Answer:

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

A restaurant mixes homemade barbecue sauce with their smoked pulled pork using a ratio of two cups of sauce for every four pounds of shredded pulled pork. Write two rates to represent this relationship.

1. Angle AOC has what measurement according to the protractor?

In order to buy the microscope, we plan to walk dogs after school, charging $3 per dog. To reward the dogs, we will buy a box of treats for $5 as we start the business. The price of the microscope is $254. How many dogs do the friends need to walk in order to have enough money to buy the microscope?

What expression represents 16 more than 5 times a number, n?

Lines v and w are parallel. Which statement can you NOT deduce from this information?m∠2+m∠5=180m∠3+m∠8=180∠4-∠7∠1=∠8

1. Angle AOC has what measurement according to the protractor?

In order to buy the microscope, we plan to walk dogs after school, charging $3 per dog. To reward the dogs, we will buy a box of treats for $5 as we start the business. The price of the microscope is $254. How many dogs do the friends need to walk in order to have enough money to buy the microscope?

What expression represents 16 more than 5 times a number, n?

Lines v and w are parallel. Which statement can you NOT deduce from this information?m∠2+m∠5=180m∠3+m∠8=180∠4-∠7∠1=∠8

The statement B is true the corresponding lines are proportional and the angles are congruent. The question with graph is A. AB with MN; BC with NL; AC with NL

Show us the maze and we will help

games won by B: games won by C = 4:3

Team B has won 8 games.

In total, how many games have the three teams won?

**Answer:**

A = 24

B = 8

C = 6

**Step-by-step explanation:**

4:3 from B:C

8:6

8 games won by B and 6 games won by C.

3:1 from A:B

24:8

24 by A and 8 by B

Team A won 24 games, Team B won 8 games and Team C won 6 games. So, the total games won by all three teams is 38.

From the problem, we know that the ratio of games won by Team A to Team B is 3:1, and the ratio of games won by Team B to Team C is 4:3. We also know that Team B has won 8 games.

Since the ratio of Team B to Team A is 1:3, Team A must have won 3 times as many games as Team B. Therefore, Team A has won 3 * 8 = **24 games**.

The ratio of games won by Team B to Team C is 4:3. This means Team B won 4 games for every 3 games Team C won. Since Team B won 8 games, Team C must have won 3/4 as many games as Team B. Therefore, Team C won 3/4 * 8 = **6 games**.

So, in total, the three teams won 24 + 8 + 6 = **38 games**.

#SPJ3

A. 1/14

B. 1/27

C. 13/14

D. 13/27

E. 14/27

The **probability** that the person** chosen** is a **boy** is 14/27.

Number of girls = 13

Number of boys = 14

Total students = 27

**Probability** is a** measure **of the** likelihood **of **occurrence** of an** event**.

**P(event) = Favorable outcomes / total outcomes**

Favourable outcomes = 14 because there are 14 boys

Total outcomes =27

So, the** probability **that the person** chosen** is a** boy **will be given by:

P(boy)=14/27

So, the **probability** that the person** chosen** is a **boy** is 14/27.

Hence, the **probability** that the person** chosen** is a **boy** is 14/27.

To get more about **probability** visit:

**Answer:**

E

**Step-by-step explanation:**

It's E because you have to add 13 and 14 and as you can see there's 14 boys so it's E.

**Answer:**

3x-3 I think that's it.

**Step-by-step explanation:**

**Answer:**

The vertex is (1, -4)

**Step-by-step explanation:**

the answer is 7 + 35v

**Answer:**

7 + 35v

**Step-by-step explanation:**

7 × 1 + 5v × 7

**7 + 35v**

**Hope this helps and have a nice life d:**