What is sum of 109 and h as an algebraic expression

) An instructor gives his class a set of 18 problems with the information that the next quiz will consist of a random selection

RSB [31]

Answer:

The probability the he or she will answer correctly is 1.5%

Step-by-step explanation:

In all, there are 18 problems. In this question, the order of which the problems are sorted for the quiz makes no difference. For example, if the question A of the quiz is P1 and question B P2, and question A P2 and question B P1, it is the same thing.

There are 18 problems and 9 are going to be selected. So, there is going to be a combination of 9 elements from a set of 18 elements.

A combination of n elements from a set of m objects has the following formula:

$C_{(m,n)} = \frac{m!}{n!(m-n)!}$

In this question, m = 18, n = 9. So the total number of possibilities is:

$T_{p} = C_{(18,9)} = \frac{18!}{9!(18-9)!} = 48620$

Now we have to calculate the number of desired outcomes. This number is a combination of 9 elements from a set of 13 elements(13 is the number of problems that the student has figured out how to do).

Now, m = 13, n = 9. The number of desired possibilities is:

$D_{p} = C_{(13,9)} = \frac{13!}{9!(13-9)!} = 715$

The probability is the number of desired possibilities divided by the number of total possibilities. So

$P = \frac{715}{48620} = 0.015 = 1.5%$

The probability the he or she will answer correctly is 1.5%

3 0

3 years ago

Which equation has solution x = -3?

vovangra [49]

<span>If the answer is incorrect , please delete.

Answer is B and D

have a nice days.........</span>

8 0

3 years ago

Which fraction represents the decimal 0. ModifyingAbove 1 2 with Bar? One-twelfth StartFraction 3 Over 25 EndFraction StartFract

mestny [16]

The considered decimal number is expressed by the fraction given by: Option C: 4/33

<h3>How to convert from decimal to fraction?</h3>

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point (if its finite), then we write 10 raised to that many power as denominator, and the considered number without any decimal point as numerator.

For example:

$0.99 = \dfrac{99}{10^2} = \dfrac{99}{100}$

(10 raised to power k = 1 followed by k zeroes)

<h3>What is the sum of an infinite geometric series?</h3>

The sum of an infinite geometric series having the initial term "a" and the multiplication per term is done by "r" such that r < 1

is given by

$S_{\infty} = \dfrac{a}{1-r}$

The series would look like $a+ ar+ ar^2+\cdots$

For the considered case, the given decimal number is

$0.\overline{12} = 0.121212\cdots$

We can check all the options available one by one, so as to know which one ends up giving this pattern, or we can use another technique as shown below.

$0.12121... = (0.1 + 0.001 + 0.00001 + ... ) + (0.02 + 0.0002 + 0.000002 + ... )$

Each of the two series obtained are geometric series with the multiplication factor as 1/100

Using the sum formula for evaluation of an infinite geometric series, and the fact that initial term of first series is 0.1 and that of second series is 0.02, we get:
$0.121212... = \dfrac{0.1}{1-1/100} + \dfrac{0.02}{1 - 1/100} = \dfrac{1}{99/100}(\dfrac{1}{10} + \dfrac{2}{100})\\0.121212... = \dfrac{100}{99}\times(\dfrac{10}{100} + \dfrac{2}{100})\\\\\\0.121212 ... = \dfrac{12}{99} = \dfrac{4}{33}$

Thus, the considered decimal number is expressed by the fraction given by: Option C: 4/33

Learn more about geometric series here:

brainly.com/question/16037289

4 0

2 years ago

How do u solve 5x+3=4 <br> Y=-3x

kogti [31]

The information from the first equation gives you the information needed for the second. To solve the first equation you must rearrange the equation to isolate X. In order to do that you can first move the 3 to the other side of the equation by subtracting it from both sides (5x + 3 - 3 = 4 - 3) and then simplify that to (5x = 4 - 3) and further to (5x = 1). Then to move the 5 you must divide both sides by 5 so you get (5x/5 = 1/5) which can be simplified to (x = 1/5)

From this you can use the X value and input it into the second equation
Y = -3(1/5) and then solve for Y.

Hope this helps!

6 0

3 years ago

Read 2 more answers

If EF bisects CD, CG = 5x-1, GD = 7x-13, EF=6x-4, and GF = 13, find EG (MUST SHOW WORK)

iogann1982 [59]

Answer:

EG = 19

Explanation:

Given that a line segment CD. EF bisects the line CD at point G.

Length of CG = 5x-1

Length of GD = 7x - 13

We know that CG = GD

5x-1 = 7x-13

Solve for x,

2x = 12

x = 6

Now given that,

EF = 6x-4

GF = 13

EF = EG + GF

6x - 4 = EG + 13

EG = 6x - 4 - 13

EG = 6x - 17

put the value of x = 6, in order to find the EG

EG = 6*6 - 17

EG = 19

That's the final answer.

I hope it will help you.

3 0

3 years ago