Paula is painting a henhouse. If a can of paint will cover 24 square feet, how many cans of paint does she need to buy? Explain

Step-by-step explanation:

A = {0,1,2,3}

a): R = {(0,0),(2,2),(3,3)}

R displays antisymmetry, as whenever (a,b)∈R, it follows that a=b.

R lacks reflexivity since (1,1) ∉ R even though 1 ∈ A.

R is transitive; therefore, if (a,b)∈R and (b, c) ∈ R, then a=b=c and (a,c)=(a,a)∈R.

R fails to be a partial ordering due to its lack of reflexivity.

b): R = {(0,0),(1,1),(2,0),(2,2),(2,3),(3,3)}

R is antisymmetric because if (a,b)∈R and (b, a) ∈ R, then a must equal b (e.g., (2,0) ∈ R and (0,2) ∉ R; likewise, (2,3) ∈ R and (3,2) ∉ R).

R is reflexive since each (a,a) resides in R for all elements a ∈ A.

R is transitive; if (a,b)∈R and (b,c)∈R, it implies (a,c) exists in R or identical to (a,b) in R.

R qualifies as a partial ordering due to its reflexivity, antisymmetry, and transitivity.

c): R =  {(0,0),(1,1),(1,2),(2,2),(3,1),(3,3)}

R is reflexive as (a,a)∈R is true for every a ∈ A.

R is antisymmetric; if (a,b)∈R holds and if also (b,a)∈R, then a invariably equals b (e.g., (1,2)∈R while (2,1) ∉ R; similarly for (3,1) and (1,3)).  

R fails transitivity because (3,1) ∈ R and (1,2) ∈ R, but (3,2) ∉ R.

R is not a partial ordering due to transitivity not being satisfied.

d): R =  {(0,0),(1,1),(1,2),(1,3),(2,0),(2,2),(2,3), (3,0),(3,3)}

R exhibits reflexivity since (a,a)∈R for each element a ∈ A.

R displays antisymmetry, as if (a,b)∈R and (b,a)∈R then a must equal b (e.g., (1,2)∈R and (2,1)∉R; similarly validated for others).

R is not transitive because (1,2)∈R and (2,0)∈R, but (1,0)∉R.

R is not a partial ordering due to transitivity issues.

e):  R = { ( 0, 0 ), ( 0, 1 ), ( 0, 2 ), ( 0, 3 ), ( 1, 0 ), ( 1, 1 ), ( 1, 2 ), ( 1, 3 ), ( 2, 0 ), ( 2, 2 ), ( 3, 3 ) }

R proves to be reflexive, given that (a,a)∈R for all a∈A.

R is not antisymmetric since both (1,0)∈R and (0,1)∈R hold while 0 is distinct from 1.

R lacks transitivity, as (2,0)∈R and (0,3)∈R, while (2,3)∉R.

R cannot be classified as a partial ordering as it fails in both antisymmetry and transitivity.

Hello from MrBillDoesMath!

Answer:

-52. None of the alternatives presented is accurate

Discussion:

Based on standard mathematical operations, none of the given solutions is correct. The calculation results in

2*3 + 4- 62 =                => * before + and -

(2*3) + 4 - 62=             => 2*3 = 6

6 + 4 -62 =                   => 6 + 4 = 10

10 - 62 =

-52

Thank you,

MrB

Jack swims a total distance of 9*25.0m=225.0 meters in 2 minutes and 34.5 seconds.

The time duration of 2 minutes and 34.5 seconds can be converted to seconds: 2*60sec +34.5 sec= 154.5 s


Jill completes 10*25.0m = 250 m also in 154.5 s.










Therefore,
the speed of Jack calculates to: 225.0 meters / 154.5 s =(225/154.5) m/s = 1.46 m/s

the speed of Jill calculates to: 250.0 meters / 154.5 s =(250/154.5) m/s = 1.62 m/s


Assuming both Jack and Jill start from point 0 moving in the positive direction,

an even number of lengths results in a Displacement of 0, while an odd number results in a Displacement of 25 m


Thus, Jill's average Velocity is 0,

and Jack's average velocity is 25/154.5 = 0.16 m/s

Answer:

Jack's Average Speed: 1.46 m/s

Jill's Average Speed: 1.62 m/s

Jack's Average Velocity: 0

Jill's Average Velocity: 0.16 m/s

H (t) = - 16t ^ 2 + 16t + 480
To address this, we first set the polynomial to zero to find its roots.
So we have:
0 = -16t ^ 2 + 16t + 480
This leads us to the roots of the polynomial:
t1 = -5
t2 = 6
We disregard the negative root since time cannot be less than zero.
Final answer:
Rose takes about
t = 6 seconds