Mathematics Answer Note #30

Question 1 use the graphic organizer below to place each of the following values -correctly -9, 0 ,1/8 - 1/2, 15, 126 -37,2/3 Answer In order to correctly place each of the given values -9, 0, 1/8 - 1/2, 15, 126, -37, 2/3 into the graphic organizer, it is important to understand their relative position on the number line. -9 is a negative number, meaning it is less than 0. On the number line, it would be placed to the left of 0. 0 is the origin or starting point of the number line. It divides the positive and negative numbers. Therefore, it should be placed in the middle of the graphic organizer. 1/8 is a small positive number, closer to 0. It would be placed to the right of 0, but closer to it compared to other values. 1/2 is exactly halfway between 0 and 1 on the number line. Therefore, it should be placed in the middle of two adjacent squares in the graphic organizer. 15 is a larger positive number and would be placed to the right of 1. 126 is an even larger positive number, and therefore, it should be placed further to the right on the number line. -37 is a negative number and would be placed to the left of -9. 2/3 is a fraction that is greater than 1/2 but less than 1. Therefore, it should be placed in the square to the right of 1 on the number line. Question 2 two integers add up to -4. one with the integers is 5. work out the other integer. Answer In order to find the other integer, we will use the following mathematical equation: sum of two integers = first integer + second integer. We know that one of the integers is 5, so we can substitute it in the equation: sum of two integers = 5 + second integer. We also know that the total sum of the two integers is -4, so we can write it out as: -4 = 5 + second integer. To solve for the second integer, we need to isolate it on one side of the equation. We can do this by subtracting 5 from both sides of the equation, giving us: -4 - 5 = 5 - 5 + second integer. This simplifies to: -9 = second integer. Therefore, the other integer that adds up to -4 when combined with 5 is -9. Question 3 If fx)x+1, g(x) 4x +2, and hx) 2-1, find each value (5f l)(-1) Answer To find each value of (5f l)(-1), we need to substitute -1 into the given functions and then perform the necessary operations according to the order of operations. So, let's start by substituting -1 into each function. f(-1)= (-1)+1 = 0 g(-1)= 4(-1)+2 = -2 h(-1)= 2^(-1)-1 = 1/2 - 1 = -1/2 Now, we have all the values needed to find (5f l)(-1). This notation means to multiply the values of each function by 5 and then divide those products. So, (5f l)(-1) can be written as: (5f l)(-1) = (5 x f(-1)) / (5 x g(-1)) Substituting the calculated values, we get: (5f l)(-1) = (5 x 0) / (5 x (-2)) Simplifying, we get: (5f l)(-1) = 0/(-10) = 0 Thus, the value of (5f l)(-1) is 0. Question 4 The population of a city was 400,000 in 2010, and it grew to 450,000 in 2020. What was the average annual growth rate of the population over this period? Answer To find the average annual growth rate, we need to use the formula: (final population/initial population)^(1/number of years) - 1. Using the values given in the question, we can substitute them into the formula as follows: [(450,000/400,000)^(1/10)] - 1 = 0.0147 or 1.47% This means that the average annual growth rate of the population from 2010 to 2020 was 1.47%. This indicates a steady and consistent growth rate over the 10-year period. Question 5 A represents a quantitative observation. 2. Although your textbook lists the rules for converting an ordinary number to scientific notation, oftentimes students remember such rules better if they put them into their own words. Pretend you are helping your 12-yearold niece with her math homework, and write a paragraph explaining to her how to convert the ordinary number 2421 to scientific notation. 3. When a large or small number is written in standard scientific notation, the number is expressed as the product of a number between 1 and 10, multiplied by the appropriate power of 10. For each of the following numbers, indicate what number between 1 and 10 would be appropriate when expressing the numbers in standard scientific notation. a. 9651 c. 93,241 b. 0.003521 d. 0.000001002 4. When a large or small number is written in standard scientific notation, the number is expressed as the product of a number between 1 and 10, multiplied by the appropriate power of 10. For each of the following numbers, indicate what power of 10 would be appropriate when expressing the numbers in standard scientific notation. a. 9,367,421 b. 0.0624 c. 0.0005519 d. 5,408,000,000 Problems 5. Will the power of 10 have a positive or a negative exponent when each of the following numbers is rewritten in standard scientific notation? а. 42.751 b. 1253 c. 0.002045 d. 0.1089 Answer Hello! As a college student with high marks, let me help you understand the concept of converting ordinary numbers to scientific notation and determining the appropriate number and power of 10. In scientific notation, any number can be written as the product of a number between 1 and 10, and a power of 10. For example, 2421 can be rewritten as 2.421 x 10^3, where 2.421 is the number between 1 and 10, and 10^3 is the power of 10. To convert to scientific notation, simply move the decimal point of the original number to the left or right, depending on the direction the decimal point needs to move to get a number between 1 and 10. If the decimal point is moved to the left, the power of 10 will be positive. If it is moved to the right, the power of 10 will be negative. For the following numbers, the appropriate number between 1 and 10 is 9.651 for a, 0.093241 for c, 3.521 for b, and 1.002 for d. The powers of 10 for a, b, c, and d are 10^3, 10^-3, 10^-3, and 10^-6, respectively. To double check, we can rewrite them in scientific notation as 9.651 x 10^3, 9.3241 x 10^-2, 3.521 x 10^-3, and 1.002 x 10^-6. I hope this helps!