Which area is larger: a circle of radius 3cm or a square of length 5cm? A rectangle and a square have the same perimeter: Math for IT Assignment, MU, Ireland

Question 1

• Which area is larger: a circle of radius 3cm or a square of length 5cm?
• A rectangle and a square have the same perimeter. If the Length and Width of the rectangle are 4cm and 20cm respectively, what is the length of the square?
• A sphere of volume 288πcm³ was melted into a cylinder of height 2cm
  (i) Calculate the radius of the cylinder
  (ii) How many cones of height 3cm and radius 4cm could instead be made from the sphere if it was melted?

Question 2

• Using the numbers from 0 to 9, how many 4-digit passwords can be made if the last two digits are even numbers and repeats are allowed?
• In Minecraft, you can barter with Piglins to receive different items. These items have different probabilities of occurring with the important item for speedrunners being Ender Pearls, with approximately a 2.18% chance of being dropped per trade. You make 3 trades in a row.
  What is the probability of getting Ender Pearls all three times?
• A bag of marbles contains 4 red, 3 green, and 1 blue marble
  (i) What is the probability of drawing the blue marble?
  (ii) What is the probability of drawing two of the same-colored marbles, one after the other, if the first marble is not replaced?

Question 3

The following are the number of goals scored by the top 10 teams in the Premier League during the 2017/18 season:

(i) What type of data is the above information?
(ii) What is the median number of goals scored?
(iii) What is the mean number of goals scored?
(iv) When the number of goals that the bottom 10 teams scored is added in, the mean instead becomes 50.9 goals. How many goals did the bottom 10 teams score in total?