I see you've uploaded two images with math problems. Let me assist you with each one:

First Image:

This problem involves polygraph tests, where:

• 250 polygraph tests are given each month,
• 4% of applicants are former criminals, and
• The polygraph test has a 90% accuracy rate.

a) How many of the former criminals will make it through the polygraph test without being caught?

• 90% accuracy rate means that the test correctly detects 90% of criminals.
• Out of 4% of the 250 applicants, the number of criminals is: $0.04 \times 250 = 10 \text{ former criminals}$
• Since 90% of the criminals will be caught, the remaining 10% will not: $10 \times 0.10 = 1 \text{ former criminal will not be caught.}$

b) How many applicants that are not lying will be falsely accused?

• 96% of applicants are not criminals (since 4% are criminals).
• For these non-criminals, 10% of them will be falsely accused due to the 90% accuracy: $0.96 \times 250 = 240 \text{ non-criminal applicants}$ $240 \times 0.10 = 24 \text{ non-criminals falsely accused.}$

Second Image:

This one involves a city park with a rectangular playground in the center, and the questions focus on the area to be covered in grass and sand.

a) What area is to be covered in grass?

The park is shaped like a parallelogram, and the playground is rectangular. To find the area covered in grass, we first need the area of the entire park and then subtract the area of the playground.

• The area of a parallelogram is calculated as: $\text{Area of Park} = \text{Base} \times \text{Height} = 90 \, \text{m} \times 60 \, \text{m} = 5400 \, \text{m}^2$

• The area of the playground is: $\text{Area of Playground} = \text{Length} \times \text{Width} = 55 \, \text{m} \times 20 \, \text{m} = 1100 \, \text{m}^2$

• Thus, the area covered in grass is: $\text{Area of Grass} = 5400 - 1100 = 4300 \, \text{m}^2$

b) How much will it cost to buy the sand to cover the playground?

• The area of the playground is 1100 m².
• The cost of sand for 1 m² is $8.79.
• Therefore, the total cost for sand is: $1100 \times 8.79 = 9670 \, \text{dollars}$

Would you like more details on any of the steps or have other questions? Here are some additional related questions you could explore:

1. How does the polygraph test accuracy affect the overall result?
2. What are other ways to improve the accuracy of a polygraph test?
3. How would the cost of sand change if the area of the playground were larger or smaller?
4. How do you calculate the area of a parallelogram with non-rectangular shapes?
5. How can probabilities and percentages be used to predict outcomes in real-life scenarios?

Tip: Always break down the problem into smaller parts to make it easier to manage!