Which of the following is an expression for “doubling a number N and dividing by 3” ?

How much do a dozen cookies weigh?

yaroslaw [1]

0.43 oz

Hope this helps...

7 0

3 years ago

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An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of

Helga [31]

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = $\pi r^{2} \frac{h}{3}$

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

$r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm$

We will now find the volume of the cone.

Volume of cone $\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}$

We know the density of ice is 0.93 grams per $1cm^{3}$

$1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g$ (Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = $\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}$

Volume of cone being melted = New Volume - Original volume

= $\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}$

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = $\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}$

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = $5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}$

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= $\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}$

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

4 0

2 years ago

Jeremiah received $65 for his birthday and used part of it to buy 3 video games. The games cost the same amount, and he had $14

hram777 [196]

Jeremiah got $65 on birthday and spent some money on 3 video games and was left with $14.

He purchased 3 video games.

Let the cost one one video game be v.

The cost of each video game is same

So the cost of 3 video games is 3v.

Also he is left with $14 after paying for three games.

Hence

3v + 14 = 65

Subtracting 14 from both sides

3v + 14 -14 = 65-14

3v = 51

Dividing by 3 on both sides

v = 51/3

v = 17

Hence the cost of each video game is $17

5 0

3 years ago

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Write the equation of the line that passes through the points (-2,3) and (-2,5),

Ad libitum [116K]

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$x = - 2$

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6 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2x%7D" id="TexFormula1" title="\frac{3}{2x}" alt="\frac{3}{2x}" align="absmid

defon

Answer:

x=35/78

Step-by-step explanation:

3/2x-11/5=(7/8)*(64/49)

3/2x-11/5=8/7

3/2x=8/7+11/5

3/2x=117/35

x=(35*3)/(2*117)

x=35/78

3 0

3 years ago