Mathematics Answer Note #22

Question 1 Ms. Glenn's students post to their class blogs every day. The blog her morning class writes has 1,960 views. The blog her afternoon class writes has 656 more views than that. How many views do both blogs have altogether? Answer According to the given information, the blog post by Ms. Glenn's morning class has 1,960 views and the blog post by her afternoon class has 656 more views than that. To calculate the total number of views for both blogs, we can use the formula A + (A + 656) = 2A + 656, where A represents the number of views for the morning class blog. Using this formula, we can rewrite the equation as 2A + 656 = Total views. To find the value of A, we can subtract 656 from both sides of the equation, giving us 2A = Total views - 656. Then, dividing both sides by 2, we get A = (Total views - 656) / 2. Therefore, the total number of views for both blogs can be calculated by plugging in the value of A into the formula, which gives us Total views = 1,960 + [(1,960 + 656) / 2]. Simplifying the equation, we get Total views = 1,960 + 1,960 / 2 + 656 / 2. Solving this, we get a total of 3,616 views for both blogs combined. Question 2 Brody needs to be at work at 6:40 A.M. It takes him 35 minutes to get ready in the morning and 50 minutes to drive to work. What is the latest time Brody can get up in the morning without being late for work? Answer Brody's latest time to get up in the morning without being late for work would be 5:15 A.M. This would allow him 25 minutes to get ready and 50 minutes for his commute, arriving at work at precisely 6:40 A.M. To determine the latest time Brody can get up in the morning, we first need to understand the time it takes him to prepare for work and the duration of his commute. According to the question, it takes Brody 35 minutes to get ready in the morning and 50 minutes to drive to work. Therefore, we can calculate the total time he needs to allocate from the moment he wakes up to the time he arrives at work by adding these two durations: 35 minutes + 50 minutes = 85 minutes. To determine the latest time Brody can get up, we need to subtract 85 minutes from his start time of 6:40 A.M. So, 6:40 A.M. - 85 minutes = 5:15 A.M. This means that Brody can wake up as late as 5:15 A.M. and still arrive at work on time. In short, the latest time Brody can get up in the morning without being late for work is 5:15 A.M. In case, Brody needs to make any stops or detours during his commute, he needs to factor in additional time for those as well. Also, it is recommended for individuals with longer commutes to allocate some extra time to avoid any unforeseen delays or accidents on the road. Question 3 What number is marked by the dot on this number line? Enter your answer as a simplified improper fraction. If the fraction is negative, enter a negative numerator. Answer The number marked by the dot on this number line is 3/2. To arrive at this answer, we can follow a few steps: 1. Identify the endpoints of the number line: We can see that the number line has 0 and 2 as its endpoints, with equal intervals marked in between. 2. Determine the number of intervals between the endpoints: We can count 3 intervals between 0 and 2. 3. Divide the distance between the endpoints by the number of intervals: 2 divided by 3 gives us 2/3, which represents the distance between any two consecutive points on the number line. 4. Count the number of intervals from the first endpoint to the marked dot: We can see that the dot is 3 intervals away from the first endpoint, 0. 5. Multiply the number of intervals by the distance between each interval: Multiplying 3 by 2/3 gives us a total distance of 2, which corresponds to the number 3/2 on the number line. Therefore, the number marked by the dot on this number line is 3/2 or 1 1/2. We can also represent this as an improper fraction, 3/2, as per the question prompt. Question 4 54,53,104 ,309,1234 ,6155 find wrong number series 1)54 2)53 3)104 4)309 5)1234 Answer After thorough analysis and research, it can be determined that the correct number series is missing and the given series does not follow any specific numerical pattern. The first two numbers, 54 and 53, are consecutive and thus suggest that the series might be based on consecutive numbers. However, the following numbers (104, 309, 1234, and 6155) do not follow any clear pattern. One possible reason for the incorrect series is a human error or typo, as the given numbers can be easily rearranged to form a consecutive series of 54, 53, 104, 510, 1234, and 6155. This rearrangement also follows a general trend of increasing by approximately 1.9 times for each subsequent number. In addition, it is important to clarify the given source of the incorrect series, as mathematical patterns can vary depending on the context and source of the data. Therefore, accuracy and reliability of the source must also be taken into consideration. Question 5 Multi Choice Type Question If the data given in both statements l and Il together are not sufficient to answer the question The question below consists of a question and two statements numbered I and Il given below it. You have to decide whether the data provided in the statements are sufficient to answer the questions Read both the statements and give an answer: How many New Year's greeting cards were sold this year in your shop? I. Last year 2935 cards were sold. Il. The number of cards sold this year was 1.2 times that of last year. • If the data in statement I alone are sufficient to answer the question, while the data in statement Il alone are not sufficient to answer the question • If the data in both statements I and Il together are necessary to answer the question If the data in statement Il alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question Answer Based on the information provided, it is not possible to accurately determine the number of New Year's greeting cards sold in my shop this year. Both statements I and II provide some information, but they do not provide enough data to come to a conclusive answer. In conclusion, based on the given information, the data in both statements I and II are not sufficient to answer the question. Further information is needed to come to a conclusive answer.