Which of the following makes this statement true: x(4 + 3) = 12 + 9?
2 answers:
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We can make a proportion to represent the woods used. On the top is cedar, and on the bottom is the redwood. On the left is what was used the first time, on the right is the current problem.
Before making the proportion, let's do a preliminary step and write all the fractions as improper fractions. We do this because we can't directly multiply or divide mixed numbers, but we can with fractions.
<-- Multiply denominator times whole number and add the leftover fraction.
Now we set up the proportion. We solve it by cross multiplying.
It may seem right to simplify the right side, but let's leave it alone. We divide both sides by 19/2.
Dividing by a fraction means multiplying by its reciprocal. Thus,
Here's where not simplifying really pays off. We can simplify NOW and the terms go away more easily. The 19s go away and simplify to 1, and the 2 and 4 simplify to 1 and 2. All this happens by dividing out common numbers.
Now we multiply all the tops and all the bottoms.
R = 23 * 1 * 1 / 3 * 2 * 1
R = 23 / 6
While R is 23/6, we need to make it a mixed number. The way we made mixed numbers as improper fractions happens here, except in reverse.
23 ÷ 6 = 3 with a remainder of 5, as 3 × 6 + 5 = 23. Thus, .
As a result, feet of redwood is needed.
Answer: 90.82%
Step-by-step explanation:
Given : The distribution of the amount of a certain brand of soda in 16 OZ bottles is approximately normal .
Mean :
Standard deviation:
Let X be the random variable that represents the amount of soda in bottles.
Formula for z-score :
Z-score for 16 oz:
Using the standard normal z-distribution table , the probability that the soda bottles that contain more than the 16 OZ is given by :_
Hence, the percentage of the soda bottles that contain more than the 16 OZ advertised is 90.82% .