Solve log x = 4. (help pls)

Eighteen telephones have just been received at an authorized service center. Six of these telephones are cellular, six are cordl

Karo-lina-s [1.5K]

Full Question

Eighteen telephones have just been received at an authorized service center. Six of these telephones are cellular, six are cordless, and the other six are corded phones. Suppose that these components are randomly allocated the numbers 1, 2, . . . , 18 to establish the order in which they will be serviced.

What is the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced?

What is the probability that two phones of each type are among the first six serviced?

Answer:

a. 0.149

b. 0.182

Step-by-step explanation:

Given

Number of telephone= 18

Number of cellular= 6

Number of cordless = 6

Number of corded = 6

a.

There are 18C6 ways of choosing 6 phones

18C6 = 18564

From the Question, there are 3 types of telephone (cordless, Corded and cellular)

There are 3C2 ways of choosing 2 out of 3 types of television

3C2 = 3

There are 12C6 ways of choosing last 6 phones from just 2 types (2 types = 6 + 6 = 12)

12C6 = 924

There are 2 * 6C6 * 6C0 ways of choosing none from any of these two types of phones

2 * 6C6 * 6C0 = 2 * 1 * 1 = 2.

So, the probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced is

3 * (924 - 2) / 18564

= 3 * 922/18564

= 2766/18564

= 0.149

b)

There are 6C2 * 6C2 * 6C2 ways of choosing 2 cellular, 2 cordless, 2 corded phones

= (6C2)³

= 3375

So, the probability that two phones of each type are among the first six serviced is

= 3375/18564

= 0.182

5 0

3 years ago

If p= 6-2y, work out p when y=-5

Blizzard [7]

You should change the y by the number given
P=6-2*-5
P=16

5 0

2 years ago

Read 2 more answers

If a rectangle has an area of x^2+x-20 and a width of x-4, what is the length?

Mrac [35]

Answer:

This (x - 5) represents the length of the rectangle.

Step-by-step explanation:

The formula for the area of a rectangle of length L and width W is A = L * W.

Here, the width is x - 4 and the area is x^2 + x - 20. Dividing the width (x - 4) into the area results in an expression for the length:

x - 4 / x^2 + x - 20

Let's use synthetic division here. It's a little faster than long division.

If the divisor in long division is x - 4, we know immediately that the divisor in synthetic division is 4:

4 / 1 1 -20

4 20

--------------------

1 5 0

This synthetic division results in a remainder of 0. This tells us that 4 (or the corresponding (x - 4) is indeed a root of the polynomial x^2 + x - 20, and so *(x - 4) is a factor. From the coefficients 1 and 5 we can construct the other factor: (x - 5). This (x - 5) represents the length of the rectangle.

4 0

2 years ago

Which expression is equivalent to (16 x Superscript 8 Baseline y Superscript negative 12 Baseline) Superscript one-half?.

loris [4]

To solve the problem we must know the Basic Rules of Exponentiation.

<h2>Basic Rules of Exponentiation</h2>

$x^ax^b = x^{(a+b)}$
$\dfrac{x^a}{x^b} = x^{(a-b)}$
$(a^a)^b =x^{(a\times b)}$
$(xy)^a = x^ay^a$

$x^{\frac{3}{4}} = \sqrt[4]{x^3}= (\sqrt[3]{x})^4$

The solution of the expression is $\dfrac{4x^4}{y^6}$ .

<h2>Explanation</h2>

Given to us

$(16x^8y^{12})^{\frac{1}{2}}$

Solution

We know that 16 can be reduced to $2^4$ ,

$=(2^4x^8y^{12})^{\frac{1}{2}}$

Using identity $(xy)^a = x^ay^a$ ,

$=(2^4)^{\frac{1}{2}}(x^8)^{\frac{1}{2}}(y^{12})^{\frac{1}{2}}$

Using identity $(a^a)^b =x^{(a\times b)}$ ,

$=(2^{4\times \frac{1}{2}})\ (x^{8\times\frac{1}{2}})\ (y^{12\times{\frac{1}{2}}})$

Solving further

$=2^2x^4y^{-6}$

Using identity $\dfrac{x^a}{x^b} = x^{(a-b)}$ ,

$=\dfrac{2^2x^4}{y^6}$

$=\dfrac{4x^4}{y^6}$

Hence, the solution of the expression is $\dfrac{4x^4}{y^6}$ .

Learn more about Exponentiation:

brainly.com/question/2193820

8 0

2 years ago

Which number line correctly shows 4. 5 + 2. 5? A number line going from 0 to 4. 5 in increments of 0. 5. An arrow goes from 0 to

sesenic [268]

So none of the options is actually correct from the given operation of:

4.5 + 2.5

This actually would be represented with a line that goes from 0 to 4.5, and then from 4.5 to 7.

The number line should start at 0 and then move to the first number (because of the commutative property of the sum, it can move to any one of the two numbers).

Once there, it moves accordingly to the other number.

So it moves first from 0 to 4.5, then the second number is 2.5, then it moves another 2.5 units to the right until the:

4.5 + 2.5 = 7

Concluding, <u><em>it moves from 0 to 4.5, then from 4.5 to 7.</em></u>

Notice that none of the options represent this, this may be because the sign of one of the two numbers is incorrect or something like that.

For example, if we had the operation:

4.5 - 2.5

Then the line starts at 0 and then goes to 4.5, then moves left 2.5 units to 4.5 - 2.5 = 2

In this case, the correct option should be:

<u><em>"An arrow goes from 0 to 4. 5 and then backwards from 4. 5 to 2."</em></u>

If you want to learn more about number lines, you can read:

brainly.com/question/13189025

3 0

2 years ago