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Questions in mathematics

📝 Answered - Using Logarithmic Regression Examine the data below for a stalk of corn. | Day, $x$ | 9 | 12 | 22 | 40 | | :-------- | :- | :- | :- | :- | | Height, $y$ (in) | 5 | 17 | 45 | 60 | Use logarithmic regression to find an equation of the form [tex]$y=a+b \ln (x)$[/tex] to model the data. [tex]a=[/tex] [tex]b=[/tex]

📝 Answered - Solve $\frac{x^2-81}{x+9} \div \frac{x^2+11 x+18}{x+2}$. Completely simplify your answer and state any restrictions on the variable. A. $\frac{x-9}{x+9}, x \neq-9, x \neq-2$ B. $\frac{x-9}{x+2}, x \neq-9, x \neq-2$ C. $1, x \neq-9, x \neq-2$ D. $\frac{x+9}{x-9}, x \neq-9, x \neq-2$

📝 Answered - Let f be Riemann integrable on [a,b]. For a ≤ x ≤ b, define \[F(x) = \int_a^x f(t) dt.\] Then F is continuous on [a,b]. Furthermore, if f is continuous at a point x_0 in [a,b], then F is differentiable at x_0, and F'(x_0) = f(x_0). Proof:

📝 Answered - In a complex function f(x, y) = u(x, y) + i v(x, y) where i is the imaginary unit, and x, y, u(x, y), and v(x, y) are real. If f(x, y) is analytic, then which of the following equations is/are TRUE? (a) ∂²u/∂x² + ∂²u/∂y² = 0 (b) ∂²v/∂x² + ∂²v/∂y² = 0 (c) ∂²u/∂x² + ∂²v/∂y² = 0 (d) (∂u/∂x)(∂v/∂x) + (∂u/∂y)(∂v/∂y) = 0

📝 Answered - Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. Which of these statements are true? Check all that apply. - There are 20C3 possible ways to choose three books to read. - There are 5C3 possible ways to choose three mysteries to read. - There are 15C3 possible ways to choose three books that are not all mysteries. - The probability that Mariah will choose 3 mysteries can be expressed as \( \frac{1}{5C3} \).

📝 Answered - Calculate the value of the expression: 16 ÷ 4 of 4 × [3 ÷ 4 of {4 × 3 ÷ (3 + 3)}] ÷ (2 ÷ 4 of 8)

📝 Answered - What is the equation of the line that is parallel to the given line and passes through the point $(-2,2)$? $y=\frac{1}{5} x+4$ A. $y=\frac{1}{5} x+\frac{12}{5}$ B. $y=-5 x+4$ C. $y=-5 x+\frac{12}{5}$

📝 Answered - Which statement could be used to explain why the function [tex]h(x)=x^3[/tex] has an inverse relation that is also a function? A. The graph of [tex]h(x)[/tex] passes the vertical line test. B. The graph of the inverse of [tex]h(x)[/tex] is a vertical line. C. The graph of the inverse of [tex]h(x)[/tex] passes the horizontal line test. D. The graph of [tex]h(x)[/tex] passes the horizontal line test.

📝 Answered - For what values of [tex]$m$[/tex] does the graph of [tex]$y=3 x^2+7 x+m$[/tex] have two [tex]$x$[/tex]-intercepts? A. [tex]$m>\frac{25}{3}$[/tex] B. [tex]$m<\frac{25}{3}$[/tex] C. [tex]$m<\frac{49}{12}$[/tex] D. [tex]$m>\frac{49}{12}$[/tex]

📝 Answered - Select the best answer for the question. Evaluate the determinant for the following matrix: $\left[\begin{array}{rr}3 & -5 \\ 1 & 1\end{array}\right]$ A. -4 B. 5 C. -2 D. 8