What is 5x + 2

A caterer makes 15 3/4 quarts of tomato soup. He pours 2 cups of soup into each bowl. How many quarts of soup are in each bowl?

Sindrei [870]

ANSWER:

There are 0.5 quarts in each bowl. There are 31 fully filled bowls. And left over soup is 1 cup of soup.

SOLUTION:

Given, a caterer makes $15 \frac{3}{4}$ which is equal to $\frac{63}{4}$ quarts of tomato soup.

He pours 2 cups of soup into each bowl.

Now let us find how many quarts of soup are in each bowl?

We know that, 1 us liquid quart equals to 4 us cups.

Then, 1 quart = 4 cups

1 cup = $\frac{1}{4}$ quarts

Here, in each bowl caterer pours two cups,

So, 2 cups = $2 \times \frac{1}{4}$ quarts

$= \frac{1}{2} = 0.5 quarts$

Hence, there are 0.5 quarts in each bowl.

Now let us find how many 2-cup bowls of soup can the caterer fill to the top?

From above part, we know that, each bowl has 0.5 quarts.

Then, total bowls with 2- cups of soup = $\frac{\text {total soup}}{\text {soup in one bowl}}$

$=\frac{\frac{63}{4}}{\frac{1}{2}}$

$=\frac{63}{4} \times \frac{2}{1}$$=\frac{63}{2}$$=31.5$$

Here, 0.5 means that a bowl which is not filled to the top. So there are 31 fully filled bowls.

Now, let us find how many cups of soup are left over?

From above part we saw that, there are 31 fully filled bowls but there is a bowl with 0.5 quarts and which is not fully filled.

So, it is the amount of soup which is left over. i.e. 0.5 times of a bowl.

We know that, each bowl will have two cups.

Here left over bowl has half of it filled with soup

So the left over soup is 1 cup of soup.

5 0

3 years ago

How to find the area of combined shapes

Elodia [21]

You can split the combined shape into separate shapes and find the area of each of those. once you have done that add all of the areas together and that will get you your combined shapes area.

3 0

3 years ago

Three numbers between 80 and 100 are prime numbers. What numbers are they? Eight numbers between 31 and 41 are composite numbers

Flura [38]

83, 89, and 97 are three primes between 80 and 100.

The primes between 30 and 50 are 31, 37, 41, 43, and 47, all of which are odd. All other numbers between 30 and 50 are composite.

To mentally find 2*50*25, you could either first multiply 25 by 2, to get 50*50, which can easily be calculated as 2500, or you could multiply the 50 by 2, for a result of 100*25, which is clearly also 2500.

5 0

3 years ago

I have 8 slices of pizza in a box, all 8 are triangle shaped, my perimeter is 43.98 Octagon with each edge 5.49 inches. So, I ne

kondor19780726 [428]

Answer:

1) The area of the circle pizza is approximately 161.64 in.²

2) The area of the octagon shaped pizza is approximately 145.52 square inches

Step-by-step explanation:

The 8 slices of pizza combine to form the composite octagon

The parameters of the pizza are;

The perimeter of the octagon = 43.98 inches

The length of each (outer) edge of the octagon = 5.49 inches

The outer edge of the octagon = The base of the triangle shaped pizza

Let θ represent the vertex angle of the triangle shaped pizza

Therefore, we have;

θ = (The angle at the center point of the pizza)/8 = 360°/8 = 45°

The vertex angle of the triangle shaped pizza, θ = 45°

We note that a triangle shaped pizza is isosceles shaped, therefore, the base angles are given as follows;

The base angles of a piece of pizza = (180° - (angle at vertex))/2

∴ The base angles of a piece of pizza = (180° - 45°)/2 = 67.5°

The length, 'l', of the other sides of the triangle shaped pizza is given by sine rule as follows;

l/(sin 67.5°) = 5.49/(sin(45°)

∴ l = (sin 67.5°) × 5.49/(sin(45°)

l = (sin 67.5°) × 5.49/(sin(45°) ≈ 7.173

The length of the other sides of the triangle shaped pizza, l ≈ 7.173 inches

1) The length of the other sides of the triangle shaped pizza, l = The radius of the circle, r

The area of the circle = π·l²

∴ The area of the circle ≈ π × (7.173 in.)² ≈ 161.64 in.²

2) The area of each triangle piece of pizza is given as follows;

The area of a triangle, A = 1/2×l·b·sin(C)

∴ A = 1/2× 5.49 × 7.173 × sin(67.5°) ≈ 18.19

The area of each triangle piece of pizza, A ≈ 18.19 inches²

The total area of 8 slices of octagon shaped pizza, TA ≈ 8 × A

∴ TA ≈ 8 × 18.19 inches² ≈ 145.52 inches²

The total area of 8 slices of octagon shaped pizza, TA ≈ 145.52 inches²

4 0

2 years ago

PLEASE HElp asap Solve for x. x = [?] X + 19 7x + 9

Bess [88]

X + 19 + 7x + 9 = 180
8x + 28 = 180
8x = 180 - 28
8x = 152
X = 152 : 8
X = 19

3 0

3 years ago

What is 5x + 2 - 4x +3