How do you write 6.75 as a mixed number in simplest form?

Which expressions are equivalent to (5⋅x)⋅3 ? Drag and drop the equivalent expressions into the box. 3⋅(5⋅x)5⋅3+x⋅35⋅(x⋅3)15x5⋅3

aivan3 [116]

Okay, so here are the answers..

1. 3 • (5 • x)

2. 5 • (x • 3)

3. 15x

You're welcome, and I took the test. :T

8 0

4 years ago

A system of equations is shown. 0.6d+0.05e=-4.5 -0.12d+0.3e=2.76 d= e=

Drupady [299]

I would multiply to get rid of the decimals and work with whole numbers.
Since we have numbers that are "hundredths", we would need to multiply every number by 100.
60d + 5e = -450
-12d + 30e = 276 Now that the decimals are gone, if we multiply the second equation by 5 the "d's" will cancel.
60d + 5e = -450
-60d + 150e = 1380
155e = 930
e = 6
Now plug 6 back in for e and solve for d.
60d + 5(6) = -450
60d + 30 = -450
60d = -480
d = -8
(-8, 6)
If you'd rather work it with decimals just let me know.

4 0

3 years ago

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

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