| Topic | Problem | Solution |
|---|---|---|
| None | Convert $\frac{1}{3}$ To decimal and explain how | Divide the numerator by the denominator: \(\frac{1}{3} = 1 \div 3\) |
| None | $\int \frac{1}{x^{2}-1} d x$ | Perform partial fraction decomposition: \(\frac{1}{x^2 - 1} = \frac{1/2}{x - 1} - \frac{1/2}{x + 1}… |
| None | $-\frac{1}{2}-3=$ | \(-\frac{1}{2} - 3 = -\frac{1}{2} - \frac{6}{2}\) |
| None | $\begin{array}{l}y=-x+3 \\ y=6 x-4\end{array}$ | Set the two equations equal to each other: \(-x + 3 = 6x - 4\) |
| None | e 7 : solve the following differential equation :… | Find the characteristic equation: \(r^2 - 1 = 0\) |
| None | $\left(\frac{x+3}{(x+1)}\right)^{\prime}$ | Given function: \(\frac{x+3}{x+1}\) |
| None | $5^{6} \cdot 5^{2} \cdot 5^{3}$ | Multiply the numbers with the same base and add the exponents: \(5^{6} \cdot 5^{2} \cdot 5^{3} = 5^… |
| None | Problem 02. X-rays for human applications can be … | Calculate the energy of the n=1 and n=2 orbitals for Tungsten using the formula: \(E_n = -\frac{Z^2… |
| None | In a certain Algebra 2 class of 24 students, 6 of… | Let x be the number of students who play both sports. Then, we have the equation: \(6 + 16 - x = 18… |
| None | Question 7 of 29 If a normal distribution has a m… | Given a normal distribution with mean \(\mu = 104\) and standard deviation \(\sigma = 4\), we want … |
| None | Question 6 of 29 There are 8 seniors on the high … | This is a combination problem because the order of the co-captains does not matter. We need to find… |
| None | Write the ratio for $\sin A$. \[ \sin A= \] (Type… | Recall the definition of sine in a right triangle: \(\sin A = \frac{\text{opposite side}}{\text{hyp… |
| None | You saved $\$ 20$ per mon or 20 months. Which exp… | Find the total amount of money saved by multiplying the amount saved per month by the number of mon… |
| None | Question 5 of 29 Suppose a normal distribution ha… | Calculate the z-score: $$z = \frac{x - \mu}{\sigma} = \frac{47 - 50}{3} = -1$$ |
| None | In $\triangle \mathrm{PQR}, p=99 \mathrm{~cm}, r=… | Use the Law of Cosines to find the length of side q: \(q = \sqrt{p^2 + r^2 - 2pr \cos{R}}\) |
| None | Let the region $\mathrm{R}$ be the area enclosed … | Find the intersection points of \(f(x) = 2\sqrt{x}\) and \(g(x) = 2x\) to determine the limits of i… |
| None | Let the region $\mathrm{R}$ be the area enclosed … | Find the points of intersection between \(f(x) = 3x^2\) and \(g(x) = 4x\) by setting \(f(x) = g(x)\) |
| None | Let the region $\mathrm{R}$ be the area enclosed … | Find the intersection points of \(f(x) = e^x\) and \(y = 3\) to determine the limits of integration… |
| None | Let the region $\mathrm{R}$ be the area enclosed … | Find the intersection points of the function \(f(x) = x^2 - 2\) and the horizontal line \(y = 6\) t… |
| None | Find the derivative using the chain rule. \[ f(a)… | Find the derivative of the outer function: \(\frac{1}{2\sqrt{8a^7 + 6}}\) |
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