| Topic | Problem | Solution |
|---|---|---|
| None | 1. Sam needs to construct two adjacent pens again… | Let's denote the length of the fence perpendicular to the wall as \(x\), and the length of the fenc… |
| None | A cylindrical drill with radius 3 is used to bore… | Given a sphere with radius 5 and a cylindrical drill with radius 3. |
| None | Use the properties of logarithms to expand $\log … | Given the logarithmic expression \(\log \left(z y^{7}\right)\). |
| None | A specific radioactive substance follows a contin… | The formula for exponential decay is given by \(y = y_0 * e^{-kt}\), where \(y_0\) is the initial a… |
| None | Write the first five terms of the geometric seque… | The given sequence is a geometric sequence where each term is twice the previous term. The first te… |
| None | An article in a journal reports that $34 \%$ of A… | An article in a journal reports that 34% of American fathers take no responsibility for child care.… |
| None | If $z$ is a standard normal variable, find the pr… | Let $z$ be a standard normal variable, which follows a normal distribution with mean 0 and standard… |
| None | Based on a Comcast survey, there is a 0.8 probabi… | This problem is about the binomial distribution. We are given the probability of success (\(p = 0.8… |
| None | Of 1232 people who came into a blood bank to give… | Given that 1232 people came into a blood bank to give blood, out of which 397 people had high blood… |
| None | Find the critical value or values of $\chi^{2}$ b… | Given that the sample size, \(n=19\), the significance level, \(\alpha=0.025\), and the alternative… |
| None | For each ordered pair, determine whether it is a … | Given the system of equations: \[\left\{\begin{array}{c} y=2 x+1 \\ -5 x+3 y=8 \end{array}\right.\] |
| None | A genetic experiment involving peas yielded one s… | Identify the null hypothesis and the alternative hypothesis. The null hypothesis is that the propor… |
| None | What is the kernel of the linear transformation $… | The kernel of a linear transformation T, denoted as ker(T), is the set of all vectors in the domain… |
| None | Solve $v^{3}=11$ where $v$ is a real number. Simp… | The problem is asking for the cube root of 11. |
| None | $4+4$ | This is a simple addition problem. We just need to add 4 and 4 together. |
| None | The number of bacteria $P(t)$ in a certain popula… | The problem is asking for the number of bacteria after 3 hours and 8 hours. This can be found by su… |
| None | The number of milligrams $D(h)$ of a drug in a pa… | The initial amount of the drug injected can be found by evaluating the function at \(h=0\). |
| None | Use the properties of logarithms to evaluate each… | Use the properties of logarithms to evaluate each of the following expressions. |
| None | Solve the system by substitution. \[ \begin{array… | Given the system of equations: \[\begin{array}{l} 4x - y = -10 \ 2y - x = 13 \end{array}\] |
| None | Solve the system by elimination. First, clear the… | Given the system of equations: \[\frac{5 x}{2}+\frac{5 y}{3}=\frac{40}{3}\] and \[\frac{x}{4}+\frac… |
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