Thursday
July 31, 2014

# Posts by STEVE

Total # Posts: 24,044

math [linear equations]
If you can plot points, remember that two points determine a line. So, pick two easy points and plot them. Then draw a line through them. So, what's easy? How about letting x=0 or y=0? That gives us 0-y=5 y = -5 x-0=5 x=5 So, our two points are (0,-5) and (5,0) Now it shou...

College Algebra
Excuse me? You already know that the length is 20 more than the width. So, if the width is 80, the length is 100. Sure enough, 80*100 = 8000 Or, since you know the width is 80, and area = length*width 8000 = 80 * length length=100 Don't forget your algebra I now that you&#...

geometry
Trying to match the question with the choices sure stumps me. Using similar triangles, if we label the vertices of the triangle P,K,F, and the library L, then we have ∆LPF ~ ∆KLP we want the distance LP and FP, and we have LP/2 = FP/KP LP/8 = KP/FP so, LP/2 = 8/LP ...

Math Helppp
you can play around at http://davidmlane.com/hyperstat/z_table.html and do all kinds of neat Z-table stuff. Just enter your mean and std and you can see the areas (probabilities) for various kinds of calculations.

math
#1 ok, though I'd write it as 4.00t + 25.00 Lose all that "x" stuff, if for no other reason than because "x" is often used as a variable. "*" is better for explicit multiplication. #2 where did 350 come from? If t shirts are ordered, then t of...

math problem
the slope of the line is ∆y/∆x, so m = 6/7 Now you have a point and a slope, so the line is y-4 = 6/7 (x-0) or y-10 = 6/7(x-7) and you can massage them to whatever form you like, and convince yourself that they are really the same equation.

math
the fifth-root of x^20 is (x^20)^(1/5) = x^(20 * 1/5) = x^4 Because (x^4)^5 = x^20 Roots are just fractional powers.

math 1 question!!!!!!
I think I'd go with a line plot. Each column will indicate how many days have a particular number of calls. The mode will be the tallest column. Plotting with time intervals could produce the same information, but would require more analysis.

trig
you cannot draw it here. However, you can see them here: http://www.wolframalpha.com/input/?i=plot+y%3Dtan%28x%29%2C+y%3D2cos%28x%29+for+x+%3D+-pi..pi x is in radians, but the graphs look the same for degrees: http://www.wolframalpha.com/input/?i=plot+y%3Dtan%28x*pi%2F180%29%2...

Math
Twenty tires are tested to see if they last as long as the manufacturer claims they do. Three tires fail the test. Two tires are selected at random without replacement for an inspection. Find the probability that both tires fail the test. Which is greater, the probability that...

Trigonometry, can someone check this please
money is no excuse. you evidently have the internet. A simple google search will provide oodles of explanations and examples. One key fact, which I found one of my students was having trouble with: For the purposes of the trig functions, the hypotenuse is not a side! When look...

Trigonometry, can someone check this please
you have posted quite a few of these, and I think you have missed them all. Better review the definitions of the basic trig function. For this one, you want arcsin(50/120)

Algebra/can you ck my work
variance of 4 means std of 2. 5 is below the mean by 2.5 std. P(Z < -2.5) = .0062 = 0.62% Think about it. Your answer indicates that virtually all of the pieces are defective. That would surely not ever be tolerated in a real-world situation. Take a visit to http://davidmla...

college algebra
If two numbers multiply to produce a product of zero, then one of them must be zero. So, if (w-80)(w+100)=0, then either w-80 = 0 w=80 or w+100 = 0 w = -100 Now pick the value that makes sense for this problem. Then check your conclusion by plugging in the value and seeing whe...

college algebra
you have the right idea, but you should have said w(w+20) = 8000 w^2+20w = 8000 w^2+20w-8000 = 0 (w-80)(w+100) = 0 ...

