<u><em>Answer:</em></u>
b.Each electrician charges a different base fee:
<u><em>Explanation:</em></u>
<u>Each of the equations has two parts:</u>
1- base fee that is independent of any variable (this would be the number that has no variable next to it)
2- an hourly rate depending on the number of hours x (this would be the number that has an x next to it)
<u>For the first electrician:</u>
y = 25x + 30
base fee = $30
hourly rate = $25
<u>For the second electrician:</u>
y = 30x + 25
base fee = $25
hourly rate = $30
<u>For the third electrician:</u>
y = 25x + 20
base fee = $20
hourly rate = $25
<u>Now, let's check the choices:</u>
<span><u>a.Each electrician charges a different hourly rate:</u>
</span>This is incorrect as electricians 1 and 3 charge the same hourly rate ($25)
<span><u>b.Each electrician charges a different base fee:</u>
This is correct as all three base fees are different ($30, $20 and $25)
</span><span><u>c.All three electricians charge the same hourly rate:</u>
This is incorrect as electrician 2 has a different hourly rate
</span><span><u>d. All three electricians charge the same base fee:</u>
This is incorrect as the base fees for the three electricians are different ($30, $25 and $20)
Hope this helps :)</span>
It is given that 
.
Now, know that in 180 degrees there are 
radians. This can be written as:
radians
radians (dividing both sides by 180)
Thus, to find the measure of the given angle of 
in radians, we will have to multiply the above equation by 135. Thus, we get:
radians
radians
Thus, equivalent to the radian measure of angle a is 2.356
Answer:
0.7 ; 0.65 ; 0.115
Step-by-step explanation:
Step-by-step explanation:
P(A) = 0.5 ; P(B) = 0.3
P(not successful) = P(B') = 1 - 0.3 = 0.7 ; P(A') = 1 - 0.5 = 0.5
1.)
Both events are independent events, hence the outcome of one does not depend on the other. That is the failure of the Asian project has nothing to do with the European project.
Probability that European project isn't successful;
P(B') = 1 - P(B) = 1 - 0.3 = 0.7
2.)
Probability that atleast one of the 2 projects is successful :
P(AUB) = P(A) + P(B) - P(AnB)
P(AnB) = P(A) * P(B) = 0.5 * 0.3 = 0.15
P(AUB) = 0.5 + 0.3 - 0.15 = 0.65
3.)
Probability that only the Asian project is successful, given that atleast one of the two projects is successful :
[P(A) - P(AnB)] ÷ P(AuB)
[0.5 * 0.15] ÷ 0.65
= 0.075 ÷ 0.65
= 0.1153846
= 0.115
Answer:
See Below
Step-by-step explanation:
The function is a piecewise function defined as:
a)
We need to find the limit of the function as t goes to infinity. This means what is the max value of fish in the pond given times goes to infinity (on an on).
We will take the 2nd part of the equation since t falls into that range, t is infinity, which is definitely greater than 8.
This means the maximum number of fish at this pond is 1600, no matter how long it goes on.
b)
A function is continuous at a point if we have the limit and the functional value at that point same.
Functional value at t = 8 is (we use 2nd part of equation):
We do have a value and limit also goes to this as t approaches 8.
So, function is continuous at t = 8
c)
We want to find is there a "time" when the number of fishes in the pond is 250, during t from 0 to 6. We plug in 250 into N(t) and try to find t. Make sure to use the 1st part of the piece-wise function. Shown below:
The time is 4 years when the number of fishes in the pond is 250
Annually: Total Amount= $1,611.76 Interest Amount= $711.76
Semiannually: Total Amount= $1,625.50 Interest Amount= $725.50
Quarterly: Total Amount= $1,632.62 Interest Amount= $732.62
