Which point is a solution to the system of inequalities below?
1 answer:
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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!
Answer:
A: The transformations are a rotation and a translation.
Step-by-step explanation:
The function f(x) is shown in the attachment as a dashed red line. The function g(x) is shown as the blue line.
The two lines have different slopes. The change in slope can be accomplished by horizontal or vertical scaling, or by rotation. The offered answer choices only include <em>rotation</em> as an option for changing the slope.
The two lines have different intercepts. To move the line from one intercept to another, generally translation is involved.
The simplest transformation is rotation and translation.
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<em>Comment on the answer choices</em>
If the reflection is done across a line other than an axis, or if the rotation is done about a point other than the origin, then <em>any combination of rotation, reflection, and translation can be used to make the transformation seen</em>. (Translation alone is not sufficient.)
For example, reflecting the line across the bisector of the angle between the lines (a line with a slope of (√13 -2)/3 through (5, 5)) will give the desired transformation in one step.
Similarly, a rotation of about 33.69° about the point (5, 5) will give the transformation in on step. (That angle is 45°-arctan(1/5).)
The name is the second option y= (2/3)x +5. Hope this helps
