Let s = the number of soldiers produced each week and t = the number of trains, The Profit equation is: P = $4s + $2.5t The constraints are: 3s + 2t ≤ 120 (No more than 120 hours of finishing labor available per week) 2s +...

Linear program (answer)

Let s = the number of soldiers produced each week and t = the number of trains, The Profit equation is: P = $4s + $2.5t The constraints are: 3s + 2t ≤ 120 (No more than 120 hours of finishing labor available per week) 2s +...

Let v = the number of vans and m = the number of motorcycles. The ratio of the number of vans to the number of motorcycles is 11:15 v/m = 11/15 v = (11/15)m Each van has 4 wheels and each motorcycle has 2 wheels.All of the vans and motorcycles have a total...

The equation of a parabola is a quadratic. Use the vertex form: y = a(x-h)2 + k where "a" is a constant (to be determined) and (h,k) is the location of the vertex. The problem tells you the location of the vertex, (h,k) = (2,1) so the equation is: y...

Explain E=mc2 (answer)

E = mc2 E = energy m = mass c = the speed of light E = mc2 is the mass-energy equivalence equation. It tells us that mass and energy are the same thing (energy) and provides the exchange rate between the two (c2). It's like dollars and euros are both types...

Average total cost question (answer)

Average cost = 8000/x + 35 + 0.7x. (a) Express the average-cost formula as a single fraction. You need to put all three terms over a common denominator, in this case x: Average cost = 8000/x + 35x/x + 0.7x2/x = (0.7x2+35x+8000)/x (b) Write...

Is this table linear or nonlinear? (answer)

It is a "function" because each x-value has one and only one y-value. However, it is a non-linear function. A linear function has a constant rate of change, Δy/Δx.

A = (1/2)*b*h 63 = (1/2)*3h*h Can you finish it from here?

polynomial (answer)

t is the elapsed time since the athlete stopped exercising. So when he first stops exercising the elapsed time is zero. Plug t=0 into the polynomial to get the heart rate

Speed = miles/hour Miles = 6 Hours = 2/3 + 1/6 = 4/6 + 1/6 = 5/6 Speed = (6 miles)/(5/6 hours) Can you finish it from here?

If the slant height of the cone is 24 cm and its height is 21 cm .then find the volume of the cone . (answer)

The volume of a cone is: V = pi*r2*h/3 where: V = Volume pi = 3.14159... r == radius of the base circle of the cone h = height = 21 cm We know everything except for r, the radius of the base circle. We are given the slant height,...

Dividing inequality (answer)

The answer is B. If you multiply or divide both sides of an inequality by a negative number, it reverses the inequality. This is an important rule that you need to remember when working with inequalities. Example: -4x > 24 -4x/-4 < 24/-4 ...

Geometry Math (answer)

You don't say whether the rotation is clockwise or counterclockwise - it makes a difference. Here are the rules: For 270o CW, (x, y) rotates to (-y, x) For 270o CCW, (x, y) rotates to (y, -x) Check out this Wyzant resource on geometric transformations. https://www.wyzant.c...

Polynomial Function (answer)

Just replace the x with 3a then do the operations f(x) = 2x4 - x3 + 6x2 - 7x - 5 f(3a) = 2(3a)4 - (3a)3 + 6(3a)2 - 7(3a) - 5 Can you finish it from here? Hint: (3a)4 = 34*a4 = 81a4

The answer is (b), Mass is the measure of the amount of matter in an object.

h(b) = h0(0.8)b where: h(b) = the height of the ball after b bounces < 1 m h0 = initial height of the ball = 9 m b = number of bounces h(b) = h0(0.8)b 1 = 9*(0.8)b 1/9 = (0.8)b log(1/9) = log(0.8b) log(1/9) = b*log(0.8) ...

Simplification of expression (answer)

3√(8x4/y) Note that 8 = 23 and x4 = x3*x = 3√(23x3x/y) = 2x 3√(x/y) Rationalize the denominator = 2x 3√(x/y) * 3√(y2/y2) =...

The term "essential" comes from the word "essence", meaning "the basic, real, and invariable nature of a thing ..." (from Dictionary.com). So what is "the invariable nature" or essence of an atom? In other words, what makes an atom an atom? ...

In similar figures, the ratios of corresponding sides are equal: FJ/AE = GH/BC 20/5 = GH/40 Solve for GH

solve each equation. function (answer)

√(-4 - 13k) = 10 Square both sides to get rid of the square root: -4 - 13k = 100 Add 4 to both sides -13k = 104 Divide both sides by -13: ...

Volume= width*length*height. Let x = width, y = height. Since V = 10 m3: 10 = x*2x*y = 2x2y 5/x2 = y (This is your substitution equation) The cost of the container is: ...

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