| Topic | Problem | Solution |
|---|---|---|
| None | An object is moving with velocity (in $\mathrm{ft… | The velocity of the object is given by the function \(v(t) = t^{2} + t - 12\) in ft/sec. |
| None | If $\int_{0}^{1} f(x) d x=-3$ and $\int_{1}^{6} f… | We are given that \(\int_{0}^{1} f(x) d x=-3\) and \(\int_{1}^{6} f(x) d x=-8\). |
| None | 42. Two students were chosen at random from each … | Two students were chosen at random from each first period class and asked to complete a survey abou… |
| None | Evaluate the Integral $\int(x+1)^{3} d x$ | The integral of a function can be found using the power rule for integration, which states that the… |
| None | 43. The antenna of a parabolic dish is 20 meters … | The parabolic dish is a parabola that opens downwards. The standard form of a parabola that opens d… |
| None | 40. Compute $\log _{4} 5$ using the change-of-bas… | Given the problem to compute \(\log _{4} 5\), we can use the change-of-base formula. |
| None | 41. Simplify $\left(x^{2}+5 x+5\right)-\left(2 x^… | Given the expression \(\left(x^{2}+5 x+5\right)-\left(2 x^{2}+6\right)\). |
| None | 38. Convert $\frac{5 \pi}{6}$ to degrees. | To convert radians to degrees, we can use the formula: Degrees = Radians * \(\frac{180}{\pi}\) |
| None | 39. What is the inverse of $f(x)=\sqrt{x+2}$ ? | Let's denote the inverse of \(f(x)\) as \(g(x)\). So we can evaluate \(f\) at \(g(x)\) to get \(f(g… |
| None | Two dies are rolled. Find the probability of the … | The problem is asking for the probability of two events happening together: rolling less than 4 on … |
| None | $\begin{array}{l}(4 x+12) \\ (80-x)\end{array}$ w… | The given expressions represent the slopes of two lines. For two lines to be parallel, their slopes… |
| None | 37. The scores on a statistics test are normally … | The problem is asking for the percentage of students who scored between 77 and 83 on a statistics t… |
| None | 36. How many two-letter code words can be made fr… | The problem is asking for the number of two-letter code words that can be made from the letters 'MA… |
| None | 35. A bag contains three chocolate candies and tw… | The problem is asking for the probability of drawing all three chocolate candies in three consecuti… |
| None | 34. What is the probability of drawing a club or … | The probability of an event is calculated by dividing the number of favorable outcomes by the total… |
| None | Simplify $\sin ^{2} x+\sin ^{2} x \cot ^{2} x$ | Rewrite the given expression as \(\sin ^{2} x+\sin ^{2} x \frac{\cos ^{2} x}{\sin ^{2} x}\) |
| None | 32. Describe the transformation of the graph of $… | The function \(f(x)=\frac{1}{2} \sin x+2\) is a transformation of the function \(g(x)=\sin x\). |
| None | 30. Solve $\frac{3}{x+3}+\frac{2}{2 x-6}=\frac{7}… | Solve the equation \(\frac{3}{x+3}+\frac{2}{2x-6}=\frac{7}{8}\) for \(x\). |
| None | 29. The rate you run to your friend's house is in… | The problem states that the rate at which you run to your friend's house is inversely proportional … |
| None | For $f(x)=4 x-9$ and $g(x)=\frac{1}{4}(x+9)$, fin… | Given functions are $f(x)=4 x-9$ and $g(x)=\frac{1}{4}(x+9)$. |
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