# Posts by Reiny

Total # Posts: 39,979

Math
Triangle AOB is isosceles, with angle OAB = angle OBA which makes each of them 40°

Math
Your number should have at least one perfect square as a factor, or else there is no advantage in separating the radical into factors e.g. ?24 = ?4*?6 = 2?6 ?24 = ?2*?12 ----> not simplified ?24 = ?3*?8 = ?3*?4*?2 = 2*?3*?2 = 2?6 ----> long way to get my first answer ?72...

math
Bread - 3 Spreads - 5 Veggies - C(7,3)= 35 Multiply them

math
https://www.jiskha.com/display.cgi?id=1441287038

math
see first question in Related Questions below.

Maths
7056 = (2*2*2*2)*(3*3)*(7*7) = 16*9*49 so ?7056 = 4*3*7 = 84

math
in your sequence, a = 88, d = -3 so you want a + (n-1)d = -17 88 + (n-1)(-3) = -17 88 - 3n + 3 = -17 -3n = -108 n = 36 state your conclusion

Math
what method have you learned ? The last one is trivial. What two numbers have a sum of -10 and a product of 24 ? I would "guess" at -6 and -4 So x = -6 or x = -4 One foolproof method, but not necessarily the best, is decomposition. multiply the coefficients of the x^...

Math
18 = 2*3*3 25 = 5*5 35 = 5*7 LCM = 2*3*3*5*5*7 = 3150 how about 3150k < 9999 k < 3.1 so largest 4 digit with above properties is 3*3150 = 9450 test it with your calculator. 1008 = 2*2*2*2*3*3*7 = 16 * 9 * 7 the first two factors are perfect square, so to make the last ...

cont'd - Calculus 2
correction: for ln (1 + x) = x ? x^2/2 + x^3/3 - x^4/4 + x^5/5 ..... x is between -1 and +1 e.g. let x = .46 on my calculator: ln(1.46) = .378436... using the above formula: ln(1.46) = .46 - (.46)^2/2 + (.46)^3/3 - (.46)^4/4 .... = .37545... using 4 terms

Calculus 2
let's look at the last one: ln (1 + x) = x ? x^2/2 + x^3/3 - x^4/4 + x^5/5 ..... of course x ? -1 this should be in your text, in your class notes, or you can easily look it up For the other two, how about just looking at the general binomial expansion: 2/(1+x)^3 = 2(1+x...

Math
"How many miles does Ernie walk when he hikes on the trail" You just stated he walked 1/6 mile Did you mean, how many miles does Ernie walk per hour when he hikes on the trail? rate = distance / time = (1/6) / (1/12) = 2

Math
I didn't say that 24 was the only answer, there is no unique answer. It is the answer only if we let m = 1 and n = 5 Since, as Scott pointed out, you did not state a second equation 9m + 3n can only be expressed in terms of either m or n

Math
from 2m + n= 7 n = 7 - 2m now plug that into 9m+3n = 9n + 3(7-2m) = 9n +21 - 6m = 3m + 21 your way should have said: m = (7 - n)/2 then 9m + 3n = 9(7-n)/2 + 3n = (63 - 9n)/2 + 6n/2 = (63 - 3n)/2 checking: if we let n = 5, then from yours m = 1 and 9m + 3n = (63 - 15)/2 = 24...

Math
clearly, yes

Math
I interpret 5x and 9y =28 as 5x + 9y = 25 since x and y must be positive integers, 5x could only have values of 5, 10, 15, 20, 25 9y could only have values of 9, 18, 27 now what number from the first set added to a number of the second set yields a sum of 28 ?

Calculus
yes

Algebra
I will assume you mean: f(x) = (2-3x)/(5-2x) and you want to know the value of a so that f(a) = 36 so (2-3a)/(5-2a) = 36 2 - 3a = 180 - 72a 69a = 178 a = 178/69 check my answer on your calculator by evaluating f(178/69)

Calculus
Use implicit differentiation. e^y -y=x^2 -2 e^y (dy/dx) - dy/dx = 2x dy/dx( e^y - 1) = 2x dy/dx = 2x/(e^y -1) so for the point (2,0), dy/dx = 2(2) / (e^0 - 1) = 4/0 this tells me that at (2,0) the tangent slope is undefined, thus the tangent will be a vertical line The ...

