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Questions in mathematics

📝 Answered - Which is equivalent to $\sqrt[3]{8}^{\frac{1}{4} x}$ ? A. $8^{\frac{3}{4} x}$ B. $\sqrt[7]{8}^x$ C. $\sqrt[12]{8^x}$ D. $8^{\frac{3}{4 x}}$

📝 Answered - A population has mean [tex]$\mu=10$[/tex] and standard deviation [tex]$\sigma=3$[/tex]. Round the answers to two decimal places as needed. (a) Find the [tex]$z$[/tex]-score for a population value of 1. The [tex]$z$[/tex]-score for a population value of 1 is ______.

📝 Answered - Algebraic fraction [tex]$\frac{4}{x^2+3 x+2} \div \frac{2}{x^2-1}$[/tex] is given. Factorize: [tex]$x^2+3 x+2$[/tex] and [tex]$x^2-1$[/tex] Convert the fraction into the lowest term.

📝 Answered - Solve. $\frac{x+9}{9}=\frac{x-1}{8}$

📝 Answered - Given: [tex]$m \angle ADE =60^{\circ}$[/tex] and [tex]$m \angle CDF =(3 x+15)^{\circ}$[/tex] Prove: [tex]$x=15$[/tex] What is the missing statement and the missing reason in step 5? Statements | Reasons --- | --- 1. [tex]$m \angle A D E=60^{\circ}$[/tex] | 1. Given 2. [tex]$m \angle C D F=(3 x+15)^{\circ}$[/tex] | 2. Given 3. [tex]$\angle A D E$[/tex] and [tex]$\angle C D F$[/tex] are vert. [tex]$\angle s$[/tex] | 3. def. of vert. [tex]$\angle s$[/tex] 4. [tex]$\angle A D E=\angle C D F$[/tex] | 4. vert. [tex]$\angle s a$[/tex] 5. [tex]$\angle A D E=m \angle C D F$[/tex] | 5. def. of a 6. | 6. ? 7. [tex]$45=3 x$[/tex] | 7. subtr. prop. 8. [tex]$15=x$[/tex] | 8. div. prop. Statement: [tex]$60=3 x+15$[/tex]; Reason: substitution Statement: [tex]$x=15$[/tex]; Reason: subtraction property of equality Statement: [tex]$60=3 x+15$[/tex]; Reason: transitive property Statement: [tex]$x=15$[/tex]; Reason: subtraction and division properties of equality

📝 Answered - A quadratic sequence begins: [tex]$5,20,45,80,125, \ldots$[/tex] Work out the [tex]$n^{\text {th }}$[/tex] term rule for this sequence.

📝 Answered - Which equation describes a parabola that opens up or down and whose vertex is at the point $(h, v)$? A. $x=a(y-h)^2+v$ B. $x=a(y-v)^2+h$ C. $y=a(x-v)^2+h$ D. $y=a(x-h)^2+v$

📝 Answered - 4. In each of the following, find a system of equations and find [tex]$x$[/tex] and [tex]$y$[/tex]. a. [tex]$\left(\begin{array}{cc}3 & 0 \\ 0 & -2\end{array}\right)\binom{x}{y}=\binom{12}{8}$[/tex] b. [tex]$\left(\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right)\binom{x}{y}=\binom{8}{1}$[/tex] c. [tex]$\left(\begin{array}{ll}x & y \\ y & x\end{array}\right)\binom{3}{1}=\binom{5}{-1}$[/tex] d. [tex]$\left(\begin{array}{cr}x+1 & 3 \\ \frac{1}{2} & -y\end{array}\right)\binom{2}{1}=\binom{11}{0}$[/tex] 5. Given [tex]$\left(\begin{array}{rr}3 & 1 \\ 2 & -1\end{array}\right)\binom{x}{y}=\binom{9}{1}$[/tex] find a system of equations in [tex]$x$[/tex] and [tex]$y$[/tex]. Hence find [tex]$x$[/tex] and [tex]$y$[/tex]. 6. If [tex]$A=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right)$[/tex], find [tex]$p, q$[/tex] such that [tex]$A^2=p A+q I$[/tex]. ([tex]$A^2=A A$[/tex] and [tex]$I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$[/tex].

📝 Answered - If $(x+8)$ is a factor of $f(x)$, which of the following must be true? A. Both $x=-8$ and $x=8$ are roots of $f(x)$. B. Neither $x=-8$ nor $x=8$ is a root of $f(x)$. C. $f(-8)=0$ D. $f(8)=0

📝 Answered - The theoretical probability of a couple having a baby girl is [tex]$\frac{1}{2}$[/tex]. What is [tex]$P$[/tex](girl, girl, girl)? A. [tex]$\frac{1}{8}$[/tex] B. [tex]$\frac{1}{6}$[/tex] C. [tex]$\frac{1}{3}$[/tex] D. [tex]$\frac{3}{8}$[/tex]