Please helpp ASAP 100 points extra and brainleist

What are the dimensions of the prism and what is the volume

Bess [88]

Answer:

in steps

Step-by-step explanation:

base width: 1/2 x 5 = 2.5

base length: 1/2 x 4 = 2

height: 1/2 x 3 = 1.5

Volume: lwh = 2.5 x 2 x 1.5 = 7.5 in³

5 0

3 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:

Pre-Algebra

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

Algebra I

Coordinate Planes

Coordinates (x, y) → (s, P)

Functions

Function Notation

Terms/Coefficients

Factoring/Expanding

Quadratics

Algebra II

Coordinate Planes

Maximums/Minimums

Calculus

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:

Step 1: Define

Identify

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

Step 2: Differentiate

[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: $\displaystyle P' = -\frac{3s^2}{10} + 12s$

Step 3: 1st Derivative Test

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

∴ s = 0, 40 are our critical numbers.

Step 4: Find Profit

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

We see that we will have a bigger profit when we spend s = $40.

∴ The maximum profit is $3600.

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

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation (Applications)

5 0

3 years ago

Warm-Up

Sveta_85 [38]

Answer:

Graph # 3

Step-by-step explanation:

-2x + 5y > 15 Let x = 0 solve for y

-2(0) + 5y = 15 change the > to an =

5y = 15

y =3 Point (0, 5) is on the graph

Graph # 3 is correct because the y-intercept is 5

x y

0 3 -2(0) + 5y = 15; 5y = 15

5 5 -2(5) + 5y = 15; -10 + 5y = 15; 5y = 25; y = 5

10 7 -2(10) + 5y = 15; -20 + 5y = 15; 5y = 35; y = 7

The graph > the line is dotted and you will shade above the line

4 0

3 years ago

A bakery sold 111 cupcakes in one day. The head baker predicted he would sell 91 cupcakes that day. What was the percent error o

Yuliya22 [10]

$111-91=20-error\\\\\begin{array}{ccc}91&-&100\%\\\\20&-&p\%\end{array}\ \ \ |cross\ multiply\\\\\\91p=100\cdot20\\91p=2000\ \ \ \ |divide\ both\ sides\ by\ 91\\\\\boxed{p\approx21.98\ (\%)}\leftarrow answer$

3 0

3 years ago

Someone please help !!easy !

r-ruslan [8.4K]

Answer:

B) 0, 4, 8, 12

Step-by-step explanation:

If you buy no pumpkins is costs $0. If you buy one pumpkin it costs $4. If you buy two pumpkins it costs $8. If you buy three pumpkins it costs $12.

4 0

3 years ago