College Algebra
x^2-9x-1 = 0 x^2-9x = 1 x^2 - 9x + 81/4 = 1 + 81/4 (x - 9/2)^2 = 85/4 x - 9/2 = ±√85/2 x = 9/2 ±√85/2 = 1/2 (9±√85) 2x^2+17x+2 = 0 2x^2+17x = -2 2(x^2+17/2 x) = -1 x^2 + 17/2 + 289/16 = -1 + 289/16 (x + 17/4)^2 = 273/16 x + 17/4 = ±...

Algebra 1
(x+a)(x+b) = x^2 + (a+b)x + ab If a>0 and b<0, then ab<0 so there's no way that n can be positive if a and b have different signs.

Simplify Polynomials
18x^2+6+4x-15x^2-4+13x (18-15)x^2 + (4+13)x + (6-4) 3x^2 + 17x + 2 3x^2+6-2x+5x-4x^2+9 (3-4)x^2 + (-2+5)x + (6+9) -x^2 + 3x + 15 3x^2+3x-7x+3-5x^+2 (3-5)x^2 + (3-7)x + (3+2) -2x^2 - 4x + 5 -5 is the coefficient of x -4 is the coefficient of x^2 (m^2-m-4)+(m-5) m^2 + (-1+1)m + ...

Algebra Math
the 3 movies use 3.6+2.8+4.1 = 10.5 GB So, his available space will be 8.25+2.3 = 10.55 GB

algebra math
9pts/6wks = 3/2 pts/wk

check set up trigonometry
Nope. cot28 = x/360

Math
Hmmm. I don't see an obvious application of the law of sines here. However, if we consider the distance directly to the plane, and call the first one x and the second one y, then 1000/x = sin52° 1000/y = sin16° Then we want the distance z given by the law of cosine...

check my set up please, trig
(105-5)/x = sin43°

algebra
1/2 (2x+4)(x+3) = 56 x^2+5x-50 = 0 (x+10)(x-5) = 0 ...

Math
1.5km/16km = 3/32

Calculus
e=2.718 so, the abs error is 2.718-2.68 = 0.038 as a % error, that is .038/e = 1.39%

Geometry
If the point directly below the top of the tree is x feet from the base, then we have h/(x+10) = tan61° h/x = tan78° eliminating x, we get the height h/tan61° - 10 = h/tan78° h = 10(cot61°-cot78°)

Math
csc60° * cot 30° * tan 60° = 2/√3 * √3 * √3 = 2√3 2sec^2 45° cos30° = 2*2*√3/2 = 2√3

Geometry
(25/35)^3 = (5/7)^3

math
4D coefficients require a variable. The 6 is just a constant, not a coefficient of x. 7A Total is just the sum: 6t+2 + 9t-6 = (6+9)t+(2-6) = 15t-4 15A (1.8 x 10^1)(7 x 10^5) = (1.8x7)x10^(1+5) = 12.6x10^6 = 1.26x10^7 18D -x(5x-4) = -x*5x -x(-4) = -5x^2 + 4x Look again at your ...

Algebra
If x is the smaller voltage, then x+32 is the larger one. x + x+32 = 126 Now find x, and you have the smaller voltage.

Maths
since the right side of the intervals are at 9,10,11 just add up (1)* f(9)+f(10)+f(11) Again use the right sides, of width 2/3 each, to get (2/3)*(f(-7/3)+f(-5/3)+f(-1)) Do the left sums similarly, using the appropriate widths.

Geometry
9 edges Euler's formula: V-E+F = 2

math(urgent)
.75p = 1200, so the original price p=1600 Since the profit was 10% of 1200, the cost was 1080. At 1600, the profit would be 520, or 32.5% of the selling price. I gotta admire you syntax on that (c) part. That simply cannot be how the question was worded . . .

MATH GEO URGENT
Since opposite angles are supplementary, we have 2x+4x = 180 x = 30 and the angles are 60,90,120,90

math 1 question!!!!!!

