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2 years ago

Ten students enter a math contest. In how many ways can 1st, 2nd, and 3rd place trophies be awarded?

1 answer:

4 0

After one of them is chosen for 1st, there are only 9 choices for 2nd, and then there are only 8 choices for 3rd... and so on. There are 720 different ways to pick 1st, 2nd, and 3rd place from among 10 original students

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Find the perimeter of this problem

GrogVix [38]

Answer: 119 4/7

Step-by-step explanation:

Add all the sides together.

4 0

3 years ago

This figure represents the base of a fish tank that is 8 inches high.

Igoryamba

The volume of the fish tank is 408 in³

To solve the volume of the fish tank, we need to understand what is the volume of plane shapes.

<h3>What is the volume of plane shapes?</h3>

The volume of plane shapes resembles a 3-dimensional space showing the area enclosed by the shape.

From the figure given:

The figure can be differentiated into two shapes;

A rectangle
A triangle

The volume of the rectangle is known as:

= Length × Breadth
= 7 inches × 6 inches
= 42 inches²

The volume of the triangle is:

= 1/2 × base × height
= 1/2 × 3 × 6
= 9 inches²

The total volume of the base of the fish tank now is:

= 42 inches² + 9 inches²
= 51 inches²

Now, the volume of the fish tank is:

= Height × base of the fish tank
= 8 inches × 51 inches²
= 408 in³

Learn more about the volume of plane shapes here:

brainly.com/question/20475473

7 0

2 years ago

Prove: The difference of the reciprocals

murzikaleks [220]

Step-by-step explanation:

let two successive integers n, n+1

difference of the reciprocals:

$\frac{1}{n}-\frac{1}{n+1} \\=\frac{(n+1)-n}{(n)(n+1)}\\=\frac{1}{(n)(n+1)}\\=\frac{1}{(n)}\frac{1}{(n+1)}\\$

7 0

2 years ago

Use the given information to find the unknown value:y varies directly as the square of z. When x = 2, then y= 20. Find y when 2

Vladimir79 [104]

Answer

y = 45 when x = 3

Step-by-step explanation:

$\begin{gathered} \text{Given that y varies directly as the square of x} \\ \text{This implies that there is a positive relationship betwe}en\text{ y and the square of z} \\ \text{Mathematically, this can be expressed as} \\ y\text{ }\propto x^2 \\ To\text{ turn this expression into an equation, we n}eed\text{ to introduce a proportionality constant k} \\ y=kx^2 \\ \text{ According to the question, y = 20 and x = 2} \\ \text{From the above informaion we can find our k} \\ y=kx^2 \\ 20\text{ = k }\cdot2^2 \\ 20\text{ = k }\cdot\text{ 4} \\ \text{Divide both sides by 4} \\ \frac{20}{4}\text{ = }\frac{k\cdot\text{ 4}}{4} \\ k\text{ = 5} \\ \text{ Find y when }x\text{ = 3} \\ y=kx^2 \\ y\text{ = 5 }\cdot(3)^2 \\ y\text{ = 5 }\cdot\text{ 9} \\ y\text{ = 45} \end{gathered}$

8 0

1 year ago

Um...help please??????

Ket [755]

Answer:

Step-by-step explanation:

64inches

7 0

2 years ago

Read 2 more answers