A gardener has three flowering shrubs and four nonflowering shrubs, where all shrubs are distinguishable from one another. He must plant these shrubs in a row using an alternating pattern, that is, a shrub must be of a different type from that on either side. How many ways can he plant these shrubs? If he has to plant these shrubs in a circle using the same pattern, how many ways can he plant this circle? Note that one nonflowering shrub will be left out at the end.

Either way you can in 144 ways.

Step-by-step explanation:

According to the statement we have 3 flowering shrubs and 3 flowerless shrubs.

We name them as follows:

S = flowering shrub

N = non flowering shrub

Now the only pattern in which these bushes can be arranged alternately  as follows:

N-S-N-S-N-S-N

Therefore, to calculate the number of forms it would be:

Number of shapes: 4 * 3 * 3 * 2 * 2 * 1 * 1 = 144

Which means there are 144 ways.

Now if we organize them in a circle in the same way

again it would be the same number of ways to organize them: 144 ways.

This is because the nun's last blooming shrub is left outside.

Last option is correct i.e

The left side of the equation will result in a rational number, which could be a non-perfect square.

Step-by-step explanation:

Given that the Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse by the formula

we have to tell if a is a rational number and b is a rational number, why could c be an irrational number.

As, a and b both are rational then their squares are also rational and the addition of two rational numbers are also rational.

Therefore, the only option which gives the c irrational is the square root of .

Hence, last option is correct i.e

The left side of the equation will result in a rational number, which could be a non-perfect square.