Math
of 17 terms, the middle term is term 9 so a + 8d = 5 -----> a = 5-8d sum(17) = (17/2)(2a + 16d) = (17/2)(10-16d + 16d) = (17/2)(10) = 85

math
I will interpret this as: In the xy-plane, the center of a circle has coordinates ( 6,10) and the circle touches the y-axis at one point only. What is the radius of the circle. If you make a sketch of the circle that has a centre of (6,10) and touches the y-axis, you can see ...

math
In my diagram, I have PS as the longer of the parallel sides. From Q and R, draw perpendiculars to meet PS at M and N respectively. So I have two equal triangles and a rectangle. In triangle PQM, PM/6 = cosx ----> PM = 6cosx QM/6 = sinx -----> QM = 6sinx area = 2 ...

math
I think this is a binomial distribution question. prob(knows) = 12/26 = 6/13 prob(not know) = 7/13 prob(students knows at least 8 of 10) = prob(8of10) + prob(9of10) + prob(10of10) = C(10,8)(6/13)^8 (7/13)^2 + C(10,9) (6/13)^9 (7/13) + C(10,10) (6/10)^10 = (you do the button ...

math
3 negatives: -1/3, -1/4, - 789/25987 3 positives: 3/11, 3/5555, 187/500 test by finding the decimal equivalent for each one. Do they fall between -.5 and .375 ? (see, I can type "between" without any problems, why can't you?)

Math
prob(win) = .1 prob(not win) = .9 prob(at least 5 of 50) = 1 - (prob(none of 50) + prob(1 of 50) + prob(2 of 50) + prob(3of50) + prob(4of50) ) = 1 - (.9^50 + 50(.1) (.9)^49 + 1225(.1)^2 (.9)^48 + 19600(.1)^3 (.9)^47 + 230300(.1)^4 (.9)^46 ) = .5688 check my arithmetic, I did ...

math
re-arrange the first to say: y = 4x-6 Now sub that into the 2nd: 2x + 3(4x-6) = 5 solve for x, then sub into y = 4x-6 or write down the first: 4x - y = 6 double the second: 4x + 6y = 10 subtract them: -7y = -4 y = 4/7 sub back into the first you should of course get the same ...

math
e.g -5/7, -2/3, -12345/12355, etc a lot of them. What is the mathematical name for "a lot of them" ?

maths
re-type using mathematic symbols Make sure you use brackets if they matter e.g. 8ki^-1 ? (8ki)^-1

maths
We can divide by every rational number except ....

maths
area of rectangle ÷ one side = the other side, so .... (120/49) ÷ (10/7) = ....

Math
words spelled correctly by Elise --- x words spelled correctly by Chris --- x+5 solve for x: x + x+5 = 27

Math
I will do the first, then you show me how you did the second. x^2 + 7x = 4 x^2 + 7x - 4 = 0 a = 1, b = 7, c = -4 x = (-b ± ?(b^2 - 4ac) ) / (2a) = (-7 ± ?(49 - 4(1)(-4))/2 = (-7 ± ?65)/2

math
Zero is a real number.

math
prob(John wins) = 4/5 -----> prob(John loses) = 1/5 Since the events do not depend on each other, what do we do with the probabilities in Prob(Megan winds AND John loses) ??

Math
Use your definitions and formulas a + 2d = -12 a + 6d = 8 subtract the two equations, and find d once you have d, go back into the first equation to find a then find a + 9d

math
Let the number be x (x+1)(x-4) = 36 x^2 - 3x - 4 = 36 x^2 - 3x - 40 = 0 (x-8)(x+5) = 0 x = 8 or x = -5 check: if the number is 8 then is 9 times 4 = 36 ? yes If the number id -5, is -4 times -9 = 36 ?, yes the number could be 8 or it could be -5

Maths
yes -3?/4 radians = -135° -135° is in quadrant III by the CAST rule. -135° is in the same position as 225° or (180° + 45°) . the equivalent angle in standard position is 45° so tan (-135°) = tan (-3?/4) = 1

Calculus
I made a diagram showing a diagonal WE I placed P along an arc called a so that the central angle is 2Ø I joined PW and let PW = x Recall that the central angle subtended by an arc is twice the angle subtended at the circle, so angle PWE = Ø recall arc = r x ...

