Questions in mathematics

Questions in mathematics

📝 Answered - The length of a rectangle is 12 in. and the perimeter is 56 in. Find the width of the rectangle. A) 16 in. B) 32 in. C) 22 in.

📝 Answered - For statements $p$ and $q$, show that $(p \wedge \neg q) \wedge(p \wedge q)$ is a contradiction.

📝 Answered - Solve $2 x^2-6 x+10=0$ by completing the square. A) $x=3 / 2+i \sqrt{5}, x=3 / 2-i \sqrt{5}$ B) $x=3 / 2+1 / 2 i \sqrt{11}, x=3 / 2-1 / 2 i \sqrt{11}$ C) $x=3+i, x=3-i$ D) $x=3+i \sqrt{11}, x=3-i \sqrt{11}$

📝 Answered - Which expression is equivalent to [tex]$6 x^3+3 y^2-5 x^3+2 y^2$[/tex]? A) [tex]$x^6+3 y^4$[/tex] B) [tex]$6 x^6 y^4$[/tex] C) [tex]$6 x^3 y^2$[/tex] D) [tex]$x^3+5 y^2$[/tex]

📝 Answered - Which expression is equivalent to $\sqrt{8 x^7 y^8}$? Assume $x \geq 0$. A. $x y^2 \sqrt{8 x^3}$ B. $2 x^2 y^2 \sqrt{x y^2}$ C. $2 x^3 y^4 \sqrt{2 x}$ D. $4 x^3 y^4 \sqrt{x}$

📝 Answered - a) Find the mean, median, and mode of $163, 149, 155, 162, 168, 168$. b) Solve the equation $2^{2x} - 9(2^x) + 8 = 0$. c) Express $3 \sin \theta + 5 \cos \theta$ in the form $R \sin (\theta + \alpha)$, and hence solve the equation $3 \sin \theta + 5 \cos \theta = 4$, for values of $\theta$ between $0^{\circ}$ and $360^{\circ}$.

📝 Answered - Graph the solution to the inequality [tex]n-3 \leq 7[/tex].

📝 Answered - Write the decimals. a. [tex]$\frac{16}{100}$[/tex] b. [tex]$\frac{7}{100}$[/tex] c. [tex]$1 \frac{25}{100}$[/tex]

📝 Answered - What word describes the "4" in the expression [tex]$4 x-10$[/tex]? A) Sum B) Product C) Coefficient D) Term

📝 Answered - A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, [tex]14 \%[/tex] chose chocolate pie, and the margin of error was given as [tex]\pm 3[/tex] percentage points. What values do [tex]\hat{p}[/tex], [tex]\hat{q}[/tex], [tex]n[/tex], [tex]E[/tex], and [tex]p[/tex] represent? If the confidence level is [tex]95 \%[/tex], what is the value of [tex]\alpha[/tex]?