Find each product. −15(0)

In late 2011 the Gallup organization surveyed a random sample of 2007 American adults and asked them what they thought about China’s relationship with the United States. 76% of those surveyed said that China was either “friendly” or “an ally.” Gallup reported the following statement along with the survey results: “For results based on the total sample size of 2007 adults, one can say with 95% confidence that the margin of error attributable to sampling and other random effects is

$$\pm 2.68$$

percentage points.” Compute the margin of error for a sample size of 1000.

$$\text { Prove that } Q ( \sqrt { 2 } , \sqrt [ 3 ] { 2 } , \sqrt [ 4 ] { 2 } , \ldots ) \text { is an algebraic extension of } Q \text { but }\text { not a finite extension of } Q$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I find it helpful to begin the problem-solving process by restating the problem in my own words.

Sketch the graph of a function f whose derivative f' has the given description. f'(x) makes the sign transitions +, -, +, -.

How many units is it from - 5 to +5 on a number line?

Determine the matrix representation

$$[ T ] _ { B } ^ { C }$$

for the given linear transformation T and ordered bases B and C.

$$T : P _ { 2 } ( \mathbb { R } ) \rightarrow P _ { 3 } ( \mathbb { R } )$$

given by

$$T ( p ( x ) ) = ( x + 1 ) p ( x ),$$

$$\left. \begin{array} { l } (a){ B = \left\{ 1 , x , x ^ { 2 } \right\} ; C = \left\{ 1 , x , x ^ { 2 } , x ^ { 3 } \right\} }, \\ (b){ B = \left\{ 1 , x - 1 , ( x - 1 ) ^ { 2 } \right\} }; \\ { C = \left\{ 1 , x - 1 , ( x - 1 ) ^ { 2 } , ( x - 1 ) ^ { 3 }. \right\} } \end{array} \right.$$

How do you define ∫∫D f(x, y) dA if D is a bounded region that is not a rectangle?

Tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.

$$y = \frac { 1 } { 2 } ( x + 1 ) + 5 \quad \text { Down } 5 , \text { right } 1$$

State whether the domain of the following functions must be restricted to ensure that its inverse is a function. Give an appropriate restriction where needed.

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

Correct the definition of the italicized term, if correction is needed, so that it is in a form acceptable for publication:

A subset $H$ of a set $S$ is $\textit{closed}$ under a binary operation $\ast$ on $S$ if and only if $(a \ast b) \in H$ for all $a,b \in S$.

Respond verbal or written explanations. Explain how to use Euler diagrams to determine whether or not an argument is valid.

How does the arrangement or atoms differ in a crystalline and a noncrystalline substance?

professor of stan kaye describes lighting design as a ____________ art form.