A dance floor is made from square wooden tiles with a side length of 1 foot. The floor can be laid out as a square or as a rectangle. The width of the rectangular floor is 10 feet less than the width of the square floor, and its length is 15 feet greater than the length of the square floor. The perimeter of the rectangular dance floor is 130 feet. What are the length and width of the dance floor? Explain your reasoning.

Write the expression as a complex number in standard form.

$$\left( 8 - 2 i ^ { 4 } \right) + \left( 3 - 7 i ^ { 8 } \right) - \left( 4 + i ^ { 9 } \right)$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

$$\log \left( \frac { x } { 100 } \right)$$

Compute the standard deviation for each set of sample data.

$$85, 75, 62, 78, 100$$

To determine if topiramate is a safe and effective treatment for alcohol dependence, researchers conducted a 14-week trial of 371 men and women aged 18 to 65 years diagnosed with alcohol dependence. In this double-blind, randomized, placebo-controlled experiment, subjects were randomly given either 300 milligrams (mg) of topiramate (183 subjects) or a placebo (188 subjects) daily, along with a weekly compliance enhancement intervention. The variable used to determine the effectiveness of the treatment was self-reported percentage of heavy drinking days. Results indicated that topiramate was more effective than placebo at reducing the percentage of heavy drinking days. The researchers concluded that topiramate is a promising treatment for alcohol dependence.

What does it mean for the experiment to be placebo-controlled?

With a height of 67 in., William McKinley was the shortest president of the past century. The presidents of the past century have a mean height of 71.5 in. and a standard deviation of 2.1 in. Convert McKinley's height to a z score.

Solve each equation. Check your answer.

$$\frac { \sqrt { x - 7 } } { 3 } = 1$$

Determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis? (b) fails to reject the null hypothesis? A sports drink maker claims that the mean calorie content of its beverages is 72 calories per serving.

A projectile’s launch speed is five times its speed at maximum height. Find launch angle

$$θ_0$$

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Based on the pattern shown in the graph, what will the unemployment rate do after 2013?

The numbers are all rational. Write each number as a ratio of two integers. 4.6037

Write a quadratic function in standard form for the given set of zeros. 3 and 3.

Simplify each quotient. Write your answer in scientific notation.

$$\frac { 4.2 \times 10 ^ { 8 } } { 2.1 \times 10 ^ { 11 } }$$

¿A que hora son las noticias? ________________________________.