First, write put the information into an equation
2*(x+9) = 3*(x-7)
distribute the 2 and 3
2x + 18 = 3x - 21
Combine like terms (Xs and munbers) (in this case, it's easier to add 15 to both sides and subtract 2x from both sides so both sides end up being positive)
33 = x
x=33
Answer:
Strength and direction of the relationship.
Step-by-step explanation:
Given that A study finds a correlation coefficient of r = .32. This number gives you information about which of the following?
Group of answer choices Type of relationship and importance Statistical validity and external validity Statistical significance and effect size Strength and direction of the relationship.
We know that correlation coefficient represented by r is a measure of association between two variables. r can lie between -1 and 1. While negative correlation suggests inverse relationship positive a positive association.
0 correlation means the two variables are independent.
If nearer to 0, it represents weak correlation and nearer to 1 than 0 represents strong correlation.
Here r =0.32 a weak positive correlation
r represents
Strength and direction of the relationship.
A combination is an unordered arrangement of r distinct objects in a set of n objects. To find the number of permutations, we use the following equation:
n!/((n-r)!r!)
In this case, there could be 0, 1, 2, 3, 4, or all 5 cards discarded. There is only one possible combination each for 0 or 5 cards being discarded (either none of them or all of them). We will be the above equation to find the number of combination s for 1, 2, 3, and 4 discarded cards.
5!/((5-1)!1!) = 5!/(4!*1!) = (5*4*3*2*1)/(4*3*2*1*1) = 5
5!/((5-2)!2!) = 5!/(3!2!) = (5*4*3*2*1)/(3*2*1*2*1) = 10
5!/((5-3)!3!) = 5!/(2!3!) = (5*4*3*2*1)/(2*1*3*2*1) = 10
5!/((5-4)!4!) = 5!/(1!4!) = (5*4*3*2*1)/(1*4*3*2*1) = 5
Notice that discarding 1 or discarding 4 have the same number of combinations, as do discarding 2 or 3. This is being they are inverses of each other. That is, if we discard 2 cards there will be 3 left, or if we discard 3 there will be 2 left.
Now we add together the combinations
1 + 5 + 10 + 10 + 5 + 1 = 32 choices combinations to discard.
The answer is 32.
-------------------------------
Note: There is also an equation for permutations which is:
n!/(n-r)!
Notice it is very similar to combinations. The only difference is that a permutation is an ORDERED arrangement while a combination is UNORDERED.
We used combinations rather than permutations because the order of the cards does not matter in this case. For example, we could discard the ace of spades followed by the jack of diamonds, or we could discard the jack or diamonds followed by the ace of spades. These two instances are the same combination of cards but a different permutation. We do not care about the order.
I hope this helps! If you have any questions, let me know :)
To find how much she can run in one minute we’re going to divide 800 by 5, to which we get 160.
She runs 160 meters in one minute.
We want to know how many meters she can run in 9 minutes.
160 * 9 = 1,440
She can run 1,440 meters in 9 minutes.
