This Venn diagram shows the pizza topping preferences for 9 students

The question is:

Examine a differential equation expressed as

y′ = f(αt + βy + γ),

where α, β, and γ are constants. Employ the variable change

z = αt + βy + γ to reformulate the differential equation as a separable equation of the type z′ = g(z).

Answer:

The equation

y′ = f(αt + βy + γ)

can be rephrased as

dy/dt = f(αt + βy + γ).

Our goal is to rewrite this differential equation in the form

z' = g(z), that is dz/dt = g(z).

First, be aware that

dz/dt = (dz/dy) * (dy/dt)...................(1)

Utilizing the substitution

z = αt + βy + γ

as specified,

dz/dy = β..........................................(2)

dy/dt = f(αt + βy + γ) = f(z)............(3)

From equations (2) and (3),

dz/dt = β.f(z) = g(z)

Thus,

z' = g(z)

Where g(z) = βf(z).

Answer:

The result is 2

Step-by-step explanation:

A segment requires at least 2 points for its construction.

In geometry, a line segment refers to a section of a line defined by two unique endpoints, encompassing all points located along the line segment between these endpoints.

Answer:

Confidence Interval

Lower Limit = $4,233.3

Upper Limit = $4,766.7

With 95% certainty, SoftBus can anticipate that the average profit per customer will fall within the range of $4,233.30 to $4,766.7, based on the provided sample data.

Step-by-step explanation:

The z-score corresponding to 95% is 1.96

             Profit         Mean      Square Root

                           Difference    of MD

P1        $5,000       $500        $250,000

P2         4,500          0              0

P3         4,000       -500         $250,000

Total $13,500                        $500,000

Mean $4,500 ($13,500/3)    $166,667 ($500,000/3)

Standard Deviation = Square root of $166,667 = 408.2

Margin of error = (z-score * standard deviation)/n

= (1.96 * 408.2)/3

= 266.7

= $266.7

Confidence Interval = Sample mean +/- Margin of error

= $4,500 +/- 266.7

Lower Limit = $4,233.3 ($4,500 - $266.7)

Upper Limit = $4,766.7 ($4,500 + $266.7)