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Questions in mathematics

📝 Answered - A survey is conducted to study the favorite sport of individuals in different age groups. The two-way table is given below: | | Football | Basketball | Baseball | Total | | :------------------ | :------- | :--------- | :------- | :---- | | $8 - 12 ~ yrs$ | 10 | 12 | 10 | $32$ | | $13 - 17 ~ yrs$ | 8 | 6 | 24 | $38$ | | $18 - 22 ~ yrs$ | 16 | 2 | 12 | $30$ | | Total | $34$ | $20$ | $46$ | $100$ | What is the probability that a randomly selected person from this survey is 13 to 17 years old, given their favorite sport is football? $P(13-17 yrs | \text { Football })=[?] %$ Round your answer to the nearest whole percent.

📝 Answered - How many 5-digit odd numbers can be formed using the digits 3, 4, 5, 6, 7, 8, and 9 if: i) repetition of digits is not allowed? ii) repetition of digits is allowed? How many ways can four boys and three girls be seated in a row containing seven seats if: a) they may sit anywhere? b) all three girls are together? c) the boys and girls must alternate? d) the girls are to occupy odd seats?

📝 Answered - Which statement could be used to explain why $f(x)=2 x-3$ has an inverse relation that is a function? A. The graph of $f(x)$ passes the vertical line test. B. $f(x)$ is a one-to-one function. C. The graph of the inverse of $f(x)$ passes the horizontal line test. D. $f(x)$ is not a function.

📝 Answered - The shoe sizes of a group of middle school girls are shown. If a shoe size of 7 is added to the data, how does the IQR change?

📝 Answered - Which of the following describes the transformations of [tex]g(x)=-(2)^{x+4}-2[/tex] from the parent function [tex]f(x)=2^x[/tex] ? A. shift 4 units left, reflect over the [tex]x[/tex]-axis, shift 2 units down B. shift 4 units left, reflect over the [tex]y[/tex]-axis, shift 2 units down C. shift 4 units right, reflect over the [tex]x[/tex]-axis, shift 2 units down D. shift 4 units right, reflect over the [tex]y[/tex]-axis, shift 2 units down

📝 Answered - Solve the equation by using substitution: 5) [tex](t+4)^2-(t+4)-12=0[/tex] A) {4,-3} 6) Find the distance between the A) 244

📝 Answered - Which statement is true about the graphs of the two lines [tex]y=-\frac{4}{5} x+2[/tex] and [tex]y=-\frac{5}{4} x-\frac{1}{2}[/tex]? The lines are perpendicular to each other because [tex]-\frac{4}{5}[/tex] and [tex]-\frac{5}{4}[/tex] are opposite reciprocals of each other. The lines are perpendicular to each other because 2 and [tex]-\frac{1}{2}[/tex] are opposite reclprocats of each other. The lines are neither parallel nor perpendicular to each other because [tex]-\frac{4}{5}[/tex] and [tex]-\frac{5}{4}[/tex] are not opposite reciprocals of each other. The lines are neither parallel nor perpendicular to each other because 2 and [tex]-\frac{1}{2}[/tex] are not opposite reciprocals of each other.

📝 Answered - The equation [tex]$y=45 x$[/tex] represents the number of miles, [tex]$y$[/tex], Mr. Miller's car can travel using [tex]$x$[/tex] gallons of gas. Which data display represents a car that gets more miles per gallon than Mr. Miller's car? A. Gas Mileage | Number of Gallons | Number of Miles | | :---------------- | :---------------- | | 2 | 96 | | 4 | 192 | | 6 | 288 | B. Gas Mileage | Number of Gallons | Number of Miles | | :---------------- | :---------------- | | 5 | 195 | | 10 | 390 | | 15 | 585 | C.

📝 Answered - Which of the following describes the domain of the piecewise function [tex]g(x)=\left\{\begin{array}{lll}\frac{x^2+3 x}{x^2+x-6} & \text { for } & x\ \textless \ 3 \\ \log _2(x+5) & \text { for } & x \geq 3\end{array}\right.[/tex] ? A. [tex](-\infty, \infty)[/tex] B. [tex](-\infty, 2) \cup(2, \infty)[/tex] C. [tex](-\infty, 2) \cup(2,3) \cup(3, \infty)[/tex] D. [tex](-\infty,-3) \cup(-3,2) \cup(2, \infty)[/tex]

📝 Answered - A polygon is graphed on a coordinate plane. The polygon is transformed according to the rule [tex]$T_{(2,3)}$[/tex]. Which transformations produce the same result? [tex]$T_{(2,2)} \circ T_{(3,3)}$[/tex] [tex]$T_{(2,3)} \circ T_{(2,3)}$[/tex] [tex]$T_{(1,-4)} \circ T_{(-3,1)}$[/tex] [tex]$T_{(-1,4)} \circ T_{(3,-1)}$[/tex]