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!
Answer:
about 5 milliliters
Step-by-step explanation:
36 miles per hour if he ran 12 miles in 20 minuets and there are 60 minuets in an hour, then multiply the # by 3
In the coordinate plane, the length of the line segment that connects points at (0, -1) and (-7, -2) is 7.07 units.
<u>Step-by-step explanation:</u>
Here we have ,in coordinate plane we are given two points (0,-1 ) & ( -7,-2 ).
From Straight line concept, we know that Distance between any two pints in a plane i.e distance between points
and
is given by:
, Here
=
and
= ![(-7,-2)](https://tex.z-dn.net/?f=%28-7%2C-2%29)
Putting values in above formula we get:
⇒![D = \sqrt{(x_1 - x_2)^{2} + ( y_1-y_2)^{2}}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E%7B2%7D%20%2B%20%28%20y_1-y_2%29%5E%7B2%7D%7D)
⇒![D = \sqrt{(0 - (-7))^{2} + ( -1-(-2))^{2}}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%280%20-%20%28-7%29%29%5E%7B2%7D%20%2B%20%28%20-1-%28-2%29%29%5E%7B2%7D%7D)
⇒![D = \sqrt{7^{2} + 1^{2}}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B7%5E%7B2%7D%20%2B%201%5E%7B2%7D%7D)
= ![7.07 units](https://tex.z-dn.net/?f=7.07%20units)
∴In the coordinate plane, the length of the line segment that connects points at 0, -1 and. -7, -2 is
.