Statistics/ is this how I do it.
add and divide by 5 gives the mean, not the range the range is hi-low = 103-83=20 The mean is 96.4 To find the std, (1) take the difference of each value from the mean (2) square that difference (3) add up all those squares (4) take the square root. That is the std. Better rev...

Math
X is 5 by 10 Y:x = 4/3, so Y is 20/3 by 40/3 and its perimeter is thus 40 or X is 5 by 10, so its perimeter is 30 Y:X = 4:3, so its perimeter is 40

math
6b/3a + b/a = 6b/3a + 3b/3a = 9b/3a = 3b/a or 6b/3a + b/a = 2b/a + b/a = 3b/a

math
well, what's 1000000/600 * 14 ?

math
just multiply by the dimensions: 60m * 25m * 7m = 10500 m^3

math
Looks like this question has been done several times. Check the Related Questions links below.

Algebra 1
Same old parenthesis-free exposition. Surely by now you can factor the expressions and eliminate common factors. Take a look at http://www.wolframalpha.com/input/?i=%28%283h^3+-+6h%29%2F%2810g^2%29%29+*+%28%284g%29%2F%28g^2+-+2g%29+%29 and notice how the parentheses make thing...

math
how many from 11:35 to 12:00? how many from 12:00 to 12:50? Now add them up...

math
34/d = cos 72° now just solve for d.

HELP!!!!
correct

Math HELP
Just read the words and write as symbols. The number of apples in an apple tree n after subtracting by 6, n-6 multiplying by 6, (n-6)*6 dividing by 6, (n-6)*6/6 equals 6. (n-6)*6/6 = 6 n-6 = 6 n = 12 books = x a = x/2 + 1 b = (x-a)/2 + 2 c = (x-a-b)/2 + 3 x-a-b-c = 3 make all ...

MATH
LCD = (k-3)(k+3) = k^2-9

math
well, clearly, a is 11 or 18 b is 5 Now pick the correct answer.

trig
you are correct

Geometry
well, you know that each sphere holds 3392.92/30 = 113.097 so, now you know that 4/3 pi r^3 = 113.097, so r = 3

math
4770(1+r/4)^(4*3) = 8233 (1+r/4)^12 = 1.726 1+r/4 = 1.0465 r/4 = .0465 r = .186 = 18.6%

Math
6700(1+.046/2)^(2*15) = 13253.90

algebra
Do you mean (x^10 + 5x^9 + 4x^8)/(x+2) ? If so, then you have x^8(x^2+5x+4)/(x+2) x^8(x+1)(x+4)/(x+2) but I don't see what that has to do with the Binomial Theorem.

Math
Draw a Venn diagram. Look for the intersections. For this problem, let the two circles represent how many people eat meat an d fish, respectively. In this case, 2 eat both. So, put a 2 in the place where the two circles intersect. Now, since we know that 6 eat meat, and we'...

#1 I get 2n^2/(n-6) #2 (2x^2 + 8x + 6)/x / (2x^2 + 2x)/(x^3 - x^2) 2(x+1)(x+3)/x / 2x(x+1)/x^2(x-1) (x+3)/(x-1) #3 8b^3c/b^2c / (4b^2 + 4b) 8b / 4b(b+1) 2/(b+1) Next time, show your steps. You are evidently taking some wrong turns.

Man, you gotta start using parentheses. Can't you see how hard it is to separate the terms and factors? #1 and #2 are ok #3 3h(h^2-2)/10g^2 * 4g/g(g-2) I suspect a couple of typos, so I will say it's (3g^2-6g)/10g^2 * 4g/(g^2-2g) 3g(g-2)/10g^2 * 4g/g(g-2) 3(g-2)/10g * ...

Trig
If you measure the temperatures and plot them, the curve is sinusoidal. This is mainly because the earth is a sphere rotating in space, relative to the sun. As the sunlight hits the surface, it causes the temperatures to rise, but then the earth turns away, and they fall again...

