FredR

The preimage is the original position before translation, or P(-1,5)

17 years ago

First off, the word equation implies both sides of the expression are equal. a > b implies a - b > 0 If c is < 0 then c(a - b) < 0 or ca - cb < 0 or ca < cb

17 years ago

The period is the inverse of the frequency, so it would be reduced to half.

17 years ago

ME = 2 sqrt(.56(1-.56)/400) = 2 sqrt(.56(.44)/400) = 2 sqrt(.2464/400) = 2 sqrt(0.000616) = 2 x .0248 = 0.0496 or 4.96 percent margin of sampling error

17 years ago

Low German is an archaic dialect of the german language spoken in northern Germany. The terrain there is relatively flat, hence the name "Low".

17 years ago

The mean of the given numbers is 16.8. SD=sqrt(1/N sum((x-mean)^2)) =sqrt(1/9*((21-16.8)^2+(13-16.8)^2... =7.3

17 years ago

A first order polynomial has just one root: -9x-15 = 0 or -9x = 15 or x = -15/9

17 years ago

Length/Width = = 10.75/18.5 = 1075/1850

17 years ago

Log10x = -7 is the same as 10^-7 = x or x = 0.0000001

17 years ago

a circle has 360 degrees or 2 pi radians, so: radians = 2.7*pi/180

17 years ago

The problem asked for the ratio of length to width, with the length being the smaller of the two numbers. Therefore, the ratio would have to be less than one. If you are allowed to round off, then the nearest whole number ratio would be one. If you want t...

17 years ago

human hrs = 160, or 2x+6y=160 machine hrs = 200, or 2x+9y=200 minimum of 15 pants, or y>=15 must make more shirts than pants, or x>=y the maximum profit is where the equation 25x+55y=profit has a local maximum. One way to determine this is using the 1st d...

17 years ago

If you take a sample of air in your neighborhood and compare the concentration of various contaminants with the maximum allowed values, the maximum allowed values would be the air quality standards. If you measure the output of various compounds from a pi...

17 years ago

screen height = h screen width = w h = w*3/4 (1) 27 = sqrt(h^2+w^2) = sqrt((3w/4)^2+w^2) solve this equation for w calculate h from (1) movie width = screen width movie height = m m=w/2 darkened strip = (h-m)/2

17 years ago

(x-h)^2/a^2+(y-k)^2/b^2=1 is the equation for an ellipse, where (h,k) is the center, a is the semimajor axis, and b is the semiminor axis.

17 years ago

I got a maximum profit of $4200 with 40 pants and 80 shirts.

17 years ago

2x-4y+5=a so rearranging, -4y=a-2x-5 or y=-a/4+2x/4+5/4 The slope of this line is 2/4. A line normal to this would have a slope of minus the inverse, or -4/2, or -2. So the equation of normal line would be: y=-2x

17 years ago

Since the equation is for a line, you really only need two points. If you plug x=0 into the equation, the value of y is also zero. This gives you the first point (0,0). For x=1, y=k, so the second point is (0,k). The graph of the equation is a line passin...

17 years ago

A line from the center of the curve to the midpoint of the chord is 8ft. If h=half of the chord length then 10^2=h^2+8^2, or h=sqrt(10^2-8^2) = 6 the chord length is 2*h or 12ft.

17 years ago

I believe an easement is correct.

17 years ago

Decrease in liabilities of $71,000

17 years ago

Cash 10,000 debit Brown, Equity 10,000 credit

17 years ago

"Record wages expense incurred and to be paid next month" Payable implies an expense you owe.

17 years ago

Assuming compound interest with a period of 1 year, the annual rate would be 4.3%

17 years ago

Frederick the Great

17 years ago

z-score = (raw score - mean)/standard deviation

17 years ago

The three angles of a triangle equal 180 degrees. The third angle is 80 degrees. Therefore, it is not a right triangle.

17 years ago

to convert degrees to rad, multiply by pi and divide by 180.

