Two students walk in the same direction along a straight path, at a constant speed - one at .90 m/s and the other at 1.90 m/s.a.

Answer:

B - Taking the cube root of y

Step-by-step explanation:

The information provided is:

y = ax^3

Using that information

we now find the cube root of y

The computation is as follows:

y1/3 = a1/3 × x

Thus

From the above equation, a linear relationship can be observed between the cube root of y and x.

Consequently, option B is the correct choice.

Therefore, the other options are incorrect.

Answer:

a) 20 different arrangements

b) 10 different arrangements

Step-by-step explanation:

When the order of selection is significant, we utilize permutations to determine the number of arrangements; if the order does not matter, we apply combinations.

For part a)

We must select 2 items from a collection of 5, considering that order matters. This is a permutation scenario, thus we calculate 5P2.

The general formula for permutations of n items taken r at a time is:

By inserting n=5 and r=2, we have:

Hence, it is possible to select 2 items from a group of 5 when the selection order is relevant.

For part b)

Since the order of selection is unimportant, we use combinations to calculate the number of ways of selecting 2 items from 5, represented as 5C2.

The general formula for combinations of n items taken r at a time is:

Plugging n=5 and r=2 into the formula results in:

This demonstrates that we can choose 2 items from a collection of 5 when the order of selection is not significant.

Answer:

14.2 hectares

Step-by-step explanation:

Fund Mexico reports that monarch butterflies occupied 1.13 hectares in one winter and 4.01 hectares the next winter (one year later)

The Geometric growth formula is

(Pt/ Po)^1/t

Where Pt = Size after t years = 4.01 hectares

Po = Initial size = 1.13

t = time = 1

=( 4.01/1.13 )^1/1

= 3.5486725664

Thus, the geometric growth rate is 3.5486725664.

The area they will occupy in hectares after one more year = Current area × Geometric growth rate

= 4.01 ×3.5486725664

= 14.230176991 hectares

Approximately equal to 14.2