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NARA [144]
2 years ago
6

Write the expression below as a single logarithm in simplest form. logo 7 – log, 7

Mathematics
1 answer:
Svet_ta [14]2 years ago
5 0

Given:

The given expression is:

\log_b7-\log_b7

To find:

The single logarithm expression for the given expression.

Solution:

Quotient property of logarithm:

\log_bm-\log_bn=\log_b\left(\dfrac{m}{n}\right)

We have,

\log_b7-\log_b7

Using quotient property of logarithm, we get

\log_b7-\log_b7=\log_b\left(\dfrac{7}{7}\right)

\log_b7-\log_b7=\log_b\left(1\right)

Therefore, the required expression is \log_b\left(1\right).

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25 POINTS!!!!Which of the following statements are true? Select all that apply.
ella [17]

Answer:

A+B=B+A

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Step-by-step explanation:

6 0
3 years ago
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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

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2 years ago
PLEASE HELP!
Kay [80]

Answer:

77 inches

Step-by-step explanation:

Given

1 inch = 3 miles in map

We are also given the actual distance between City A and City B = 231 miles.

In order to get the distance in inches = Distance between City A and City B in miles/ 3

We are dividing the distance by 3 to get the distance in inches.

So,

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= 77 inches

4 0
3 years ago
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Find the polynomial of lowest degree with only real coefficients and having the given zeros. -7i and square root of 2
mario62 [17]

Answer:

x³ - (√2)x² + 49x - 49√2

Step-by-step explanation:

If one root is -7i, another root must be 7i.  You can't just have one root with i.  The other roos is √2, so there are 3 roots.  

x = -7i       is one root,

   (x + 7i) = 0    is the factor

x = 7i       is one root

  (x - 7i) = 0     is the factor

x = √2      is one root

    (x - √2) = 0   is the factor

So the factors are...

(x + 7i)(x - 7i)(x - √2) = 0

Multiply these out to find the polynomial...

(x + 7i)(x - 7i) =  x² + 7i - 7i - 49i²

Which simplifies to

  x² - 49i²        since i² = -1 , we have

    x² - 49(-1)  

 

      x² + 49

Now we have...

(x² + 49)(x - √2) = 0

Now foil this out...

 x²(x) - x²(-√2) + 49(x) + 49(-√2) = 0

     x³ + (√2)x² + 49x - 49√2

7 0
3 years ago
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