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Vera_Pavlovna [14]
3 years ago
10

An orange juice company sells a can of frozen orange juice that measures 9.4 centimeters in height and 5.2 centimeters in diamet

er. The company wants to sell a larger can of juice. The height of the can is kept at 9.4 cm, but the diameter is increased to 8.5 cm. About how many times more juice will the new can hold?
Image is the same question w/ a model.

Mathematics
1 answer:
drek231 [11]3 years ago
3 0
<h2>Hello!</h2>

The answer is:

The third option:

2.7 times as much.

<h2>Why?</h2>

To calculate how many more juice will the new can hold, we need to calculate the old can volume to the new can volume.

So, calculating we have:

Old can:

Since the cans have a right cylinder shape, we can calculate their volume using the following formula:

Volume_{RightCylinder}=Volume_{Can}=\pi r^{2} h

Where,

r=radius=\frac{diameter}{2}\\h=height

We are given the old can dimensions:

radius=\frac{5.2cm}{2}=2.6cm\\\\height=9.4cm

So, calculating the volume, we have:

Volume_{Can}=\pi *2.6cm^{2} *9.4cm=199.7cm^{3}

We have that the volume of the old can is:

Volume_{Can}=199.7cm^{2}

New can:

We are given the new can dimensions, the diameter is increased but the height is the same, so:

radius=\frac{8.5cm}{2}=4.25cm\\\\height=9.4cm

Calculating we have:

Volume_{Can}=\pi *4.25cm^{2} *9.4cm=533.40cm^{3}

Now, dividing the volume of the new can by the old can volume to know how many times more juice will the new can hold, we have:

\frac{533.4cm^{3} }{199.7cm^{3}}=2.67=2.7

Hence, we have that the new can hold 2.7 more juice than the old can, so, the answer is the third option:

2.7 times as much.

Have a nice day!

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eimsori [14]

Answer:

1) Slope-intercept form

2) 9200

3) 2 months

4) (0,200)

Step-by-step explanation:

A shelter had 200 animals in foster homes at the beginning of spring and the number of animals in foster homes at the end of the summer could be represented by  

y=3000x+200 ............ (1)

Where x is the number of months and y is the number of animals.

1) The equation (1) is written in the slope-intercept form of a straight line equation.

2) After 3 months means x = 3 and the number of animals in the foster home after 3 months will be (3000 ×3 + 200) = 9200 (Answer)

3) Let after x months the animal population will become 6200.

So, 6200 = 3000x + 200

⇒ 3000x = 6000

⇒ x = 2 months (Answer)  

4) If we put x = 0 in equation (1), then we get y = 200.

So, (0,200) is a point on the graph of the line. (Answer)

5 0
3 years ago
A truck begins a trip of 1675 miles. The truck averages 55 miles per hour, including stops. create a table, a graph, and an equa
lawyer [7]
Let
x be the distance that the truck has left to travel
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The digits 1, 7, and 8 and 2 copies of the digit 5 are all arranged to form a 5-digit integer. How many different integers can b
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Step-by-step explanation:

You have 5 digits.Youdonot say if duplication is allowed. I will assume not

For the first digit you have 5 choices. One of the 5 digits is gone.

You now have 4 digits to choose from. You pick one. Now you have but 3 left.

The total answer if 5*4*3*2*1 = 120

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Find vertex of f(x)=(x+3)(x-5)
astra-53 [7]

The x coordinate of the vertex will be the average of the two zeros, here -3 and 5, so x=(-3+5)/2 = 1, f(1)=(1+3)(1-5) = -16.

Answer: (1, -16)

Let's do it some other ways.  How about completing the square to turn f in to vertex form?

f(x) = (x+3)(x-5) = x² - 2x - 15 = (x² - 2x + 1) - 1 - 15 = (x-1)² - 16

and now we can read off (1, -16) as the vertex.

The other method is the vertex is x= - b/2a =  - (-2)/2(1) = 1.

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