The masses and coordinates of three spheres are as follows: 20 kg, x = 0.50 m, y = 1.0 m; 40 kg, x = -1.0 m, y = -1.0 m; 60 kg, x = 0 m, y = -0.50 m. What is the magnitude of the gravitational force on a 20 kg sphere located at the origin due to these three spheres?

ABCD is a rectangle. Find the length of each diagonal.

$$A C = \frac { 3 c } { 9 } \text { and } B D = 4 - c$$

Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth. C = 375.3 cm

Let $X_1$ and $X_2$ have the joint pmf $p \left( x _ { 1 } , x _ { 2 } \right) = x _ { 1 } x _ { 2 } / 36 , x _ { 1 } = 1,2,3$ and $x_2 = 1, 2, 3,$ zero elsewhere. Find first the joint pmf of $Y_1 = X_1X_2$ and $Y_2 = X_2,$ and then find the marginal pmf of $Y_1.$

Determine whether the statements that follow are true or false, and justify your answer: There exists a matrix $A$ such that

$$\begin{bmatrix} 1 &2\\1 &2 \end{bmatrix}A=\begin{bmatrix} 1 &1\\1 &1 \end{bmatrix}.$$

The average density of Earth is 5.52 g/cm3. What is its density in

kg/m3;

Use a change of variables to evaluate the following integrals.

$$\int _ { 0 } ^ { 2 } x ^ { 3 } \sqrt { 16 - x ^ { 4 } } d x$$

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Objective Function

$$z = 2 x + 4 y$$

Constraints

$$\left\{ \begin{array} { l } { x \geq 0 , y \geq 0 } \\ { x + 3 y \geq 6 } \\ { x + y \geq 3 } \\ { x + y \leq 9 } \end{array} \right.$$

Find the derivative using the appropriate rule or combination of rules.

$$y = \sin \left( x ^ { 2 } \right) \cos \left( x ^ { 2 } \right)$$

Solve the inequality: h - 16 ≤ -24

Write the function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer. f(x) = |x| - 3; vertical shrink by a factor of 1/3

Evaluate the expression for the given value of the variable.

$$5j - 3j · 5$$

when

$$j = 10$$

The weight of a fruit fly is about

$$1.3 \times 10 ^ { - 4 }$$

pound. How much would one million fruit flies weigh?

Determine whether the trinomial is a perfect square trinomial. If so, factor it.

$$4 x ^ { 2 } - 3 x + 9$$