ity of being born on any as any other day, find the least number of people to Res the probability > 50% that two people at the party were born on t same day of the month. A. 7 В. С. D. 12. E. 15 x2 +15xy= x + 15y y2x 14. How many solutions does the system have? xy= 15x +y А. 1 в. 2 С. 3 D.
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Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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- Globally, 35% of all ridged brittleshell tortoises have spots on their shells. A herpetologist in Citition collects a sample of 38 ridged brittlesell tortoises and finds that 16 of them have spots on their shells. The herpetologist would like to test the claim that the proportion of ridged brittleshell tortoises in Cititon with spots on their shells is greater than 35%. The herpetologist ends up rejecting the null hypothesis. If the actual proportion of ridged brittleshell tortoises in Cititon with spots on their shells is 41%, then what type of error, if any, has occurred? In the problem above, what is the test statistic?A student wondered what proportion of a large jar of thousands of marbles were red and speculated that it was 0.30. She took a random sample of 50 marbles and got 18 red marbles, for a sample proportion of 0.36. Below is a dotplot of 100 simulated samples of drawing 50 marbles from a population that is set up to have the proportion of "red marbles" to be 0.30. Based on this dotplot, would getting a sample of 50 marbles to have a 0.36 proportion of red marbles be significant evidence that the true proportion of red marbles in the whole jar is greater than 0.30?Suppose that we identify 155 women 50 to 54 years of age who have both a mother and a sister with a history of breast cancer. 18 of these women themselves have developed breast cancer at some time in their lives. If we assume that the proportion of breast cancer cases in women whose mothers have had breast cancer is 8%, does having a sister with the disease increase the risk? Find the p-value.
- Sarah believes that completely cutting caffeine out of a person’s diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah’s claim at the 0.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine 18 24 22…Sarah believes that completely cutting caffeine out of a person’s diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah’s claim at the 0.10 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine 16 21 21…Sarah believes that completely cutting caffeine out of a person’s diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah’s claim at the 0.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine 20 17 16…
- Sarah believes that completely cutting caffeine out of a person’s diet will allow him or her more restful sleep at night. In fact, she believes that, on average, adults will have more than two additional nights of restful sleep in a four-week period after removing caffeine from their diets. She randomly selects 8 adults to help her test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days, and then cut back to no caffeinated beverages for the following 28 days. During each period, the participants record the numbers of nights of restful sleep that they had. The following table gives the results of the study. Test Sarah’s claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let the period before removing caffeine be Population 1 and let the period after removing caffeine be Population 2. Numbers of Nights of Restful Sleep in a Four-Week Period With Caffeine 20 19 18…When Alexa takes her 1st free throw in a game, she has a 40 percent chance to score.She has a 70 percent chance of scoring on her next throw if she scored on the earlierone, but only a 20 percent chance if she didn't score on the previous one. Assumeshe needs to make 3 free throws in a row, the first of which she misses. What is theprobability that she will score at least once on one of the following two throws?Suppose a local symphony decides to raise money by raffling an HD television worth 500$, a dinner for two worth 100$, and 2 CD's worth 15$ each. A total of 3000 tickets are sold at 2$ each. Find the expected payback for a person who buys one ticket in the raffle.
- Teens who vape are likely to develop pneumonia 60% of the time, whereas teens who don’t vape are likely to develop pneumonia 3% of the time. About 20% of the teen population vapes. If you learn that a teen has pneumonia, what is the likely hood that they vape?Recent studies have shown that about 39.4% of American adults fit the medical definition of being obese. A large medical clinic would like to estimate what percentage of their patients are obese, so they take a random sample of 600 patients and find that 204 are obese. Suppose that in truth, the same percentage holds for the patients of the medical clinic as for the general population, 39.4%. Give a numerical value for each of the following. (a) the population proportion, p, of obese patients in the medical clinic p = (b) the proportion of obese patients, p̂, for the sample of 600 patients p̂ = (c) the standard error, s.e., of p̂ (Round your answer to four decimal places.) s.e.(p̂) = (d) the mean of the sampling distribution of p̂ (e) the standard deviation, s.d., of the sampling distribution of p̂ (Round your answer to four decimal places.)For 30 recent Academy Award ceremonies, ages of Best Supporting Actors (x) and ages of Best Supporting Actresses (y) are recorded.The 30 paired ages yield x¯ = 52.1 years, y¯ = 37.3 years, r = 0.076, P-value = 0.691, and y^ = 33.4 + 0.0587x. Find the best predicted value (age of Best Supporting Actress in 1982), when the age of the Best Supporting Actor (x) was 44 years.