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Questions in mathematics

📝 Answered - A survey was conducted at a high school to study school sports in different grade levels. The data gathered is in the two-way table below: | | Football | Baseball | Soccer | Total | | :-------- | :------- | :------- | :----- | :---- | | Freshman | 2 | 6 | 0 | 8 | | Sophomore | 3 | 2 | 1 | 6 | | Junior | 4 | 0 | 5 | 9 | | Senior | 1 | 2 | 4 | 7 | | Total | 10 | 10 | 10 | 30 | Based on this table, what is the relative frequency that a student is a junior who plays football?

📝 Answered - Holly is thinking of a number. $\frac{3}{4}$ of Holly's number is 39. Work out the number Holly is thinking of.

📝 Answered - Convert the decimal 0.984 to a fraction. A. [tex]$\frac{984}{100}$[/tex] B. [tex]$\frac{984}{1000}$[/tex] C. [tex]$\frac{984}{999}$[/tex] D. [tex]$\frac{984}{99}$[/tex]

📝 Answered - Find the 7th term of this geometric sequence. [tex] \begin{array}{c} 2,8,32,128, \ldots \ a_7=[?] \end{array} [/tex]

📝 Answered - What is the sum of the first five terms of the geometric sequence in which a₁ = 3 and r=1/3? Express your answer as an improper fraction using the slash (/) key and no spaces.

📝 Answered - Solve the system of equations: [tex] \begin{array}{l} 2.5 y+3 x=27 \\ 5 x-2.5 y=5 \end{array} [/tex] What equation is the result of adding the two equations? What is the solution to the system?

📝 Answered - Solve $S I=P(1+r t)$ for $P$. $P=\frac{S I}{1+r t}$ Given the formula in the format to input into the calculator. Type your answer with a negative exponent $P=$

📝 Answered - Find the logarithm using the change of base formula. [tex]$\log _8 18$[/tex] [tex]$\log _8 18=$ $\square$[/tex] (Round to four decimal places as needed.)

📝 Answered - Which pair of vectors is orthogonal? A. [tex]u =\langle-3,2\rangle[/tex] and [tex]v =\langle-2,1\rangle[/tex] B. [tex]u =\langle 1,5\rangle[/tex] and [tex]v =\langle-5,1\rangle[/tex] C. [tex]u =\langle 2,1)[/tex] and [tex]v =\langle-4,3\rangle[/tex] D. [tex]u =\langle 2,3\rangle[/tex] and [tex]v =\langle 3,1\rangle[/tex]

📝 Answered - Find the sum of the following geometric series: [tex]$\sqrt{2}+\frac{1}{\sqrt{2}}+\frac{1}{2 \sqrt{2}}+\ldots \text { to } 8 \text { term }$[/tex]