| Topic | Problem | Solution |
|---|---|---|
| None | A particle $P$ moves on the positive $x$-axis. Th… | Integrate the velocity function to find the position function: \(x(t) = \frac{2}{3}t^3 - \frac{9}{2… |
| None | Consider the circuit, in which three resistors of… | Apply Kirchhoff's Voltage Law (KVL) to the two loops in the circuit: Loop 1: \(V - I_1 R - I_2 2R =… |
| None | Select all the true equations. A. $\cos (15)=\sin… | Evaluate each equation using trigonometric functions: |
| None | Given that $f(\theta)=\cos (n \theta)$ has the sa… | Find the value of n such that the period of \(f(\theta) = \cos(n\theta)\) is the same as the period… |
| None | $(4)$ 6. Commercial airplanes often fly around $3… | Convert 30000 feet to miles: \(\frac{30000}{5280}\) |
| None | 5 For a normal distribution, $P(X \leq 23.8)=91.9… | Given probabilities: $P(X \leq 23.8) = 91.92%$ and $P(X \leq 17.15) = 30.85%$ |
| None | 4 Find the cumulative distribution function for t… | Find the cumulative distribution function (CDF) by integrating the given probability density functi… |
| None | Which of the following can be used to calculate t… | Calculate the height using the sine function: height = distance * sin(angle) |
| None | Three children are throwing a disc in the park. T… | Find the x and y components of each throw: \(x_1 = -16.57\), \(y_1 = -7.03\), \(x_2 = 8.92\), \(y_2… |
| None | $\frac{6 n}{n^{2}-9}-\frac{3}{n+3}$ | Factor the denominator of the first term: $\frac{6n}{(n-3)(n+3)} - \frac{3}{n+3}$ |
| None | Simplify $\frac{\sqrt{x\left(x^{2 n+1}\right)}}{\… | Rewrite the expression using exponents: \(\frac{x^{\frac{1}{2}}x^{\frac{2n+1}{2}}}{x^{n}}\) |
| None | e un seul logarithme, l'expression suivante: \[ 2… | Apply property 1: \( 10\log{x} - 12\log{2x^3} + 12\log{4x^4} \) |
| None | Solve the system of equations using technology: \… | Set the two equations equal to each other: \( (4x - 1)^2 - 1 = -4x + 1 \) |
| None | Un bocal contient 7 bonbons bleus, 3 jaunes et 10… | Calculer la probabilité de tirer un bonbon bleu : \(\frac{7}{20}\) soit \(0.35\) |
| None | Un cylindre a un rayon de $22 \mathrm{~cm}$ à la … | 1. Calculate the area of one of the bases: A = π * r^2 = 3.1416 * (22)^2 = \(1520.53 cm^2\) |
| None | 9.67 A vinyl record that is initially turning at … | Convert initial angular velocity from rpm to rad/s: \(\omega_{i} = 33.33 \times \frac{2\pi}{60} = 3… |
| None | The area of the circle below is $59 \mathrm{~cm}^… | Find the area of the minor sector OAB: \(Area_{OAB} = Area_{circle} \times Fraction\) |
| None | The radius of the circle below is $22 \mathrm{~mm… | Given the radius of the circle is 22 mm, we can calculate the area using the formula: Area = \(\pi … |
| None | In $\triangle \mathrm{MNO}, m=89$ inches, $n=30$ … | Using the Law of Cosines: \(89^2 = 30^2 + 71^2 - 2(30)(71)\cos(M)\) |
| None | A survey was given to a randorn sample of voters … | Given percentage: \(55%\) and margin of error: \(3.5%\) |
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