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Posts by Reiny

Total # Posts: 38,338

math
Really? How can you claim that it is negative, after having it shown that it is positive. Look at the calculation.

math
first one: slope = (5-1)/(6-3) = 4/3 how did you get it to be negative? 2nd: slope = (-5-(-6))/(-3-(-3)) = 1/0 can't divide by zero, so "undefined"

Algebra
t(1) = 3 = 1x3 t(2) = 8 = 2x4 t(3) = 15 = 3x5 t(4) = 24 = 4x6 t(5) = 35 = 5x7 .. looks like t(n) = n x (n+2) so t(11) = 11x13 = 143

Pre calculus
term(1) = 1^2 -2 = -1 term(2) = 2^2 - 2 = 2 term(3) = 3^2 - 2 = 7 term(4) = 4^2 - 2 = 14 ... term(n) = n^2 - 2 62 = 8^2 - 2 , so we have 8 terms sigma (n^2 - 2) for 1 to n = n(n+1)(2n+1)/6 - 2n recalling that sum n^2 = n(n+1)(2n+1)/6 checking for sum(5) = 5(6)(11)/6 - 10 = 55-...

Probability
odds are defined slightly different from probability. odds in favour of some event = prob(of that event) : prob (not that event) so odds in favour of rain on Sept 21 = .358 : .642 = 358 : 642 reduce to lowest term ratio

Math (ugh)
Don't know what the hangup is between mixed fractions and "improper" fractions mixed fractions may be nice to look at, but they are basically useless for arithmetic calculations and must be changed to improper fractions so, 3 3/4 x 2 4/5 = (15/4)(14/5) = (3/2)(7/...

Math 1
80x^4 - 60x^3 - 60x^2 - 45x This one looks more promising. = 5x(16x^3 - 12x^2 - 12x - 9) let f(x) = 16x^3 - 12x^2 - 12x - 9 f(±1) ? 0 f(±3) ? 0 tried ±3/2, ±3/4, ±3/8, ±3/16 found f(3/2) = 16(27/8) - 12(9/4) - 12(3/2) - 9 = 54 - 27 - ...

Math1
Well, let's look at everything again. clearly x^2 is a common factor. Look at the numbers, start with the 24 24 = 3*8 = 3*2*2*2 so the 195 is only divisible by 3 but not 28, so the HCF is x^2 195x^5 + 168x^4 - 28x^3 - 24x^2 = x^2(195x^3 + 168x^2 - 28x - 24)

Math
review your rules of exponents as it applies to division of powers. This one is a straightforward application of one of those rules. If this is for a test, you MUST know this. btw, x^9/x^2 is the same as x^9 ÷ x^2

algebra
did you mean log(2x-6)^256=4 ?? according to the numbers, I will assume so. You must know your rules of logs by definition 256 log (2x-6) = 4 log (2x-6) = 1/64 2x-6 = 10^(1/64) 2x-6 = 1.0366329.. 2x = 7.0366... x = 3.518316... round to whatever accuracy you want. that answer ...

Statistics
I only answered part b) since a) is very simple a) would be .51^7 = .0089741 I have no idea how yo got 8.9741, the digits are the same, but no probability can be greater than 1. for b) the answer correct to 4 decimals is .0494, your is correct only to 3 decimals

Statistics
prob(b) = .51 prob(x) = .49 , where x is "not blue eyes" one such case could be xxbxxxx , which would be (.51)(.49^6) but there are 7 such cases, so prob(your event) = 7(.51)(.49^6) = .... in stats notation: C(7,1)(.51)(.49)^6

maths
R = k/r^2 when R = .24, r = .05 .24 = k/.0025 k = .006 when r = .04 R = .006(1/.0016) = .375

calculus
done, look back

clculus
dy/dx = 2x at (-2,4), slope = -4 equation of tangent: y-4 = -4(x+2) y = -4x -4 let x = t y = -4t - 4

Maths
Assuming you mean: 4x^2 - 5x - 1 = 0 x = (5 ± ?41)/8 so alpha = (5+?41)/8 and beta = (5-?41)/8 a^2b = (5+?41)/8 * (5+?41)/8 * (5-?41)/8 = (5+?41)/8 * (25 - 41)/64 = (5+?41)/8 * (-16/64) = (-5-?41)/32 GAURAV concluded that a = 1, b = 1/4 but those are not the zeros of ...

Math
What is 6x15 ?

