Question

Which of the following expressions accurately represents the relationship between a numerical value 'x' and 155√x?

A. 13 < 155√x < 14
B. 14 < 155√x < 15
C. 12 < 155√x < 13
D. 11 < 155√x < 12

Answer 1

The expression that accurately represents the relationship between a numerical value 'x' and 155√x is 0.009 > x > 0.008. Therefore, the correct option is C. 12 < 155√x < 13.

Step-by-step explanation:

The relationship between a numerical value 'x' and 155√x can be determined by comparing the given options. We can find the range by solving inequalities for 'x'.

1. If 13 < 155√x < 14, then dividing all the terms by 155 gives 13/155 < √x < 14/155. Squaring the inequality gives (13/155)^2 < x < (14/155)^2. Thus, 0.011 > x > 0.010.
2. If 14 < 155√x < 15, then dividing all the terms by 155 gives 14/155 < √x < 15/155. Squaring the inequality gives (14/155)^2 < x < (15/155)^2. Thus, 0.012 > x > 0.011.
3. If 12 < 155√x < 13, then dividing all the terms by 155 gives 12/155 < √x < 13/155. Squaring the inequality gives (12/155)^2 < x < (13/155)^2. Thus, 0.009 > x > 0.008.
4. If 11 < 155√x < 12, then dividing all the terms by 155 gives 11/155 < √x < 12/155. Squaring the inequality gives (11/155)^2 < x < (12/155)^2. Thus, 0.007 > x > 0.006.

Based on these calculations, the expression that accurately represents the relationship is 0.009 > x > 0.008. Therefore, the correct option is C. 12 < 155√x < 13.