Sum of ratios: 3 + 7 + 2 = 12

Measure of smallest; sum of angles in triangle = 180

Smallest: (2/12)* 180 = 30

30°

**Answer:**

a. T1 = -4 , T2 = -4/3 , T3 = -4/9 , T4 = -4/27

b. It is converge

c. The sum to ∞ = -6

**Step-by-step explanation:**

a.

∵ Tn = -4(1/3)^(n-1)

∵ The lower n = 1

∵ The geometric series Tn = a(r)^(n-1)

∴ T1 = a , T2 = ar , T3 = ar² , T4 = ar³

∴ a = -4 , r = 1/3

∴ T1 = **-4**

∴ T2 = -4(1/3) = **-4/3**

∴ T3 = -4(1/3)² = **-4/9**

∴ T4 = -4(1/3)³ = **-4/27**

b.

r = **1/3**

∴ **-1** < r < **1**

∴ It is **converge** because the value of **1/3** when **n** is a very **large**

number will approach to **zero**

c.

∵ The sum of the geometric series = a(1-(r)^n)/1-r

∵ **r^n** ≅ **0** when **n** is a very **large** number

∴ The sum to **∞** = a/1 - r = -4/(1 - 1/3) = -4/(2/3) = **-6**

**Answer:**

**Type of music Country Rock & roll Blues **

**Observed number** 11 17 8

**Probabilities P(x)** 11/36 17/36 8/36

**Step-by-step explanation:**

The probabilities can be calculated as

P(x)= observed number of times/ Total number of times.

The probability distribution for the type of music restaurant playing is

Type of music Country Rock & roll Blues Total

Observed number 11 17 8 36

Probabilities P(x) 11/36 17/36 8/36 1

**Answer: if the iguana is five feet it would be 60 inches**

It would be 30 if the angles are interior or exterior.