14.54 = 0 + c , c = 14.54 N = .83t + 14.54 , where t is in years since 2004 and N is ...
*February 20, 2015*

**correction _ Last help Thanks**

Argghhh! the odds AGAINST drawing an S = 7 : 3
*February 20, 2015*

**Last help Thanks**

prob of drawing an S = 4/11 prob of NOT drawing an S = 1 - 4/11 = 7/11 So the odds in favour of drawing an S = (4/11) : (7/11) = 4 : 7 So the odds AGAINST drawing an S = 3 : 7 I would say, "Karen, read the question carefully"
*February 20, 2015*

**help please**

odds in favour of some event = probability of that event happening : probability of the event NOT happening so if the odds of something happening is 3: 4 then the probability of the event happening is 3/7 in general if the odds of something is a : b then prob of that something...
*February 20, 2015*

**math**

total amount invested ---- x Fatuma's share = x/4 Ali's share = (2/5)(3x/4) = 3x/10 Hassan's share = (3/2)(x/4) = 3x/8 so far they have: x/4 + 3x/10 + 3x/8 = 10x/40 + 9x/40 + 15x/40 = 37x/40 so they are still short 3x/40 3x/40 < 3x/8 by 60000 3x/40 = 3x/8 - ...
*February 20, 2015*

**math**

sinØ= 2/3 , Ø is in quad I in my triangle, x = ? , y = 2, r = 3 x^2 + 2^2 = 3^2 x^2 = 5 x = √5 tanØ = y/x = 2/√5 or, if rationalized, 2√5 /5
*February 20, 2015*

**Math**

5 gifts take 1.5 rollos 1 gift takes 1.5/5 rolls 9 gifts take 9(1.5/5) rolls or 2.7 rolls or 9/5 = x/1.5 x = 1.5(9/5) = 2.7
*February 20, 2015*

**Algebra**

let the side parallel to the house be y ft let each of the other two sides by x ft so 2x + y = 164 y = 164 - 2x area = xy = x(164 - 2x = -2x^2 + 164x This is a downwards opening parabola, so we need its vertex. Either 1. complete the square 2. use Calculus 3. use " the x ...
*February 20, 2015*

**math.help pls**

all you have to look at is B(5,-6,-1) If you are using the standard position of x-axis towards and away from you, the y-axis left and right, and the z-axis up and down, then B ---> 2 units back, 3 units right, and 1 unit up ---> B' (3, -3, 0) , then B'(3,-3,0...
*February 20, 2015*

**Math Help**

3u ∙ v = <6,6> ∙ <-3,4> = -18 + 24 = 6 (u ∙ 2v)w = ( <2,2> ∙ <-6,8>)<1,-2> = (-12 + 16)<1,-2> = 4<1,-2>= <4,-8>
*February 20, 2015*

**Math**

i = .035/365 = .00009589.. (I store this in my calculator memory so I don't lose any accuracy) amount = 28000(1 + .00009589..)^68 = 28183.16 for the 2nd problem, the 3000 earns interest for 20 + 30 or 50 days the 650 for 10+30 or 40 days then 1200 for 12 days amount = 3000...
*February 20, 2015*

**Math**

1. dot product u ∙ v = |u| |v| cosØ, where Ø is the angle between them, so <2,-3> ∙ <1,-2> = √13 √5 cosØ 2+6 = √13√5cosØ cosØ = 8/(√13√5) = .99227... Ø = appr 7.1° do #2 ...
*February 20, 2015*

**Maths**

Of course not. It only increases by 3 for this question since this arithmetic series has a common difference of 3 It depends totally on the sequence
*February 20, 2015*

**Maths**

Nothing very exciting. It just blows up, getting bigger and bigger You are just adding 3 to each new term added.
*February 20, 2015*

**Math**

in general: <a, b> ∙ <c, d> = ac + bd so <0, 3> ∙ <4, -2> = 0 + (-6) = -6 repeat for #2
*February 20, 2015*

