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Questions in mathematics

[Jawaban] A. Round off to the nearest hundred: 1. 2246 = 2300 2. 5134 = 5100 3. 3321 = 2300 4. 5461 = 5500 5. 7458 = 7500 6. 8492 = 8500 B. Round off to the nearest thousand: 1. 20890 = 2. 14201 = 3. 9050 = 4. 85419 = 5. 75923 = 6. 92504 = C. Round off to the nearest ten-thousand: 1. 245667 = 2. 379420 =

[Jawaban] Dirk and his friends set out to sea on their annual fishing trip. There is a proportional relationship between the time (in hours) Dirk and his friends spend sailing, x, and their distance from shore (in miles), y. Write an equation for the relationship between x and y. Simplify any fractions. y = kx

[Jawaban] Lauren describes a parabola where the focus has a positive, nonzero [tex]$x$[/tex] coordinate. Which parabola(s) could Lauren be describing? Check all that apply. [tex]$x^2=4 y$[/tex] [tex]$x^2=-6 y$[/tex] [tex]$y^2=x$[/tex] [tex]$y^2=10 x$[/tex] [tex]$y^2=-3 x$[/tex] [tex]$y^2=5 x$[/tex]

[Jawaban] The table below shows the saturated thickness (water level) in five-year intervals. Water Levels in the Ogallala Aquifer \begin{tabular}{|c|c|} \hline Year & Saturated Thickness \\ \hline 1975 & $32.77 m(107.5 t )$ \\ \hline 1980 & $28.11 m(95.5 t )$ \\ \hline 1985 & $25.68 m(84.25 t )$ \\ \hline 1990 & $22.48 m(73.75 t )$ \\ \hline 1995 & $19.43 m(63.75 t )$ \\ \hline 2000 & $16.84 m(55.25 t )$ \\ \hline 2005 & $14.15 m(47.75 t )$ \\ \hline 2010 & $12.27 m(40.25 t )$ \\ \hline \end{tabular} If water continues to be used at the current rate, what will the saturated thickness be in 2020?

[Jawaban] Determine whether the statement is true or false. If [tex]$f$[/tex] is increasing and [tex]$f(x)>0$[/tex] on [tex]$I$[/tex], then [tex]$g(x)=\frac{1}{f(x)}$[/tex] is decreasing on [tex]$I$[/tex].

[Jawaban] Show that: [tex]$2 \sin ^2\left(\frac{\pi}{4}-\frac{\theta}{2}\right)=1-\sin \theta$[/tex]

[Jawaban] $2.7 \times(-3) \times(-1.2)$ A) -9.72 B) 10.8 C) -10.8 D) 9.72

[Jawaban] Select the correct answer. One factor of the polynomial $3 x^3+20 x^2-21 x+88$ is $(x+8)$. What is the other factor of the polynomial? (Note: Use long division.) A. $\left(3 x^2-4 x+11\right)$ B. $\left(3 x^2-4 x\right)$ C. $\left(3 x^2+11\right)$ D. $\left(3 x^2+4 x-11\right)$

[Jawaban] Use the Ratio Test to determine whether [tex]$\sum_{n=1}^{\infty} a_n$[/tex] converges, where [tex]$a_n$[/tex] is given. State if the ratio test is inconclusive. [tex]$\sum_{n=1}^{\infty} \frac{(2 n)!}{\left(\frac{n}{e}\right)^{2 n}}$[/tex] Identify [tex]$a_n$[/tex]. [tex]$\frac{(2 n)!}{\left(\frac{n}{e}\right)^{2 n}}$[/tex] Evaluate the following limit. [tex]$\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_n}\right|$[/tex] Since [tex]$\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_n}\right|$[/tex] ? Select.

[Jawaban] Which is the exponential form of [tex]$\log _b 35=3$[/tex] ? [tex]$b^{35}=3$[/tex] [tex]$b^3=35$[/tex] [tex]$35^3=b$[/tex] [tex]$3^b=35$[/tex]