17 years ago

Taylor series is as follows: f(x)=f(a)+f'(a)(x-a)/1!+f''(a)(x-a)^2/2!+f'''(a)(x-a)^3/3!+...

17 years ago

compound interest formula is: FV=PV(1+(r/n))^(nT) As n approaches infinity, this formula becomes: FV=PV*e^(rt) for the 1st $1000 invested: FV=1000*e^(.07*20) for the 2nd $1000 invested: FV=1000*e^(.07*19) and so on for 20 years. The sum total of future va...

17 years ago

sin(a)/cos(a)=tan(a) tan(a)*cos(a)=sin(a)*cos(a)/cos(a)=sin(a)

17 years ago

if c is one of the legs of the triangle then it equals four. If it is the hypotenuse then it equals: c=sqrt(5^2+3^2)

17 years ago

More information is needed besides the mean to answer the question.

17 years ago

1/2N2+3/2H2 => NH3 or 1/3N2+H2 => 2/3NH3 so 12*2/3 = 8 moles HN3

17 years ago

circumference = pi*D = 10m, so D = 10m/pi = 3.183m radius = D/2 = 1.59m

17 years ago

I'm not sure I understand what angle the 56.4 degrees represents, but assuming it is the difference in horizontal azimuth to the pillar from the 1st setup to the 2nd setup then solution is: If the distance to the pillar is "P" then: tan(56.4)=10/P or P=10...

17 years ago

4^(2x-5)=2^2*(2x-5) 8^(x-3)=2^3*(x-3) so 2(2x-5)=3(x-3) simplifying, 4x-10=3x-9 x=1

17 years ago

the formula for water is H2O. Therefore, two atoms of hydrogen are released for each atom of oxygen. You could test the gases by putting them in a balloon and seeing which one floats.

17 years ago

two more equations are: m1+m2=M v2-v1=20m/s

17 years ago

Area = A x B Total length = 3000 = A + 2B B = (3000-A)/2 so, Area = A x (3000-A)/2 = = 3000A/2 - (1/2)A^2 take 1st derivative 0 = 1500 - A and solve for A A = 1500 and B = 750

15 years ago

dx/dt = 2 inches/min V = x^3 so, dV/dt = 2^3 = 8 cubic inches/min

15 years ago

y = (x-2)^2 y = x^2-4x -4 dy = 2xdx - 4dx so, dy/dx = 2x-4 dx/dt = 2 so, dy/dt = dy/dx dx/dt = 2(2x-4) = 4x-8 for x=1 then dy/dt = 4(1)-8 = -4 units per second

15 years ago

(a) 3y = x - 10 substitute in the 2nd equation 3(x-2) = x - 10 3x - 6 = x - 10 simplifing... 2x = -4 or x = -2 and y = -4 this is a unique solution (b) this system has infinitely many solutions and cannot be solved without more information. 3x + 3y = 15 d...

15 years ago

the probability that the 1st marble is red is 10/13. So, the probability that both marbles are red is (10/13)^2 or (100/169)

15 years ago

Moles of solute = 16 g / 60 g/M = = 0.267 M volume of H2O = 39g/1.3 g/ml = 30 ml = 0.03 l molarity = 0.267 M / 0.03 l = 8.89 M/l

15 years ago

It would take 10 minutes.

15 years ago

sin(a+b)/cos(a)cos(b) = = (sin(a)cos(b)+cos(a)sin(b))/cos(a)cos(b) = sin(a)cos(b)/(cos(a)cos(b) + cos(a)sin(b)/(cos(a)cos(b) = sin(a)/cos(a) + sin(b)/cos(b) = tan(a) + tan(b)

15 years ago

dmA/dt = cmB^2/mA where c is a constant mB=m-mA so dmA/dt = c (m-mA)^2/mA = (c/mA)(mA^2-2mmA+m^2) = cmA-2cm+cm^2/mA integrate with respect to t

15 years ago

cos(x)=15/17 so x = arccos(15/17) tan(76) = 13/x so x = 13/tan(76)

15 years ago

c = # of chest freezers u = # of upright freezers c+u>=100 or u >= 100-c assume a total of 100 units cost = 250c + 400u = 250c +400(100-c) = 250c + 40000 - 400c = 40000 - 150c = 800 - 3c so obviously the more type c units, the lower the total cost. profit...

