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Questions in mathematics

[Done] Work out and simplify where possible. a) $8 \times \frac{1}{5}$ b) $\frac{1}{8} \times 15$

[Done] Solve this system of linear equations. Write your answer as an ordered pair, $(x, y)$. $\begin{array}{l} 6 x+4 y=24 \\ 6 x+3 y=21 \end{array}$

[Done] 1. Condense $5 \log _3(x)+2 \log _3(4 x)-\log _3 8 x^5$ 2. Prove the hyperbolic identity $ch ^2- sh ^2=1$ 3. A cylindrical container has a radius of 7 m and a vertical height of 20 m. a) Calculate the amount of water the container can hold in litres. b) If the container has a mass of 1320 kg, calculate the density of the material used in making the container. 4. The following marks were scored by engineering students in mathematics test | Marks | $40-44$ | $45-49$ | $50-54$ | $55-59$ | $60-64$ | $65-69$ | $70-74$ | | :-------- | :------ | :------ | :------ | :------ | :------ | :------ | :------ | | frequency | 3 | 8 | 12 | 15 | 19 | 8 | 9 | State the; I) Modal class II) Modal frequency Calculate the; I) Mean mark II) Median mark III) Variance 5. Determine the modulus and argument of the complex number $z=\frac{9+3 j}{1+2 j}$

[Done] Simplify the following: $\left(p^{2+3 n}\right)\left(p^{2 n}\right)$

[Done] Adam's car traveled 465.3 miles on 16.5 gallons of gas. Which equation can be used to determine the average number of miles that the car traveled on each gallon of gas? [tex]$16.5 x=465.3$[/tex] [tex]$\frac{x}{16.5}=485.3$[/tex] [tex]$465.3 x=16.5$[/tex] [tex]$\frac{x}{465.3}=16.5$[/tex]

[Done] Which of the following is a logarithmic function? $y=\log _3 x$ $y=3^x$ $y=x+3$ $y=x^3$

[Done] Determine whether the equation defines y as a function of x. [tex]y=9 x^2-7 x+6[/tex] Does the equation define [tex]y[/tex] as a function of [tex]x[/tex]? A. Yes B. No

[Done] At a game show, there are 8 people (including you and your friend) in the front row. The host randomly chooses 3 people from the front row to be contestants. The order in which they are chosen does not matter. There are [tex]$B _8 C _3=56$[/tex] total ways to choose the 3 contestants. What is the probability that you and your friend are both chosen? A. [tex]$\frac{6}{56}$[/tex] B. [tex]$\frac{3}{56}$[/tex] C. [tex]$\frac{2}{56}$[/tex]

[Done] Multiply. 3x * 4x^9 * v^2 * 2v^6 Simplify your answer as much as possible.

[Done] There are four steps for converting the equation $x^2+y^2+12 x+2 y-1=0$ into standard form by completing the square. Complete the last step. 1. Group the $x$ terms together and the $y$ terms together, and move the constant term to the other side of the equation. $x^2+12 x+y^2+2 y=1$ 2. Determine $(b \div 2)^2$ for the $x$ and $y$ terms. $(12 \div 2)^2=36 \text { and }(2 \div 2)^2=1$ 3. Add the values to both sides of the equation. $x^2+12 x+36+y^2+2 y+1=1+36+1$ 4. Write each trinomial as a binomial squared, and simplify the right side. $(x+\square)^2+(y+\square)^2=\square