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Mekhanik [1.2K]

3 years ago

15

If numbers 1,2,3,4,5 are to be used in a five number code, how many different codes are possible if repetitions are not permitte

d

1 answer:

Alex73 [517]3 years ago

4 0

5x4x3x2x1=120 different codes possible
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If log2 5 = k, determine an expression for log32 5 in terms of k.

lukranit [14]

Answer:

$log_3_2(5)=\frac{1}{5} k$

Step-by-step explanation:

Let's start by using change of base property:

$log_b(x)=\frac{log_a(x)}{log_a(b)}$

So, for $log_2(5)$

$log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)$

Now, using change of base for $log_3_2(5)$

$log_3_2(5)=\frac{log(5)}{log(32)}$

You can express $32$ as:

$2^5$

Using reduction of power property:

$log_z(x^y)=ylog_z(x)$

$log(32)=log(2^5)=5log(2)$

Therefore:

$log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)$

As you can see the only difference between (1) and (2) is the coefficient $\frac{1}{5}$ :

So:

$\frac{log(5)}{log(2)} =k\\$

$log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k$

6 0

3 years ago

What is the equation of the midline for the function f(x)? f(x)=1/2 cos(x)+5

ivolga24 [154]

Answer:

y = 5

Step-by-step explanation:

That "+5" elevates the graph of this cosine function 5 units above the x axis, and thus the "midline" you wanted is y = 5.

6 0

3 years ago

What can you predict regarding the probability of the

natka813 [3]

Answer:

The frequency does not change with more trials

Step-by-step explanation:

To predict: the probability of the coin landing heads up

Solution:

Probability refers to the chances that an event will occur in an experiment. The value of probability lies between 0 and 1. 0 indicates impossible event and 1 indicates a sure event. The probability of an event can not be greater than 1.

When a coin is tossed, there are two possible outcomes: heads (H), tails (T).

In case of the probability of the coin landing heads up, the frequency does not change with more trials.

6 0

3 years ago

Read 2 more answers

Using the diagram below, translate the figure 3 units to the left and 2 units up. Graph the translated figure and provide the tr

aleksandrvk [35]

Bah ahaha because i’m trying to get answers to m

8 0

3 years ago

Six friends, four boys and two girls, went to a movie theater. They wanted to sit in a way so no girl sits on either first or la

mel-nik [20]

Answer:

120 ways

Step-by-step explanation:

Since no girl wil sit either first or last

Hence, in all irrespective whether boy or girl = (6 - 1)! = 5! = 5 X 4 X 3 X 2 = 120

∴ Number of arrangements = 120 ways

8 0

3 years ago