15 years ago

A = amt invested at 8.5% B = amt invested at 10% A + B = 50000 or A = 50000 - B income = 0.085A + 0.10B = 4700 substitute A in terms of B and solve

15 years ago

for example, for x = 2, y = 0 x = 3, y = -1/3 x = 4, y = -2/3 x = 5, y = -1

15 years ago

= (y/3)(y^2+5y+6) = (y/3)(y+2)(y+3)

15 years ago

= (18+4)r^2 +7s = 22r^2+7s

15 years ago

the graph of y=sin(theta) is moved vertically along the y axis a distance of q to obtain y=sin(theta)+q.

15 years ago

The formulas given look like they are for sinusoids and not circles.

15 years ago

16-15.2 = 0.8 0.8/0.03 = n = 26 standard deviations so, erf(n/sqrt(2)) = approximately 1 so, 50% of the data would be between 15.2 and 16.

15 years ago

x = original # of tickets y = original price you have 2 equations: xy = 180 (x-2)(y+9)=180+36 substitute equation 1 into 2 and solve.

15 years ago

# of ways of selecting winning quintuple = permutations of 5 objects = 5! = 5 x 4 x 3 x 2 x 1 probability of winning = n!/(r!(n-r)!) = 44!/(5!39!)

15 years ago

9cos^2(t)+3cos(t)=0 subtract 3cos(t) from both sides 9cos^2(t)=-3cos(t) divide both sides by 3cos(t) 3cos(t)=-1 cos(t)=-1/3 t=arccos(-1/3)

15 years ago

1) it is not correct. The second term would be log3(-2) and you can't take the log of a negative number. 2) it is not correct. The base angle would be 45 degrees, so the cotangent would be 1.

15 years ago

csc=1/sin cot=cos/sin so, csc^2-1/cotcsc = ((1/sin^2)-1)sin/(cos/sin) = sin((sin/sin^2)-sin)/(cos) = (sin^2/sin^2-sin^2)/cos = (1-sin^2)/cos = cos^2/cos = cos A ((sin^2/sin^2)-sin/(sin^2 cos)

15 years ago

NO. 500 = A - A x 0.28 = A (1-.28) = .72A so, A = 500/0.72 = 694

15 years ago

dist from station to trains = D ta = time in hours from when A passes station to when trains A & B meet. D = 80ta D = 88(ta-15/60) solve for ta Time at catch-up = 1:20 AM + ta

15 years ago

yes, it could be. You just need to change the sign, so you would have 8-y over y-4 PLUS 7y-9 over y-4

15 years ago

Permutations of 9 objects taken 5 at a time = 9!/(9-5)! where 4! = 4x3x2x1 and 9! = 9x8x7x6x5x4x3x2x1

15 years ago

It looks right to me. The easiest way to check is to plug the number back into the formula: e^.6931 = 2 2*2-3 = 4-3 = 1

15 years ago

a = angular acceleration I = rotational inertia w = angular velocity v = linear velocity Torque = RxFT = Ia so, a = RxFT/I = (R/I)(4t-0.10t^2) w = integral(a) with respect to t v= wR

15 years ago

180+arctan(12/-5) = 112.6

15 years ago

if you are traveling along the leg of the star, the deflection angle is the angle you have to turn to get to the next leg. d = deflection angle at a point = 180 - 12 = 168 since there are points, the total point deflection angle at the points is 1680. x =...

15 years ago

12.60 - 23.00 = A A / -1.30 = standard deviation

15 years ago

Newton's law of gravitation: F = G m1 m2 /r^2 let m2 = mass of ice cube and s = G m1/r^2 so, F = s m2 rearranging, s = m2/F let V = orbital speed centripetal acceleration = V^2/r For an object to remain in orbit s must equal the centripetal acceleration s...

