lesson #44\n1. find the prime factorization of 56.\n2. if a data set has an even number of data points, the…

lesson #44\n1. find the prime factorization of 56.\n2. if a data set has an even number of data points, the median falls between two values. find the average of the middle two values. find the median of the data in the box.\nexample: 0, 1, 2, 3, 3, 4\nlower half upper half\nthe median is between 2 and 3.\n2 + 3 = 5 and 5÷2 = 2.5\nmedian = 2.5\n1. 6.ns.4\n56÷2 = 28, 28÷2 = 14\n14÷2 = 7\n2×2×2×7 = 2³×7\n2³×7\n2. 6.sp.5\ndata set 3 3 5 7 8 8\n4. 6.ns.2\n5. 6.sp.3

lesson #44\n1. find the prime factorization of 56.\n2. if a data set has an even number of data points, the median falls between two values. find the average of the middle two values. find the median of the data in the box.\nexample: 0, 1, 2, 3, 3, 4\nlower half upper half\nthe median is between 2 and 3.\n2 + 3 = 5 and 5÷2 = 2.5\nmedian = 2.5\n1. 6.ns.4\n56÷2 = 28, 28÷2 = 14\n14÷2 = 7\n2×2×2×7 = 2³×7\n2³×7\n2. 6.sp.5\ndata set 3 3 5 7 8 8\n4. 6.ns.2\n5. 6.sp.3

Answer

Explanation:

Step1: Prime - factorize 56

Divide 56 by the smallest prime number 2. $56\div2 = 28$, then $28\div2=14$, and $14\div2 = 7$. Since 7 is a prime number, the prime - factorization of 56 is $2\times2\times2\times7=2^{3}\times7$.

Step2: Find the median of the data set {3, 3, 5, 7, 8, 8}

First, arrange the data set in ascending order (already in ascending order here). The data set has 6 (an even number) data points. The middle two values are the 3rd and 4th values. The 3rd value is 5 and the 4th value is 7. Calculate the average of the middle two values: $\frac{5 + 7}{2}=\frac{12}{2}=6$.

Answer:

  1. $2^{3}\times7$
  2. 6