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Questions in mathematics

📝 Answered - Simplify: $\frac{3}{4}$ of $\left(\frac{11}{15}-\overline{\frac{3}{5}-\frac{1}{3}}\right) \div 1 \frac{2}{5}$

📝 Answered - What is the solution to the system of equations? [tex] \begin{array}{l} y=\frac{2}{3} x+3 \\ x=-2 \end{array} [/tex]

📝 Answered - The length of a rectangle is 10 more than three times its width. The perimeter of the rectangle is 108. Find the dimensions of the rectangle.

📝 Answered - Write the next three multiples of 17. $17, 34, 51, 68, 85$, ____, ____, ____.

📝 Answered - [tex]\sqrt{25 a^2 b^2} \times \sqrt[3]{27 a^3}[/tex]

📝 Answered - Round to 3 significant figures. $901.234$

📝 Answered - (a) A continuous random variable [tex]$x$[/tex] has a probability density function defined [tex]f(x)=\left\{\begin{array}{cc} k\left(x-\frac{1}{a}\right), & 0 \leq x \leq 3 \\ 0, & \text { elsewhere }\\ \end{array}\right.[/tex] Given that [tex]$P ( x \geq 1)=0.8$[/tex], determine the: (i) values of the constants a and k ; (ii) mean of [tex]$x$[/tex].

📝 Answered - Simplify the expression $5(x-3)(x^2+4x+1)$.

📝 Answered - Which of the following cannot be a right-angled triangle? A. [tex]$3 cm, 4 cm, 5 cm$[/tex] B. [tex]$2 cm, 1 cm, \sqrt{5 cm}$[/tex] C. [tex]$400 mm, 300 mm, 500 mm$[/tex] D. [tex]$9 cm, 15 cm, 12 cm$[/tex].

📝 Answered - For each ($P, V$) pair, type the pressure in the x column and the volume in the y-column. Then click 'Resize window to fit data.' Choose the power regression option. Copy the equation, using three significant figures, to match the data. [tex]\begin{array}{l}< V=51.4 \quad \checkmark \ P^{\wedge}-1.00 \quad X \Rightarrow-0.999 \end{array}[/tex] Notice that the exponent is very close to -1. The equation is essentially in the form of [tex]V=k P^{-1}[/tex] Is this a proportion, an inverse proportion, a linear relationship, a quadratic relationship, or a direct proportion?