<img src="https://tex.z-dn.net/?f=%28%20%5Cfrac%7B8%7D%7B11%7D%29%20%7B%7D%5E%7B7%20-%202%20%5Ctimes%203%20-%201%7D%20" id="TexF

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3 years ago

ormula1" title="( \frac{8}{11}) {}^{7 - 2 \times 3 - 1} " alt="( \frac{8}{11}) {}^{7 - 2 \times 3 - 1} " align="absmiddle" class="latex-formula">
find the answer

Mathematics

1 answer:

Darya [45]3 years ago

6 0

Answer:

Step-by-step explanation:

$(\frac{8}{11})^{7- 2*3 - 1} = (\frac{8}{11})^{7- 6 - 1}\\\\=(\frac{8}{11})^{7- 7}\\\\=(\frac{8}{11})^{0}\\\\=1$

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if the hieght and radius of the cone is tripled then find the ratio of Volume of the new cone and of that of original

solniwko [45]

$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
r=\stackrel{3\times r}{3r}\\
h=\stackrel{3\times h}{3h}
\end{cases}\implies V=\cfrac{\pi (3r)^2(3h)}{3}
\\\\\\
V=\cfrac{\pi (3^2r^2)(3h)}{3}\implies V=\cfrac{\pi (9r^2)(3h)}{3}\implies V=27\left( \cfrac{\pi r^2 h}{3} \right)$

notice the original, and the new one, with the tripled "r" and "h" is just, whatever the original was times 27, namely 27 times as large as the original.

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3 years ago

What is the focus of the parabola

Blizzard [7]

Answer:

(-4,1)

Step-by-step explanation:

The given parabola is

$y = - \frac{1}{4} {x}^{2} - 2x - 2$

When we rewrite in vertex form, we get;

$y = - \frac{1}{4} {(x + 4)}^{2} + 2$

${(x + 4)}^{2} = - 4( y - 2)$

When we compare to:

${(x - h)}^{2} = 4p( y - k)$

We have 4p=-4

This means p=-1

But the vertex is at:

(-4,2)

Since it is a vertical parabola that opens down, the focus is one unit(|p|=1) below the vertex.

Hence the focus is (-4,1)

7 0

4 years ago

Find the area of the figure

Eduardwww [97]

Answer:

132cm²

Step-by-step explanation:

You can find the area of the entire shape by calculating the area of seperate smaller shapes.

You can split them up into 2 rectangles, one with a base of 7cm and height of 4cm, and another one with a base of 7cm and height of 8cm. You also have 2 triangles, with a base of 19cm - 7cm / 2 = 6cm since it is the entire bottom line subtracted by the top; they will have a height of 8cm each.

To calculate the rectangles areas, simply do length x width, which are:

4cm x 7cm = 28cm²

8cm x 7cm = 56cm²

Next, since the triangles are similar in measurements, instead of doing the normal calculation to find the area of a triangle, you can do base times height again, which is:

6cm x 8cm = 48cm²

Add all the answers together to get the final area, which is 132cm².

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3 years ago

a circular picture whose diameter is 4 decimeter is framed in a rectangle board with dimension of 6 decimeter by 4 decimeter wha

avanturin [10]

Answer is $\bf \dfrac{80}{7}$ dm².

In order to calculate the area of the board that can be seen, we need to calculate the area of the the rectangular board and the circular frame. The difference of both's area is the required answer.

Refer to the attachment for step by step solution. :)

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3 years ago

POSSIBLE OUTCOMES!!!

Ganezh [65]

The probability of drawing two blue marbles if the first marble is not replaced is 1/5

<h3>How to determine the probabilities?</h3>

<u>The probability of tossing a head and drawing a red marble</u>

The given parameters are:

White = 1

Blue =3

Red = 2

Total = 6

The probability of a head is

P(Head)= 1/2

The probability of drawing a red marble is

P(Red)= 2/6 = 1/3

The required probability is

P = P(Head) * P(Red)

This gives

P = 1/2 * 1/3

P =1/6

<u>The probability of drawing two blue marbles if the first marble is not replaced.</u>

Here, we have:

P(B1) = 3/6 = 1/2

P(B2) = 2/5

The required probability is

P = P(B1) * P(B2)

This gives

P = 1/2 * 2/5

P =1/5

Hence, the probability of drawing two blue marbles if the first marble is not replaced is 1/5