Mathematical And Numerical Reasoning 2026 Njfp Job

To solve for \( n \), we isolate the term in the brackets:\[ \frac{7}{8}(n-6) = \frac{21}{2} \]Multiply both sides by the reciprocal of \( 7/8 \), which is \( 8/7 \):\[ n-6 = \frac{21}{2} \times \frac{8}{7} \]\[ n-6 = 3 \times 4 \]\[ n-6 = 12 \]Finally, add 6 to both sides:\[ n = 12 + 6 = 18 \]

We are given the inequality \( A > 50 \). Using the formula \( nA = 360 \), we can express \( A \) as \( 360/n \):\[ \frac{360}{n} > 50 \]Multiply both sides by \( n \) and divide by 50:\[ \frac{360}{50} > n \]\[ 7.2 > n \]Since \( n \) must be an integer (as a polygon cannot have a fraction of a side), the largest whole number less than 7.2 is 7. Thus, the greatest number of sides a regular polygon can have while maintaining an exterior angle greater than 50° is 7.

First, calculate the variable cost based on time. There are 60 minutes in an hour, so 3 hours equals 180 minutes. Since she charges per 30-minute block:\[ \text{Number of 30-min blocks} = \frac{180}{30} = 6 \text{ blocks} \]Now, calculate the total cost for these blocks:\[ 6 \times 7.50 = $45.00 \]Finally, add the flat daily fee:\[ $45.00 + $25.00 = $70.00 \]

We can solve this using the substitution method. From the second equation, isolate \( x \):\[ 2y - x = -19 \implies x = 2y + 19 \]Substitute this into the first equation:\[ 3(2y + 19) + 4y = -23 \]\[ 6y + 57 + 4y = -23 \]\[ 10y = -23 - 57 \]\[ 10y = -80 \implies y = -8 \]Now, find \( x \) by substituting \( y = -8 \) back into our isolated \( x \) equation:\[ x = 2(-8) + 19 = -16 + 19 = 3 \]The solution is (3, -8).

The volume of the rectangular tank is calculated as:\[ V = L \times W \times H = 6 \times 4 \times 3 = 72\text{m}^3 \]Calculating one-third of this volume:\[ \frac{1}{3} \times 72 = 24\text{m}^3 \]

To convert a fraction to a percentage, multiply by 100: \[ \frac{3}{4} \times 100 = 75\% \]

Using the relative speed formula where \( L \) is train length and \( V \) is train speed: \[ L = (V - 4.5) \times 8.4 = (V - 5.4) \times 8.5 \] Solving for \( V \): \[ 8.4V - 37.8 = 8.5V - 45.9 \] \[ 0.1V = 8.1 \implies V = 81 \text{ km/hr} \]