Adjacent Angles<span> are </span>two angles<span> that share a common vertex, a common side, and no common interior points. (They share a vertex and side, but </span>do<span> not overlap.) A </span>Linear Pair<span> is </span>two<span> adjacent</span>angles<span> whose non-common sides </span>form<span> opposite rays. ... ∠1 and ∠3 are not </span>vertical angles<span> (they are a </span>linear pair<span>).</span>
Answer:
D Numbers that can be written as fractions
Step-by-step explanation:
A <em>rational</em> number is one that can be written as a <em>ratio</em>: a fraction with integer numerator and denominator.
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The term "decimal" as used here is sufficiently non-specific that we cannot seriously consider it to be part of a suitable answer. A terminating or repeating decimal will be a rational number. A non-terminating, non-repeating decimal will not be a rational number.
While integers and whole numbers are included in the set of rational numbers, by themselves, they do not constitute the best description of the set of rational numbers.
Answer:
The inverse of function 
is ![\mathbf{f^{-1} (x)=\sqrt[5]{x}+7}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%5E%7B-1%7D%20%28x%29%3D%5Csqrt%5B5%5D%7Bx%7D%2B7%7D)
Option A is correct option.
Step-by-step explanation:
For the function , Find 
For finding inverse of x,
First let:
Now replace x with y and y with x
Now, solve for y
Taking 5th square root on both sides
![\sqrt[5]{x}=\sqrt[5]{(y+7)^5}\\\sqrt[5]{x}=y+7\\=> y+7=\sqrt[5]{x}\\y=\sqrt[5]{x}-7](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%7D%3D%5Csqrt%5B5%5D%7B%28y%2B7%29%5E5%7D%5C%5C%5Csqrt%5B5%5D%7Bx%7D%3Dy%2B7%5C%5C%3D%3E%20y%2B7%3D%5Csqrt%5B5%5D%7Bx%7D%5C%5Cy%3D%5Csqrt%5B5%5D%7Bx%7D-7)
Now, replace y with
![f^{-1} (x)=\sqrt[5]{x}+7](https://tex.z-dn.net/?f=f%5E%7B-1%7D%20%28x%29%3D%5Csqrt%5B5%5D%7Bx%7D%2B7)
So, the inverse of function is
Option A is correct option.
Let events
A=Nathan has allergy
~A=Nathan does not have allergy
T=Nathan tests positive
~T=Nathan does not test positive
We are given
P(A)=0.75 [ probability that Nathan is allergic ]
P(T|A)=0.98 [probability of testing positive given Nathan is allergic to Penicillin]
We want to calculate probability that Nathan is allergic AND tests positive
P(T n A)
From definition of conditional probability,
P(T|A)=P(T n A)/P(A)
substitute known values,
0.98 = P(T n A) / 0.75
solving for P(T n A)
P(T n A) = 0.75*0.98 = 0.735
Answer:
work is shown and pictured
