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IgorLugansk [536]
2 years ago
14

Simplify -2i sq.root -12

Mathematics
1 answer:
Darina [25.2K]2 years ago
6 0

Answer:

= 4sqrt3

Step-by-step explanation:

-2i sqrt -12

= -2i * i sqrt12 <-- i^2 = -1

= -2i^2sqrt12

= -2(-1)sqrt12

= 2sqrt12

= 2 * 2 sqrt3

= 4sqrt3

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3 years ago
18 tens 20 ones = ______hundreds
Elis [28]

Answer:

200

Step-by-step explanation:

18 × 10 = 180

20 × 1 = 20

180 + 20 = 200

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Abigail heard on the weather report that there is a 40% chance that it will rain tomorrow and a 50% chance that it will be cloud
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7 0
3 years ago
A bacteria culture begins with 4 bacteria which double in size every hour. How many bacteria exist in the culture after 8 hours?
Shalnov [3]

Answer:

Option C. 1,024 bacteria

Step-by-step explanation:

We are given that a bacteria culture begins with 4 bacteria which double in size every hour. And we have to find that how many bacteria exist in the culture after 8 hours;

So, Number of bacteria after one hour = 4 * 2 = 8

     Number of bacteria after two hours = 8 * 2 = 16

     Number of bacteria after three hours = 16 * 2 = 32

     Number of bacteria after four hours = 32 * 2 = 64

     Number of bacteria after five hours = 64 * 2 = 128

     Number of bacteria after six hours = 128 * 2 = 256

     Number of bacteria after seven hours = 256 * 2 = 512

     Number of bacteria after eight hours = 512 * 2 = 1,024

Therefore, 1,024 bacteria exist in the culture after 8 hours .    

7 0
3 years ago
Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,
kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

V_{flask}=V_{sphere}+V_{cylinder}.

Use following formulas to determine volumes of sphere and cylinder:

V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

  • V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;
  • V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;
  • V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.

Then

\dfrac{V_{\text{new flask}}}{V_{\text{flask}}} =\dfrac{8}{1}=8.

Answer 2: correct choice is D.


8 0
3 years ago
Read 2 more answers
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