Answer:
The fourth graph is the graph of 
Step-by-step explanation:
As this inequality has a
, we know two things:
The graph must have a solid line as that signifies that it includes the value.
The shaded area must be less than 2.
The fourth graph is the only one that meets our criteria
Answer:
Step-by-step explanation:
Hello!
The variable of interest is the readings on thermometers. This variable is normally distributed with mean μ= 0 degrees C and standard deviation σ= 1.00 degrees C.
The objective is to find the readings that are in the top 3.3% of the distribution and the lowest 3.3% of the distribution.
Symbolically:
The lower value P(X≤a)=0.033
Top value P(X≥b)=0.033
(see attachment)
Lower value:
The accumulated probability until "a" is 0.03, since the variable has a normal distribution, to reach the value of temperature that has the lowest 3.3%, you have to work under the standard normal distribution.
First we look the Z value corresponding to 0.033 of probability:
Z= -1.838
Now you reverste the standardization using the formula Z= (a-μ)/δ
a= (Z*δ)+μ
a= (-1.838*1)+0
a= -1.838
Top value:
P(X≥b)=0.033
This value has 0.033 of the distribution above it then 1 - 0.033= 0.967
is below it.
You can rewrite the expression as:
P(X≤b)=0.967
Now you have to look the value of Z that corresponds to 0.967 of accumulated probability:
b= (Z*δ)+μ
b= (1.838*1)+0
b= 1.838
The cutoff values that separates rejected thermometers from the others are -1.838 and 1.838 degrees C.
I hope it helps!
x+2 > 10 solves to x > 8 after we subtract 2 from both sides
So set A is the set of real numbers that are larger than 8. The value 8 itself is not in set A. The same can be said about 5 as well.
Set B is the set of values that are larger than 5 since 2x > 10 turns into x > 5 after dividing both sides by 2. The value x = 5 is not in set B since x > 5 would turn into 5 > 5 which is false. The values x = 6, x = 8, and x = 9 are in set B.
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Summarizing everything, we can say...
5 is not in set A. True
5 is in set B. False
6 is in set A. False
6 is not in set B. False
8 is not in set A. True
8 is in set B. True
9 is in set A. True
9 is not in set B. False
The least common multiple (or LCM) of 9 and 12 is 36