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Brittany B.

UC Berkeley student with years of tutoring experience

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Question:

A grocery store must pay $1500 a month to rent their facilities and makes and average of $64 per customer who visits. Write an equation which models the store's profits, where S represents the total profit and C represents the number of customers. In addition, determine the minimum number of customers they must have visit in a month and spend the average amount in order for the store to break even.

Brittany B.

Answer:

S = 64C - 1500 (explanation: the store makes an average of $64 per costumer, so this is accounted for in the equation by 64 times C, the number of customers. However, to find the store's profits, we must also subtract their expenses, which include the rent of $1500). To find how many customers they need to visit to break even, we take S = 0 and solve for C. 0 = 64C - 1500 1500 = 64C C = 1500/64 C = 23.4375 but since we cant have .4375 of a person, we round up to 24 customers.

Literature

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Question:

What is one motif that appears in Shakespeare's Hamlet? How is it used/what does it signify?

Brittany B.

Answer:

Hearing and ears are a common motif in Hamlet. References to these things often signify deceit and the power that words have to corrupt and even kill. Notable uses include the fact that King Hamlet was killed by poison poured in his ear, and the following quote spoken to Hamlet by his father's ghost: "So the whole ear of Denmark is by a forgèd process of my death rankly abused" (Act 1 scene 5).

Calculus

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Question:

What is the fundamental theorem of calculus? What does it tell us and what can we find with this knowledge?

Brittany B.

Answer:

The fundamental theorem of calculus states that the integral of a continuous function f over the closed interval [a, b] is equal to F(a) - F(b), where F is the antiderivative of f. From this, we can find the area under the curve f from point a to b.

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