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3 years ago

Lucy had 12 books. She gave 3 books to Michael. How many books does Lucy have now?

Mathematics

2 answers:

Artemon [7]3 years ago

6 0

12-3=9 :) hope this helps

Mice21 [21]3 years ago

4 0

Lucy started with 12 books and gave 3 which is 12-3=9
Lucy has 9 books m

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A source of information randomly generates symbols from a four letter alphabet {w, x, y, z }. The probability of each symbol is

koban [17]

The expected length of code for one encoded symbol is

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha\ell_\alpha$

where $p_\alpha$ is the probability of picking the letter $\alpha$ , and $\ell_\alpha$ is the length of code needed to encode $\alpha$ . $p_\alpha$ is given to us, and we have

$\begin{cases}\ell_w=1\\\ell_x=2\\\ell_y=\ell_z=3\end{cases}$

so that we expect a contribution of

$\dfrac12+\dfrac24+\dfrac{2\cdot3}8=\dfrac{11}8=1.375$

bits to the code per encoded letter. For a string of length $n$ , we would then expect $E[L]=1.375n$ .

By definition of variance, we have

$\mathrm{Var}[L]=E\left[(L-E[L])^2\right]=E[L^2]-E[L]^2$

For a string consisting of one letter, we have

$\displaystyle\sum_{\alpha\in\{w,x,y,z\}}p_\alpha{\ell_\alpha}^2=\dfrac12+\dfrac{2^2}4+\dfrac{2\cdot3^2}8=\dfrac{15}4$

so that the variance for the length such a string is

$\dfrac{15}4-\left(\dfrac{11}8\right)^2=\dfrac{119}{64}\approx1.859$

"squared" bits per encoded letter. For a string of length $n$ , we would get $\mathrm{Var}[L]=1.859n$ .

5 0

3 years ago

Please help i give 15 points for the answer

Paraphin [41]

Answer:

2 and 9/10

Step-by-step explanation:

3 1/2- 3/5=2 9/10

5 0

3 years ago

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Olivia has 48 slices of ham and 36 slices of cheese to make sandwiches.

serious [3.7K]

The greatest number of sandwiches that Olivia can make is 12.

3 slices of cheese will be on each sandwich

Solution:

Given that, Olivia has 48 slices of ham and 36 slices of cheese to make sandwiches.

We have to find what is the greatest number of sandwiches that Olivia can make? And how many slices of cheese will be on each sandwich?

Let the number of sandwiches be "n"

Then, number of slices of ham per sandwich $=\frac{48}{n}$

And, number of slices of cheese per sandwich $=\frac{36}{n}$

As slices can’t be fractions, "n" should be a factor of 48 and 36. So now let us find H.C.F of 48 and 36 as we want greatest number of sandwiches that Olivia can make.

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36

The common factors are those which appear on both factors of 48 and 36 are 1, 2, 4, 6, and 12.

Out of these common factors, 12 is the greatest

So, H.C.F of 48 and 36 is 12, which means n = 12

Then, number of cheese slices per sandwich $=\frac{36}{12}=3$

Hence, 12 sandwiches can be made with 3 slices of cheese per sandwich.

8 0

4 years ago

Store a sells 12 juice bottles for 4 and stor b sells 18 bottles for 6 dollars are they equivalent

patriot [66]

Answer:

Yes

Step-by-step explanation:

They are equivalent because they both have the GCF of 3. 3x4=12 3x6=18

Hope it helps!

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3 years ago

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What is 5.8×10^6 seconds in minutes?

Wewaii [24]

Answer:

9.66 x 10⁴ minutes

Step-by-step explanation:

To convert seconds into minutes, simply divide by 60.

=> 5.8 x 10⁶ / 60

=> 580 x 10⁴ / 60

=> 29 x 10⁴ / 3

=> 9.66 x 10⁴ minutes

3 0

2 years ago

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