Step-by-step explanation:
a) 7!
If there are no restrictions, answer is 7! as it is the permutation of all animals.
b) 4! x 3!
As cats are 6 and Dogs are 5, thus 1st and last must be cats in order to have alternate arrangements. Therefore the only choices are the order of the cats among themselves and the order of the dogs among themselves. There
are 4! permutations of the cats and 3! permutations of the dogs,
so there are a total of 4! x 3! possible arrangements of the suites.
c) 3! x 5!
There are 3! possible arrangements of the dogs among themselves. Now, if we consider the dogs as one ”object” together, then we can think of arranging the 4 cats together with this 1 additional object. There are 5! such arrangements possible, so there are a total of 3! · 5! possible arrangements of the suites.
d) 2 x 4! x 3!
As required that all the cats must be together and all the dogs must be together, either the cats are all before the dogs or the dogs are all before the cats. There are two possible arrangements thus two times of both possibilities is the answer i.e. 2 x 4! x 3!
By definition, the average rate of change is given by:

We evaluate each of the functions in the given interval.
We have then:
For f (x) = x ^ 2 + 3x:
Evaluating for x = -2:

Evaluating for x = 3:

Then, the AVR is:




For f (x) = 3x - 8:
Evaluating for x =4:

Evaluating for x = 5:

Then, the AVR is:



For f (x) = x ^ 2 - 2x:
Evaluating for x = -3:

Evaluating for x = 4:

Then, the AVR is:




For f (x) = x ^ 2 - 5:
Evaluating for x = -1:

Evaluating for x = 1:

Then, the AVR is:




Answer:
from the greatest to the least value based on the average rate of change in the specified interval:
f(x) = x^2 + 3x interval: [-2, 3]
f(x) = 3x - 8 interval: [4, 5]
f(x) = x^2 - 5 interval: [-1, 1]
f(x) = x^2 - 2x interval: [-3, 4]
Mukat gets 40, Usha gets 8
Step-by-step explanation:
Mukat = 5 × Usha
After Mukat gives Usha 16 books ,Usha gets (16 + initial number of books) and Mukat gets (5 × Usha - 16)
Then Mukat = final number of books for Usha
5 × Usha - 16 = Usha + 16
(5 × Usha ) - Usha = 16+16
4 × Usha = 32
Usha = 8 i.e her number of books.
Mukat = 5×8=40.
I HOPE IT'S OK
Let's solve for d.
fd=(7)(1.06)d
Step 1: Add -7.42d to both sides.
df+−7.42d=7.42d+−7.42d
df−7.42d=0
Step 2: Factor out variable d.
d(f−7.42)=0
Step 3: Divide both sides by f-7.42.
d(f−7.42)f−7.42=0f−7.42
d=0f−7.42
Answer:
d=0f−7.42
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