Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible: crosses the x-axis at -1,0, and 4; lies below the x-axis between -1 and 0; lies above the x-axis between 0 and 4.

The lengths of all sides of a triangle are integers when measured in decimeters. one of the sides has length of 1 dm and another of 3 dm. find the perimeter of the triangle.'

Consider a cube that has sides of length l. now consider putting the largest sphere you can inside this cube without any point on the sphere lying outside of the cube. the volume ratio -volume of the sphere/ volume of the cube is 1. 5.2 × 10−1 2. 3.8 × 10−1 3. 1.9 4. 2.5 × 10−1 5. 3.8

Unaware that 35% of the 10000 voters in his constituency support him, a politician decides to estimate his political strength. a sample of 200 voters shows that 40% support him. a. what is the population? b. what is the parameter of interest? state its value c. what is the statistics of the interest? state its value d. compare your answers in (b) and (c) is it surprising they are different? if the politician were to sample another 200 voters, which of the two numbers would most likely change? explain