Shane and Abha earned a team badge that required their team to collect no less than 20002000 cans for recycling. Abha collected

To determine which functions depict the arithmetic sequence 8, 1.5, -5, -11.5,... follow these steps:

<span>f(n) = –6.5n + 14.5... correct
f(1) = 8
f(2) = 1.5
f(3) = -5
f(4) = -11.5

f(n) = –1.5n + 9.5... incorrect
f(1) = 8
f(2) = 6.5

f(n) = 6.5n + 1.5... incorrect
f(1) = 8
f(2) = 14.5

f(1) = 8, f(n + 1) = f(n) – 6.5... correct
f(2) = 8 - 6.5 = 1.5
f(3) = 1.5 - 6.5 = -5
f(4) = -5 - 6.5 = -11.5

f(1) = 8, f(n + 1) = f(n) – 1.5... incorrect
f(2) = 8 - 1.5 = 6.5

f(1) = 8, f(n + 1) = f(n) + 6.5... incorrect
f(2) = 8 + 6.5 = 14.5

The valid functions are:
</span>f(n) = –6.5n + 14.5 and f(1) = 8, f(n + 1) = f(n) – 6.5.

The gross margin would be reduced to 34%.

To determine the time interval δt, we must subtract the starting time from the ending time. In this scenario, the first value in the coordinates signifies time:

δt=50 - 0
δt= 50s

The time interval is 50s.

We are given the triangle

△ABC, with m∠A=60° and m∠C=45°, and AB=8.

To start, we will calculate all angles and sides.

Finding angle B:

The total of all angles in a triangle equals 180.

m∠A + m∠B + m∠C = 180.

Substituting the known values,

60° + m∠B + 45° = 180.

This gives us m∠B = 75°.

Calculating BC:

Using the law of sines,

We can substitute in the values.

Finding AC:

Now we'll input the values.

Calculating Perimeter:

We substitute values here as well.

Calculating Area:

Using the area formula,

we can then insert values.

...............Answer

48 divided by 3 equals 16 (cups)
Adding 16 and 16 gives 32 (which is double the number of cups)
Thus, the number of plates is 16.