1. math fit is a tutoring company for high school students taking algebra 1, algebra 2,
geometry, pre-calculus and calculus. the profit this company makes in a year is
given by the expression 0.2(2000 + 350s), where s is the total number of students
enrolled.
part a: use the distributive property to write an equivalent expression.
part b: what is the company's yearly profit if its enrollment is 50 students?

Part A: Profit = 400 + 70 s,  Part B : $3900

Step-by-step explanation:

Part A:

We know that the expression is: 0.2 ( 2000 + 350 s ). Using the distributive property :

Profit = 0.2 · 2000 + 0.2 · 350 s = 400 + 70 s

Part B :

The company's yearly profit when: s = 50 ( the total number of students )

P ( 50 ) = 400 + 70 · 50 = 400 + 3500 = $3900

A) 0.2*(2000 + 350s) = 400 + 70s

B) $3900

Step-by-step explanation:

A) Given the expression: 0.2*(2000 + 350s). Applying the distributive property of multiplication over addition, we get:

0.2*(2000 + 350s) = 0.2*2000 + 0.2*350s = 400 + 70s

B) Replacing s = 50 into the equation:

0.2*[2000 + 350(50)] = 0.2*[2000 +  17500] = 0.2* 19500 =  $3900

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.