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Questions in mathematics

[Done] An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

[Done] Identify all of the following solutions of [tex]$\sqrt{x+8}-6=x$[/tex]. A. None of the above B. [tex]$x=-7$[/tex] C. [tex]$x=-4$[/tex] D. [tex]$x=-4$[/tex] and [tex]$x=-7$[/tex]

[Done] Use the equation to find the length of the missing leg measure. [tex]a^2+16^2=20^2[/tex] 1. Evaluate powers: [tex]a^2+256=400[/tex] 2. Undo addition: [tex]a^2=144[/tex] 3. Undo the square: [tex]a=\sqrt{144}[/tex] What is the length of the missing leg measure? [tex]a=[/tex] $\square$ units

[Done] Which of the following is equivalent to [tex]$\log _3(b) \cdot \log _b(27)$[/tex]? A. 3 B. 9 C. [tex]$\log (9)$[/tex] D. [tex]$\log _b(3)$[/tex]

[Done] Noah is working on a geometry problem that involves finding the volume of a sphere with a diameter of 9 units. His work is shown below. [tex]\begin{array}{l} V=\frac{4}{3} \pi r^3 \\ V=\frac{4}{3} \pi(9)^3 \\ V=\frac{4}{3} \pi(729) \\ V=972 \pi \text { cubic units }\\ \end{array}[/tex] Is Noah's work correct? Explain. A. Yes, Noah's calculations are correct. B. No, Noah did not simplify correctly. C. No, Noah used the diameter instead of the radius in the calculations. D. No, Noah did not use the correct formula for volume of a sphere.

[Done] David expressed the ratio of the number of books that he owns to the number of DVDs that he owns as 27:11. Which statement could be true based upon this relationship? A. David has 11 books and 27 DVDs. B. David has 11 DVDs and 27 books. C. David has 11 DVDs and 27 items total. D. David has 11 books and 27 items total.

[Done] $\lim _{x \rightarrow-\infty} \frac{\sqrt{x^2+7 x}}{12-4 x}=$

[Done] A division problem is shown below. 4 and one-third divided by 5 and 1/6. The reciprocal of a fraction must be found to solve the problem. What is the reciprocal fraction that is required? Options: - 6/31 - 3/13 - 13/3 - 31/6

[Done] No smoking: The General Social Survey conducted a poll of 691 adults in which the subjects were asked whether they agree that the government should prohibit smoking in public places. In addition, each was asked how many people lived in his or her household. The results are summarized in the following contingency table. | Household Size | 1 | 2 | 3 | 4 | 5 | | :------------- | :-- | :-- | :-- | :-- | :-- | | Agree | 66 | 107 | 37 | 29 | 31 | | No Opinion | 27 | 55 | 30 | 19 | 29 | | Disagree | 52 | 80 | 47 | 50 | 32 | Test the hypothesis of independence. Use the α = 0.05 level of significance and the P-value method with the TI-84 Plus calculator. What do you conclude? (a) State the null and alternate hypotheses. H0: Household size and opinion are independent. H1: Household size and opinion are dependent.

[Done] Three museums charge an entrance fee based on the number of visitors in the group. The table lists the fees charged by the museums. At which museum is the entrance fee proportional to the number of visitors? \begin{tabular}{|r|r|r|r|r|r|} \hline \multicolumn{2}{|c|}{ Museum A } & \multicolumn{2}{c|}{ Museum B } & \multicolumn{2}{c|}{ Museum C } \\ \hline Visitors & Fee ($) & Visitors & Fee ($) & Visitors & Fee ($) \\ \hline 2 & 4 & 1 & 2 & 3 & 4 \\ \hline 3 & 5 & 4 & 8 & 12 & 16 \\ \hline 4 & 6 & 6 & 11 & 18 & 24 \\ \hline \end{tabular} A. museum $A$ B. museum B C. museum C D. museum $A$ and museum $B$