MATHEMATICS HIGH SCHOOL

A rectangular swimming pool with a flat bottom is 20 feet by 12 feet. How long will it take to fill the swimming pool to 5 feet if water is being pumped into the pool at 30 cubic feet per minute?

Answers

Answer 1

Answer:

The given dimensions of the rectangular swimming pool are =

Length = 20 feet

Width = 12 feet

Height upto which the water should be filled up = 5 feet

So, the total volume of water needed to fill the pool will be =

$20*12*5=1200$ cubic feet

The water is pumped at a speed of = 30 cubic feet per minute.

So, to fill 1200 cubic feet, the time taken will be = $(1200)/(30) =40$

Hence, it will take 40 minutes to fill the pool.

Answer 2

Answer: 20 feet * 12 feet * 5 feet
= 20 * 12 * 5 feet ^3
= 1200 feet^3

1200 feet^3 / (30 feet^3 / minute)
= (1200 / 30) minutes
= (120 / 3) minutes
= 40 minutes

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A grocery store manager uses 1/2 crate of apples for every 3/4 crate if oranges in a fruit display. How many crates of oranges will she need if she uses 2 1/2 crates of apples?

Answers

Answer:

15/4

Step-by-step explanation:

This is a proportion question

It says 1/2 crates of apple are used for every 3/4 crates of oranges

For 5/2 crates of apple, x crates of oranges will be needed.

To get x, we simply multiply 1/2 by x and equate it to 3/4 multiplied by 5/2

This means: 0.5x = 0.75 × 2.5

x = ( 0.75 × 2.5 ) ÷ 0.5 = 3.75

Hence for 5/2 crates for apple, she will need 15/4 crates of oranges.

Answer:

Step-by-step explanation:

You would first make a proportion.

.5/.75 = 2.5/x

So, .5x = 1.875

x = 15/4

Persons younger than 18 years old are not eligible to vote. Let a be age in years. Which inequality models this situation?

A.
a < 18 and a may be a negative number

B.
a < 18 and a must be a positive number

C.
a > 18 and a may be a negative number

D.
a > 18 and a must be a positive number

Answers

D 18 and must be a positive number

Describe the structure of roman law during the republic and explain its impact on the world?

Answers

Answer:

The structure of Roman law during the Republic was characterized by the Twelve Tables, legal procedures emphasizing due process, the development of jurisprudence, and its influence on legal systems globally. Roman law's principles of transparency, fairness, and universal application have had a lasting impact on the world, shaping legal systems and promoting justice and equal rights

Step-by-step explanation:

1. Twelve Tables: The Twelve Tables were a set of laws codified in the 5th century BCE. They established the foundation of Roman law and were publicly displayed to ensure transparency and equal treatment under the law. The Twelve Tables covered various aspects of civil law, such as property rights, contracts, and family law.

2. Legal Procedures: Roman law emphasized legal procedures and due process. It provided individuals with the right to a fair trial and allowed them to present evidence and arguments in their defense. This emphasis on legal procedures contributed to the development of the concept of "innocent until proven guilty" and influenced legal systems around the world.

3. Jurisprudence: Roman law developed a system of legal interpretation and principles known as jurisprudence. Jurisprudence involved the study and application of legal principles derived from previous court decisions and legal writings. This system of jurisprudence laid the foundation for legal reasoning and the development of legal principles that have influenced modern legal systems.

4. Influence on Western Legal Systems: Roman law had a profound impact on the development of legal systems in Europe and beyond. Many principles and concepts of Roman law, such as the distinction between public and private law, the idea of legal rights, and the concept of legal personhood, were incorporated into later legal systems. Roman law formed the basis for civil law systems in many countries, including those in continental Europe and Latin America.

5. Universal Application: One of the most significant contributions of Roman law was its universal application. Roman law aimed to provide legal rights and protections to all individuals, regardless of their social status or origin. This concept of universal application and equal treatment under the law had a lasting impact on legal systems worldwide, promoting the idea of legal equality and justice for all.

In summary, the structure of Roman law during the Republic was characterized by the codification of laws, an emphasis on legal procedures and due process, the development of jurisprudence, and its influence on legal systems globally. Roman law's principles of transparency, fairness, and universal application have had a lasting impact on the world, shaping legal systems and promoting the concepts of justice and equal rights.

Simplify each radical expression. Leave in radical form. Show your work

Answers

1. √45n^5 = √ 9 * √5 * √n^5 = 3 * n * n * √n * √5 = 3n^2√5n
2. √75 + √3 = √15 * √3 + √3 = √5 * √3 * √3 + √3 = 3√5 + √3
3. √7 (√14 + √3) = √7 * √14 + √7 * √3 = √7 * √7 * √2 + √7 * √3 = 7√2 + 7√3

I believe these are the solutions

Answer:

√45n^5
$√(45n) ^(5)$

AB+C=50
BC+A=41
What is A, B, C

Answers

For the given system of equations, when B = 2, the values are A = 133 and C = -216. Values will vary with different choices of B.

To solve for the values of A, B, and C in the system of equations:

AB + C = 50

BC + A = 41

We can use a systematic approach. Let's first isolate one variable in one equation and then substitute it into the other equation.

From the first equation (AB + C = 50), we can isolate C:

C = 50 - AB

Now, substitute this expression for C into the second equation:

B(50 - AB) + A = 41

Expand and simplify:

50B - $AB^2$ + A = 41

Rearrange terms:

$AB^2$ - 50B + A = 41

Now, let's consider this as a quadratic equation in terms of A and solve for A:

A = 41 - $AB^2$ + 50B

Now that we have expressions for A and C in terms of B, we can choose a value for B, and then calculate the corresponding values of A and C. For instance, let's say B = 2:

A = 41 - (2)( $2^2$ ) + 50(2) = 41 - 8 + 100 = 133