Find a value for w so that the equation has (a) two solutions and (b) three solutions. Explain your reasoning.

$$5 x ^ { 3 } + w x ^ { 2 } + 80 x = 0$$

$$w - 3 \frac { 2 } { 3 } = 1 \frac { 1 } { 2 }$$

Write the vocabulary word that best completes the following sentence: Although the newspaper editor laughed at him, Wright somehow knew ___________ that the man was amused, not scornful.

The Centers for Disease Control and Prevention say that about 19.5% of teenagers smoke tobacco (down from a high of 38% in 1997). A college has 522 students in its freshman class. Is it likely that more than 25% of them are smokers? Explain.

Calculate the indefinite integral.

$$\int \left( 4 x ^ { 3 } - 2 x ^ { 2 } \right) d x$$

The volume of a cylinder is given by the formula $V=\pi r^{2} h$ where $h$ is the height of the cylinder and $r$ is the radius.

a) Find the volume of a cylindrical post of length $7.5~\mathrm{ m}$ and a diameter of $30 \mathrm{~cm}$.
b) Make $r$ the subject of the formula.
c) A cylinder of height $75 \mathrm{~cm}$ has a volume of $6000\mathrm{~cm}^{3}$ find its radius correct to $3$ s.f.

Without using any type of writing instrument, what can you do to make the following incorrect statement a correct statement? XI+I=X

Which of the following sciences is not considered a natural science? a. biology, b. astronomy, c. physics, d. computer science.

Use the unit circle to evaluate the six trigonometric functions of

$$\theta.$$

$$\theta = 540 ^ { \circ }$$

$$\begin{array}{l} \text{Find the differential of the function.} \end{array}$$

$$f ( x ) = \frac { 2 x ^ { 2 } + 1 } { x + 1 }$$

A map has a scale of 1 inch: 50 mile. Use the given map distance to find the actual distance. 3 inches

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Parametric equations let me think of a curve as a path traced out by a moving point.

Can you find all the missing parts of a triangle using the Law of Sines if you know the lengths of all three sides? Explain.

Solve each of the following equations. a. (1/6)x + 2/3 = (1/4)x - 1/3 b. 0.15(w + 2) = 0.3 + 0.2w c. 8x/6 = 72/54 d. 3(2x - 7) = 5x + 17 + x