MAth
Of course the bisector of angle C is 45° let the bisector hit AB at P in triangle BCP tan 45 = BP/15 BP = 15tan45 = 15 continue

alg II
yes, and yes

Calculus
yes

geometry please help!!!!
I made a rough sketch. For the total surface area I see two equal trapezoids, and 4 rectangles. the rectangles are: 14 by 10 , 8 by 10 and 2 of 5 by 10 the area of the trapezoid = (1/2)(8+14)/2 finish the arithmetic and use the correct units

math help please check my answer
tan Ø = 60/25 = 2.4 Ø = tan^-1 (2.4) = 67.38..° = 67° to the nearest degree

math
I disagree, Odds and probability are defined slightly different. The odds of some event happening = prob( event) : prob(not the event) so if prob(a 21 ) = 1/38 then the prob(not a 21 ) = 1 - 1/38 = 37/38 odds in favour of a 21 = (1/38) / (37/38) = (1/38)(38/37) = 1 : 37

Pre calc
Or for the 2nd Cos 2x cosx -sin 2xsinx = 0 Cos(2x + x) = 0 cos 3x = 0 3x = pi/2 or 3x = 3pi/2 x = pi/6 or x = pi/2 The period of cos 3x = 2pi/3 So add multiples of that together Steve's other answers

math
the sixth term of an arithmetic progression is 37 ---> a+5d = 37 5d = 37-a sum of the first six term is 147 ---> (6/2)(2a + 5d) = 147 3(2a + 37-a) = 147 a +37 = 49 a = 12 d = 5 If you had a question, take it from there

Math
Juan's present age --- x Ben's present age ---- x+4 in two years: Juan ----- x+2 Ben -------x=4+2 = x+6 x+2 + x+6 = 50 continue

MAth
2l + 2w = 240 l + w = 120 l = 120-w new length = 1.1l new width = .8w 2(1.1l) + 2(.8w) = 240 1.1l + .8w= 120 1.1(120-w) + .8w = 120 11(120-w) + 8w = 1200 1320 - 11w + 8w = 1200 -3w = -120 w = 40 then l = 120-40 =80 state a proper conclusion

Mathmatics
slope of line Q = (-8+2)/(-8+10) = -6/2 = -3 slope of line R = (a-2)/(10-1) = (a-2)/9 but they are perpendicular, so (a-2)/9 = -1/3 continue

Mathmatics
let B be (x,y) for the x: (x-3)/(12-x) = 2/1 x - 3 = 24 - 2x 3x = 27 x = 9 find the y in the same way

Mathmatics
slope AB = m = (1+7)/(-8+12) = 8/4 = 2 using (2,5) y-5 = 2(x-2)

Maths
sub in the two points to set up two equations for (0,3) 3 = a b^0, but b^0 = 1 so a = 3 for (2,12) 12 = 3 b^2 4 = b^2 b = ± 2, but we need b> 0 a = 3 , b = 2 ---> y = 3 (2)^x

math
dc/dq=0.08q^2-1.8q+2.5 c = (.08/3) q^3 - .9 q^2 + 2.5q + 5000 plug in 1000 for q

math
I would expand it first, y = 4x^-2 + x^-5 now it is elementary.

Mathematics
Surface area of original = 2(11)(6) + 2(11)(4) + 2(6)(4) cm^2 = 268 cm^2 volume of original = (11)(6)(4) cm^3 = 264 cm^3 For a cube to hold 264 cm^3, each side must be 264^(1/3) or 6.415... cm long surface area of the cube = 6(6.415...)^2 = appr 246.92 cm^2 (I only rounded ...

QMI
amount = 2000(1.1^35 - 1)/.1 = ....

precalculus
p = 32 e^(kt) , where k is a constant when t = 3, p = 200 32 e^(3k) = 200 e^(3k) = 6.25 3k = ln 6.25 k = appr .61086 p = 32 e^(.61086 t)

Trig
Fish at a depth of 45 km in Lake Ontario ???? I live about 45 minutes from Lake Ontario, and let me guarantee you that lake is not that deep, lol. Anyway ..... I will assume you meant 45 m. let the line be l m long cos 45 = 46/l ----- ( 1 m above the water + 45 l = 46 m) l = ...

precalculus
If I read it correctly you want 230000(.95)^t = 150000(1.11)^t 23(.95^t) = 15(1.11)^t take logs of both sides and use log rules log 23 + t log .95 = log 15 + t log 1.11 log 23 - log 15 = t(log 1.11 - log .95) carry on

math
What are you trying to do ?? is it 6 = e^(5r) or the way you typed it?

math
correct, but remember that q will be half-years so you will have to divide q by 2 to get the number of years

College Algebra
good grief! I just did this for you a few minutes ago!!!!

