Afamily lines up for a photograph. in each of the following situations, how many ways are there for the family to line up so that the mother is next to at least one of her daughters? (a) the family consists of two parents, two daughters and two sons. solution call the daughters a and b. the number of ways the family can line up with the mother next to a is 2-5! . the number of ways the family can line up with the mother next to b is 2.5! to determine the number of ways in which the family can line up in which the mother is next to both a and b, first decide whether a is to the left and b is to the right of the mother or whether a is to the right and b is to the left of the mother (2 choices). once this decision has been made, stick the daughters to either side of the mother. the number of items to permute is now four: father, two sons, and the daughter-mother-daughter unit. there are 4! ways to permute the four people/groups. thus, there are 2-4! ways to line up the family so that the mother is next to both daughters. use the inclusion-exclusion principle to determine the number of ways to line up the family so that the mother is next to one or both of her daughters: 2.5! + 2.5! - 2.4! 45! -2.4! (b) the family consists of two parents, three daughters and four sons.

a: 1/6, j: 1/4

step-by-step explanation: you are welcome

i believe the answer is c.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%