**math**

either 2 men or 2 women. with no restriction: number of choices = C(5,2) = 10 number choices of 2 women = C(2,2) = 1 number of choices of 2 men = C(3,2) = 3 prob of 2 of same sex = 4/10 = 2/5 prob of 2 of opposite sex = 1 - 2/5 = 3/5
*February 20, 2015*

**math**

L1: y-2 = 5(x-1) y-2 = 5x-5 5x - y = 3 L2: x + 5y = c from L1, when x = 4, y = 17 so (4,17) into L2 4 + 85 = c = 89 L2: x + 5y = 89 or y = (-1/5)x + 89/5
*February 20, 2015*

**trignometry**

Iwill read that as 1/(1 - cscx) - 1/(1 + cscx) = -2tanx secx LS = (1 + cscx - (1 - cscx))/(1 - csc^2 x) = 2cscx/(-cot^2 x) = -2 (1/sinx)(tan^2 x) = -2(1/sinx)(sin^2 x/cos^2 x) = -2 cscx/cos^2 x = -2 cscx sec^2 x = RS
*February 20, 2015*

**math**

90/x = 5^2/10^2 90/x = 25/100 = 1/4 x = 360
*February 20, 2015*

**math**

follow the same method I showed you in your other post with a similar concept Except here you have areas instead of volumes Hint: areas of similar shapes area proportional to the square of their corresponding sides.
*February 20, 2015*

**Math**

prob of grey = 87/100 number of greys in 220 = (87/100)(220) = appr 191
*February 20, 2015*

**Math**

number = (1/50)(750) = 15
*February 20, 2015*

**maths**

visualize the box cut open and laid out flat on a table. What do you see ? Calculate the area of each of the 5 rectangles and add them up
*February 20, 2015*

**Math**

prob of 4 spades = C(13,4)/C(52,4) = 715/270725 = 11/4165
*February 19, 2015*

**Math**

original square is x by x cm new rectangle is x by x/2 2( x + x/2) = 24.9 2x + x = 24.9 x = 8.3 the square piece is 8.3 by 8.3 cm
*February 19, 2015*

**Math**

volume of similar solids is proportional to the cube of their corresponding sides 240/x = 92^3/23^3 240/x = 778688/12167 778688x = 12167(240) x = 3.75 or 3.8 to the nearest tenth
*February 19, 2015*

**Math (Probability)**

You want the 8 of hearts, then an Ace prob = (1/52)(4/51) = 1/663
*February 19, 2015*

**Algebra 2**

t3 = ar^2 = -75 t6 = ar^5 = -9375 divide them r^3 = 125 r = 5 in ar^2 = -75 a(25) = -75 a = -3 term(n) = -3(5)^(n-1)
*February 19, 2015*

**Math**

I assume the median is 87 z-score = (91-87)/4.01 = ....
*February 19, 2015*

**math**

You are basically going through the development of the formula, using a specific example You seem to have a typo your: 3²+3³+3to the power of 6+...to 20 terms makes little sense I will assume we have S(20) = 3^2 + 3^3 + ... + 3^21 multiply both sides by 3 3S(20) = 3^...
*February 19, 2015*

**MATH**

Typo: you have Sn=n/2[a+1] clearly should be : Sn=n/2[a+l] let S(n) = a + (a+d) + (a+2d) + ... +(l-2d) + (l-d) + l , for n terms we could just write this turned around S(n) = l + (l-d) + (l-2d) + ... + (a+2d) + (a+d) + a add these two equations 2S(n) = a+l + (a+d+l-d...
*February 19, 2015*

**MATH**

I will assume that you are adding the corresponding terms of each sequence, that is .. new sequence: t1 = a+a t2 = a+d + ar t3 = a+2d + ar^2 etc so a+a = 4 a+d + ar = 20 but d=-2 and r=3 2a = 4 a = 2 So all is known t3 = 2 - 4 + 2(9) = 16 check: AS: 2, 0, -2, -4, .. GS: 2, 6, ...
*February 19, 2015*

