| Topic | Problem | Solution |
|---|---|---|
| None | \[ \left[\begin{array}{rrrr} -3 & 6 & -1 & -10 \\… | The given matrix represents a system of linear equations. Each row in the matrix corresponds to one… |
| None | Marissa went shopping for holiday presents. She b… | Translate the problem into two equations based on the given information: \(C + O = 14\) and \(12C +… |
| None | \( (x+9)^{2}+(2 x-8)^{2}=x^{2} \) | \( (x+9)^{2}-(x^{2})=(2x-8)^{2} \) |
| None | $\left\{\begin{array}{l}4 x+6 y-6 z=36 \\ 2 x+y-2… | We are given the system of linear equations: \[\begin{cases} 4x+6y-6z=36 \ 2x+y-2z=13 \ 2x+3y-2z=15… |
| None | Rewrite the equation in terms of base $e$. Expres… | Rewrite the equation in terms of base \(e\). Using the property of logarithms that states \(a^b = e… |
| None | The logistic growth function $\mathrm{P}(\mathrm{… | The logistic growth function \(P(x)=\frac{90}{1+271 e^{-0.122 x}}\) models the percentage, \(P(x)\)… |
| None | $\left\{\begin{array}{l}4 x-9 y-4 z=-59 \\ -7 x+5… | We are given a system of linear equations with three variables: \(4x - 9y - 4z = -59\), \(-7x + 5y … |
| None | $\begin{aligned} 4 x-9 y-4 z & =-59 \\ -7 x+5 y+z… | We are given a system of linear equations with three variables: \(4x - 9y - 4z = -59\), \(-7x + 5y … |
| None | Calculate the volume of the cylinder Give your an… | The volume of a cylinder can be calculated using the formula: Volume = \(\pi\) * radius^2 * height |
| None | Jane took $30 \mathrm{~min}$ to drive her boat up… | Let's denote the boat speed in still water as x (km/hr). The distance she travelled upstream and do… |
| None | Margaret drove to a business appointment at $70 \… | Margaret drove to a business appointment at a speed of 70 mph. Her average speed on the return trip… |
| None | When Fritz drives to work his trip takes 36 minut… | Let's denote the distance Fritz travels to work as \(d\), Fritz's driving speed as \(s\), the time … |
| None | \( (2 x+7)^{2}+(4 x-7)^{2}=4 x^{2} \) | \( \text{Expand the squares}\: (2x+7)^{2} = 4x^{2} + 28x + 49 \) |
| None | $\int_{\frac{1}{2}}^{2} \frac{\pi x\left(4 x^{2}+… | We are given the definite integral problem: \(\int_{\frac{1}{2}}^{2} \frac{\pi x\left(4 x^{2}+3\rig… |
| None | The difference between seven times a number and 9… | Translate the problem into a mathematical equation. The statement 'seven times a number' can be rep… |
| None | Based on a poll, $40 \%$ of adults believe in rei… | Given that the probability of an adult believing in reincarnation is 40%, we are asked to find the … |
| None | Part 3 of 4 Based on a poll, $40 \%$ of adults be… | The question asks for the probability that at least 4 of the selected adults believe in reincarnati… |
| None | Based on a poll, among adults who regret getting … | This problem is about the binomial distribution. The binomial distribution model is appropriate for… |
| None | Locate any intercepts of the function. 4) $f(x)=\… | First, we need to understand the function $f(x)$, which is defined in three parts: $f(x)=1$ for $-2… |
| None | $\int_{\frac{1}{2}}^{1} 2 \pi\left(\frac{x^{3}}{2… | This is a definite integral problem. The integral is from \(\frac{1}{2}\) to 1 of a function. The f… |
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