Everyone thought that Martha Mathy was trying to start a new fashion trend when she started wearing socks that did not match. her "look" started to catch on, and pretty soon all the kids at her school were wearing mixed-up socks, too. Rita Writer, a reporter for the school paper, interviewed Martha about the new sock trend. " Wat gave you the idea to wear mismatched socks?" Rita Asked.

"Its simple mathematics," Martha replied. "you see, I have 18 socks at home but no two are the same. with just these 18 socks, I can create over 100 unique pairs of mismatched socks." Rita found this hard to believe, so she checked it out. Was Martha correct?

Answers

Answer 1

Answer:

There are 153 combinations

Combinations - any two from eighteen is given by the formula 18C2 or 18! / (2!*16!)

= 18 * 17 / 2 = 153

OK that is the maths - now the explanation

The first sock can be any of 18

The second sock can be any of 17 (one already been selected and they must be mismatched)

Therefore there are 18*17 = 306 permutations she could make

However the question asks for "combinations" not "permutations"

A green sock on the right foot and a yellow sock on the left foot is deemed to be a different "permutation" to a yellow sock on the right foot and a green sock on the left foot. HOWEVER, they are regarded as the same "combination" in both cases you have one green and one yellow sock.

Therefore for combinations we must divide the 306 permutations calculated above by 2 = 153

FYI Walton has incorrectly given you the value of 18!. That would only apply if Martha Mathy had 18 feet!


Related Questions


Find the slope of the line through the points (-2, -3) and (2, 1).

Answers

Answer:

1

Step-by-step explanation:

i did it

mark invested a certain amount at 5 % simple interest per year after 10 year he received an interest of 50000 how much did he invest​

Answers

Answer:

100,000

Step-by-step explanation:

The sum of two consecutive even integers is 98 find the larger number

Answers

Answer:

50

Step-by-step explanation:

Let's say the smaller number is x then

x + x + 2 = 98

2x+2 = 98

2x = 96

x = 48

==> 48, 50

The sum of two consecutive even integers is 98 has 50 as larger number.

Given that the sum of two consecutive even integers is 98, we need to find the larger number,

Let's denote the two consecutive even integers as x and x + 2. According to the given information, their sum is 98.

So we can write the equation:

x + (x + 2) = 98

Simplifying the equation:

2x + 2 = 98

Subtracting 2 from both sides:

2x = 96

Dividing both sides by 2:

x = 48

Therefore, the larger number (x + 2) is:

48 + 2 = 50

So, the larger number is 50.

Learn more about Consecutive Numbers click;

https://brainly.com/question/29775116

#SPJ4

Jack knows that one-third of his total trip is 640 miles. How far is Jack's total trip?

Answers


If one-third of his total trip is 640

You would multiply 640 by 3 to find out how far his total trip is.

640 x 3 = 1,920

5) Un pedazo de pizza cuesta $30, un jugo cuesta $15. ¿Cuánto de deben sobrar de
$500 al comprar 5 pedazos de pizza y 5 jugos?​

Answers

275
Explicación: 30 por 5 es 150 por la pizza
15 por 5 es 75. 150+75=225.
500-225=275

Answer:

I think it is 275 if you are subtracting

Show your work and explain how you can determine which is a better deal:
10 ounces of orange juice for $2.40 or 8 ounces for $2.08?

Answers

divide 10 by 2.40 it gives you a decimal 4.16 and go on. Round it and its 4.20.

At the grocery store, almonds ore on soe for
$3.8 per pound What is the price of 4.5pounds??

Answers

Answer:

$17.10

Step-by-step explanation:

Almonds being on sale

$3.8 per pound

4.5 pounds

___________________

We know that for every pound, the cost is three dollars and eighty cents, we are looking for 4.5 pounds in total.

Multiply the amount per pound to the amount of pounds being asked :

3.8 * 4.5

$17.10

can someone help me?

Answers

9514 1404 393

Answer:

  8.39

Step-by-step explanation:

In the right triangle, the hypotenuse and side opposite the angle are shown. The applicable trig relation is ...

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse × Sin

  x cm = (15 cm)×sin(34°)

  x ≈ 8.39

A family has four children. If the genders of these children are listed in the order they are born, there are sixteen possible outcomes: BBBB, BBBG, BBGB, BGBB, GBBB, BGBG, GBGB, BGGB, GBBG, BBGG, GGBB, BGGG, GBGG, GGBG, GGGB, and GGGG. Assume these outcomes are equally likely. Let represent the number of children that are girls. Find the probability distribution of . Part: 0 / 20 of 2 Parts Complete Part 1 of 2 Your Answer is incorrect (a) Find the number of possible values for the random variable . There are possible values for the random variable .