Math
let the number of 50 cent increases be n Now: number sold = 60 price per mug = 4 after increase: number sold = 60 - 6n selling price = 400 + 50n Profit = Revenue - cost = (60-6n)(400+50n) - 250(60-6n) = (60-6n)(400+50n - 250) = (60-6n)(150 + 50n) = - 300n^2 + 2100n + 9000 if ...

Math
correct see my answer to the same question a few minutes ago

Math
1st prize = 100,000 2nd prize = (.6)(10,000) = 6,000 3rd prize = (.6)^2 (10000) = 3600 ... 6th prize = (.6)^5 (10,000) = .....

Maths
You are correct so far, r = ?2 all you need is Ø, and you almost got it tanØ = -1 we know that tan ?/4 = +1, (tan 45° = 1) and we also know that 1 - i would form an angle in quadrant IV so Ø must be 2? - ?/4 = 7?/4 so 1 - i = ?2cos 7?/4 + ?2sin 7?/4 or...

Precal12
Thanks Steve, good catch.

Precal12
(n+1)C(n-1) = 28 (n+1)! / ((n+1-n+1)! (n-1)! ) = 28 (n+1)! / (2! (n-1)! ) = 28 (n+1)(n)(n-1)!/(2! (n-1)! ) = 28 n(n+1)/2 = 28 n^2 + n = 56 n^2 + n- 56 = 0 (n-8)(n+7) = 0 n = 8 or n = -7 , but n ? 0 n = 8 another way would be to realize that n+1 and n-1 have a difference of 2. ...

Math/Pre-calculus
Did not see Damon's answer, I had the page open all this time.

Math/Pre-calculus
I think you have a typo or a flaw in your equation. P(t) = P0 e^(k/t) makes no sense at t = 0 and since you are asking for the initial value P0, that would assume we need t = 0 in our calculation. That would make our result undefined. Fix your problem.

Math
the concept of odds is not quite the same as probability odds in favour of some event = prob(the event) : prob(not the event) prob(rain for 3 days) = .3^3 = 27/1000 = .027 prob(no rain on any of the 3 days) = 1-.027 = .973 or 973/1000 so odds in favour of no rain at all = 973/...

Math
I will assume you want the measure of the angles of triangle ADC Well, the angles of a triangle must add up to 180° Just noticed your given data makes no sense. Where does angle B enter the picture? You said "triangle ADC"

Math
40 = 1 x 40 = 2 x 20 = .....

Math
The LCF of 14 and 35 is .... ?

Math
What is the HCF of 18 and 27 ?? (lucky that falls between 1 and 10)

math
Present age: Dana ----- x Michael ---- x - 63 7 years ago: Dana ---- x-7 Michael --- x-63-7 = x-70 x-7 = 4(x-70) x-7 = 4x - 280 -3x = -273 x = 91 So Dana is now 91 and Michael is 28 check: 7 years ago , Dana was 84 and Michael was 21 Was Dana 4 times as old as Michael ?? , YES

math
NO You have to use the formula for "amount of an annuity" i = .02/4 = .005 n = 10(4) = 40 amount = 1000( 1.005^40 - 1)/.005 = \$44,158.85 What are you doing with, Total = 1220.79 40,000 + 1220.79 = 41,220.79 ?????

MATHS
x(1.05)^2.5 - x = 416.2 solve for x

Maths
2 years, 8 months = 1 + 8/12 = 5/3 years interest = 6300(1.07)^(5/3) - 6300

Math
for loan A, i = .12/12 = .01, n = 12 for loan B, i = .125, n = 1 rate for A = 1.01^12 - 1 = .1268.. rate for B = 1.125 - 1 = .125 so what do you think?

A nice sequence of videos by Sal Khan of the Khan Academy. Sal has a knack of explaining things in simple terms. (one of the best sites on the entire internet, this is what makes the internet a good thing) https://www.khanacademy.org/math/arithmetic-home/multiply-divide/mult-...

math 106
Why are you even using ANY calculator for this question As Ms Sue told you, and you should know, I = PRT 60 = 500(3/100)T 60 = 15T T = 60/15 = 4 , and I didn't touch a calculator.

math 106
4 consecutive questions posted in about 10 minutes without showing any effort or work on your part. This does not fly here, since you clearly just want somebody to do an assignment for you. Where are you running into difficulties? e.g. this question is a very straightforward ...

mathhelop
you have two ordered pairs of the type (h, p) namely (90,100) and (25, -30) slope = (-30-100)/(25-90) = 2 p-100 = 2(h-90) p = 2h - 80 , which is what Scott had

Algebra 2
start with y = 5sin (?x) period = 2?/k 6? = 2?/k 6?k = 2? k = 1/3 so far: y = 5 sin ( (1/3)x ) midline is y=?2 , so we have to drop our curve down by 2 units so far: y = 5 sin ( (1/3)x ) - 2 Testing this for x = 0 y = 5(0) - 2 = -2 y = 5sin (x/3) - 2 will do it check: http://...

