Write the number in i-form. $\sqrt{-48}$

A machine produces bolts with an average diameter of 0.25 in. and a standard deviation of 0.02 in. What is the probability that a bolt will be produced with a diameter greater than 0.3 in.?

Use the Zero-Factor Property to solve the equation. (3x - 2)(4x + 1)(x + 9) = 0

$$2 x + 3 y = 12$$

$$x - y = 1$$

Find the Laplace transform of the given piecewise defined function.

$$f(t)=\left\{\begin{array}{ll} 0, & 0 \leq t<2 \\ 2, & t \geq 2 \end{array}\right.$$

Find the solution of the initial value problem. Discuss the interval of existence and provide a sketch of your solution. $(2 x+3) y^{\prime}=y+(2 x+3)^{1 / 2}$, y(-1)=0

Let $f(x)=x^{2}+1.$ Find (a) $f((1,3]).$ (b) $f([-1,0] \cup[2,4]).$ (c) $f^{-1}([-1,1])$ (d) $f^{-1}([-2,3])$ (e) $f^{-1}([5,10])$ (f) $f^{-1}([-1,5] \cup[17,26])$

Determine the values of a and b that satisfy the equation. 5 - 4i = (a + 3) + (b - 1)i

Determine whether each of the following arguments is valid or invalid. If it is valid, give a proof. If it is invalid, give an assignment of truth values to the variables that makes the premises true and the conclusion false. The Yankees will be in the World Series or the Phillies won't be there. If the Phillies are not in the World Series, the National League cannot win. In fact, the National League wins. Therefore, the Yankees are in the World Series.

Solve the equation and check your solution. $\sqrt{y}=7$

A soup kitchen makes 16 gallons of soup. Each day, a quarter of the soup is served and the rest is saved for the next day. Write the first five terms of the sequence of the number of fluid ounces of soup left each day. Write an equation that represents the nth term of the sequence. When is all the soup gone?

Given the function $\phi$, place the ordinary differential equation $\phi\left(t, y, y^{\prime}\right)=0$ in normal form. $\phi(x, y, z)=x z-2 y-x^{2}$

Find the general solution of the given differential equation. In each case, sketch at least six members of the family of solution curves. $y^{\prime}=t^{2} e^{3 t}$

Rationalize the denominator and simplify further, if possible.

$$\frac{21 x^{2}}{\sqrt{7 x}}$$