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4 years ago

Simplify the expression given below.

Mathematics

1 answer:

svet-max [94.6K]4 years ago

4 0

Answer:

Option B. $\frac{1}{3x+1}$ .

Step-by-step explanation:

The given expression is $\frac{x+2}{x^{3}+2x^{2}-9x-18}\div \frac{3x+1}{x^{2}-9}$

In this expression we will simplify $\frac{x+2}{x^{3}+2x^{2}-9x-18}$ first.

= $\frac{x+2}{x^{2}(x+2)-9(x+2)}$

$=\frac{x+2}{(x+2)(x^{2}-9)}$

$=\frac{1}{x^{2}-9}$

Now we can rewrite the given expression as

$=\frac{1}{x^{2}-9}\div \frac{3x+1}{x^{2}-9}$

$=\frac{1}{x^{2}-9}\times \frac{x^{2}-9}{3x+1}$

$= \frac{1}{3x+1}$

So option B. $\frac{1}{3x+1}$ is the right answer.

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What is the mean score, rounded to the nearest hundredth? What is the median score? 95,45,37,82,90,100,91,78,67,84,85,85,82,91,9

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Answers:
______________________________________________________
Question 1) The answer is: " 81.92 " .
________________________________________________________
The mean score, rounded to the nearest hundredth, is: " 81.92 " .
________________________________________________________
Question #2)
_______________________________________________________
The answer is: " 84.5 " .
_____________________________________________________
The median score is: " 84.5 " .
_______________________________________________________
Explanation:
_______________________________________________________
Let us order these numbers — from the data set provided — from least to greatest:
_______________________________________________________
3: 7
4: 5
5: 9
6: 7 9
7: 6 7 8
8: 2 2 4 4 5 5 8
9: 0 1 1 2 2 3 5
100, 100 {note: "100" occurs TWICE} .
____________________________________________________
From least to greatest, the numbers in the data set provided are:
____________________________________________________
→ { 37, 45, 59, 67, 69, 76, 77, 78, 82, 82, 84, 84, 85, 85, 88, 90, 91, 91, 92, 92, 93, 95, 100, 100 } ;

Note: By counting the number of values, we find that there are "24" values in the data set.
_________________________________________________________

Question 1) "What is the mean score, roiunded to the nearest hundredth?"

Assuming that the values provided in the data set given refer to "scores" :

→To calculate the "mean" of the values in the data, we find the sum of the values in the data set; that is, we add up the values in the data set provided.

→ Then we take that value; & divide that value by the number of values in the data set provide. This value is the "mean" . We are then asked to round the "mean" to the nearest hundredth.
_______________________________________________________
→ As such:

The "mean" =

{ 37 + 45 + 59 + 67 + 69 + 76 + 77 + 78 + 82 + 82 + 84 + 84 + 85 + 85 + 88 + 90 + 91 + 91 + 92+ 92 + 93 + 95 + 100 + 100} / 24 ;

= { 1942 } / 24 ;

= 80.9166666666666667 ;

→ We are asked to round to the "nearest hundredth" (that is; nearest "two (2) decimal places") ;

→ Take the answer, to the nearest 3 (three) decimal places. If the 3rd decimal place is less than "5" (i.e. from "0 to "4") ; we "round down" (i.e. keep the original 2 (two) decimal places. If the 3rd decimal place is "5" or greater (i.e. from "5" to "9"); we "round up" that is we write the answer by changing the second decimal place to the next sequential highest digit.

→ Given our calculated answer, to the "nearest three decimal places" ;

 → " 80.916..... " ;

→ We notice that the "third decimal place" is "6" ;

 → which is from "5 to 9" ; so we "round up" ; and write the answer, rounded to the "nearest hundredth" ; as

→ " 81.92 " .
_______________________________________________________
The answer is: " 81.92 " .
_______________________________________________________
Answer: The mean score, rounded to the nearest hundredth, is: " 81.92 " .
_______________________________________________________

Question #2) :
_______________________________________________________
To find the median score:

1) When the data set is arranged from least to greatest, the "median" value is the value that occurs in the "middle" of the data set. This occurs when there is an "odd number" of values in the data set.

2) When there is an "even number" of values in the data set (as in our case—in which there are "24 values" in the data set given):

We find the "median value" by finding the "two values" that appear in the "middle" of the data set [when the values in the data set are arranged from least to greatest]; and then finding the "mean" of these two (2) values {refer to explanation above}.
_____________________________________________________
In our given data set, with values arranged from least to greatest:
_____________________________________________________
→ { 37, 45, 59, 67, 69, 76, 77, 78, 82, 82, 84, 84, 85, 85, 88, 90, 91, 91, 92, 92, 93, 95, 100, 100 } ;
_____________________________________________________
 → The two (2) numbers in the "middle" of the data set are: "84" and "85".

The "mean" of "84" and "85":

→ {84 + 85} / 2 = {169} / 2 = "84.5 " .

→ Alternately, by inspection: "What is the "mean" of "84" and "85" ?

→ "What number is in the middle of "84" and "85" ?

The answer is: " 84.5 "; because this would be "84 $\frac{1}{2}$ " .
_______________________________________________________
The median is: " 84.5 " .
_______________________________________________________

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