Algebra
6e^-x = 3 e^-x = 1/2 e^x = 2 x = ln 2 32(1.5)^x = 640 1.5^x = 20 x ln 1.5 = ln 20 x = ln20/ln1.5 and similarly for the others. If you get stuck, come on back and show what steps you took. Just remember that log and exponents are inverse operations. Just as with roots, if you k...

algebra
speed = distance/time So, you want 20/1.2 - 20/1.6 = ?

geometry
The slope of a line does not change. The length expands by the dilation factor.

algebra
so, how many watts per decibel? Divide that into 2.42*10^-5 what's this "cross"? Can't you say "times", or use the multiplication symbol?

math
(1) The sides are x and y, so y = 400-x The area is thus a = xy = x(400-x) (2) If the side x is parallel to the water, x+2y = 400, so y = (400-x)/2 and the area is a = xy = x*(400-x)/2 (3) x+y=200, so the area is a = xy = x(200-x) If you need to find the maximum area, just rem...

algebra
3 = x-3 6 = x As for the other, I can't quite decode your weird text. I can say that ln e = 1 ln √n = 1/2 ln n ln a - ln b = ln(a/b) If you have ln e = ln √6 - 3ln x 1 = ln√6 - ln x^3 1 = ln √(6/x^6) e = √(6/x^6) 6/x^6 = e^2 x^6 = 6/e^2 x = (6...

Precalculus
y=2*pi*x*(25-x)^2

college algebra
If the numbers are x-1,x,x+1, then 3x = 651 x = 217 So, the numbers are 216,217,218 Don't know what was all that stuff with factors of 651. Looks like you need to study what "sum" and "consecutive" mean. The two paychecks are p and .75p. So, p + .75p = ...

Algebra
Reference angles are always measured from the x-axis. So, since 3pi/4 = pi - pi/4, the reference angle is pi/4. Better go back and review that topic some.

college algebra
you are mixing up all kinds of unrelated numbers, and then throwing darts at the calculations. If x is the slower rate, then 3x is the faster rate. So far so good. Now consider that distance = time * speed, and the total distance covered is 64 miles. Since the time for both ri...

MATH
a rational number can be written as a fraction. Any terminating or repeating decimal is also rational. √5 is not rational. There is no fraction which is exactly equal to √5. The decimal value goes on forever and never repeats. It is easy to prove that √5 is i...

Math - incomplete
don't you see that there's something missing here?

Algebra 2
OK. You do understand that if the sides of the rectangle are x and y, then the area is a = xy right? Given the equation of a parabola, can you find the vertex? If y = ax^2+bx+c, then the vertex is at x = -b/2a So, in each case, figure out what x and y are, express the area a a...

Algebra 2
(1) The sides are x and y, so y = 400-x The area is thus a = xy = x(400-x) (2) If the side x is parallel to the water, x+2y = 400, so y = (400-x)/2 and the area is a = xy = x*(400-x)/2 (3) x+y=200, so the area is a = xy = x(200-x) If you need to find the maximum area, just rem...

Geometry
the car moves as far as 10 times the circumference of the wheel. C = pi*d, so C = 22pi = 69.11 inches so, the car moves 691.1 inches, or 57.6 ft

Algebra
correct

Math
v = 15000 * .7^t

Algebra, math
If the plane's speed is p and the wind's speed is w, then 1200/(p+w) = 3 1200/(p-w) = 4 rearrange to get 3p+3w = 1200 4p-4w = 1200 or, p+w = 400 p-w = 300 Now just solve for p and w.

How many terms are in the following polynomial?
the powers don't really matter. The terms are separated by the + and - signs. So, just count them and add 1.

Math
You are correct in counting 2 coefficients. But, they are both positive, so (b) is correct.