**math**

Use the formulas for both "sum of terms" and "sum of infinite number of terms" Sum to infinity = a/(1-r) a/(1-r) = 243 , ---- #1 ( I recognized 243 as 3^5) a = 243 - 243r sum(5) = a(1 - r^5)/(1-r) 242 = a(1 - r^5)/(1-r) ---- #2 divide #2 by #1 1-r^5 = 242/...
*February 19, 2015*

**Algebra 2**

∑ 2n/(n+4) , where n = 1 to 5 write n=1 underneath the sigma symbol and 5 above it
*February 18, 2015*

**Math Help Please**

You must mean: (4x^3 + 5x^2 - 12x + 27)/(x + 3) I did a synthetic division and got 4x^2 - 7x + 9 , which is A since none of the answers had a remainder, you knew the division had to be exact, so it had to look like this (4x^3 + 5x^2 - 12x + 27) = (x+3)(4x^2 .... +9) so it had ...
*February 18, 2015*

**math**

going to the theatre C = 12.5n, where n is the number of movies seen buying a player, then renting C = 125 + 1.95n 12.5n = 125 + 1.95n 10.55n = 125 n = 11.8 I will let you interpret that decimal answer
*February 18, 2015*

**algebra**

let the side parallel to the barn be y yards then the other two sides are x yards each 2x + y = 25 y = 25-2x area = xy = x(25-2x) = 25x - 2x^2 which graphs as a downwards parabola, so the vertex has to be found. quickest way: the x of the vertex is -b/(2a) = -25/-4 = 6.25 then...
*February 18, 2015*

**ALGEBRA**

unless [ ] is defined as something special, f(2) = 2*(-1)^2 = 2*(1) = 2
*February 18, 2015*

**math**

reflection of P(-3,5) in the x-axis ----> R(-3,-5) which is in quadrant III P(-3,5) reflected in the y-axis---> S(3,5) , which is in quad I
*February 18, 2015*

**Jonie, Pamela, Spartans - math**

Why are you changing names, and what could you not understand about my answer here: http://www.jiskha.com/display.cgi?id=1424281591
*February 18, 2015*

**Math**

the resultant vector is (9-1 , 3-11) = (8,-8) This is generally considered in component form check with your textbook how they write the vector. Some authors avoid the standard round brackets ( ..., ...) to avoid confusion with a point. Some use this form [8,-8] others use <...
*February 18, 2015*

**Calculus**

not an easy problem follow these steps: http://mathworld.wolfram.com/SphericalCap.html or http://en.wikipedia.org/wiki/Spherical_cap or http://keisan.casio.com/has10/SpecExec.cgi?id=system/2006/1223382199
*February 18, 2015*

**math**

I hope Mr. Howard put in the closing brackets. 3(20x + 8) = 60x + 24 4(15x)+6) = 60x + 48 so what is your opinion ?
*February 18, 2015*

**Math**

so what did your calculator say? remember the angle could have been in quadrant IV also. so 360-(whatever your calculator said)°
*February 18, 2015*

**Algebra 2**

sum(7) = (7/2)(2(26) + 6(18)) = 560
*February 18, 2015*

**Algebra 2**

so you want 16+20+24+...100 number of terms = ?? you have an AS, where a = 16 , d=4 term(n) = a+(n-1)d 100 = 16 + (n-1)(4) 84 = 4n - 4 88 = 4n n = 22 so we want S(22) = (22/2)(first + last) = 11(16+100) = 1276
*February 18, 2015*

**Algebra not algabra**

(3a+2)^3 = (3a+2)(9a^2 + 12a + 4) = 27a^3 + 36a^2 + 12a + 18a^2 + 24a + 8 = 27a^3 + 54a^2 + 36a + 8 or , using the binomial expansion = 1(3a)^3 + 3(3a)^2 (2) + 3(3a)(2^2) = 1(2^3) = 27a^3 + 54a^2 + 36a + 8
*February 18, 2015*

**Math**

N = N(M) + N(S) + N(R) - N(M and S) - N(M and R) - N(S and R) + N(M and S and R) = 36+28+12 - 15 - 12 - 8 + 4 = 45 If the question is, How many did not buy any type of book, then it would be 59-45 or 14 You did not state a question. You could draw a Venn diagram and all ...
*February 18, 2015*