# Posts by Reiny

Total # Posts: 38,776

**Maths**

Let's compare the value of $1 at the end of 10 years at both types of interest: compound: Value = 1(1.06)^10 simple: let the rate be r interest = 1(10)(r) = 10r value = 1 + 10r so 1 + 10r = 1.06^10 10r = 1.790847... - 1 r = .0790847... rate = 7.91% to 2 decimals

**Math**

the general term of an AS is a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms so : a = 0 a+9d = 15 0+9d = 15 d = 15/9 = 5/3 For 10 to be one of the terms a + (n-1)d = 10 0 + (n-1)(5/3) = 10 times 3: 5(n-1) = 30 5n-5 = 30 5n = 35 n...

**Algebra**

(x-1/2)-(x-2/2)+(x-3/2)-...-(x-100/2) = x - 1/2 - x + 2/2 + x - 3/2 - .... - x + 100/2 = x-x+x-x+x-....-x -1/2 + 2/2 - 3/2 - ... + 100/2 looking at the last term, we see there are 100 terms, so the x's drop out = -1/2 + 2/2 - 3/2 - ... + 100/2 = (-1/2)(1 - 2 + 3 - .... + ...

**3rd Math fraction answer conflict**

You are correct at 36/7 another way to look at it: there are 12 half-hours in 6 hours. Have Katie look at a clock. So the length is 12*(6/7) = 36/7 inches

**Math**

In your trig repertoire , you should know the 3 basic trig values of angles 0°, 30°, 45°, 60°, 90° by knowing the ratio of sides of the 30-60-90 and the 45-45-90 degree triangles. This is very very important in any further study of trig. I will do the only...

**Math**

FG----> 25+6.5n, where n is the number of games GB ---> 57 + 2.5n 25 + 6.5n = 57 + 2.5n 6.5n - 2.5n = 57 - 25 carry on

**Math**

hint: sure looks like the coach is collecting $22 from each player. So on Friday, he collects from 2 players, or $ .....? So from p players, he collects $ .... ?

**Math Help**

The order does not matter, so this is a "combination" problem Number of possible 4 cards from the reds = C(26,4) or 26!/(22!4!) number of possible 4 cards from all = C(52,4) or 52!/(48!4!) prob(your event = C(26,4)/C(52,4) = 14950/270725 = 46/833 = appr .055

**Math (Probability)**

Prob(a one) = 1/6 prob(a one) twice = (1/6)(1/6) = (1/6)^2 .. prob(a one) ten times = (1/6)^10 = 1/60466176 = appr .000000016 These are independent events, that is, the die has no memory of what happened before, so each roll is a new event e.g. suppose we flip a coin 3 times. ...

**Math - Calc/Algebra/Trig**

your derivative is ok -4cos^2(x)sin(x)+sin(x) = 0 sinx( -4cos^2 x + 1 ) = 0 sinx = 0 ----> x = 0, ±?, ±2?, ... or 4cos^2 x = 1 cos^2 x = 1/4 cosx = ± 1/2 so x is in any of the 4 quadrants x = ±?/3, ±2?/3 , 4?/3, ±5?/3

**math**

"The sum of the 9th term is 117" makes no sense. Do you mean : the sum of the first 9 terms is 117 or The 9th term is 117 ?

**Math(Please help!)**

You should have an idea what y = 1/x looks like, y = 1/(x+6) simply shifts the y = 1/x six units to the left. the 5 instead of the 1 means that the y value is 5 times as great, so it rises faster or there is a vertical stretch by a factor of 5 e.g. the point (1,1) on y = 1/x ...

**Math**

From your diagram, you should see than tan30° = 20/x, where x is the distance you need. However, a tower 20 cm high ???? You probably meant 20 metres.

**Math**

7. correct 8. area = 29 side = ?29 which is between 5 and 6 since 5^2 = 25 and 6^2= 36 , and your 29 falls between those two

**Algebra**

consecutive odd numbers are 2 apart let the first be x then the 2nd is x+2 and the third is x+4 "the sum of 4 times the largest is -191" makes no sense, "sum" is the result of addition , not multiplication If you meant that the result of 4 times the largest...

