| Topic | Problem | Solution |
|---|---|---|
| None | Given the equation $3 x^{3}+2 x^{2} y-4 y^{3}=0$,… | Given the equation $F(x, y)=3 x^{3}+2 x^{2} y-4 y^{3}=0$, we are asked to find $\frac{d y}{d x}$. |
| None | Reduce the following ratio to its smallest terms.… | The question is asking to reduce the given ratio to its smallest terms. This can be done by finding… |
| None | After two consecutive years of $8 \%$ losses, wha… | Let's denote the initial value of the stock as \(x\). After the first year, the value of the stock … |
| None | The result of slicing through the center of the s… | The volume of a solid can be calculated by integrating the area of the cross sections. In this case… |
| None | UCF students pay an average of $\mu=1,222$ dollar… | The problem is asking for the probability that the mean cost of books for 36 students exceeds a cer… |
| None | By rewriting the formula for the multiplication r… | We are given the probability of event A (flight departs on time) as 0.89, event B (flight arrives o… |
| None | Compute the gradient of the following function an… | The gradient of a function $f(x, y)$ is given by the vector of its partial derivatives, i.e., $\nab… |
| None | 9. Use the discriminate to determine the number o… | The given equation is not a quadratic equation. A quadratic equation is of the form $ax^2 + bx + c … |
| None | 11. Consider the function $f(x, y)=x^{2}-4 y^{2}-… | First, we need to find the gradient of the function \(f(x, y)=x^{2}-4 y^{2}-8\), which is a vector … |
| None | Use the two-path test to prove that the following… | Consider the function \(f(x, y)=\frac{x+2 y}{x-2 y}\). |
| None | 8. A cab charges $\$ 0.10$ per mile and a flat fe… | The question is asking for an equation that models the price of a cab ride. The price is determined… |
| None | $\sum_{x=0}^{16} 6(x ; 19,0.7)-\sum_{x=0}^{15} 6(… | The problem is about the sum of a function \(6(x ; 19,0.7)\) from \(x=0\) to \(x=16\) minus the sum… |
| None | The shape of a dome can be modeled by the equatio… | The shape of a dome can be modeled by the equation \(h=-2 d^{2}+100\) where \(h\) is the height (in… |
| None | $\sum_{x=0}^{5} b(x ; 12,8)$ | The problem is asking for the sum of binomial probabilities for x ranging from 0 to 5, given 12 tri… |
| None | Subtract $\frac{6}{7}$ from $\frac{4}{3}$. | Subtract \(\frac{6}{7}\) from \(\frac{4}{3}\). |
| None | Find the missing denominator. \[ \frac{7}{8}=\fra… | The problem is asking for the missing denominator in the equation \(\frac{7}{8} = \frac{21}{?}\). |
| None | Re-write the given number by placing negative sig… | Given the number \(\frac{-3}{14}\). |
| None | The SAT scores $(x)$ of Florida high school stude… | The SAT scores of Florida high school students are normally distributed with mean \(\mu=1,308\) and… |
| None | $y=x^{2}-3 x+5$ | The given equation is a quadratic equation in the form of \(ax^{2}+bx+c=0\). Here, \(a=1\), \(b=-3\… |
| None | $A-(x+3)^{2}=-4 x-15$ | Expand the equation: \(A - (x + 3)^2 = -4x - 15 \Rightarrow A - x^2 - 6x - 9 = -4x - 15\) |
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