Questions in mathematics

Questions in mathematics

📝 Answered - Which expression results when the change of base formula is applied to [tex]$\log _4(x+2)$[/tex] ? [tex]$\frac{\log (x+2)}{\log 4}$[/tex] [tex]$\frac{\log 4}{\log (x+2)}$[/tex] [tex]$\frac{\log 4}{\log x+2}$[/tex] [tex]$\frac{\log x+2}{\log 4}$[/tex]

📝 Answered - A manufacturer has determined that the total cost [tex]$C$[/tex] of operating a factory is [tex]$C=0.5 x^2+15 x+5000$[/tex] where [tex]$x$[/tex] is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is [tex]$\frac{C}{x}$[/tex]). [tex]$x=$[/tex] units

📝 Answered - The center of a circle circumscribed about a triangle is outside the triangle. What type of triangle is it? A. Obtuse B. Acute C. Scalene D. Right

📝 Answered - Factor the polynomial function [tex]6 x^3+41 x^2+80 x+48[/tex], graphed below. [tex]f(x)=[/tex]

📝 Answered - What is the solution of [tex]log _x 729=3[/tex]?

📝 Answered - What is the midpoint M given $Q (-2,-4)$ and $R (6,10)$? A. $(-4,-7)$ B. $(1,-2)$ C. $(2,3)$ D. $(-3,8)$

📝 Answered - You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures: | 26.8 | 18.9 | 33.3 | 15.3 | 35.9 | 10 | 21.8 | 8.6 | 23.3 | 36.6 | 16.2 | 6.1 | Find the [tex]$95 \%$[/tex] confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.

📝 Answered - What is the solution of [tex]$3 x+5=2 x-7 ?$[/tex] A. the [tex]$x$[/tex]-coordinates of the intersection point of the lines [tex]$y=3 x+5$[/tex] and [tex]$y=2 x-7$[/tex] B. the [tex]$x$[/tex]-coordinates of the [tex]$x$[/tex]-intercepts of the lines [tex]$y=3 x+5$[/tex] and [tex]$y=2 x-7$[/tex] C. the [tex]$y$[/tex]-coordinate of the intersection point of the lines [tex]$y=3 x+5$[/tex] and [tex]$y=2 x-7$[/tex] D. the [tex]$y$[/tex]-coordinates of the [tex]$y$[/tex]-intercepts of the lines [tex]$y=3 x+5$[/tex] and [tex]$y=2 x-7$[/tex]

📝 Answered - Solve the system of linear equations by graphing. Round the solution to the nearest tenth. [tex]\begin{array}{l} y=-0.25 x+4.7 \\ y=4.9 x-1.64 \end{array}[/tex] The approximate solution to the system is ( $\square$ , $\square$ ).

📝 Answered - The table shows the number of goals scored by a football team in each league match during a season. \begin{tabular}{|c|c|} \hline Number of goals scored & Frequency \\ \hline 0 & 2 \\ \hline 1 & 10 \\ \hline 2 & 7 \\ \hline 3 & 6 \\ \hline 4 & 3 \\ \hline 5 & 2 \\ \hline \end{tabular} a) Calculate the number of league games the team played over the season. (1 mark) b) Calculate the total number of goals scored by the team during the season. (2 marks) c) Calculate the mean average number of goals scored per match during the season.