Help College Algebra
At what will the ball be ... ????? Time ?? set -16t^(2)+128t = 213 and solve 16t^2 - 128t + 213 = 0 you will get two answers, one positive and one negative. Reject the negative answer.

College Algebra
Besides that , it was already answered.

College Algebra
V = (1/3)? r^2 , solve for r 3V/? = r^2 r = ±?(3V/r)

algebra
a) x = 5y ? 3 5y = x+3 y = (1/5)x + 3/5 b) the slope is 1/5, they are the same equation c) they are the same equation

Algebra
d=kt^2 kt^2 = d t^2 = d/k t = ± ?(d/k)

Algebra
part one, height = 32 -16t^2 + 32t = 32 t^2 - t +1 = 0 by the formula: t = (1 ± ?-3)/2 , not real so it will never reach a height of 32 ft we can see that by noting that the x-intercepts are 0 and 2 so the vertex is at t = 1 max height is h(1) = -16+32 = 16 I also ...

metric unit
behold the beauty of the metric system 48567 kg = 48.567 tons

Math
clearly B

Math
No, this is an example of Binomial Distribution. You are planting 7 plants, and you want the prob that exactly 1 does not grow. Suppose it is the 3rd plant which did not grow. GGNGGGG, where G stands for grow, N for not grow. That specific probability is (.7)(.7)(.3)(.7)(.7)(....

Math
same question here: http://www.jiskha.com/display.cgi?id=1445605410

francis
the 8th term of an A.P is twice the 5th term ----> a + 7d = 2(a+4d) a+7d = 2a + 8d a = -d 12th term = a + 11d = -d + 11d = 10d e.g. let d = 4, then a = -4 term(8) = -4 + 7(4) = 24 term(5) = -4 + 4(4) = 12 so term 8 is twice term 5 term 12 = -4+11(4) = 40 which is 10d or 10(...

Math
I would just use a simple ratio. 29/35 : 6/35 = 29 : 6 since 3 5/12 = 41/12 so x/(41/12) = 6/29 29x = 6(41/12) = 41/2 x = 41/58 quarts needed to finish the job

Maths
surface area = 2 circles + 1 rectangle = 2?r^2 + (2?r)(h) = 2?(5^2) + 2?(5)(15) = 50? + 150? = 200? cm^2 1 m^2 = 10000 cm^2 so our surface area = 200?/10000 m^2 cost = 4500(200?/10000) naira = 90? naira = ..... I will let you do the arithmetic

Maths
rest of distance = 1 - (3/8 + 3/5) = 1 - 39/40 = 1/40 (1/40)x = 2 x = 80 km so he went (3/5)(80) km by bus = .....

Maths
volume = length x width x height = (85)(62)(36) cm^3 = .. continue

maths
done here http://www.jiskha.com/display.cgi?id=1492480948

arithmatic series
quotient of the larger number and the smaller number is just a list of the terms e.g. a,b,c,d,.. the series is the sum of those arithmetic terms a+b+c+d+..

math
larger --- L smaller --- 74-L "quotient of the larger number and the smaller number" ---> L/(74 - L)

math
done here http://www.jiskha.com/display.cgi?id=1492424429

math
15, 15+d, 15+2d, 15+3d, 15+4d, 87 87 - (15+4d) = d 72 - 4d = d 5d = 72 d = 72/5 = 14.4 15, 29.4, 43.8, 58.2, 72.6, 87

math
a = -13 , d = 5 term(n) = a + (n-1)d = -13 + 5(n-1) = -13 + 5n - 5 = 5n - 18

maths
you have an AS sum = 4000 + 5000 + 6000 + .. sum(n) = (n/2)(8000 + (n-1)(1000) ) = 60000 n(8000 + 1000n - 1000) = 120000 1000n(7 + n) = 120000 n(n+7) = 120 n^2 + 7n - 120 = 0 (n - 8)(n + 15) = 0 n = 8 or n = -15, ignore the negative They can be late 8 days

correction - Calculus
I jumped to conclusion when I subbed in the 0 (4/(1/3) (x+1)^(1/3) from 0 to x = 12(x+1)^1/3 from 0 to x should have given me: 12 (x+1)^(1/3) - 12(1)^(1/3) = 12 (x+1)^(1/3) - 12 f(x) = 12 (x+1)^(1/3) - 12 f(26) = 12(3) - 12 = 24

Calculus
so you want f(x)= ? 4 (x+1)^(-2/3) dx from 0 to x = (4/(1/3) (x+1)^(1/3) from 0 to x = 12(x+1)^1/3 so f(26) = 12(27)^(1/3) = 12(3) = 36

math
a metre and a centimetre are units of length if I told you that a nickel has a mass of about 5 grams, and a quart of milk has a mass of about 1 kg, what is your conclusion ?

