The term "closed" in math means that if you take two items from a set, do some operation, then you'll always get another value in the same set (sometimes you may get the same value as used before). For example, adding two whole numbers leads to another whole number. We therefore say "the set of whole numbers is closed under addition". This applies to integers as well because integers are positive and negative whole numbers. So we can say that integers are closed under addition.
Integers are not closed under division. Take two integers like 2 an 5 and divide: 2/5 = 0.4 which is not an integer. Integers don't have decimal parts.
The set of whole numbers is {0,1,2,3,...} and we can subtract the two values 1 and 2 to get 1-2 = -1. The order matters here. Subtracting a larger value from a smaller leads to a negative. The value -1 is not in the set of whole numbers. So we can say that whole numbers is not closed under subtraction
Finally, the set of irrational numbers is closed under addition. Adding any two irrational numbers leads to another irrational number. For instance, pi+sqrt(2) = 3.142 + 1.414 = 4.556; I'm using rounded decimals as approximate values. An irrational number is one where we cannot write it as a fraction of integers. Contrast that with a rational number in which we can write it as a fraction of integers. Example: 10 = 10/1 is a rational number.
Answer:
A t-score of 2.0244 should be used to find the 99% confidence interval for the population mean
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 39 - 1 = 38
Now, we have to find a value of T, which is found looking at the t table, with 38 degrees of freedom(y-axis) and a confidence level of 0.99(
). So we have T = 2.0244.
A t-score of 2.0244 should be used to find the 99% confidence interval for the population mean
Answer:
I think the answer is A.Negative
Step-by-step explanation:
From x=-5 to x=0 the slope is decreasing and from x=1 to x=6 it keeps decreasing.
Answer:
See below
Step-by-step explanation:
When we talk about the function 
, the domain and codomain are generally defaulted to be subsets of the Real set. Once 
and 
such that 
for 
. Therefore,
![\[\sqrt{\cdot}: \mathbb R_{\geq 0} \to \mathbb R_{\geq 0} \]](https://tex.z-dn.net/?f=%5C%5B%5Csqrt%7B%5Ccdot%7D%3A%20%5Cmathbb%20R_%7B%5Cgeq%200%7D%20%5Cto%20%5Cmathbb%20R_%7B%5Cgeq%200%7D%20%5C%5D)
![\[x \mapsto \sqrt{x}\]](https://tex.z-dn.net/?f=%5C%5Bx%20%5Cmapsto%20%5Csqrt%7Bx%7D%5C%5D)
But this table just shows the perfect square solutions.
Answer:
11
Step-by-step explanation:
I just assumed D is the midpoint; and if D is the midpoint,
GD=DH, GD+DH=GH
5.5+5.5=11
