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Questions in mathematics

📝 Answered - (Prove that) : $\frac{5^x-5^{x-1}}{4 \times 5^{x-1}}=1$

📝 Answered - The sum of three numbers in an A.P. is 15. If 1, 4, and 19 are added to them respectively, the resulting numbers are in G.P. Find the initial three numbers.

📝 Answered - Consider a situation in which [tex]$P(X)=\frac{4}{5}$[/tex] and [tex]$P(Y)=\frac{1}{4}$[/tex]. If [tex]$P(X$[/tex] and [tex]$Y)$[/tex] is [tex]$=\frac{1}{5}$[/tex], which best describes the events? A. They are independent because [tex]$P(X) \cdot P(Y)=P(X$[/tex] and [tex]$Y)$[/tex]. B. They are independent because [tex]$P( X )+P( Y )=P( X$[/tex] and Y [tex]$)$[/tex]. C. They are dependent because [tex]$P( X ) \cdot P( Y )=P( X$[/tex] and Y [tex]$)$[/tex]. D. They are dependent because [tex]$P(X)+P(Y)=P(X$[/tex] and [tex]$Y)$[/tex].

📝 Answered - Which of the binomials below is a factor of this trinomial? [tex]5 x^2+15 x-50[/tex] A. [tex]x+10[/tex] B. [tex]x+2[/tex] C. [tex]x-10[/tex] D. [tex]x-2[/tex]

📝 Answered - Consider the following function: [tex]y=9 x-5 \tan (x), \quad\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)[/tex] Find the first and second derivatives. [tex]\begin{array}{l} y^{\prime}(x)=\square \\ y^{\prime}(x)=\square \end{array}[/tex] Find any values of [tex]c[/tex] such that [tex]y^{\prime}(c)=0[/tex]. (Enter your answer as a comma-separated list. If any answer does not exist, enter DNE.) [tex]c=\square[/tex] Determine the open intervals on which the graph of the function is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) concave upward [tex]\square[/tex] concave downward [tex]\square[/tex]

📝 Answered - Evaluate $33-5 \times 6$

📝 Answered - The vertex form of the equation of a parabola is $x=8(y-1)^2-15$. What is the standard form of the equation? A. $x=8 y^2-6 y-22$ B. $x=8 y^2-16 y-7$ C. $x=16 y^2-4 y+32$ D. $x=16 y^2-2 y-16$

📝 Answered - If [tex]f(x)=3 x^2+1[/tex] and [tex]g(x)=1-x[/tex], what is the value of [tex](f-g)(2)[/tex]?

📝 Answered - There are two pizzas. Conor ate $[1 / 4]$ of a pizza, Brandon $[2 / 8]$, Tyler $[3 / 4]$, and Audrey $[4 / 8]$. Who ate the most of the two pizzas?

📝 Answered - Chin was shown the graph of a line that contained point $(1,7)$. He wrote $f(x)=4 x+3$ to correctly represent the line. Which of these equations could represent the same line? A. $y-7=3(x-1)$ B. $y-1=3(x-7)$ C. $y-7=4(x-1)$ D. $y-1=4(x-7)$