Math
children --- x adults ------2x Joe + wife + 4 children = 56 2x + 2x + 4x = 56 x = 7 state your conclusion.

math
in y = mx + b, the rate of change or slope is m consider y = 3 as y = 0x + 3 so the rate of change is zero, or "y does not change", it is always 3

Math
1000 words per 5 minutes = 1000/5 words per 1 minute or simply 200 words/min (you had 5/1000 which is not 200, but 1/200)

Math
or, using algebra let the two amounts invested by 6x and 7x (notice 6x : 7x = 6 : 7 ) then 6x + 7x = 260 13x = 260 x = 20 then 6x = 6(20) = 120 and 7x = 7(20) = 140 the same answers obtained by Ms Sue

Statistics
I will assume that you are working from "tables", so we need the z-score for 1550 z-score = (1550 - 1500)/200 = .25 look at http://math.arizona.edu/~rsims/ma464/standardnormaltable.pdf and find .25 (2nd page , find .2 in 1st column, then under .05) to find .59871 ...

Statistics
P(-2>Z and Z<-1) or more commonly written as P(-2 > Z <-1) wants you to find the probability that the z-score of the normal binomial distribution lies between -2 and -1 X~N(3,4) or X~N(3,2^2) means X is normally distributed with a mean of 3 and a standard deviation...

Math
in d = 25h the distance travelled "depends" on the time taken, so ......

Math
for a mean of 541, with a sd of 89 we would have: 541-89 <---> 541+89 (one standard deviation) 452 <---> 630 ---------68% 452-89 <---> 630+89 (two standard deviations) 363 <---> 719 -------- 95% since 541 is the mean 363<---> 541 would be 1/2 of ...

Steve to the rescue
Of course, why didn't I think of that 2 data values --- linear 3 data values --- quadratic 4 data values --- cubic etc

series maths steve reiny bob reiny steve!!!
Looking at only 3 terms, they are not in AP they are not in GP looking for some pattern: 8 = 4*2 20 = 4*5 52 = 4*13 I see nothing special about 2, 5, 13 2 = 1+1 5 = 4+1 13 = 12+1 still nothing

math
meant to say at the end: I get 2 pairs of solution for a and d, one will work, the other causes a 0 to show up in a GP, which is not possible.

math
let the four number be a, a+d, a+2d , a+3d then given: a+5, a+d+6, a+2d+9, a+3d+15 are in GP then (a+d+6)^2 = (a+5)(a+2d+9) a^2 + d^2 + 36 + 2ad + 12a + 12d = a^2 + 2ad + 9a + 5a + 10d + 45 d^2 - 2a + 2d = 9 a = (d^2 + 2d - 9)/2 (a+2d+9)^2 = (a+d+6)(a+3d+15) I get: - 3a + d^2...

financial mathematics
perhaps "alternative facts" are even entering the world of math, lol, strange times

financial mathematics
i = .16/4 = .04 n = 5(4) = 20 PV = payment (1 - (1+i)^-n)/i P( 1 - 1.04^-20)/.04 = 1000 P = .04(1000)/(1 - 1.04^-20) = 73.58

maths
After you make your sketch and draw the parallogram, I would use the cosine law: |R|^2 = 16^2 + 16^2 - 2(16)(16)cos 120° = 512 - 256(-1/2) = 640 |R| = ?640 = appr 25.3

Pre calc
tanØ = 2?10/9 recall tanØ = y/x in the corresponding right-angled triangle we are also given that cscØ is negative, so Ø must be in III then y = -2?10 and x = -9 r^2 = 40 + 81 =121 r = 11 x = -9, y = -2?10, r = 11 sinØ = -2?10/11, cosØ...

Pre-Algebra
simple case of Pythagoras h^2 + 16^2 = 20^2 solve for h

math
amount invested at 3% --- x intereste at that = .03x amount invested at 5% ---- 16000 - x interest at that = .05(16000-x) they are equal, so solve .03x = .05(16000 - x) 3x = 5(16000-x) carry on

MATHS
The width of the pathway is the unknown, let it be x m so make a sketch and you will see that the length of the whole thing is 120 + 2x and the width is 50+2x area of the whole thing = (120+2x)(50+2x) = 4x^2 + 340x + 6000 If the garden area is 6000, and the pathway is also ...

