Tutor profile: David B.
To solve, take the square root of 121, but not x. Remember that when multiplying under a square root with variables, the square roots of the variables are taken separately from square roots of the number. The variable 'x' doesn't have a square root, so it's still under the square root sign in the final answer. The square root of 121 is 11, so 11 is written in front of the square root sign. $$\sqrt(121x)$$ = 11$$\sqrt(x)$$ Nothing further can be simplified, so 11 multiplied by the square root of 'x' is the final answer.
A health expert is conducting a study to determine if the proportion of adults who exercise regularly has increased in recent years. It's known that the proportion of adults who exercise regularly is 0.11. To test this, the researcher gathers a random sample of 200 adults and asks them whether or not they exercise regularly. They find the sample proportion of adults who regularly exercise is 0.14. The data is approximately normal. Does this sample provide evidence that the proportion of adults who regularly exercise has increased at a significance level of 0.10?
There are multiple methods that can be used to find an answer including Z-tables, ti-83/84 calculators, Excel, Statcrunch, etc. The best method to use depends on the way you're solving in class. For this example, I'll be solving with Statcrunch while explaining the general process behind the solution. I'll start by re-writing all of the important values in the problem. The hypothesized proportion = 0.11, the sample proportion = 0.14, the sample size = 200, and the level of significance is 0.10. First thing is to identify the hypotheses. The health expert wants to determine if the true proportion of adults who regularly exercised has increased. That let's us know the alternative hypothesis is p > 0.11. The null hypothesis is that the proportion hasn't changed, p = 0.11. The sample is approximately normal, so we can calculate the Z statistic for the sample and then compare the p-value to the level of significance stated in the problem. The goal of the test is to determine if the sample proportion found is extreme enough to justify accepting the alternative hypothesis that the proportion of adults who regularly exercise has increased. Since there is a greater than sign towards 'p', this is a right-tail Z-test. To calculate in Statcrunch, go to the following: Stat (on the top row) -> Proportion Stats -> One-Sample -> With Summary You'll be prompted to enter the "# of successes" and "# of observations". The # of observations is given in the problem as the sample size, 200. The # of successes is found by multiplying the given sample proportion with the # of observations. # of successes = 200 * 0.14 = 28 This means 28 out of 200 adults in the sample exercise regularly. After entering the values into the boxes, perform the hypothesis test for 'p' by entering the hypothesized proportion in the box and then changing the sign of the alternative hypothesis to ">". Then click "calculate" at the bottom right. Z statistic = 1.3559538 p-value = 0.0876 The p-value of 0.0876 is less than the significance level of 0.10. This means we reject the null hypothesis in favor of the alternative, and conclude that the sample does provide evidence that the proportion of adults who exercise regularly has increased.
A farmer can harvest 50 square feet of wheat per hour. If the farmer has 4750 square feet of wheat to harvest, how long will it take the farmer to harvest all of the wheat?
Rate of harvest = R = 50 square feet per hour Total harvest = T = 4750 square feet Number of hours = H We'll solve for the unknown variable, H, by creating an equation relating all the values listed above. T = R * H Substitute all known values for the variable letters. 4750 = 50 * H Solve for H by dividing both sides of the equation by 50. (4750 / 50) = (50 * H) / 50 95 = H It will take 95 hours for the farmer to harvest 4750 square feet of wheat at a rate of 50 square feet per hour.
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