Mathematics Answer Note #55

Question 1 Write a Explicit Function to represent the sequence, the sequence starts at 1. Example: f(n)=3(2)^n or f(n)=3n+5 claire has 300$ in an amount .she decides she gonna take out half of whats left in there at the end of each month Answer The explicit function for this sequence would be f(n) = 300(0.5)^n, where n represents the number of months and f(n) represents the amount of money remaining in Claire's account after n months. This function follows the pattern of halving the previous amount each month. To better understand this function, let us consider a specific example. If n=1, then f(n) = 300(0.5)^1 = 150. This means that after the first month, Claire will have 150 dollars remaining in her account. If n=2, then f(n) = 300(0.5)^2 = 75. After the second month, Claire will have 75 dollars remaining in her account. This pattern continues, with the amount of money remaining in Claire's account halving each month. Calculation breakdown: Step 1: Determine the starting amount of money. In this case, the starting amount is $300. Step 2: Determine the rate at which the amount is decreasing. In this case, the rate is 0.5 or 50%. Step 3: Determine the number of months, represented by the variable n. Step 4: Use the formula f(n) = 300(0.5)^n to calculate the amount of money remaining in Claire's account after n months. Question 2 One through 28. How could you organize the data to answer your questions or right? Answer to complete something Answer Organizing data is crucial when trying to find answers or complete a task. In order to answer this question, I would first gather all the necessary data and then proceed with organizing it in a systematic manner. Here are the steps I would take to organize the data: 1. Determine the type of data: The first step is to identify whether the data is quantitative or qualitative. Quantitative data is numerical and can include data such as age, weight, and test scores. On the other hand, qualitative data is descriptive and includes data such as gender, occupation, and race. This step is important as it helps in choosing the appropriate method of organizing the data. 2. Choose an appropriate data layout: There are various ways to organize data such as tables, graphs, and charts. Depending on the type of data and the questions at hand, I would select the most suitable data layout. For numerical data, a table would be a better option, whereas for categorical data a bar graph or pie chart would be more effective. 3. Grouping and categorizing the data: This step involves arranging the data into groups or categories based on similar characteristics. For example, if the data is about the age of students, it can be grouped into categories such as 15-18, 19-22, 23-26, and so on. This step helps in identifying patterns and trends in the data. 4. Calculations if needed: If the question at hand requires calculations, I would perform them at this stage. It is important to show all the steps and provide a clear explanation to ensure accuracy and understanding. 5. Use of software: In today's digital age, software programs such as Microsoft Excel or SPSS can be helpful in organizing and analyzing data. These programs have various tools and functions that make data organization and analysis more efficient. Question 3 Calculate the volume of a cylinder of a radius 50mm and height 25 cm in cubic meters Answer According to the formula for calculating the volume of a cylinder, V=πr^2h, where π is the constant pi, r is the radius, and h is the height, the volume in cubic meters can be calculated by converting the given measurements to the appropriate units. Firstly, we need to convert the radius from millimeters to meters. As 1 meter is equal to 1000 millimeters, the radius of 50mm can be expressed as 50/1000 = 0.05 meters. Next, the height needs to be converted from centimeters to meters. As 1 meter is equal to 100 centimeters, the height of 25 cm can be expressed as 25/100 = 0.25 meters. Substituting the converted values into the formula, we get: V=π(0.05)^2(0.25) = 0.00785π m^3 Using a calculator to approximate pi to 3.14, we get the volume as 0.0246445 m^3. Therefore, the volume of the cylinder with a radius of 50mm and height of 25 cm is approximately 0.0246445 cubic meters. Question 4 Calculate the circumference of a circle of a radius of 6 cm Answer The circumference of a circle can be calculated using the formula C=2πr, where C is the circumference and r is the radius of the circle. In this case, the radius is given as 6 cm. So, we can substitute the value of 6 cm for r in the formula as follows: C=2π(6 cm) C=12π cm Therefore, the circumference of the circle with a radius of 6 cm is 12π cm. This can be further simplified to approximately 37.7 cm. Step-by-step breakdown: 1. The formula for calculating the circumference of a circle is C=2πr, where C is the circumference and r is the radius. 2. The given radius is 6 cm. 3. Substitute the value of 6 cm for r in the formula. 4. Multiply the radius by 2π, which can also be written as 2 times π. 5. Simplify the equation by multiplying 2 and 6 to get 12. 6. The final result is 12π cm. This can be further simplified to approximately 37.7 cm by using the value of π as 3.14. Question 5 Calculate the volume of a rectangular box which is 30cm long 25cm wide and 15cm high in cubic meters Answer The volume of a rectangular box can be calculated by multiplying its length, width, and height. Therefore, to calculate the volume of a rectangular box that is 30cm long, 25cm wide, and 15cm high, we use the formula V = l × w × h. Where V is the volume, l is the length, w is the width, and h is the height.