15 years ago

using the Pythagorean theorem, opposite side = sqrt(13^2-12^2) sin x = opposite side / 13 tan x = opposite side / 12

15 years ago

It doesn't look right to me sec Q - 1/sec Q = 1/cos - cos = 1/cos - cos^2/cos = (1-cos^2)/cos = sin^2/cos

15 years ago

rearranging the given line, y = (9/5)x - 4/5 (1) which has the form y = mx + b (2) where m is the slope and b is the y intercept. The new line would have the same slope to be parallel, so it would have the form: y = (9/5)x + b (3) to solve for b, input th...

15 years ago

let the 3 dimensions be a, b, and c where a and b are the bottom edges and c is the height. v is the volume s is the surface area a = 7b v = abc = 7b^2c or rearranging, c = v/7b^2 s = ab + 2ac + 2bc = 7b^2 + 14bc + 2bc = 7b^2 + 16bc = 7b^2 + 16bv/7b^2 = 7...

15 years ago

if you bisect one of the angles, you have a right triangle with a hypotenuse of 1 cm and a short leg of 0.5 cm. Using the Pythagorean theorem, the height would be: height = square root (1^2 - 0.5^2)

15 years ago

It could be interpreted as the azimuth, which in surveying applications is typically measured in a clockwise direction from north.

15 years ago

Oops. Thanks for the correction.

15 years ago

Assuming an ideal spring (linear) and using Hooke's law, the force generated by the spring is: F = -kx (1) where x is the distance the spring is stretched from the rest position. So, substituting the info into (1) you get: -10 = -k(2) or k = 5 lb/in work...

15 years ago

From 1920 to 1980 is 60 years. The record was shortened by 1.2 seconds. The slope of the line is the rise over the run, or: -1.2/60 for t=0, R(t) = 46.6 so the y intercept is 46.6. The format of a line is y = mx + b where m is the slope and b is the y int...

15 years ago

a)centripetal acceleration is v^2/r. In this case, v is 30 mi/hr and r = 200 ft. The inertial force would be: F = ma = mv^2/r (1) This would be the friction force required to keep the car on its path. b) The static friction is: F = uN (2) where u is the s...

15 years ago

cos(A) -1 = 0 or cos(A) = 1 arccos(1) = A = 0

15 years ago

sin = opposite / hypotenuse so, hypotenuse = 8 opposite leg = 7 adjacent leg = sqrt(8^2 - 7^2) = sqrt(15) 1/cot = tan tan = opposite / adjacent = 7/sqrt(15) in the 4th quadrant the tangent is negative, so add a minus sign: 1/cot(theta) = -7/sqrt(15)

15 years ago

It doesn't seem like there is enough information to determine the answer

15 years ago

distance = velocity x time or time = distance / velocity total time=d1/v1+d2/v2=2.5 hrs (1) where d1 = car distance = 30 (2) v1 = car speed d2 = train distance = 120 - d1 (3) v2 = train velocity = v1+20 (4) combine (1), (2), (3), and (4) and solve for v1

15 years ago

x = original # of pieces w = gave to wife = 10x/100 m = gave to meg = 3 (x-w-m)/4 = j = gave to joe 18 = x - w - m - j combine and solve for x

15 years ago

A+B = 60 (1) A/3 = B/2 A = 3B/2 (2) combine (1) and (2) 3B/2+B = 60 3B/2+2B/2 = 60 5B/2 = 60 B = 24 A = 36

15 years ago

u = 2d or u - 2d = 0 u + d = 5 so the matrix would be 1 -2 0 1 1 5 add -1 times the 1st row to the 2nd row. Then you get 1 -2 0 0 3 5 multiply the 2nd row by 1/3: 1 -2 0 0 1 5/3 The 2nd row tells us that d = 5/3, so u = 10/3

15 years ago