A. Describe the connection of the pattern of outcomes to Pascal’s triangle.

B. Look at the increase in values. What is the pattern in the number of total possible outcomes?

The answer to the question is;

A. The pattern of outcomes of 0 heads, 1 head, 2 heads ... n heads when arranged in the Pascal's triangle is given by the row of the triangles with the lowest at the edges and highest  outcome in the middle potion of the rows in the Pascal's triangle.

B. The number of total possible outcomes in a row n is 2ⁿ.

Step-by-step explanation:

To solve the question, we note that.

Pascal's triangle is an important sequence of numbers formed by starting with 1 at the top of the triangle followed by 1s on the outer edges of the triangle and the numbers directly below two adjacent numbers is the sum of the two adjacent numbers.

In probability theory, such as in throwing a coin,  Pascal's triangle indicates the number of possible heads obtained when n number of coins is thrown, that is, 0 heads, 1 head 2 heads etc. as follows

Number of coins                          Possible head outcome             Total outcome

0 coin                                                      1                                                 1

1 coin                                                      1  1                                               2

2 coins                                                  1  2 1                                             4

3 coins                                                 1  3  3 1                                          8

4 coins                                               1  4  6 4  1                                       16

The above triangle means that when

0 coin is flipped, the number of 0 heads is  1

1 coin  is flipped, the number of 0 heads is 1 (T) and 1 head is 1 (H)

2 coins are flipped, the number of 0 heads is 1, (TT), 1 head is 2 (TH), (HT) and 2 heads is 1 (HH)

3 coins are flipped 0 heads = 1 (TTT), 1 head = 3, (TTH), (THT), (HTT), the number of 2 heads = 3, (HHT), (HTH), (TTH) and the number of 3 heads = 1, (HHH).

B. The pattern in the number of total possible outcomes is

1, 2, 4, 8, 16 which is =2 raised to the power of the number of coin tossed for a particular row as follows

Number of coin tossed = 0  = 2⁰ = 1 = Total possible outcome

Number of coin tossed = 1  =  2¹ =  2 = Total possible outcomes

Number of coin tossed = 2  = 2² = 4 = Total possible outcomes

Number of coin tossed = 3  = 2³ = 8 = Total possible outcomes

Number of coin tossed = 4  = 2⁴ = 16 = Total possible outcomes

Therefore total number of possible outcome = 2ⁿ where n = number of coins tossed.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500