College Algebra
better to use time = distance/speed, since we are adding up times here. d/35 + 15 + d/50 = 41 17/350 d = 26 d = 26 * 350/17 d = 9100/17 = 535.29 check: 535.29/35 = 15.294 535.29/50 = 10.706 total driving time is 26 hours, as expected.

MATH PLZ HELP
NO. The answer is 10/14 since there are 10 not-pink erasers out of 14 total.

MATH PLZ HELP
how many of the erasers are not pink? How many total erasers are there? P(~pink) = #~pink/#total

Math
No reason to try to use decimals. Fractions are exact. Your addition is correct.

Maths ,science
12000(1+.065)^5

Trig
The angle is θ, where tanθ = (173-5)/50

statistics
75 is 5 std from the mean of 60, so 1 std must be 3.

Test and Measures
In that case, you need to review what the Z table means. Without that, you have no context. A Z score of zero means that the value is 0 std away from the mean. In this case, it means that the score is the same as the mean, or 65. If such a question is assigned, it can only ind...

Test and Measures
what score is 0 std from the mean of 65?

science
Each mole of Pb(NO3)2 will make one mole of PbO So, how many moles of Pb(NO3)2 are in 4.0 grams? What is the mass of that many moles of PbO

Geometry
you need factors of 39 which differ by 10. I suggest 3 and 13. So, x^2-10x-39 = (x-13)(x+3)

math
initial velocity is 800 ft/s upward it does not change the equation. initial position is 0, since it was fired from the ground (height=0) It falls back to the ground when h=0. So, solve for t in 800t-16t^2 = 0 Solve for t in 800-16t^2 = 6400 (why are there two solutions?) Same...

geometry
If the length is x, then 20/x = sin 75.5° Now just solve for x.

math
1/a + 1/b + 1/c = 2 If we let a <= b <= c, then there's always the easy case where a=1 b=2 c=2 I guess that's the only one, since if any of the three values is 3 or more, then the fractions can't add up to 2.

Algebra
x^2+6x+8 = 0 (x+2)(x+4) = 0 Since (x+a)(x+b) = x^2 + (a+b)x + ab you are looking for factors of 8 that add up to 6. 5w^2-3 = 0 5w^2 = 3 w^2 = 3/5 w = ±√(3/5)

Math
If she started with x dollars, 4/9 x = 20b x = 45b 10b + 5d = 5/9 x We want the ratio d/b. So, 10b + 5d = 5/9 * 45b 10b + 5d = 25b 5d = 15b d/b = 3

math
The cat runs 4/7 as fast as the dog. So, if the dog has to run x meters, the cat will have run 4/7 x during that time. x = 12 + 4/7 x 3/7 x = 12 x = 28 That is, the cat will have run 16 meters while the dog runs 28 meters, having made up the cat's 12-meter head start.

Take a look at the last terms: x and 3x-2 So, for all the other places where x is given, y = 3x-2 Where y is given, x = (y+2)/3 Now just fill in the blanks.

Math
a = -12 d = 3 S = n/2 (-12 + 39) Your mission, should you choose to accept it, is to figure out how many terms there are (n) from -12 to 39

math
If there are x ounces of the cheap tea, then the rest (32-x) is expensive. The cost of the mix must be the total of the costs of the components, so 3.99x + 8.99(32-x) = 5.99*32 Now just solve for x.

algebra
2x-x^3 >= 0 x(2-x^2) >= 0 This function crosses the x-axis at the roots, which are at x = -√2, 0, √2 Now, you know that y is negative for large negative x, so y < 0 in (-∞,-√2) y >= 0 in [-√2,0] y < 0 in (0,√2) y >= 0 in [&...

College Algebra
The common denominator is 2(x-2). If you multiply through by that, you get x - 7*2(x-2) = 1*2 Now just proceed normally: x - 14x + 28 = 2 -13x = -26 x = 2 For the next one, you must be interpreting the equation as 1/(2y) + 4 = 1/(7y) if you multiply by 14y, you get y + 4*14y =...

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