an art collector bought 20 paintings at an art fair, and wants to know the average price of the paintings ahe purchased at the fair. She adds the prices of all the paintingsand dividesthis number by 20 to find an average price of $3550. Is this price a sample mean or a population mean, and which symbol would be used to donate it?

The calculated mean price is a sample mean and it is denoted by x.

Step-by-step explanation:

Given that

Mean price of paintings = $3550

Number of paintings = 20

In order to decide whether it is a population mean or a sample mean we have to understand the terms first.

Population:

Population is the overall collection from which a sample or observations are taken.

Sample:

The small or less number of observations that we take from a large population to perform data analysis is called sample.

In the given scenario, all the paintings at the art fair are population while the number of paintings that the art collector bought is a sample.

Hence,

The calculated mean price is a sample mean and it is denoted by x.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