1. How is Unilever applying its understanding of internal consumer processes in the psychological core to market its products?

Let $S$ be the set of complex numbers of the form $a + bi,$ where $a$ and $b$ are integers. We say that $z \in S$ is a unit if t

lakkis [162]

Answer:

Number of units possible in S are 4.

Explanation:

Given S is a set of complex number of the form $a+bi$ where a and b are integers.

$z\in S$ is a unit if $w\in z$ exists such that $zw=1$ .

To find:

Number of units possible = ?

Solution:

Given that:

$zw = 1$

Taking modulus both sides:

$|zw| = |1|$

Using the property that modulus of product of two complex numbers is equal to their individual modulus multiplied.

i.e.

$|z_1z_2|=|z_1|.|z_2|$

So,

$|zw| = |1|\\\Rightarrow |zw| =|z|.|w| =1\\\Rightarrow |z|=\dfrac{1}{|w|}$ ......... (1)

Let $z=a+bi$

Then modulus of z is $|z| = \sqrt{a^2+b^2}$

Given that a and b are integers, so the equation (1) can be true only when $|z| = |w| =1$ (Reciprocal of 1 is 1). Modulus can be equal only when one of the following is satisfied:

(a = 1, b = 0) , (a = -1, b = 0), (a = 0, b = 1) OR (a = 0, b = -1)

So, the possible complex numbers can be:

$1.\ 1 + 0i = 1\\2.\ -1 + 0i = -1\\3.\ 0+ 1i = i\\4.\ 0 -1i = -i$

Hence, number of units possible in S are 4.

6 0

3 years ago

Thyme, Inc. owns 16,000 of Sage Co.'s 20,000 outstanding common shares. The carrying value of Sage's equity is $500,000. Sage su

DedPeter [7]

Answer:

The total non controlling interest after the additional shares are issued is equal to $252,000.

Explanation:

Before the issue Sage co's had 20,000 shares with total equity value of $500,000. After the issue of 5000 shares worth $200,000, the total number of shares and equity would be -

Total number of shares = 25,000 ( 20,0000 + 5000 )

Total equity value = $700,000

Now Thyme inc owns 16,000 number of shares , which means that minority holds 9000 number of shares . Now the price per share would be =

TOTAL EQUITY / NUMBER OF SHARES

$700,000 / 25,000

= $28

NON CONTROLLING INTEREST = Minority shares x Price per shares

= 9000 x $28

= $252,000

8 0

3 years ago

Type the correct answer in the box. Spell all words correctly. In which book of accounts do businesses record their daily financ

Marysya12 [62]

Answer:

Journal.

Explanation:

Businesses record their daily financial transactions in a journal, also known as the businessperson's diary.

A journal entry involves the process of keeping the records of business transactions made by an organization.

The journal entry is used by bookkeepers and accountants. Ideally, it is important that a journal has all of following informations; date, reference number, debit balance, credit balance and transaction description.

In Accounting, most businesses use a double-entry account system and as such, the total amount debited must equal the total amount credited in a journal entry.

6 0

3 years ago

Your company has just taken out a 1-year installment loan for $82,500 at a nominal rate of 12.0% but with equal end-of-month pay

Bas_tet [7]

Answer:

89.63% of 2nd month payment will go towards the payment of principal.

Explanation:

Loan Payament per month = r ( PV ) / 1 - ( 1 + r )^-n

r = rate per period = 12% per year = 1% per month

n = number months = 12 months

PV = present value of all payments = $82,500

P = payment per month = ?

P = 1% ( $82,500 ) / 1 - ( 1 + 1% )^-12

P = $7,330 per month

Month Payments Principal Interest Balance

1 -7330 -6505 -825 75995

2 -7330 -6570 -760 69,425

Percentage of Principal Payment = Principal payment / totla monthly payment = $6,570 / $7,330 = 0.8963 = 89.63%

6 0

2 years ago

With only a part-time job and the need for a professional wardrobe, Rachel quickly maxed out her credit card the summer after

choli [55]

Answer:

a. It will take her 5 years to pay for her wardrobe

b. She should shop for a new card once she is done paying for this one.

c. She should shop for a new card after finishing paying for this card since going further into debt with the current card would be a bad idea. This is due to the fact that an annual interest rate of 16% is very high. The best option would therefor to finish her payments on the credit card, then shop for a new card with a lower annual interest rate.

Explanation:

Use the formula below to determine the number of months it would take Rachel to pay off her debt;

C *{1-(1+r)^(-n×t)}/(r/n)=PV

where;

C=annuity

r=annual interest rate

n=number of compounding periods in a year

t=number of years

PV=present value

In our case;

PV=$10,574

C=$260

r=16%=16/100=0.16

n=12

t=unknown

replacing;

260*{1-(1+0.16/12)^(-12×t)}/(0.16/12)=10,574

1-(1+0.16/12)^(-12×t)={10,574×(0.16/12)}/260

1-{1.013^(-12 t)}=0.542

(1-0.542)=1.013^(-12 t)

ln 0.458=-12 t (ln 1.013)

t=-ln 0.458/12×ln 1.013

t=5

It will take her 5 years to pay for her wardrobe

b. She should shop for a new card once she is done paying for this one.

c. She should shop for a new card after finishing paying for this card since going further into debt with the current card would be a bad idea. This is due to the fact that an annual interest rate of 16% is very high. The best option would therefor to finish her payments on the credit card, then shop for a new card with a lower annual interest rate.

3 0

3 years ago