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Questions in mathematics

📝 Answered - Golf Clubs R Us had a set of 10 golf clubs that were marked on sale for $590. This was a discount of 25% off the original selling price. If the golf clubs cost Golf Clubs R Us $570, what was their profit? Follow the problem-solving process and round your answer to the nearest cent, if necessary.

📝 Answered - Solve the equation. If there is no solution, select no solution. [tex]5|n|-15=40[/tex]

📝 Answered - Simplify $(8 j^3-5 j^2-5)-(6 j^3-12 j^2+8 j-7)$

📝 Answered - $\begin{array}{l}\left(-2 \frac{1}{8}\right)+\left(-3 \frac{1}{2}\right)+(+5)+(+1.125)+ \\ \left(+4 \frac{1}{2}\right)\end{array}$

📝 Answered - Work out $\frac{5}{6} \times \frac{7}{3}$. Give your answer as a fraction in its simplest form.

📝 Answered - If 2 is added to the numerator and denominator of a fraction, it becomes [tex]$\frac{9}{10}$[/tex] and if 3 is subtracted from the same numerator and denominator, it becomes [tex]$\frac{4}{5}$[/tex]. Find the fraction.

📝 Answered - Let $f(x)=x^2-7 x$ and $g(x)=6+x$. Find the following. (a) $( f + g )( x )$ (b) $( f - g )( x )$ (c) $( f \cdot g )( x )$ (d) $\left(\frac{f}{g}\right)(x)$ (e) The domain of $\frac{f}{g}$ (a) $(f+g)(x)=x^2-6 x+6$ (Simplify your answer. Do not factor.) (b) $(f-g)(x)=$ $\square$ (Simplify your answer. Do not factor.)

📝 Answered - Write the equation of the circle in standard form. Then identify the center and radius of the circle. [tex]x^2+y^2-10 x+8 y+37=0[/tex] center: ( $\square$, $\square$ ) radius: $\square$

📝 Answered - (a) A continuous random variable $x$ 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 $x$.

📝 Answered - A hunter climbs on a tree of unknown height and aims to shoot an antelope at an angle of depression [tex]$38^{\circ}$[/tex]. Given that the horizontal distance of the hunter from the antelope is [tex]$1,500 m$[/tex], calculate the height of the tree, correct to the nearest whole number. [Hint: [tex]$\tan 38^{\circ}=0.7813, \quad \operatorname{Cos} 38^{\circ}=0.7880$, $\sin 38^{\circ}=0.6157[/tex]]