| Topic | Problem | Solution |
|---|---|---|
| None | List all the permutations of five objects $x, y, … | First, we need to understand the question. It asks for all the permutations of five objects $x, y, … |
| None | A golf-course architect has six linden trees, fiv… | The problem is a permutation problem with repetition. The total number of trees is 6 (linden) + 5 (… |
| None | The two conversion factors for the equality 1 in … | The question is asking whether the two conversion factors for the equality 1 in = 2.54 cm are corre… |
| None | $\log _{2}(x)+\log _{2}(x-12)=6$ | Given the logarithmic equation \(\log _{2}(x)+\log _{2}(x-12)=6\) |
| None | How many different simple random samples of size … | We are asked to find the number of ways to choose 5 items from a set of 51 items. This is a problem… |
| None | In an election, suppose that $35 \%$ of voters su… | This problem is about the normal distribution. The mean of the distribution is the actual proportio… |
| None | In an certain species of newt, offspring are born… | Given that the proportion of green newts, denoted as p, is 0.45 and the sample size, denoted as n, … |
| None | 4 The position $s$ of a point (in miles) is given… | The position $s$ of a point (in miles) is given as a function of time $t$ (in minutes): $s=t^{3}-3 … |
| None | 2 Locate all extrema for the function $y=x^{2}-6 … | First, we need to find the derivative of the function \(y=x^{2}-6 x+5\). The derivative is \(f'(x) … |
| None | Which number is the smallest? $4.38 \times 10^{3}… | The question is asking for the smallest number among the given options. To find the smallest number… |
| None | If a balloon has a volume of 21.6 cups, what is t… | We are given that the volume of a balloon is 21.6 cups and we are asked to convert this volume into… |
| None | A lottery exists where palls numbered 1 to 19 are… | A lottery exists where balls numbered 1 to 19 are placed in an urn. To win, you must match the four… |
| None | Suppose 31 cars start at a car race. In how many … | Suppose 31 cars start at a car race. We want to find out in how many ways the top 3 cars can finish… |
| None | Which length is the longest? $12 \mathrm{~m}$ $12… | Convert all the lengths to the same unit, meters, using the following conversion rates: 1 m = 1 m, … |
| None | \( (-a)^{4}\left[\frac{(-a)^{3} \sqrt[6]{729}}{3 … | \( (-a)^{4}\left[\frac{(-a)^{3} \sqrt[6]{729}}{3 a}\right]^{2} = (-a)^{4}(\frac{(-a)^{3} \sqrt[6]{7… |
| None | grals to find $\int_{1}^{8} f(x) d x$ for the fol… | The integral of a piecewise function from a to b can be found by breaking the integral into two par… |
| None | A salesperson must travel to four cities to promo… | A salesperson must travel to four cities to promote a new marketing campaign. How many different tr… |
| None | Suppose you just received a shipment of thirteen … | We have a total of 13 televisions, out of which 2 are defective and 11 are working. |
| None | When $5.5490 \times 10^{8}$ is correctly rounded … | The given number is \(5.5490 \times 10^{8}\). |
| None | The measurement $78,005,760$ expressed correctly … | First, we need to express the number $78,005,760$ in scientific notation. Scientific notation is a … |
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