Algebra 1
I would reduce it first to x^2 + x - 12 = 0 then: a = 1, b = 1, c = -12 so... x = (-1 ± ?(1 - 4(1)(-12))/2 = (-1 ± ?49)/2 = (-1 ± 7)/2 = 3 or -4

Math
I am glad to see that the present value of the house of \$180,000 has nothing to do with the rest of the question. You also did not state what the rate of interest is, but from you partial solution I will surmise it is 7% The questions you asked can be answered as you did, ...

MATHS
for a set of n elements, the number of subsets is 2§n 2^n = 254 solve for n , BUT, since the number of elements must be a whole number, I suspect a typo, or else the question is bogus. 2^8 = 256 2^7 = 128

algerbra 2
2500 e^(.08t) = 7500 e^(.08t) = 3 take ln of both sides and solve for t

math
You should know the basic formulas for these. "the second term of an arithmetic sequence is -2" ---> a+d = -2 "the fourth term is 6" ---> a+5d = 6 subtract the two equations, that will give you d sub back into the first equation to get a then find a+6d

maths
You have to use brackets Surely you meant: (2+5?7)/(2-5?7) = a + ?7 b on the left side, multiply by (2+5?7)/(2+5?7) then match up the coefficients of the rational terms and match the coefficients of the irrational terms let me know what you got 2. I don't know what "5...

maths
since ?448 = 8?7, which is clearly irrational, then -16/8?7 = -2/?7 is clearly irrational You probably meant (?3-1)/(?3+1) , but in the outcome it would not make any difference as to irrational vs rational (?3-1)/(?3+1) = (?3-1)/(?3+1) * (?3-1)/(?3-1) = (3 - 2?3 + 1)/(3-1) = 2...

math
Just fill in the information. "my millions place is 5" ----> 5 xxx xxx "my ten thousands and hundreds place is the smallest odd number" ---> 5 xx1 1xx etc

math
blue marbles ----- x red marbles ---- (3/5)x total = x + (3/5)x = 8x/5 ratio of red : total = 3x/5 : 8x/5 = 3x : 8x = 3 : 8

math
number of bus rides ---- b 2.5b ? 90 b ? 90/2.5 ....

Math
2p + 2e = 150 -----> p + e = 75 p + n = 150 2n = 220 from last equation, solve for n sub that into the second equation to find p sub that into the first equation to find e and the mystery is solved.

math
width -- x length --- x+5 , it said so So, 2 widths + 2 lengths = 114 form your equation, find the width and length Area = length x width

math
Let the 3 consecutive odd numbers be x-2, x, and x+2 x+2 = -4 + 3(x-2) solve for x, and sub into my definitions for the numbers

Math
Please stick to one name 70,000 + 10,000 = ....

Math
What tools do you have? Do you know how to find the distance between two points? Do you know how to find angles of a triangle knowing the sides?

Trigonometry
Factoring looks promising: (1/(sin^2x-cos^2x))-(2/cosx-sinx) = 1/( (sinx+cosx)(sinx-cosx) ) + 2/(sinx-cosx) so (sinx+cosx)(sinx-cosx) is the LCD = 1/( (sinx+cosx)(sinx-cosx) ) + 2(sinx+cosx)/( (sinx+cosx)(sinx-cosx) ) = ( 1 + 2sinx + 2cosx)/(sin^2 x - cos^2 x) You have a typo ...

