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3 years ago

6

A pizza is to be cut into halves. Each of these halves is to be cut into sevenths. What fraction of the pizza is each of the fin

al pieces?

1 answer:

Hitman42 [59]3 years ago

7 0

Answer: $\dfrac{1}{14}$

Step-by-step explanation:

Given, A pizza is to be cut into halves.

Since half is represented by $\dfrac12$ .

So each piece is now $\dfrac12$ of the original.

if each of these halves is to be cut into sevenths, then the fraction of final pieces would be: $\dfrac{1}{2}\times\dfrac{1}{7}=\dfrac{1}{14}$ or we can say each half is divides into 7 pieces since there are two halves, so there will be 2 x 7 = 14 peices.

And the fraction of the pizza is each of the final pieces = $\dfrac{1}{14}$ .

You might be interested in

Round the following times to 1 decimal place 8.16

Mekhanik [1.2K]

The answer is 8.2 bc anything above a 5 goes up.
8.16 <<< a 6 is greater than 5. So the 1 goes up to a 2.

4 0

3 years ago

X/5=2/3=5/y<br><br> 2/3 <br> 4/9<br> 1

Mademuasel [1]

$\frac{x}{5}= \frac{2}{3} = \frac{5}{y}$
Break the equation into parts;
$\frac{x}{5} = \frac{2}{3} ; \frac{2}{3}= \frac{5}{y}$
Solving for x;
$\frac{x}{5} = \frac{2}{3}$
x= $\frac{10}{3}$
Solving for y;
$\frac{2}{3} = \frac{5}{y} 
y= \frac{3*5}{2} 
y= \frac{15}{2}$
$\frac{x}{y} = \frac{10/3}{15/2}$
$\frac{x}{y} = \frac{4}{15}$

5 0

4 years ago

an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

4 years ago

Expand 3(x+ 2.3) <br> Expand 1/3(9x-12)

Snezhnost [94]

Answer:

3x+6.9 and 3x-4

Step-by-step explanation:

since 3 x x is 3x and the sign in the bracket is addition you place it there then place 3 x 2.3

being 6.9.

1/3 x 9is 9/3 and 3 can multiply both sides to get 3/1 or 3 then bring the minus and 1/3 x 12 is 12/3 3 can multiply both sides to get 4/1 or 4

4 0

3 years ago

4. When Megan solved this system using the elimination method, she added the equations together and got the equation 4y = 16. Th

Ede4ka [16]

Hi there!

So, our two equations are:
2x + 3y = 20 and
-2x + y = 4

We can see that the x's will cancel out because they're the same number, opposite signs. Then we're left with 4y = 24.

Divide 24 by 4, which is 6.

y = 6, then we plug that in to the first equation for y:
2x + 3(6) = 20
2x + 18 = 20
2x = 2
x = 1

So, she made her first mistake when adding the equations, adding 20 and 4, she somehow got 16.

The solution to the system is (1,6).

I hope I helped!

6 0

3 years ago