A sugar cube is put into the coffee. The sugar keeps its cube shape as it dissolves. As the sugar cube dissolves, its volume decreases at the constant rate of \( \frac{1}{20} \mathrm{~cm}^{3} / \mathrm{sec} \). Let \( x(t) \) be the sidelength of the cube at time \( t \). Find the rate of change of \( x(t) \) when the volume of the cube reaches \( \frac{1}{64} \mathrm{~cm}^{3} \).

ach year, a group surveys 50,000 households to study internet usage. In one area of the study, the group is interested in nding out how many hours a day the household spends streaming video from the internet. Describe the five basic steps in statistical study with an example of their application below. D. Use the sample statistics to infer the population parameters. In this case, the group estimates how many households have internet access. A. Act on the results. In this case, we determine that we need to have more households stream internet video. B. Repeat your study. In this case, we find a new sample to discover their internet usage. C. Draw conclusions to determine what you learned and whether you achieved your goal. In this case, we discovered the average time per day that a household spends streaming internet video. D. Draw conclusions to determine what you learned and whether you achieved your goal. In this case, we learned that some households use the internet to check email.

How many different strings can be formed by reordering the letters in the word "LITTLE"?

\( a)<5>\sqrt {9<6

Solve the following system of equations. \( \left\{\begin{array}{r}3 x+2 y-z=1 \\ -2 x-2 y-4 z=-1 \\ 2 x+4 y+7 z=2\end{array}\right. \) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution is (Type integers or simplified fractions.) B. There are infinitely many solutions. The solution set is \( \{(x, y, z) \mid 3 x+2 y-z=1\} \). C. The solution set is \( \varnothing \).

he widespread use of insecticides has (A) reduced the number of wild animals (B) caused imbalance in the relationship between living beings and their environment (C) eliminated diseases by killing mosquitoes and flies () caused biological hazards