Answer:
Step-by-step explanation:
Given:
- Fuel volume = 5/6
- Each trip uses fuel = 1/12
- Number of trips to work = x
Since 1/12 of the tank is used for each trip and the starting volume is 5/6, the equation can be represented as:
By solving the equation, we find:
This means Felitz can make 10 trips to/from work with a tank filled to 5/6.
James will retain his original t toy cars along with half of (t+13) cars, resulting in a total of...
... t + (t + 13/2) = (3t + 13)/2.... cars after receiving a gift from Paul.
a) The area of a rectangle is calculated by multiplying the length by the width:
A = l·w
This formula allows us to express the width in terms of area and length. By dividing A by l, we find
A/l = w
We also recognize that the perimeter of a rectangle is the total length around it.
P = l + w + l + w
P = 2(l + w)
We aim to rewrite the perimeter formula to isolate l on one side, using the expression for w derived earlier.
P = 2(l + A/l)
By substituting the known value for A, we can express p(l) as
p(l) = 2(l + 25/l)
p(l) = 2l + 50/l
b) For lengths exceeding widths, we have
l > w
l > A/l
l² > A
l > √A
l > √25
This indicates that the domain of p(l) is
l ∈ (5, ∞)..... meters
The sphere's radius is calculated as 18 divided by 2, giving 9 cm.
Using the formula for the volume of a sphere, we find it to be 4/3 πr^3, resulting in 4/3 x π x (9)^3 which equals 972 π cubic centimeters.
If we halve the diameter, the new volume can be calculated as: 4/3 x π x (9/2)^3 equals 4/3 x π x (9)^3 x (1/2)^3, simplifying down to 1/8 of 972.
Thus, the new volume will only be 1/8 of the original volume.
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.
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