| Topic | Problem | Solution |
|---|---|---|
| None | The piston diameter of a certain hand pump is $0.… | The null hypothesis is \(H_{0} : \sigma = 0.007\). |
| None | The mass of a radioactive substance follows a con… | The problem is asking for the mass of the radioactive substance after three days. The substance dec… |
| None | Moneysaver's Bank offers a savings account that e… | Given that Moneysaver's Bank offers a savings account that earns $3 \%$ interest compounded continu… |
| None | A college offers 2 introductory courses in histor… | A college offers 2 introductory courses in history, 1 in science, 1 in mathematics, 3 in philosophy… |
| None | Solve the following inequality. \[ (x-7)^{2}(x+8)… | The inequality is a product of two factors: \((x-7)^2\) and \((x+8)\). The inequality is greater th… |
| None | Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[… | Calculate the down payment, which is 20% of the home price. So, \(\text{down payment} = 0.2 \times … |
| None | Solve the linear programming problem. Maximize an… | First, we need to find the feasible region defined by the constraints. The constraints are $2x + y … |
| None | The temperature $\mathrm{T}\left({ }^{\circ} \mat… | Given the temperature function \(T=65-12 \sqrt{25-t}\) for \(0 \leq t \leq 25\) |
| None | Find the length of the following curve. \[ y=\ln … | Given the function \(y=\ln \left(x+\sqrt{x^{2}-1}\right)\), we are asked to find the length of the … |
| None | Find the exact interest on a loan of $\$ 33,000$ … | Given a loan of $33,000 at an annual interest rate of 8% for a period of 35 days, we are to find th… |
| None | Find the arc length of the curve below on the giv… | Given the function \(y=\ln \left(x-\sqrt{x^{2}-1}\right)\), we need to find the arc length of the c… |
| None | Simplify square roots (variables) Simplify. Remov… | The square root of a number is a value that, when multiplied by itself, gives the original number. … |
| None | Write the resulting set using the listing method.… | The intersection of two sets is the set of elements that are common to both sets. In this case, we … |
| None | Evaluate the integral below by interpreting it in… | The integral represents the area under the curve of the function \(f(x) = \sqrt{3^{2}-x^{2}}\) from… |
| None | If \sum_{k=1}^{n} a_{k}=9 and \sum_{k=1}^{n} b_{k… | The first question is asking for the sum of 2 times each \(a_k\) from \(k=1\) to \(n\). Since we kn… |
| None | Given the equation below, find $\frac{d y}{d x}$.… | First, we differentiate the given equation implicitly with respect to \(x\). |
| None | Find the equation of the tangent line to the curv… | Given the equation of the curve (a lemniscate) \(2(x^{2}+y^{2})^{2}=25(x^{2}-y^{2})\) and the point… |
| None | Use implicit differentiation to find the equation… | First, we need to differentiate the given equation implicitly with respect to \(x\). The given equa… |
| None | If $f(x)=\frac{4-x^{2}}{7+x^{2}}$, find: \[ f^{\p… | Given the function \(f(x)=\frac{4-x^{2}}{7+x^{2}}\), we are asked to find its derivative \(f^{\prim… |
| None | Suppose the value $R(d)$ of $d$ dollars in euros … | Let's denote the cost in dollars to purchase and ship n purses as \(P(n) = 55n + 23\). |
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