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A librarian has 883 books to place on shelves. Each shelf holds 98 books.

egoroff_w [7]

Answer:

She will be able to fill 9 shelves with 1 book left over.

Let me know if you need more help! :)

3 0

2 years ago

Read 2 more answers

Santana went for a hike on the 21 mile South Boundary Trail. If she can hike2 miles

Katena32 [7]

Answer:

It will take santana 630 minutes or 10.5 hours to complete the 21 miles.

Step-by-step explanation:

<h3> $\frac{2}{60\\}$ $\frac{21}{y}$ y is what you are trying to find multiple her miles by the number of minutes and then divided by how many miles in 60 min. </h3><h3 /><h3 /><h3> </h3>

5 0

2 years ago

HELP ASAP!!! (The problem is on a screenshot)

Darina [25.2K]

The correct answers are A, D, and E.

7 0

2 years ago

The profit P (in thousands of dollars) for a company spending an amount s (in thousands of dollars on advertising is

sattari [20]

Answer:

The company should spend $40 to yield a maximum profit.

The point of diminishing returns is (40, 3600).

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

<u>Algebra I</u>

Coordinate Planes

Coordinates (x, y) → (s, P)

Functions

Function Notation

Terms/Coefficients

Factoring/Expanding

Quadratics

<u>Algebra II</u>

Coordinate Planes

Maximums/Minimums

<u>Calculus</u>

Derivatives

Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

1st Derivative Test - tells us where on the function f(x) does it have a relative maximum or minimum

Critical Numbers

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle P = \frac{-1}{10}s^3 + 6s^2 + 400$

<u>Step 2: Differentiate</u>

[Function] Derivative Property [Addition/Subtraction]: $\displaystyle P' = \frac{dP}{ds} \bigg[ \frac{-1}{10}s^3 \bigg] + \frac{dP}{ds} [ 6s^2 ] + \frac{dP}{ds} [ 400 ]$
[Derivative] Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle P' = \frac{-1}{10} \frac{dP}{ds} \bigg[ s^3 \bigg] + 6 \frac{dP}{ds} [ s^2 ] + \frac{dP}{ds} [ 400 ]$
[Derivative] Basic Power Rule: $\displaystyle P' = \frac{-1}{10}(3s^2) + 6(2s)$
[Derivative] Simplify: $\displaystyle P' = -\frac{3s^2}{10} + 12s$

<u>Step 3: 1st Derivative Test</u>

[Derivative] Set up: $\displaystyle 0 = -\frac{3s^2}{10} + 12s$
[Derivative] Factor: $\displaystyle 0 = \frac{-3s(s - 40)}{10}$
[Multiplication Property of Equality] Isolate <em>s </em>terms: $\displaystyle 0 = -3s(s - 40)$
[Solve] Find quadratic roots: $\displaystyle s = 0, 40$

∴ <em>s</em> = 0, 40 are our critical numbers.

<u>Step 4: Find Profit</u>

[Function] Substitute in <em>s</em> = 0: $\displaystyle P(0) = \frac{-1}{10}(0)^3 + 6(0)^2 + 400$
[Order of Operations] Evaluate: $\displaystyle P(0) = 400$
[Function] Substitute in <em>s</em> = 40: $\displaystyle P(40) = \frac{-1}{10}(40)^3 + 6(40)^2 + 400$
[Order of Operations] Evaluate: $\displaystyle P(40) = 3600$