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Mekhanik [1.2K]
3 years ago
7

A scoop of ice cream is the shape of a whole perfect sphere sits in a right cone.

Mathematics
2 answers:
Tomtit [17]3 years ago
8 0

Answer:

\large \boxed{\text{10 cm}}

Step-by-step explanation:

The volume of the sphere must equal  the volume of the cone.

\begin{array}{rcll}V_{\text{sphere}} & = & V_{\text{cone}}&\\\dfrac{4}{3} \pi r^{3}& = & \dfrac{1}{3} \pi r^{2} h&\\4 \pi r^{3} & = & \pi r^{2} h &\text{Multiplied each side by 3}\\4r & = & h&\text{Divided each side by }\pi r^{2}\\h & = & 4r \times 2.5&\text{Substituted the value of }r\\& = & \textbf{10 cm}&\\\end{array}\\\text{The height of the cone must be $\large \boxed{\textbf{10 cm}}$}

Andrei [34K]3 years ago
7 0

Answer:

  10 cm

Step-by-step explanation:

The volume of a sphere is given by the formula ...

  V = 4/3πr³

The volume of a cone is given by the formula ...

  V = 1/3πr²h

The ratio of the volume of the cone to that of the sphere is ...

  Vcone/Vsphere = (1/3πr²h)/(4/3πr³) = h/(4r)

In order for the ratio to have a value of 1, we must have ...

  h = 4r

The height of the cone must be 4×2.5 cm = 10 cm to fit all of the ice cream.

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Which equation best represents the data? y = –1.026x2 1016.402x – 162075 y = –1.036x2 1024.771x – 163710 y = 298.214x – 66317.66
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The table on the items produced by this company and the profits derived from these goods shows that the best model is y = -1.026x² + 1,016.402x - 162,075.

<h3>Which model best represents the data?</h3><h3 />

Find out the best model by testing all models assuming a given value of x. The model that gives a y value closest to the actual value is the best model.

Assuming x is 100:

= -1.026x² + 1,016.402x - 162,075

= (-1.026 x 100²) + (1,016.402 x 100) - 162,075

= -$70,694.80

Second model:

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= (-1.036 x 100²) + 1024.771 x 100 - 163710

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Third model:

=  298.214x - 66317.667

= 298.214 x 100 - 66317.667

= -$36,496.27

Fourth model:

= 196.2x - 18710

= 196.2 x 100 - 18,710

= $910

The best model is therefore the first model which shows the closest value to the actual y value of -$70,500 when x is 100.

Find out more on fitting models at brainly.com/question/2564940.

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Answer:

9 free-throws

Step-by-step explanation:

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<u>Make y the subject:</u>

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The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles. The adjacent angles are the angles which have a common vertex.

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3 years ago
A city Council consist of six democrats and eight Republicans if a committee of six people is selected find the probability of s
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Answer:

The probability of selecting three Democrats and two Republicans is 0.349

Step-by-step explanation:

Given:

The Number of Democrats = 6

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Probability of selecting 2 Democrats and 4 Republicans. = ?

Solution:

we have to select a committee of 6 people

Now the probability of selecting 2 Democrats and 4 Republicans.

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