Advanced maths
a = 9 term(n) = a + (n-1)d = 105 (n-1)d = 105 - a = 105-9 = 96 sum(n) = (n/2)(2a + (n-1)d) = 741 (n/2)(18 + 96) = 741 n/2 = 6.5 n = 13 (n-1)d = 96 12d = 96 d = 8 the terms are 9, 17, 25, ..

Maths
Suppose we have n objects. In how many ways can I take all of them of course the answer to that is 1 way. but from the theory of combinations it would be n!/( (n-n)(n!) ) = n!/(0!n!) = 1/0! but we know that has to be 1 1/0! = 1, this can only be true if we define 0! = 1 That ...

Calculus
thanks for catching that, of course when you add 1 to -2 you get -1, not -3 - sometimes the simple things mess us up! Ok, then I should have had: ln (y-1) = -1/x + c and plugging in (1,2) ln 1 = (-1/1) = c c = 1, you had that. so we get to ln (y-1) = -1/x + 1 or (x-1)/x now ...

Calculus
dy/dx = (y-1)/(x^2) dy = (y-1)/(x^2) dx dy/(y-1) = x^-2 dx the next step is where you went wrong, ln (y-1) = (-1/3)x^-3 + c check by taking the derivative. given: the point (1,2) lies on it, so ln (2-1) = (-1/3)(1^3) + c 0 = -1/3 + c c = 1/3 ln (y-1) = (-1/3)x^-3 + 1/3 = ( -1/...

correction - Statistics
C(13,4)/C(52/4) = 715/270725 = 11/4165 or appr .002641 Nonetheless' second answer is not correct, should be (13/52)(12/51)(11/50)(10/49) which comes out to the same as my answer above "drawing" cards usually means that you are holding the cards in your hand, ...

math
how about the two points (0,0,3) and (3,3,0) ? a line containing those two point has direction [3,3,-3] or [1,1,-1] if reduced let's take the dot product of [1,1,-1] and [2,3,5] = 2 + 3 - 5 = 0 so if the dot product is 0, then the vectors are perpendicular. By now you ...

math
amount = 8000(1.04)^8 + 6000(1.04)^2 = ...

algebra
If you meant: (a+b)^3 - 8 then your answer is correct

Maths
The time taken is inversely proportional to the speed t = k/v if t = 10, v = 6 10 = k/6 k = 60 when v = 8 t = 60/8 = 7.5 minutes

Maths - trigonometry
secØ sin(36+Ø) = 0 secØ = 0 or sin(36°+Ø) = 0 secØ can never be zero, secØ?1 OR secØ ? -1 so: sin(36°+Ø) = 0 36+Ø = 0° or 180° or 360° or -180° ... then Ø = -36° , Ø = 144&...

algebra
I hope you mean: (v^2+6v+8)/(v^2+v-12) ÷ ((v+2)/(2v-6) ) = (v+2)(v+4)/((v+4)(v-3) * (2(v-3)/(v+2) = 2(v+2)(v+4)(v-3) / ( (v+4)(v-3)(v+2) ) = 2 , where v ? -4,-2, 3

algebra
correct, the division was exact with no remainder. the answer is 8x^2 + 20x + 24 synthetic division confirms it: 3 | 8 - 4 - 36 - 72 ........ 24 .. 60 .. 72 .... 8..20 .. 24 ... 0 the 8, 20, 24 represents 8x^2 + 20x + 24 the 0 shows no remainder.

MATH
Why don't you try it with two different functions, e.g. f(x) = x+2 , g(x) = 2x - 1 let y = f(x) + g(x) = x+2 + 2x - 1 = 3x + 1 is this a straight line ? so what do you think about a) ??? ... c) let y = f(x) * g(x) = (x+2)(2x-1) = 2x^2 + 3x - 2 Is a quadratic a straight ...

math
Do you have a typo? did you mean: Suppose x can be expressed as a function of y by x = 5y ? 3 ?? If so, then a) x + 3= 5y y = (x+3)/5 b) since all I did was to re-arrange the equation, I don't have two equations, it is the same equation. Of course all properties such as ...

Trignometry
just set it equal to 10 10 = 12+2.83sin((2?)/365(t-800) -2 = 2.83sin((2?)/365(t-800) -2/2.83 = sin((2?)/365(t-800) -.706713... = sin((2?)/365(t-800) using my calculator set to radians, taking the inverse sine of +.706713, I get a reference angle of .78484 radians but for the ...

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