A red die and blue die are rolled. The red die has 10 sides and the blue die has 8 sides. What is the probability of rolling a 3 on the red die and a 4 on the blue die? You do not need to simplify your answer.
1/80
What is the total volume of the shape below if the height of the cylinder is 9 inches, the radius of the cylinder is 7 inches and the height of the cone is 15 inches. Use 3.14 for π.
The total volume is ______ cubic inches.
The shape described is the combination of a cylinder and a cone. The volume of a cylinder is given by V_cylinder = π * r^2 * h, where r is the radius and h is the height of the cylinder. The volume of a cone is given by V_cone = (1/3) * π * r^2 * h, where r is the radius and h is the height of the cone.
Given:
- Radius of cylinder (r) = 7 inches
- Height of cylinder (h) = 9 inches
- Height of cone (h) = 15 inches
First, calculate the volume of the cylinder:
V_cylinder = π * 7^2 * 9
V_cylinder = 3.14 * 49 * 9
V_cylinder = 1376.86 cubic inches
Next, calculate the volume of the cone:
V_cone = (1/3) * π * 7^2 * 15
V_cone = (1/3) * 3.14 * 49 * 15
V_cone = 364.65 cubic inches
The total volume of the shape is the sum of the volumes of the cylinder and the cone:
Total volume = V_cylinder + V_cone
Total volume = 1376.86 + 364.65
Total volume = 1741.51 cubic inches
Therefore, the total volume of the shape is 1741.51 cubic inches.
How much larger is the calculation of the volume of a sphere's whose radius is 69 inches if π is used instead of 3.14?
Round your answer to the nearest tenth.
The difference of using π rather than 3.14 is about ______cubic inches.
The formula for the volume of a sphere is V_sphere = (4/3) * π * r^3, where r is the radius of the sphere.
Given:
- Radius of the sphere (r) = 69 inches
First, calculate the volume of the sphere using the value of π:
V_sphere = (4/3) * π * 69^3
V_sphere = (4/3) * π * 328,509
V_sphere ≈ 437,012.7 cubic inches
Next, calculate the volume of the sphere using the rounded value of π as 3.14:
V_sphere = (4/3) * 3.14 * 69^3
V_sphere = (4/3) * 3.14 * 328,509
V_sphere ≈ 437,220.1 cubic inches
The difference between the volume calculated using π and the volume calculated using 3.14 is:
437,220.1 - 437,012.7 ≈ 207.4
Therefore, the difference of using π rather than 3.14 in the calculation is about 207.4 cubic inches.
John has three chances of throwing and hitting the target to win the prize. One hit wins John the prize. What is the probability of John not winning if any given throw has a 60% chance of hitting the target?
Since each throw is independent, the probability of not winning on any given throw when the chance of hitting the target is 60% is 1 - 0.60 = 0.40.
Thus, the probability of John not winning on any given throw is 0.40.
Since John has three chances to throw and hit the target, the probability of not winning on all three throws is calculated as:
0.40 * 0.40 * 0.40 = 0.064
Therefore, the probability of John not winning the prize in all three throws is 0.064 or 6.4%.
The baseball store has 5 different types of bats, 3 types of gloves and 3 types of cleats. Assuming you will pick exactly one of each how many different possibilities are there?
To calculate the total number of different possibilities when picking exactly one bat, one glove, and one pair of cleats, we multiply the number of options for each item.
- Number of bat options: 5
- Number of glove options: 3
- Number of cleats options: 3
Total number of possibilities = Number of bat options * Number of glove options * Number of cleats options
Total number of possibilities = 5 * 3 * 3
Total number of possibilities = 45
Therefore, there are 45 different possibilities when picking exactly one bat, one glove, and one pair of cleats from the baseball store.