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Questions in mathematics

📝 Answered - For statements p, q, and [tex]$r$[/tex], use a truth table to show that each of the following pairs of statements is logically equivalent: [tex]$P \Rightarrow(q \vee r) \text { and }(\neg r) \wedge P) \Rightarrow q \text {. }$[/tex]

📝 Answered - Simplify the following expression. [tex]$\begin{array}{c} (y+4)^2 \\ y^2+[?] y+ \end{array}$[/tex]

📝 Answered - Factor $f(x)$ into linear factors given that $k$ is a zero of $f(x)$. $f(x)=2 x^3-3 x^2-5 x+6 ; k=1$ A. $f(x)=(x-1)(x-2)(2 x+3)$ B. $f(x)=(x-1)(x+1)(2 x-6)$ C. $f(x)=(x-1)(x+2)(2 x-3)$ D. $f(x)=(x+1)(x+2)(2 x-3)$

📝 Answered - A probability experiment is conducted in which the sample space of the experiment is [tex]$S = \{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16\}$[/tex], event [tex]$F = \{9, 10, 11, 12, 13, 14\}$[/tex], and event [tex]$G = \{13, 14, 15, 16\}$[/tex]. Assume that each outcome is equally likely. List the outcomes in F or G. Find [tex]$P(F \text{ or } G)$[/tex] by counting the number of outcomes in F or G. Determine [tex]$P(F \text{ or } G)$[/tex] using the general addition rule. List the outcomes in F or G. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. F or [tex]$G = \boxed{\ }[/tex]. B. F or [tex]$G = \{\ \}[/tex] Find [tex]$P(F \text{ or } G)$[/tex] by counting the number of outcomes in F or G. [tex]$P(F \text{ or } G) = \square[/tex] (Type an integer or a decimal rounded to three decimal places as needed.) Determine [tex]$P(F \text{ or } G)$[/tex] using the general addition rule. Select the correct choice below and fill in any answer boxes within your choice. (Type the terms of your expression in the same order as they appear in the original expression. Round to three decimal places as needed.) A. [tex]$P(F \text{ or } G) = \square + \square = \square[/tex] B. [tex]$P(F \text{ or } G) = \square + \square - \square = \square[/tex]

📝 Answered - Which equation demonstrates the multiplicative identity property? [tex](-2+8)+0-4+6[/tex] [tex](-3+6)(1)-3+61[/tex] [tex](-3+6)(3+5)-10+30[/tex]

📝 Answered - Select the best answer for the question. What is step 2 in the problem-solving process? A. Read the problem. B. Do the work. C. Find a relationship between what is given and what must be found. D. Write down the facts and figures.

📝 Answered - The number of boys and girls in different grades of a school are shown in the table below. Pick the appropriate scatter plot for the data. | Grades | Boys | Girls | |---|---|---| | 8th | 20 | 25 | | 9th | 30 | 28 | | 10th | 40 | 35 | | 11th | 60 | 45 | | 12th | 80 | 65 |

📝 Answered - What is the solution to the inequality $x(x-3)>0$? A) $x \leq 0$ or $x \geq 3$ B) $0 C) $x<0$ or $x>3$ D) $x \leq 0$ and $x \geq 3$

📝 Answered - The AI Development Group has just recruited 8 math majors, 5 computer science majors, 3 physics majors, and 4 psychology majors. The company president would like to select three of them to join the Planning Department, but would like no two members to have the same major. How many choices does the president have?

📝 Answered - The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550? Use the portion of the standard normal table below to help answer the question. | z | Probability | | :----- | :---------- | | 0.00 | 0.5000 | | 0.25 | 0.5987 | | 0.35 | 0.6368 | | 0.45 | 0.6736 | | 1.00 | 0.8413 | | 1.26 | 0.8961 | | 1.35 | 0.9115 | | 1.36 | 0.9131 | A. 9% B. 24% C. 59%