Darius created a factor tree and wrote the prime factorization of 60 shown here. A factor tree of 60. 60 branches to 4 and 15. 4 branches to 2 and 2. 15 branches to 3 and 5.

60 = 2 × 3 × 5

What is Darius’s error?
Darius should have started the factor tree with 2 × 30.
Darius did not complete the factorization; 5 is a composite number.
Darius should have expressed 15 as 5 × 5, not 3 × 5.
Darius should have expressed 60 as 22 × 3 × 5, not 2 × 3 × 5.

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.1. (round your answers to four decimal places.) (a) if the distribution is normal, what is the probability that the sample mean hardness for a random sample of 8 pins is at least 51?

Points a, b, and c form a triangle. complete the statements to prove that the sum of the interior angles of triangle abc is 180

Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6: 10. which statement explains whether juliana is correct? she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio. she is correct because 6: 10 can be written as 1: 2 and there are an infinite number of ratios for 1: 2. she is not correct because the multiplication table does not include multiples of 10. she is not correct because 6: 10 is equivalent to 3: 5 and there are only 9 ratios in the multiplication table that are equivalent to 3: 5.