**math**

3/4x+5/6x=5x-125/3 the LCD is 12, so multiply each term by 12 9x + 10x = 60x - 500 easy from here.... 2(3x-7)+4(3x+2)=6(5x+9)+3 6x - 14 + 12x + 8 = 30x + 54 + 3 I am sure you an handle it from here

**Math**

For 1. , just replace the x with a+b 2. f(g(x)) = f(2x+5) = -2(2x+5)

**Math**

sum = -1/12 - 4/9 = -19/36 difference = -1/12 - (-4/9) = 13/36 (-19/36) ÷ (13/36 = -19/13

**Algebra/ please help!!!!**

40 hrs a week at $17.00 for 52 weeks = $35,360 Where does the $28,285.28 come from? No idea what the rest of the stuff is supposed to mean.

**Algebra/ please help!!!!**

So much missing information! "WAGE---$ 17.00-an hour---------ANUALLY---28,285.28" --- how many hours a week, how many working weeks in a year? "APARTMENT VALUE 17.34hrs/pay period towards an apartment value of $934/month----ANUALLY---$11,208----TOTAL-------$39,...

**algebra**

6123/x = x + (1/2)x/x times x 6123 = x^2 + (1/2)x times 2 2x^2 + x - 12246 = 0 (x - 78)(2x + 157) = 0 x = 78 or x = -157 check: 6123/78 = 78 + remainder of 39 , which is 1/2 of 78 6123/-157 ? -157 + (????) the divisor is 78

**Math(Please help!)**

Your first step should have been to simplify the expression: (x^2+x-6)/(x^2-9) = (x+3)(x-2)/( (x+3)(x-3) ) = (x-2)/(x-3), x ? 3 take over

**IB Calculus**

since a(t) = 2t - 16 when a(t) = 0 t = 8 v(8) = 64 - 16(8) + 4 = ......

**Math**

Find the volume of the large box Find the volume of the inner box Subtract the two results.

**Math and Please Help!**

nope, look up distributive property in your text or notes and look up examples

**Calculus**

V = (4/3)?r^3 dV/dt = 4? r^2 dr/dt plug in the given stuff 50 = 4?(100)^2 dr/dt dr/dt = 50/(4?(100)^2 ) = .... cm/min

**math**

The first three are rational numbers. For the last one, no idea what the ## in 250## stands for

**Math**

original: Andy ---- a Jack ----- j after first give-away: Andy ---- a/2 Jack ----- j + a/2 after 2nd give-away: Jack --- (2/3)(j + a/2) Andy ---- a/2 + (1/3)(j+a/2) (2/3)(j + a/2) = 20 2(j + a/2) = 60 2j + a = 60 *** a/2 + (1/3)(j+a/2) = 20 times 6 3a + 2(j + a/2) = 120 3a + ...

**math**

The interest in the first year would simply be .1(14,000) = $1,400 The fact of 5 equal payments for 5 years has nothing to do with this. Now for the 2nd year's interest, we need to do further calculations

**statistics and probability**

I agree with it, but I find I would like to meet that .8144 of a person.

**Math**

Hasn't the minute hand completed 1/4 of a rotation? Just look at the face of a clock

**Math**

let f(x) = x^3 + kx - 4 if x-2 is a factor, then f(2) = 0 f(2) = 8 + 2k - 4 = 0 2k = -4 k = -2

**Grade 6: money and measures**

combined rate is 15 litres per minute. amount in 6 min = 6(15) = 90 litres. volume in tank = 2400h cm^3, where h is the height = 2.4h litres, since 1000 c^3 = 1 litre so 2.4h = 90 h = 90/2.4 cm = 37.5 cm <--- the depth of water after both taps ran for 6 minutes b) Does the ...

**algebra**

let the time form 11:00 to the time of overtaking be t hrs distance gone by the truck = 54t distance gone by the van = 64(t-1) but they went the same distance, so ... 54t = 64(t-1) solve for t, and add it to 11:00

**math**

3s + 4j = 360 s + 3j = 220 -----> s = 220 - 3j sub that into the first and solve for j then find s

**algebra**

Plane's speed --- x mph wind speed ----- y mph 2(x-y) = 180 x-y = 90 1(x+y) = 180 x+y = 180 add them: 2x = 270 x = 135 back in x+y= 180 135+y=180 y = 45 state a proper conclusion.

