What law does this mathematical equation represent?

Solve the inequality and graph the solution on the real number line. Use a graphing utility to verify your solution graphically. $2 x^{3}+13 x^{2}-8 x-46 \geq 6$

Use the Fundamental Counting Principle to find the total number of outcomes for the given situation: choosing tea in regular, raspberry, lemon, or peach; sweetened or unsweetened; and in a glass or bottle

Use matrix addition to find the coordinates of each image after a translation of 3 units left and 5 units up. If possible, graph each pair of figures on the same coordinate plane. $R(9,3), S(3,6), T(3,3), U(6,-3)$

Solve each equation. Check your answer. 4d = -2.4

A study was made to determine if the subject matter in a physics course is better understood when a lab constitutes part of the course. Students were randomly selected to participate in either a 3-semesterhour course without labs or a 4-semester-hour course with labs. In the section with labs, 11 students made an average grade of 85 with a standard deviation of 4.7, and in the section without labs, 17 students made an average grade of 79 with a standard deviation of 6.1. Would you say that the laboratory course increases the average grade by as much as 8 points? Use a P-value in your conclusion and assume the populations to be approximately normally distributed with equal variances.

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What is meant by the phrase degrees of freedom as it pertains to the computation of the sample standard deviation?

Write each expression as a single radical. Then simplify your answer. $\sqrt{\sqrt[3]{128 a^{7} b}}$

Find the inverse of the given elementary matrix.

$$\left[ \begin{array} { l l l } { 1 } & { 0 } & { 0 } \\ { 0 } & { c } & { 0 } \\ { 0 } & { 0 } & { 1 } \end{array} \right] , c \neq 0$$

For these exercises, divide the interval [a, b] into n subintervals by inserting points

$$t _ { 1 } , t _ { 2 } , \ldots , t _ { n - 1 }$$

between a=

$$t_0$$

and b=

$$t_n$$

, and assume that x'(t) and y'(t) are continuous functions and that no segment of the curve x=x(t), y=y(t)

$$( a \leq t \leq b )$$

is traced more than once.

Simplify each expression.

$$\frac { y ^ { 3 } } { y ^ { 10 } }$$

Do you think Dee would agree with the speaker in Nikki Giovanni's poem? Why or why not?

(a) Write the variation equation and (b) determine the quantity indicated. C varies inversely as J. If C=7 when J=0.7, determine C when J=14.