Sure, let's find the value of [tex]\( x \)[/tex] given that the mean of the data [tex]\( x+10, 30, x+20, 4x+5, 40 \)[/tex] is 33.
The mean (average) of a set of values is calculated by dividing the sum of the values by the number of values. Given the mean is 33, we can set up our equation as follows:
[tex]\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \][/tex]
Given the values [tex]\( x+10, 30, x+20, 4x+5, 40 \)[/tex], we first express their mean:
[tex]\[ 33 = \frac{(x+10) + 30 + (x+20) + (4x+5) + 40}{5} \][/tex]
Let's simplify the numerator:
[tex]\[ 33 = \frac{x + 10 + 30 + x + 20 + 4x + 5 + 40}{5} \][/tex]
Combine like terms:
[tex]\[ 33 = \frac{6x + 105}{5} \][/tex]
To solve for [tex]\( x \)[/tex], we first clear the fraction by multiplying both sides of the equation by 5:
[tex]\[ 33 \times 5 = 6x + 105 \][/tex]
[tex]\[ 165 = 6x + 105 \][/tex]
Next, we isolate the term with [tex]\( x \)[/tex] by subtracting 105 from both sides:
[tex]\[ 165 - 105 = 6x \][/tex]
[tex]\[ 60 = 6x \][/tex]
Finally, solve for [tex]\( x \)[/tex] by dividing both sides by 6:
[tex]\[ x = \frac{60}{6} \][/tex]
[tex]\[ x = 10 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 10 \)[/tex].