**Algebra**

"and" usually suggests addition, e.g. what is 5 and 6 ? let the number be n "the sum of 4 times a number and 30" --> 4n+30 now twice that ---> 2(4n+30) = 8n + 60

**Cal 1**

S(-3) = 6(-27) + 8(9) + 5 = -85 S(-1) = 6(-1) + 8 + 5 = 7 avg velocity = (7 + 85)/(-1 + 3) = 46

**Math-Geometry**

Good job, you have 1. shown that opposite sides are parallel 2. adjacent sides form a right angle.

**Math-Geometry**

I would first of all plot the points. That would give you an idea which sides would form the rectangle. Since in a rectangle: 1. opposite sides are parallel, you can show this by finding the slopes 2. slopes of adjacent sides are negative reciprocals of each other. Use your ...

**Math**

or number of bags needed --- n amount of peanuts he bought 2n lbs number of bags he needs to buy = 2n/(5/6) = 12n/5 <---- must be a whole number the smallest number of n to make it so, is n = 5 number of bags needed = 5

**Math**

all 3 digit number divisible by 6: 102 108 114 120 126 132 138 144...978 984 990 996 How many of those are there ? (996-102)/6 + 1 = 150 or: An AG with a=102, d = 6, term(n) = 996 term(n) = a+(n-1)d 996 = 102 + 6(n-1) 6n-6 = 894 6n = 900 n = 150 Of those which ARE divisible by...

**math**

so shaded part = 6/20 = 3/10 or 30%

**math**

prob(yellow) = 1/6= x/36, so x = 6 , 6 yellows prob(orange) = 3/4 = y/36, so y = 27, 27 orange remaining 3 must be orange or 1/6 + 3/4 = 11/12 leaving 1/12 for the purple (1/12)(36) = 3 purple

**Maths**

midpoint of (-5,12) and (-1,-12) = ( (-5-1)/2 , (12-12)/2 )) = (-3, 0) I will use vectors to find the points of trisection i.e. in the ratio of 1:2 one point = (1/3)(7,10) + (2/3)(-8,-5) = (7/3, 10/3) + (-16/3 , -10/3) = (-9/3 , 0) = (-3,0) which is the midpoint of above other...

**Math**

In your sketch that you made, you will notice that the diagonals right-bisect each other, creating 4 congruent right-angled triangles. Each of them has angles 30:60:90 degrees the ratio of sides for such a triangle is 1:?3:2 where 2 is the hypotenuse Our hypotenuse is 8 so the...

**math**

I am sure you meant: f(x) = e^x b) f(6) = e^6 f(4) = e^4 avg rate of change from x=4 to x=6 = (e^6 - e^4)/(6-4) = ... , use your calculator

**Algebra**

invested at 2% --- x invested at 3% --- 7000-x .02x + .03(7000-x) = 184 carry on

**Trigonometry**

When you say "a 10 inch wheel" I will assume you have a radius of 10 arc length = rØ, where Ø is in radians 225° = 5?/4 radians 450 = r(5?/4) r = 360/? inches = appr 114.59 inches (big wheel) A point on the smaller wheel has to move 450 inches as ...

**Algebra**

4^4 x 8^8 x 16^16 are all powers of 2 = (2^2)^4 x (2^3)^8 x (2^4)^16 = 2^8 x 2^24 x 2^64 = 2^96 so what do you think?

**Algebra**

looks pretty standard to me. Perhaps you mean: |y|-2=0 |y| = 2 y = 2 or y = -2

**college algebra**

from your data, if h is the height above the water h = -4.9t^2 + 28t + 38 set h = 7 4.9t^2 - 28t - 31 = 0 use the quadratic formula to solve for t, use the positive result

**college math**

At a time of t hours after the action started, - distance remaining for the northbound car before reaching intersection is 3 - 20t - distance remaining for the westbound car before reaching the intersection is 4 - 30t let d be the distance between them d^2= (3-20t)^2 + (4-30t...

**Algebra (answer check)**

y = -x^2 + 2x + 5 the x of the vertex is -b/(2a) = -2/(-2) = 1 plug in x = -1, y = -1+2+5 = 6 vertex is (1,6) -4x^2+7x+5=0 4x^2 - 7x - 5 = 0 x = (7 ± ?129)/8 = appr (7±11)/8 = appr 18/8 or -4/8 or appr 2.5 or -1/2 your choice is good 5x^2 - 20 = 15x x^2 - 3x - 4...

