Questions in mathematics

Questions in mathematics

[Free] Use the function below to find [tex]$f(3)$[/tex]. [tex]$f(x)=\frac{1}{3} \cdot 4^x$[/tex] A. 4 B. 8 C. [tex]$\frac{16}{3}$[/tex] D. [tex]$\frac{64}{3}$[/tex]

[Free] Davis's net paycheck is $2,920.50. | Type of Tax | Amount | |---|---| | Federal | $945.00 | | State | $225.00 | | Medicare | $65.25 | | Social Security | $344.25 | Based on the information in the table, what is Davis's gross pay? A. $2,920.50 B. $2,985.75 C. $4,090.50 D. $4,500.00

[Free] Evaluate the expression. [tex]$\begin{array}{c} x=5 y=4 \ (3 x-2 y)^2 \ {[?]} \end{array}$[/tex]

[Free] The quadratic function $y=-10 x^2+160 x-430$ models a store's daily profit ($y$), in dollars, for selling T-shirts priced at $x$ dollars. A. the daily profit the company would make from the T-shirts if it gave the T-shirts away for free B. the greatest daily profit the company could make from selling the T-shirts C. a selling price that would result in the company making no profit from the T-shirts D. the selling price that would result in the company making the greatest daily profit from the T-shirts Match each item with what it represents in this situation by entering the appropriate letter in each box. $\square$ $x$-coordinate of the vertex of the function $\square$ $y$-coordinate of the vertex of the function $\square$ an $x$-intercept of the function $\square$ a $y$-intercept of the function

[Free] Write the equation you created in slope-intercept form: (2)x + (3)y = (24)

[Free] Air pressure may be represented as a function of height above the surface of the Earth as shown below: [tex]$P(h)=P_o e^{-00012 h}$[/tex] In this function, [tex]$P_0$[/tex] is air pressure at sea level, and h is measured in meters. Which of the following equations will find the height at which air pressure is 65% of the air pressure at sea level? A. [tex]$P_o=.65 P_o e^{-.00012 h}$[/tex] B. [tex]$65=h \cdot e^{-.00012}$[/tex] C. [tex]$.65 P_o=P_o e^{-.00012 h}$[/tex] D. [tex]$h=.65 e^{-0.0012}$[/tex]

[Free] Raj's bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, [tex]$y$[/tex], is a function of the time in minutes, [tex]$x$[/tex], that it has been draining. What is the range of this function? A. all real numbers such that [tex]$y \leq 40$[/tex] B. all real numbers such that [tex]$y \geq 0$[/tex] C. all real numbers such that [tex]$0 \leq y \leq 40$[/tex] D. all real numbers such that [tex]$37.75 \leq y \leq 40$[/tex]

[Free] The function $f(x)=\left(\frac{1}{5}\right)^x$ is translated up 4 units. Which equation represents the translated function? A. $g(x)=\left(\frac{1}{5}\right)^{x-4}$ B. $g(x)=\left(\frac{1}{5}\right)^{x+4}$ C. $g(x)=\left(\frac{1}{5}\right)^x+4$ D. $g(x)=\left(\frac{1}{5}\right)^x-4$

[Free] Complete the statements about the key features of the graph of [tex]f(x)=x^5-9 x^3[/tex]. As [tex]x[/tex] goes to negative infinity, [tex]f(x)[/tex] goes to $\square$ infinity, and as [tex]x[/tex] goes to positive infinity, [tex]f(x)[/tex] goes to $\square$ infinity.

[Free] Find $\begin{array}{l} \lim _{x \rightarrow 0} \frac{x}{f(x)}=\square \ \lim _{x \rightarrow 0} \frac{4-4 e^x}{f(x)}=\square \end{array}$