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4 years ago

What is commutative property

1 answer:

6 0

Commutative property of addition:

The property that states the sum of an addition problem will be the same no matter the order of its numbers.
a + b = b + a

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The area of a triangle is 80. The length is 2 more than the width. Find the dimensions

Jobisdone [24]

Answer:

The width is 19 units. The length is 21 units.

Step-by-step explanation:

W=width: L=length=W+2; P=perimeter=80

P=2(L+W)

80=2(W+2+W)

40=2W+2

38=2W

19=W answer 1: The width is 19 units.

L=W+2=21 ANSWER 2: The length is 21 units.

CHECK:

P=2(L+W)

80=2(21+19)

80=2(40)

80=80

4 0

3 years ago

Lightfoot Inc., a software development firm, has stock outstanding as follows: 30,000 shares of cumulative preferred 2% stock, $

Lesechka [4]

The calculation of the dividends per share on each class of stock for each of the four years for Lightfoot Inc. are:

1st Year 2nd Year 3rd Year 4th Year

Preferred stock $0.19 $0.32 $0.99 $0.50

Common stock $0 $0 $0.79 $2.69

How is dividend per share calculated?

The dividend per share for each class of stock can be computed by dividing the total dividend distributed by the number of shares outstanding.

For cumulative preferred stock, the unpaid dividends in a year are carried forward for distribution when profits are made. Note also that preferred stock dividends enjoy preferential payment before common stock dividends.

<h3>Data and Calculations:</h3>

Cumulative preferred stock = 30,000 shares

Par value of preferred stock = $25

Dividend rate = 2%

The total value of preferred stock = $750,000 ($25 x 30,000)

Expected annual dividend for preferred stockholders = $15,000 ($750,000 x 2%)

Common stock = 38,000 shares

Par value of common stock = $75

The total value of ordinary stock = $2,850,000 ($75 x 38,000)

<h3>Dividends distribution:</h3>

1st Year 2nd Year 3rd Year 4th Year

Dividends distributed $5,700 $9,600 $59,720 $117,220

Preferred stock $5,700 $9,600 $29,700 $15,000

Preferred stock per share $0.19 $0.32 $0.99 $0.50 ($15,000/30,000)

Common stock $0 $0 $30,020 $102,220

Common stock per share $0 $0 $0.79 $2.69 ($102,220/38,000)

Thus, the dividends distribution of Lightfoot Inc. shows that the common stockholders started earning dividends after the second year.

Learn more about cumulative preferred stock dividends at brainly.com/question/14006397

#SPJ1

<h3>Question Completion:</h3>

Calculate the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "O."

6 0

2 years ago

To calculate her cat's age in "human

brilliants [131]

Answer: it is c

Step-by-step explanation:

8 0

3 years ago

Help, show work please (NO LINKS)

Reptile [31]

3.29/18= about 0.18
5.59/28= about 0.2

the best buy is option a!

4 0

3 years ago

There are three urns that each contain 10 balls. The first contains 3 white and 7 red balls, the second 8 white and 2 red, and t

malfutka [58]

Answer:

(a) 0.0520

(b) 0.3699

Step-by-step explanation:

Let $E_{1},E_{2},E_{3}$ be the events of selecting urn 1, urn 2 and urn 3 respectively.

So, $P(E_{1})=P(E_{2})=P(E_{3})=\frac{1}{3}$

Let W be the event of drawing a white ball.

Now, probability of drawing 2 white balls from urn 1 is given as:

$P(W\cap W \cap E_{1})=P(E_{1})\times P((W\cap W)/E_{1})\\P(W\cap W \cap E_{1})=\frac{1}{3}\times (\frac{3}{10})^{2}=\frac{9}{300}$

Probability of drawing 2 white balls from urn 2 is given as:

$P(W\cap W \cap E_{2})=P(E_{2})\times P((W\cap W)/E_{2})\\P(W\cap W \cap E_{2})=\frac{1}{3}\times (\frac{8}{10})^{2}=\frac{64}{300}$

Probability of drawing 2 white balls from urn 3 is given as:

$P(W\cap W \cap E_{3})=P(E_{2})\times P((W\cap W)/E_{2})=\frac{1}{3}\times 1=\frac{1}{3}$ ............. (as all balls are white only)

Now, probability of drawing 2 white balls is the sum of all the above probabilities and is given as:

$P(2W)=P(W\cap W \cap E_{1})+P(W\cap W \cap E_{2})+P(W\cap W \cap E_{3})\\P(2W)=\frac{9}{300}+\frac{64}{300}+\frac{1}{3}\\P(2W)=\frac{9}{300}+\frac{64}{300}+\frac{100}{300}=\frac{9+64+100}{300}=\frac{173}{300}$

(a)

Probability of selecting urn 1 given that 2 white balls are drawn is:

$P(E_{1}/2W)=\frac{P(E_{1})\times P(2W/E_{1})}{P(2W)}\\P(E_{1}/2W)=\frac{\frac{9}{300}}{\frac{173}{300}}=\frac{9}{173}=0.0520$

Therefore, probability of selecting urn 1 given that 2 white balls are drawn is 0.0250.

(b)

Probability of selecting urn 2 given that 2 white balls are drawn is:

$P(E_{2}/2W)=\frac{P(E_{2})\times P(2W/E_{2})}{P(2W)}\\P(E_{2}/2W)=\frac{\frac{64}{300}}{\frac{173}{300}}=\frac{64}{173}=0.3699$

Therefore, probability of selecting urn 2 given that 2 white balls are drawn is 0.3699

8 0

4 years ago