Is 0.398 a whole number, interger, rational number, irrational number, or a real number

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.

Step-by-step explanation:

-7y > 161

7y < 161

Dividing by 7 gives 1

161÷7=23

y=23

7y > -161

7÷7=1

-161÷7=-23

y=-23

Answer:

Step-by-step explanation:

Assuming a fair die is rolled.

• The sample space comprises 1, 2, 3, 4, 5, 6, with all results being equally probable.

Let X represent the collection of all outcomes. Let A represent a specific outcome.

<pThus, the probability of event A occurring is:

                                                       

Considering that the set of all possible outcomes for a singular die roll is:

Notably,

Here,  

  since 8 is not included in the sample space. Therefore, rolling an 8 is impossible within the defined outcomes.

<pThis leads to the conclusion that the probability is zero.

In other terms,

                       

                         

<pAs a result,

                   

D is the correct option since it represents a combination where neither p nor a equals zero.

The profit produced by combining sales of gold label and black label equals the total of their individual profits. From the table you find the gold label's profit and similarly from another table find the black label's profit . Adding these yields . Thus, option 5 is the correct choice.