Math
John's age ---- x Joe's age ---- (3/5)x John's age : Joe's age = x : 3x/5 = 1 : 3/5 = 5 : 3

Math
let's start with "the number of boys is 5 more than the number of girls" ---> b = g+5 and "the number of boys in a class is 10 less than twice the number of girls" ---> b = 2g - 10 so 2g - 10 = g + 5 continue

Math
let the barber's earnings be x let the apprentices' earnings be y Now, form two equations using the facts given, then solve those two equations. let me know what you get

Math
"Amira has four times 7 less than the number of Malik's books" Do you mean Amira has 28 less than Malik ??? Poor phrasing of the question.

math
x(1.1)^3 - x(1.1)^2 = 2100 solve for x hint: x is a common factor.

Math
(3/4)x = 21 solve for x, then take 4/7 of that

Maths
I suggest getting 2 ordered pairs for each equation your graph should look like this http://www.wolframalpha.com/input/?i=x%2B2y%3D9+,+2x-4y%3D2

probability
Why are your repeating your post after it has been answered previously ? As both MathMate and I stated, the theoretical probability of your event is 1/20. Since you are using experimental probability, the choice that comes closest to 1/20 would be it. Theoretical Prob = 1/20...

math
The sum of any two sides must be greater than the third side Let the third side be x x+25 >35 x > 10 x+35 > 25 x > -10 , obviously! 25 + 35 >x x < 60 so 10 < x < 60 So the third side could be any real number between 10 and 60

probability
since you did not list the choices, I can't tell "which of the following is most likely to be the experimental probability". The probability of the event you stated is (1/2)(1/10) = 1/20 which you had

Algebra 2
since the period of your sine curve should be 12 2?/k = 12 k = 6/? your equation probably should have been: f(x)=15.3sin(?x/6)+44.1 instead of what you typed. since Jan ----> x = 0 June ----> x = 5 so just sub in x = 5 and evaluate Let me know what you got.

Math probability
number of ways to get exactly two green = C(12,2) * (28,2) prob(exactly two green) = C(12,2)*C(28,2) / C(40,4) = ... prob(non-yellow) = C(35,4)/C(40,4) =

4?/3 is in quad III (240° so sec 4?/3 = -sec ?/3 cos ?/3 = 1/2, so sec 4?/3 = -2 5?/6 is in quad II (150°) so cot 5?/6 = -cot ?/6 we know tan ?/3 = 1/?3 so cot 5?/6 = -?3 3?/4 is in quad II (135°) tan 3?/4 = -1 sec4?/3*cot5?/6-tan3?/4 = sec(240°) cot(150°...

Maths
I would do it this way: x : y = 9/2 : 16/3 = 27 : 32 y : z = 25/4:17/2 = 25 : 34 The LCM(32,25) = 800 x:y = 675:800 y:z = 800:1088 x:y:z = 675 : 800 : 1088

math
you must know that term(n) = a + (n-1)d, where n is the term number, a is the first term and d is the common difference so, for the first one: n = 10, a = 1/2, d = 1/2 term(1) = 1/2 + 9(1/2) = 5 follow the same method for #2 #3 appears to have a typo, it is neither an ...

Algebra
An important identity is sin (2x) = 2sinxcosx so if sinx cosx = 1/4 2sinx cosx = 1/2 sin (2x) = 1/2 2x = 30° or 2x = 150° x = 15° or x = 75° since the period of sin (2x) = 360°/2 or 180°, other solutions are 15+180 or 195° and 75+180 or 255° in ...

math
k/2 - k/5 - k/6 =2 your LCD = 30, so multiply each term by 30 15k - 6k - 5k = 60 continue ....

math
11:40 + 12:45 = 24:25 so it would be Wednesday at 00:25

math
This is conditional probability Prob(B given A) = P(B | A) = P( A and B)/P(A) = .08/.2 = .....

math
There would be an infinite number of solutions. Any ordered pair that satisfies the equation would be a solution. If you meant: How many real number solutions does the equation 0 = -5x^2+8x-7 have? There would be no real solution, see ... http://www.wolframalpha.com/input/?i=y...

Algebra
well, I would start with: y+3 = 6(x-2) then arrange it to the form you want You did not specify which of the intercept forms you want.

math
Find (g (circle) f) (-5) can also be written as g( f(x) ) the way you typed it: f(-5) = 25+7 = 32 g(32) = 32 + 3/32 = 1027/32 which is none of the choices if you meant: g(x) = (x+3)/x then g(32) = 35/32 , which would be b) What did you do to get a) ??

statistics
Here is the perfect webpage for this type of question http://davidmlane.com/normal.html