1. Estimate the sum of \( \sqrt{115} + \sqrt{24} \) to the nearest whole integer.

2. Which of the following represents the largest numerical value?

3. If the number \( 0.00000405 \) is converted into scientific notation in the form \( a \times 10^n \), what is the value of the exponent \( n \)?

4. Calculate the result of \( (3.2 \times 10^4) + 4,500 \) and express it in standard form.

5. Which integer is closest to the computed value of \( \frac{\sqrt{200}}{2} \)?

6. Evaluate the following expression and select the correct decimal answer: \( \frac{1}{4} + 0.65 - 15\% \)

7. What is the absolute distance on a number line between \( -3.5 \) and \( \sqrt{16} \)?

8. If \( x = 4.5 \times 10^3 \) and \( y = 2.0 \times 10^2 \), what is the value of \( x - y \)?

9. A rectangle has dimensions 8 cm by 12 cm. If it is dilated by a scale factor of 2.5, what is the perimeter of the new rectangle?

10. A circle has an original area of \( 20\pi \text{ cm}^2 \). It is dilated by a scale factor of 3. What is the area of the newly dilated circle?

11. Point \( P \) is located at \( (12, -18) \). It undergoes a dilation centered at the origin, mapping to \( P'(4, -6) \). What is the scale factor of this dilation?

12. A triangle has a side of length 15. A mathematically similar triangle has a corresponding side of length 24. If another side of the first triangle is 20, what is the length of the corresponding side of the second triangle?

13. The coordinates of a shape are dilated using the rule \( (x, y) \rightarrow (1.5x, 1.5y) \). If the original area of the shape was \( 24 \text{ cm}^2 \), what is the new area?

14. A map utilizes a scale where \( 1 \text{ inch} = 15 \text{ miles} \). If two cities are measured to be \( 4.2 \text{ inches} \) apart on the map, what is their actual distance in miles?

15. Calculate the precise slope of the line passing through the coordinates \( (-4, 7) \) and \( (2, -5) \).

16. A table contains the following \( (x, y) \) data points: \( (2, 9), (4, 17), \) and \( (6, 25) \). What is the constant rate of change?

17. A linear function has a slope of \( \frac{3}{4} \) and passes through the y-axis at \( (0, -2) \). What is the exact value of \( y \) when \( x = 12 \)?

18. A plumber's billing structure charges a $45 flat diagnostic fee plus $60 per hour of labor. Calculate the total cost for a job that takes exactly 3.5 hours.

19. A line passes through the points \( (3, 10) \) and \( (6, 22) \). What is the value of its y-intercept (\(b\))?

20. If \( y \) varies directly with \( x \), and it is known that \( y = 42 \) when \( x = 6 \), compute the value of \( y \) when \( x = 11 \).

21. A car uses 8 gallons of gasoline to travel a distance of 224 miles. At this exact proportional rate, how many miles can the car travel on 13 gallons?

22. By analyzing the slopes, determine which of the following linear equations represents the steepest line graphed on a coordinate plane.

23. A line passes through the coordinates \( (5, 8) \) and \( (x, 14) \). If the slope of this line is exactly 2, solve for \( x \).

24. The total cost \( C \) to rent a moving truck is determined by the equation \( C = 0.5m + 30 \), where \( m \) is miles driven. If a customer paid a total of $105, how many miles were driven?

25. A scatterplot utilizes the trend line equation \( y = -2.5x + 80 \) to relate hours spent playing video games (\(x\)) to a math test score (\(y\)). What is the predicted test score for a student who plays 6 hours of video games?

26. A scatterplot has a line of best fit represented by \( y = 4.2x + 15 \). One of the actual data points is located at \( (5, 38) \). Calculate the difference (residual) between the actual y-value and the predicted y-value.

27. A specific data set consisting of 5 points has a calculated mean of 12. If a 6th data point with a value of 24 is added to the set, what is the new mean of the 6 numbers?

28. A factory tracking its output finds that it produces 150 units in 2 hours and 375 units in 5 hours. Assuming this data follows a perfectly linear trend, how many units are produced in 8 hours?

29. A biology student tracks their plant's height and creates the trend line \( h = 1.5w + 4 \), where \( w \) is the number of weeks. During exactly which week will the plant be predicted to reach 22 cm?

30. Two points that perfectly lie on a scatterplot's trend line are \( (2, 40) \) and \( (8, 10) \). Using the equation of this line, what is the predicted \( y \)-value when \( x = 5 \)?