To solve this problem, KROW SDAWKCAB. (That's WORK BACKWARDS spelled backwards.)
We are told that there's a 3:2 ratio of 8th graders to 7th graders in the club. Let x be the number of 7th graders in the class. We set a proportion. The proportion puts the ratio on one side, how many students on the other. Tops are the 8th graders, bottoms are the 7th graders.
You can solve it by cross multipling or by noticing what happens between the fractions. On the top how did you go from 3 to 18? You multiplied by 6. So the same thing must happen on the bottoms, and 2 * 6 = 12.
By cross multiplying, 3x = 36 and when we divide both sides by 3, we find x = 12.
Now that we know we have 12 7th graders, we can find the number of 6th graders. The process is similar with 7th graders on bottom, 6th graders on top, and x for what we do not know.
We went from 4 to 12 by multiplying 3 on the bottom, and we repeat it on the top. So 5 * 3 = 15.
Thus, there are 15 6th graders in the club.
Answer:
The constant of proportionality is 0.3, or K=0.3.
Step-by-step explanation:
The chart I attached shows points that are plotted on the proportional line. In order to find the constant of proportionality from these points, you have to divide the amount of change by the number of years. For example, 3 divided by 10 or 6 divided by 20. This results in 0.3, which means that every year, there is 0.3 centimeters of change in the sea level.
I got D.
There's a few ways to solve it; I prefer using tables, but there are functions on a TI-84 that'll do it for you too. The logic here is, you have a standard normal distribution which means right away, the mean is 0 and the standard deviation is 1. This means you can use a Z table that helps you calculate the area beneath a normal curve for a range of values. Here, your two Z scores are -1.21 and .84. You might notice that this table doesn't account for negative values, but the cool thing about a normal distribution is that we can assume symmetry, so you can just look for 1.21 and call it good. The actual calculation here is:
1 - Z-score of 1.21 - Z-score .84 ... use the table or calculator
1 - .1131 - .2005 = .6864
Because this table calculates areas to the RIGHT of the mean, you have to play around with it a little to get the bit in the middle that your graph asks for. You subtract from 1 to make sure you're getting the area in the middle and not the area of the tails in this problem.
