For the upcoming holiday season, Dorothy wants to mold 20 bars of chocolate into tiny pyramids. Each bar of chocolate contains 6

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:

(a) What will his age be after 5 years?

"5 + y" years old

(b) What was his age 6 years ago?

"y - 6" years old

(c) If his grandfather’s age is five times his, how old is his grandfather?

"5y" years old

(d) His father is 6 years older than three times his age. How old is his father?

"6 + 3y" years old

Note: Disregard the quotation marks, ""

0.96/8= $0.12 (per crayon)
0.12x30= $3.60

Answer:

The correct selection is 1.

Step-by-step explanation:

The histogram indicates that

In the 5-10 age group, there are 7 students.

In the 11-13 age group, 5 students are represented.

In the 14-18 age category, 4 students are included.

This implies that the ages of 7 students fall within the 5-10 range, 5 students within the 11-13 range, and 4 students within the 14-18 range.

The total count in the dataset is

In options 3 and 4, the counts in the datasets are fewer than 16. Hence, options 3 and 4 are invalid.

Option 2 exclusively contains data within the 5-10 range, making it incorrect as well.

In option 1,

Class intervals      elements           frequency

5-10                    5,6,7,8,9,10,10           7

11-13                  11,11,12,12,13            5

14-18                    14,14,15,16              4

Based on the above table, we can determine that data set 1 is represented in the provided histogram.

Thus, the answer is option 1.

Adult tickets sold = 75, Students = 200, Children = 75. To find the values, we use the variables for adult tickets, students, and children and set a series of equations based on the total tickets sold and both the pricing and quantity, leading to a solution of ticket counts.