To find out how much is taken from the employee's biweekly paycheck for health insurance, let's follow these steps:
1. Determine the total annual cost of the health insurance:
The total cost is given as \[tex]$6,240 per year.
2. Calculate the amount the employer pays annually:
The employer covers 70% of the total cost.
\[
\text{Employer's annual contribution} = 0.70 \times 6240 = \$[/tex]4,368
\]
3. Calculate the amount the employee pays annually:
The remainder of the total cost after the employer's contribution is the amount that the employee needs to pay.
[tex]\[
\text{Employee's annual cost} = 6240 - 4368 = \$1,872
\][/tex]
4. Determine the number of biweekly periods in a year:
There are 52 weeks in a year, and since "biweekly" means every two weeks, the number of biweekly periods is:
[tex]\[
\text{Number of biweekly periods} = \frac{52}{2} = 26
\][/tex]
5. Calculate the biweekly cost for the employee:
Divide the employee's annual cost by the number of biweekly periods to find out how much is taken from the paycheck every two weeks.
[tex]\[
\text{Employee's biweekly cost} = \frac{1872}{26} = \$72
\][/tex]
Therefore, the amount taken from the employee's biweekly paycheck for health insurance is [tex]$\boxed{72}$[/tex].