The expected value of health care without insurance is $437.25.
The expected value of health care with insurance is $1,636.40.
<h3>What are the expected values?</h3>
The expected values can be determined by multiplying the respective probabilities by its associated costs.
The expected value of health care without insurance
= (1 x 0) + (0.32 x 1050) + (0.45 x $225)
= $437.25
The expected value of health care with insurance
= (1 x 1580) + (0.32 x 75) + (0.45 x $72)
= $1,636.40
Thus, The expected value of health care without insurance is $437.25.
The expected value of health care with insurance is $1,636.40.
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The value of q(x) is 
The value of r(x) is 
Explanation:
The given expression is 
We need to rewrite the expression in the form of 
Simplifying the expression, we get,
Separating the fractions, we have,
-----------(1)
Now, we shall further simplify the term 
, we get,
Common out 5 from the numerator, we have,
Substituting the value in the equation(1), we get,
Thus, the expression 
is in the form of
Hence, we have,
and
9514 1404 393
Answer:
- red boat distance: 42 miles
- angle at lighthouse: 22°
Step-by-step explanation:
The Law of Cosines can be used to find the distance from the red boat to the lighthouse.
b² = l² +r² -2lr·cos(B)
b² = 18² +30² +2·18·30·cos(120°) = 1764
b = √1764 = 42
The distance from the red boat to the lighthouse is 42 miles.
__
The angle at the lighthouse can be found using the law of sines.
sin(L)/l = sin(B)/b
L = arcsin(l/b·sin(B)) = arcsin(18/42·sin(120°)) ≈ 21.79°
The angle between the boats measured at the lighthouse is about 22°.
Since a target is a circle and the bulls-eye is also a circle, the percent of the circle that is bulls-eye would be (Area of the bulls eye)/(Area of the target)
[tex] A = \pi r^{2} \\
d = 2r \\ r = \frac{d}{2} \\\\
\frac{ \pi ( \frac{d}{2})^{2}}{ \pi ( \frac{d}{2})^{2} }= \frac{ \pi ( \frac{3}{2})^{2}}{ \pi ( \frac{15}{2})^{2} }\\
\frac{ \pi ( \frac{3}{2})^{2} }{ \pi ( \frac{15}{2})^{2} } = \frac{ \pi (1.5)^{2} }{ \pi (7.5)^{2} } \\
\frac{ \pi (1.5)}{ \pi (7.5) } = \frac{ \pi (2.25)}{ \pi (56.25)}\\
\frac{ \pi (2.25)}{ \pi (56.25)}=\frac{2.25}{56.25}= 0.04 [tex]
So the bulls-eye takes up 4% of the target.
