Answer:
Shane must have gathered a minimum of 911 cans.
Step-by-step explanation:
Let S represent the number of cans Shane collected.
Since Abha collected 178 more cans, her total is S + 178.
The combined total should be at least 2000:
S + (S + 178) ≥ 2000
2S + 178 ≥ 2000
2S ≥ 2000 - 178
2S ≥ 1822
S ≥ 911
Therefore, Shane must have collected at least 911 cans.
Response:
(C) Fourth
Detailed reasoning:
We will create a list based on the given constraints.
Chris is last in the order, positioned right after Andy.
Frank holds the first position in line and is one spot ahead of Betty.
Mark stands in between Betty and Mary.
- Frank
- Betty
- Mark
- Mary
- Andy
- Chris
Answer:
Step-by-step explanation:
Answer:
D, 344
Step-by-step explanation:
5x6 = 30, then 30x2 = 60
6x10 = 60
5x10 = 50, and 50x4 = 200
4x6=24 (no need to divide by two as there are two triangles)
Adding these, 24+60+60+200 results in 344.
Options
- Counting rule for permutations
- Counting rule for multiple-step experiments
- Counting rule for combinations
- Counting rule for independent events
Answer:
(C) Counting rule for combinations
Step-by-step explanation:
To find the number of outcomes when selecting n objects from N objects, we apply either permutation or combination.
- If the order of selection matters, we utilize permutation.
- On the other hand, if the order of selection does not matter, we opt for combination.
Thus, the counting method employed for determining experimental outcomes when selecting n objects from N objects without regard to selection order is referred to as the counting rule for combinations.
Answer:
347.3 cubic units
Step-by-step explanation:
To calculate the volume of the empty space, we derive the total volume of the two shapes and subtract the volume of the sphere from that of the cube.
The volume of a cube is calculated as l^3.
Here, the length is given as 9, so we compute 9x9x9, resulting in 729 cubic units.
The formula for the volume of a sphere is 4/3 pi r^3.
The radius is 4.5 (half of the diameter), thus:
4/3*91.125 pi
which becomes 121.5 pi = 381.7 (to one decimal place).
Subtracting these gives us 729-381.7 = 347.3.
The volume of the empty space equals 347.3 cubic units.
The comprehensive expression in reference to the given d:
Volume of empty space = d^3 - 4/3 pi (d/2)^3
I hope this was helpful!
