Let

be the number of strawberry cupcakes, and

the number of chocolate cupcakes.
From our problem we know that the total number of cupcakes is 180, so

. We also know that the number of chocolate cupcakes is eighteen more than twice the number of strawberry cupcakes, so

, or solving for

:

.
Know we have our system of equations:

We can conclude that the correct answer is <span>
B. c + s = 180 c = 2s + 18.
Lets solve our equations to find how many cupcakes of each they have:
from our second equation we know that </span>

; lets replace that value in our first equation to find the number of strawberry cupcakes:




<span>Now that we know the number of strawberry cupcakes, lets replace that value in our second equation to find the number of chocolate cupcakes:
</span>



As a bonus, we can conclude that the <span>math club have 126 chocolate cupcakes and 54 strawberry cupcakes. </span>
Square root 3 is approximately equivalent to 1.732 therefore the answer would be B.
Answer:
E(x)=0.15
V(x)=0.3075
S(x)=0.5545
Step-by-step explanation:
The mean of a discrete variable is calculated as:

where
are the values that the variable can take and
are their respective probabilities.
So, if we call x the number of defective transistors in cartons, we can calculate the mean E(x) as:

Because there are 0 defective transistor with a probability of 0.92, 1 defective transistor with a probability of 0.03, 2 defective transistors with a probability of 0.03 and 3 defective transistors with a probability of 0.01.
At the same way, the variance V(x) is calculated as:

Where 
So, the variance V(x) is equal to:

Finally, the standard deviation is calculated as:

The first and third are correct. They are equal.
The second is incorrect. This is because 1800 meters = 1.8 km (not 18 km). The answer you should have is a "less than sign" because 1.8 km is smaller than 18 km.
To go from meters to kilometers, you move the decimal point 3 spots to the left. This is the same as dividing by 1000.
To go from kilometers to meters, you move the decimal point 3 spots to the right. This is the same as multiplying by 1000.