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Questions in mathematics

[Done] [tex]$24 a-22=-4(1-6 a)$[/tex]

[Done] Give me MCQs on identities for ICSE grade 9.

[Done] Simplify the radical expression. Write your answer in the simplest form. $2 \sqrt{48}+\sqrt{200}-\sqrt{75}-4 \sqrt{32}$

[Done] The length of the base edge of a pyramid with a regular hexagon base is represented as [tex]$x$[/tex]. The height of the pyramid is [tex]$3$[/tex] times longer than the base edge. The height of the pyramid can be represented as $\square$. The area of an equilateral triangle with length [tex]$x$[/tex] is [tex]$\frac{x^2 \sqrt{3}}{4}$[/tex] units [tex]$^2$[/tex]. The area of the hexagon base is $\square$ times the area of the equilateral triangle. The volume of the pyramid is $\square$ [tex]$x^3 \sqrt{3}$[/tex] units [tex]$^3$[/tex].

[Done] Which of the following is a biconditional statement? A) If [tex]$x \neq 5$[/tex] then [tex]$x^2 \neq 25$[/tex] B) [tex]$x=5$[/tex] if and only if [tex]$x+5=10$[/tex] C) [tex]$x=5$[/tex] if [tex]$x^2=25$[/tex] D) If [tex]$x^2=25$[/tex], then [tex]$x=5$[/tex] or [tex]$x=-5$[/tex]

[Done] Simplify: (a) [tex]$\sin \left(180^{\circ}-\theta\right)+\sin \left(360^{\circ}-\theta\right)$[/tex] (b) [tex]$\cos \left(180^{\circ}+x\right)-\cos \left(360^{\circ}-x\right)$[/tex] (c) [tex]$\frac{\tan \left(180^{\circ}- A \right)}{\tan \left(180^{\circ}+ A \right)}$[/tex] (d) [tex]$\sin \left(360^{\circ}-\alpha\right) \cdot \sin \left(180^{\circ}+\alpha\right)$[/tex] (e) [tex]$\frac{\cos \left(360^{\circ}-\theta\right) \cdot \tan \left(180^{\circ}-\theta\right)}{\cos \left(180^{\circ}-\theta\right)}$[/tex] (f) [tex]$\frac{\sin \left(180^{\circ}- B \right) \cdot \tan \left(360^{\circ}- B \right)}{\sin \left(180^{\circ}+ B \right)}$[/tex] (g) [tex]$\frac{\tan \left(360^{\circ}-x\right) \cdot \tan \left(180^{\circ}+x\right)}{\tan ^2\left(180^{\circ}-x\right)}$[/tex] (h) [tex]$\frac{\sin ^2\left(360^{\circ}-\theta\right) \cdot \cos ^2\left(360^{\circ}-\theta\right)}{\sin \left(180^{\circ}+\theta\right) \cdot \sin \left(180^{\circ}-\theta\right)}$[/tex]

[Done] Given the table: | | Sunrise | No Sunrise | Total | | :------ | :------ | :--------- | :---- | | Sunset | 14 | 12 | 26 | | No Sunset | 7 | 5 | 12 | | Total | 21 | 17 | 38 | Which is the joint relative frequency for the people who can only see the sunset? A. [tex]$\frac{5}{38}$[/tex] B. [tex]$\frac{7}{38}$[/tex] C. [tex]$\frac{12}{38}$[/tex] D. [tex]$\frac{14}{38}$[/tex]

[Done] In the triangle shown, use appropriate trigonometric rules to calculate the values of the unknowns. Express your final answer in the format: x, θ, β, and choose the correct answer from the provided options. Options: 1) 46.29, 63.71°, 12.4 units 2) 12.75 units, 68.1°, 41.9° 3) 12.40 units, 46.29°, 63.71° 4) 12.84 units, 66.3°, 43.7°

[Done] Find the product. i. 47945 x 567 iv. 56890 x 400 vii. 63250 x 149 x. 876 x 145 xiii. 8420 x 240

[Done] (2) $\frac{3}{5}$ of the men at a club meeting drank beer and $\frac{5}{8}$ drank wine. Every man drank at least one of these drinks. If 18 men drank both beer and wine, how many men attended the club meeting?