Correct answer is C -I just took the test

**Answer:**

(a) Mean = 36.05; (b) median = 37; (c) mode = 37

**Step-by-step explanation:**

I am assuming your DFT is like this:

**(a) Mean
**

The **mean **is the **sum of all the data points divided by the number of points**. I have done some of the calculations for you in the table below

**(b) Median
**

The **median** is the **middle value** in your list of observations.

Your data set contains 19 terms, so the middle is (19/2)th term.

Count down the column of cumulative frequency (cf) until cf = 9½.

The 9½th term is **37**.

Median = **37
**

** (c) Mode
**

The **mode** is the **value that appears most often** in your list of observations.

It is obvious from your table that the number that occurs most frequently is 37.

Mode = **37**

The diagram below shows that the score of 37 is predominant.

**Answer:**

**b) the coefficient of x of jamie's polynomial is 5 .**

**c) The two polynomials are :**

x³ + 4x² + 5x + 4

x³ - 2x² + 5x + 4

**Step-by-step explanation:**

consider these two Monic polynomials of degree 3:

P : x³ + ax² + bx² + c

Q : x³ + a₁x² + bx² + c

P × Q = x⁶+ (a+a₁)x⁵ + (aa₁+2b)x⁴ + (ab+a₁b+2c)x³ + (ac+a₁c+b²)x² +2bcx + c²

Now we compare the coefficients of P × Q and x⁶ + 2x⁵ +2x⁴ + 18x³ + 33x² + 40x + 16

b)

c² = 16 ⇒ c = 4 (c is positive)

2bc = 40 ⇒ 8b = 40 ⇒ b = 5 then the coefficient of x of jamie's polynomial is 5 .

c)

In order to find a and a₁ we need to solve this system:

a+a₁ = 2 a+a₁ = 2

⇔

aa₁+2b = 2 aa₁ = -8

Solve the system and you’ll get :

a = 4 and a₁ = -2 or a = -2 and a₁ = 4

Let’s choose a = 4 and a₁ = -2 then

the two polynomials are respectively:

P : x³ + ax² + bx² + c = x³ + 4x² + 5x + 4

Q : x³ + a₁x² + bx² + c = x³ - 2x² + 5x + 4