76 sodas and 34 hot dogs were sold by the vendor.
Step-by-step explanation:
Given,
Total sodas and hot dogs sold = 110
Let,
x be the number of sodas sold
y be the number of hot dogs sold
According to given statement;
x+y=110 Eqn 1
y = x-42 Eqn 2
Putting value of y from Eqn 2 in Eqn 1

Dividing both sides by 2

Putting x=76 in Eqn 1

76 sodas and 34 hot dogs were sold by the vendor.
Keywords: linear equation, substitution method
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Answer:
Step-by-step explanation:
The formula for continuous compounding is
where A(t) is the amount after all the compounding is done, P is the initial investment, r is the rate as a decimal, and t is the time in years. Filling in our info:

First raise e to the product of that power to get

Multiply those numbers together to get A(t) = $824.36
I don't want to give you the answer so here is a thorough explanation and an answer if you want it. Set this up as a proportion. Set it up as 5/5=x/12.5. Then multiply 5 by x to get 5x and 12.5 by 5. Once you have this answer, divide it by five to isolate the x. Once you have finished this, you have your answer.
I got the answer 12.5. Make sure you check this so you understand how to solve these kinds of problems.