What is the volume of this rectangular prism? 3 units 1 cubic unit 3 units
1 answer:
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I will first reveal the most obvious secret of trig: Most of the problems are 30/60/90 or 45/45/90 triangles of some sort.
The rule to remember is
has solutions
integer 
Continuing where we left off, a cosine of -1/2 is a 30/60/90 triangle in the second or third quadrant; we pick second, and a little thought tells us the angle is
.
integer
In the range we want, that's
with the plus sign and 
with the minus, so
or 
or 
The rule to remember is
Continuing where we left off, a cosine of -1/2 is a 30/60/90 triangle in the second or third quadrant; we pick second, and a little thought tells us the angle is
In the range we want, that's
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!