**Math; Calculus**

from the given data: h = -16t^2 + 55t + 6 this is a parabola, we need its vertex. the t of the vertex is -b/(2a) = -55/-32 = 55/32 seconds plug that into equation to find max height it is in the air for h > 0 let's see when h = 0 0 = -16t^2 + 55t + 6 16t^2 - 55t - 6 = 0...

**Algebra**

speed of current --- y speed of swimming ---- x x+y = 5 x-y = 2 solve, I suggest adding them, etc

**Algebra**

amount of cashews --- x lbs amount of raisins ---- 4.5 - x lbs 2.5x + 1.25(4.5-x) = 2(4.5)

**math**

let the second be x ft long then the first is x+4.25 the third is x+2.24 x + x+4.25 + x+2.24 = 10 carry on

**math**

cost price = 525 18 eggs = 1.5 dozen selling price = 23.5(26) = ... profit or loss = selling price - 525 = .... percent profit = ....

**math**

collins meant: (a+b+c)/2 = s

**number base help plz**

Steve is simply using the definition of a number with a different base. Just like 57810 = 5(10^2) + 7(10^1) + 8(10^0) 1234 = 1(4^2) + 2(4) + 3 = 16 + 8 + 3 = 24 + 3 ---> Steve noticed the multiples of 8 = 3(8) + 3 = 338

**Math**

Say what ?

**algebra**

your function is a straight line - from your equation we can tell that the slope is -2 and the line passes through (-8,7) All you need is another point and you can draw it. Why not pick something nice like x = 0 So we get: y-7 = -2(8) y = -16+7 = -9 take over

**Calculus**

A rough sketch of the two functions y = x , and y = 1+sinx will show that y = x clearly crosses y = 1 + sinx only once. So your statement is not correct. evidence: http://www.wolframalpha.com/input/?i=solve+x%3D1%2Bsin(x)

**Algebra**

x/3 + 5 = 3x/2 times 6. 2x + 30 = 9x 7x = 30 x = 30/7 check: (1/3)(30/7) + 5 = 45/7 3/2(30/7) = 45/7 my answer is correct

**math**

They do not intersect at (3,4) (3,4) does not satisfy g(x) = 2^x - 1 RS = 2^3 - 1 = 7 LS = 4, no good (3,4) work in f(x) = -5/3x + 9 RS = -5/3(3) + 9 = 4 So it does work in the other equation. did you mean g(x) = 2^(x-1) ?? RS = 2^2 = 4 = RS you must have meant that! so ...

**math**

Did you make a sketch?? The difference in their connection points is 4 m. and you have a triangle with base 10, height 4 and missing hypotenuse x^2 = 4^2 + 10^2 carry on

**Math**

Maria "guessed" correctly, I got the same answer. So none of the answers supplied are correct. Either typo or misprint.

**Matj**

I will assume the difference to be between pairs of coupons possible cases: 5,1 6,1 6,2 7,1 7,2 7,3 8,1 8,2 8,3 8,4 9,1 9,2 9,3 9,4 9,5 10,1 10,2 10,3 10,4 10,5 10,6 total 21 number of pairs = C(10,2) = 45 prob(of your event) = 21/45 = 7/15

**math**

Hint: The diagonals of a rhombus right-bisect each other. Another hint: Make a sketch. What type of triangles do you see? Do you know the legs of those triangles?

**Math**

What is the LCM of 2, 6, and 9 ?

**algebra**

time spent cyling --- x hrs times spent running --- (2.5 - x) hrs 10x + 6(2.5-x) = 21 carry on

**math**

Scott is absolutely right, if you had taken the 10 seconds to complete his calculations.

**n**

Let's use a sine curve, we could use a cosine as well amplitude is 10, so h = 10sin kt the period is 6 minutes, so 2?/k = 6 ----> k = ?/3 sofar: h = 10sin (?/3 t) this has a min of -10, but our min is to be +1, so we have to raise everything up by 11 so far: h = 10sin...

**Math**

Number of Yen remaining = 110682 - 87438.78 = 23243.22 $1100US = 110682 Yen 1 Yen = 1100/110682 = $.009938382 so 23243.22 Yen = .009938382(23243.22) = $231 or 1100/110682 = x/23243.22 x = 231

**math**

correct, only a = 0 if x = 0 then in x/y=2 0/y = 2, which cannot be, so x ? 0 if y = 0, we would be dividing by zero to get 2, which is rather silly, so y ? 0 if a = 0, x/y =2 has nothing to do with it, but x*y*0 = 0, which is true

**math**

size of original piece of material: x cm by x cm after cut-out base is (x-8) by (x-8) height = x V = x(x-8)^2 = 576 x^3 - 16x^2 + 64x - 576 = 0 Nasty equation to solve. Have you learned any methods to solve a cubic? Newton's Method is probably the best way, but you have to...

