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Questions in mathematics

📝 Answered - Consider the following function. [tex]f(x)=\frac{21}{x^2+3}[/tex] Find the first and second derivatives. [tex]\begin{array}{l} f^{\prime}(x)=\square \\ f^{\prime}(x)=\square \end{array}[/tex] Find any values of [tex]c[/tex] such that [tex]f^{\prime \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 - On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake? [tex]M=\log \left(\frac{1}{l_0}\right)[/tex] [tex]M=[/tex] the magnitude of an earthquake I = the intensity of an earthquake [tex]I_0=[/tex] the smallest seismic activity that can be measured, which is 1 A. 0.40 B. 1.02 C. 1.05 D. 2.51

📝 Answered - \frac{(-7)^0 \times 7^9}{(-7)^2(-7)^3(-7)}

📝 Answered - Read the clues and write the numbers. (a) 10 more than 4,309 (b) 100 less than the largest 4-digit number

📝 Answered - A box contains different-colored marbles. If [tex]P(blue) = \frac{1}{4}[/tex], [tex]P(green) = \frac{1}{4}[/tex], and [tex]P(blue and green) = \frac{1}{12}[/tex], which statement is true? A. The events are independent because [tex]P(blue) \cdot P(green) = P(blue and green)[/tex]. B. The events are independent because [tex]P(blue) \cdot P(green) \neq P(blue and green)[/tex]. C. The events are dependent because [tex]P(blue) \cdot P(green) = P(blue and green)[/tex]. D. The events are dependent because [tex]P(blue) \cdot P(green) \neq P(blue and green)[/tex].

📝 Answered - Determine whether the normal distribution can be used to compare the following population proportions. [tex]n_1=45, \quad n_2=29, \quad \hat{p}_1=0.689, \quad \hat{p}_2=0.897[/tex] Step 1 of 2: Calculate the four values [tex]n_1 \hat{p}_1, n_1(1-\hat{p}_1), n_2 \hat{p}_2[/tex], and [tex]n_2(1-\hat{p}_2)[/tex]. Round your answers to three decimal places, if necessary.

📝 Answered - There are rational numbers [tex]$\frac{5}{7}$[/tex] and [tex]$\frac{6}{7}$[/tex]

📝 Answered - Subtract. $\begin{array}{r} -8-(-5)= \\ 2-(-9)= \end{array}$

📝 Answered - Substitute the value of $x$ back into the equation $\frac{3}{4} x+3 -2 x=-\frac{1}{4}+\frac{1}{2} x+5$ to justify the solution. What value of $x$ is the solution? $x=\square$

📝 Answered - What are the coordinates of the vertex of the parabola described by the equation below? [tex]$y=-7(x-4)^2-5$[/tex] A. (-5,-4) B. (5,4) C. (4,-5) D. (-4,5)