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Questions in mathematics

[Terjawab] If $y=2 x e^{-3 x}$, show that $\frac{d 2 y}{d x^2}+\frac{6 d y}{d x}+9 y=0$

[Terjawab] Which of the following is equivalent to $\log _7(a) \cdot \log _b(7) ?$ Choose 1 answer: (A) $\log (7)$ (B) $\log (7 a)$ (C) $\log _a(b)$ (D) $\log _b(a)$

[Terjawab] Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying $x$-intercepts. $5 x^2=8 x+4$ Rewrite the equation in factored form. $\square$ $=0$ (Factor completely.)

[Terjawab] Simplify: $-7 z^4-2 z+2+2 z^4+5 z-5$

[Terjawab] A survey asks teachers and students whether they would like the new school mascot to be a Viking or a Patriot. This table shows the results. \begin{tabular}{|l|c|c|c|} \hline & Vikings & Patriots & Total \\ \hline Students & 80 & 20 & 100 \\ \hline Teachers & 5 & 20 & 25 \\ \hline Total & 85 & 40 & 125 \\ \hline \end{tabular} A person is randomly selected from those surveyed. Are being a student and preferring "Viking" independent events? Why or why not? A. Yes, they are independent because [tex]P(\text{student}) = 0.80[/tex] and [tex]P(\text{student} \mid \text{Viking}) = 0.68[/tex]. B. No, they are not independent because [tex]P(\text{student}) = 0.80[/tex] and [tex]P(\text{student} \mid \text{Viking}) = 0.94[/tex]. C. Yes, they are independent because [tex]P(\text{student}) = 0.80[/tex] and [tex]P(\text{student} \mid \text{Viking}) = 0.94[/tex]. D. No, they are not independent because [tex]P(\text{student}) = 0.80[/tex] and [tex]P(\text{student} \mid \text{Viking}) = 0.68[/tex].

[Terjawab] A strip of wood 78 inches long is to be cut into pieces $[3 \frac{3}{4}]$ inches long. How many pieces can be cut? A) 21 B) 20 C) 26 D) 12

[Terjawab] Tobin is solving the equation 3(x - 1.25) = 11.25. His work is shown below: 3(x - 1.25) = 11.25 3x - 3.75 = 11.25 3x - 3.75 + 3.75 = 11.25 + 3.75 3x = 15 3x times 3 = 45 times 3 x = 135 What mistake did Tobin make? Options: - Tobin did not distribute the 3 correctly. - Tobin should have subtracted 3.75 from each side. - Tobin should have divided by 3. - Tobin did not make a mistake.

[Terjawab] 1. What is the numerical coefficient of -x^5 - (-2x)^5 - (-2x^5) when simplified? 2. What is the degree of -2^3? Explain your answer. 3. Is the expression 2x^{1.5} + 3x - 18 a polynomial? Why or why not?

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

[Terjawab] Classify each of the following as a function or not a function. Select "1" for Function and "2" for Not a function. Graph of a circle. {(1, -2), (-2, 0), (-1, 2), (1, 3)} 1. Function