The solution is 85, based on the Alternate Interior Angles Theorem.
Triangle XYZ is an equilateral triangle, meaning the sector's central angle measures 120 degrees, which is equivalent to 2π/3 radians. To find the area of a sector corresponding to a central angle β, we use the formula A = (1/2)r²*β, where β is expressed in radians. For this sector, the area calculation is A = (1/2)*2²*(2π/3) = 4π/3 square units.
Response:
To settle their disagreement over who does the dishes, flip a fair coin. There is an equal 50% probability of it showing heads or tails, hence the choice will be random.
A. True. The presence of a significant outlier greater than the main group increases the mean, whereas a substantial outlier lower than the main group decreases it. B. False. Outliers distort the true mean's value. In cases where a trimmed mean is considered, the resulting mean may be correct. When outliers exist, using the median is advisable; for instance, the sale of expensive properties significantly affects the mean home prices, hence the term "median home price" is preferred. C. False. The standard deviation decreases because it indicates how data is spread. An outlier leads to greater spread, resulting in a higher standard deviation, which diminishes when the outlier is discarded as the data becomes more centralized. D. False. This assertion holds for normally distributed data that conforms to a bell curve and is centered around the mean; skewed distributions do not follow this principle. E. True. When data is described as "skewed to the right," it implies a large outlier extending the right-side tail more than anticipated, pulling the mean higher while leaving the median unchanged, causing the mean to exceed the median. This concept aligns with statement A. In conclusion, the true responses are A and E, therefore there are two correct answers.
