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Questions in mathematics

[Done] Work out $10 \times 5 \frac{1}{3}$. Give your answer as a fraction in its simplest form.

[Done] In a floor plan, the length, [tex]$l$[/tex], of a rectangular room is twice its width, [tex]$w$[/tex]. The perimeter of the room must be greater than 72 feet. Which inequality can be used to find all possible widths of the room, in feet? A. [tex]$6 w\ \textgreater \ 72$[/tex] B. [tex]$6 w\ \textless \ 72$[/tex] C. [tex]$3 w\ \textgreater \ 72$[/tex] D. [tex]$3 w\ \textless \ 72$[/tex]

[Done] Quadrilateral B: Angle A: 60° Angle B: 120° Angle C: 60° Angle D: 120° Type of Quadrilateral?

[Done] 45 storybooks 30 science books The rest are maths books. Every week, students borrow 10 storybooks, 5 science books, and 8 maths books. Questions: 1. How many maths books are there in the library? 2. How many books are borrowed in one week? 3. How many books are left in the library after one week? 4. If the same number of books is borrowed every week, how many books will be borrowed in 4 weeks?

[Done] Without finding the squares, find the units digit in the squares of the following numbers: (i) 352 (ii) 9377 (iii) 285 (iv) 4626 (v) 999

[Done] 1. Write the following numbers in words as per the Indian system of numeration. a. 5,08,943 b. 28,86,073 c. 75,92,000 d. 54,87,222 2. Write the following numbers in words as per the International system of numeration. a. 843,628 b. 8,372,131 c. 2,937,139 d. 645,231 3. Write the following numbers in figures. a. Seventy-three lakh thirty-five thousand eight hundred sixty-one b. Five lakh twenty thousand c. Ninety-nine lakh ninety-nine thousand nine hundred ninety-nine d. Four million twenty-eight thousand six hundred nineteen 4. Insert commas (,) and write the numbers as per the Indian and the International systems of numeration. a. 325640 b. 6602140 c. 1000658 d. 321012 e. 7851254

[Done] Given that $\cos \beta=-\frac{1}{\sqrt{5}}$, where $180^{\circ}<\beta<360^{\circ}$. Determine, with the aid of a sketch and without using a calculator, the value of $\sin \beta$.

[Done] Complete the table: Answer: \begin{tabular}{|c|c|}\hline Class & Class centre \\ \hline 0 - under 5 & $2.5$ \\ 5 - under 11 & \\ 11 - under 17 & \\ 17 - under 23 & \\ 23 - under 29 & \\ 29 - under 25 & \\ \hline\end{tabular}

[Done] Factor $16 x^2+40 x+25$ A. $(4 x+5)(-4 x-5)$ B. $(4 x-5)^2$ C. $(4 x+5)^2$ D. $(-4 x+5)^2$

[Done] If $s(x)=x-7$ and $t(x)=4 x^2-x+3$, which expression is equivalent to $(t \circ s)(x)$? A. $4(x-7)^2-x-7+3$ B. $4(x-7)^2-(x-7)+3$ C. $(4 x^2-x+3)-7$ D. $(4 x^2-x+3)(x-7)$