**Algebra**

x=3, so Alysia is 3 and Adam is 33 3+33 = 36

**Algebra**

Ms. Sue meant to say: x + 30+x = 36

**Algebra 1**

Yes, except since this is money in dollars you would round it to the nearest cent. $500,637.91

**Algebra 1**

What is 20000(1.05)^66 ?

**Math**

rate of first ---- x rate of 2nd ---- y 1500(3)x - 1500(3)y = 13.50 x-y = .003 the difference is .3%

**polynomial**

I don't understand how looking at the graph of y=2x³+x²+x+8 , which does not have a "nice" rational solution, will help you in solving y = 2x^3 + x^2 - x + 5. The latter also has an irrational solution. http://www.wolframalpha.com/input/?i=y%3D2x%C2%B3%...

**Maths**

you are solving, 6750(1.05)^t = 8000 1.05^t = 1.185185.. take log of both sides, and use log rules t = log 1.185185.../log 1.05 = 3.482239 so that is 3 years and .482239 years multiply the decimal part by 12 to get 3 years, 5.7868.. months so 3 years, 5 months and .7868 months...

**maths**

graphing utility?? why? 6sinx + 3cosx = 0 divide by cosx 6sinx/cosx + 3 = 0 6tanx = -3 tanx = -1/2 we know that the tangent is negative in II or IV and we know tan (.4636) = +.5 x = ?-.4636 = appr 2.678 or x = 2? - .4636 = appr 5.820 If you insist: http://www.wolframalpha.com/...

**Math**

12.5 litres takes the car 168.75 km then 1 L takes the car 168.75/12.5 km then 15 L will take the car .....

**Math**

Why do you think this question might deal with the concept of a Lowest Common Multiple ?

**Math**

How many square cm are there in 1 square metre? - then how many in 1/2 square metre ?

**Math**

simplify and re-arrange ... y-5 = (2/7)(x-11)

**Math**

of course it isn't right x = 3 would be a vertical line. A quick sketch will show you that your 2 points do not lie along a vertical line slope = m = (-8-8)/(5-3) = -16/2 = -8 equation: y-8 = -8(x-3) re-arrange to whatever form you learned.

**Slopes**

slope = m = (7-4)/(-5-0) = ... once you find m, replace it in the equation y-4 = m(x+6) arrange into the form that you are familiar with.

**Algebra II**

Don't understand your question. Don't understand your answer.

**Math**

p5^y + 5^-y = 5 p5^y + 1/5^y = 5 now replace px + 1/x = 5 times x px^2 + 1 = 5x px^2 - 5x + 1 = 0 which is what we want

**calculus**

V= (4/3)? r^3 dV/dt = 4? r^2 dr/dt when V = 64 64 = (4/3)? r^3 48/? = r^3 r = (48/?)^(1/3) = appr 2.4814 ---> I stored the 10 decimal answer in dV/dt = 4? r^2 dr/dt 20 = 4?(2.4814..)^2 dr/dt dr/dt = appr .2585 inches/min

**Math**

You must know the binomial expansion and the general term of the expansion!! 5th term = C(9,4) (4^4)(-x/5)^5 = 126 (256)(-x^5)/3125 = -32256/3125 x^5 oops, just did in descending powers, so C(9,5) 4^5 (-x/5)^4 = 126(1024)(x^4/625) = 129024/625 x^4 , in ascending order

**Maths**

distance at original speed = (1/4)(60 km = 15 km time at reduced speed = 15/36 hours = 5/12 hr = 25 minutes

**Geometry**

clearly the largest circle will have a diameter of 4 ft, or a radius of 2 ft area = ?(2^2) = 4? ft^2 = ...... In this time of calculators, using 3.14 for ? and then rounding off that rounded constant is rather silly. Most calculators have a special key for ?, use it.

**Maths**

correct your spelling and incomprehensible gibberish

**Math**

Yes, could have been easily checked by taking 20% of it.

**Math**

regular price ---- x it said the 20% discount came to $15 well, .2x = 15 x = 15/.2 = ......