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3 years ago

A juice container can hold 96 ounces. The container has 72 ounces of juice. What percentage is not in the container.

Mathematics

1 answer:

Ede4ka [16]3 years ago

8 0

Answer:

25% of the juice is not in the container.

Step-by-step explanation:

We are given the following in the question:

Total juice container can hold = 96 ounces

Amount of juice in container = 72 ounces

Amount of juice not in container =

$96-72=24\text{ ounces}$

We have to find the percentage of juice not in the container.

Percentage =

$=\dfrac{\text{Amount of juice not in container}}{\text{Total amount the container can hold}}\times 100\5\\\\=\dfrac{24}{96}\times 100\%\\\\=25\%$

Thus, 25% of the juice is not in the container.

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Find area of the shaded region.

Monica [59]

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

$\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}$

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

$\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}$

Now, we can find the area of the triangle. We can use an alternative formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

$\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)$

The area of the shaded region is equivalent to the sector minus the triangle:

$A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}$

Therefore:

$A_{\text{shaded}}=15\pi -18\sin(150)$

Use a calculator:

$A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2$

The area of the shaded region is about 38.1 square centimeters.

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Graph that represents y=4^2+3

marissa [1.9K]

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Mario has a rectangular prism completely filled with sand that has a base area of 85 cm² and a height of 15 cm. Mario pours all

just olya [345]

The base area of this second rectangular prism is 51 cm²

The rectangular prism completely filled with sand has a base area of 85cm² and height of 15cm .

<h3></h3><h3> volume of a rectangular prism</h3>

volume = Bh

where

B = base area

h = height

Since the first rectangular prism was completely filled with sand and it completely filled the second rectangular prism, it means they both have the same volume.

Therefore,

volume of the first rectangular prism = volume of the second rectangular prism.

volume = Bh

volume = 85 × 15

volume = 1275 cm³

Therefore, the base area of the second rectangular prism can be calculated as follows:

volume = Bh

1275 = 25B

B = 1275 / 25

B = 51 cm²

learn more on prism here: brainly.com/question/2517494?referrer=searchResults

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