Answers

Answer:

X : ___ 0 ____ 1 _____ 2 _____ 3 _____ 4

P(x): _ 1/16 __ 1/4 ____ 3/8 ____ 1/4 ____ 1/16

Step-by-step explanation:

Given the listed possible occurrence of boys and girls :

B = boys ; G = girls

BBBB, BBBG, BBGB, BGBB, GBBB, BGBG, GBGB, BGGB, GBBG, BBGG, GGBB, BGGG, GBGG, GGBG, GGGB, and GGGG

Let x = distribution of girls

P = required outcome / Total possible outcomes

For :

x = 0 ;(BBBB) = 1

P(x) = 1/16

x = 1 ; (BBBG, BBGB, BGBB, GBBB) = 4

P(x) = 4 / 16 = 1/4

P(x = 2) ; (BGBG, GBGB, BGGB, GBBG, BBGG, GGBB) = 6

P(x) = 6 / 16 = 3/8

P(x = 3) ; (BGGG, GBGG, GGBG, GGGB) = 4

P(x) = 4 / 16 = 1/4

P(x = 4) ; (GGGG) = 1

P(x) = 1 / 16

X : ___ 0 ____ 1 _____ 2 _____ 3 _____ 4

P(x): _ 1/16 __ 1/4 ____ 3/8 ____ 1/4 ____ 1/16

Decrease 1428g by 38.5%​

Answers

Answer:

1428 (1-0.385) = 878.22

Step-by-step explanation:

18 lollipop at the same number of lollipops on the nine tables how many levels did she pop on each table​

Answers

Answer:

2

Step-by-step explanation:

.....................

What is the slope of the line shown in the graph?

Answers

Answer:

y = -3/2x - 2.5

Step-by-step explanation:

First, identify the slope by using y-y1/x-x1

2- -1 = 3, -3 - -1 = -2 the slope is -3/2

Then, you have y = -3/2x + b

To find b, you have to plug in a value of x and y

I will use the point (-3,2) for this example.

2 = -3(-3/2) + b

2 = 9/2 + b

2 = 4.5 + b

b = -2.5

Once you assemble your equation, you should get y = -3/2x - 2.5

The fraction 4/5 is equivalent to which of the following percentages

Answers

Answer:

80 percent but could you please take a picture of the question...

Step-by-step explanation:

I need help ASAP pls

Answers

There is 4 cats and 3 dogs
/ = 4/3

Y varies directly with x. If y = 150 when x = 3, what is x when y = 600

Answers

Answer:

Step-by-step explanation:

Y varies directly with x:

y=kx

for some non-zero constant k

substitute y=150 and x=3:

150=3k

k=50

When y=600:

600=(50)x

x=12

what is the LCM of 3and 6​

Answers

Answer:

L.c.m of 3 and 6 is 6

Answer:

Lcm of 3&6 is:

3*2 & 6*1 (DONE LIKE THIS BECAUSE THAT LCM OF 3 & 6 IS FOUND TO BE 6 AS BOTH 3 & 6 HAS THE SMALLEST COMMON MULTIPLE AS 6)

6  & 6

There fore LCM is 6

i need help with

−5 × −8 =

Answers

Answer:

40

Step-by-step explanation:

-5 * (-8) = 40

Answer:

40

Step-by-step explanation:

Because multiplication of subtract will be added

To make meatloaf. mix 2 pounds of beef and 0.5 of a cup of breadcrumbs. How many pounds of beef
would you mix with 4.5 cups of breadcrumbs

Answers

Answer:

18 pounds of beef.

Step-by-step explanation:

For every 0.5 cups of breadcrumbs there's 2 pounds of beef.

0.5 x 9 = 4.5

9 x 2 = 18 or 2 x 9 = 18

multiples of two: 2 4 6 8 10 12 14 16 18

This shows that when we multiply 2 nine times we get 18!

what is 70000000000000000 divided by 100000 plus 797970605 plus 023475748392

Answers

Answer:

7.000002427×10¹⁶

Answer:  

723555545997

Step-by-step explanation:

I hope this helps, i had to use a calculator because that was a long math equation question, I mean, who else can't do that?

And plz rate it 5 starts, give brainilest, and thank me

[tex]-(x+9)2=64[/tex]

Answers

-(x+9)2=64
(-x-9)2= 64
-2x-18= 64
+18. +18
-2x = 82
/-2. /-2
x= -41

I WILL GIVE BRAILIEST IF ANSWER IS CORRECT! The sum of all the solutions to the equation (6x+k)(3x-11)=0 is 1. Find K. Please help me I don't understand what this problem means.

Answers

Answer:

k=-6x

Step-by-step explanation:

You are looking for the value of k.

Either (6x+k)=0, or (3x-11)=0 because of the Zero Product Property

We are looking for k, so we must make (6x+k)=0

Simply cancel 6x out by subtracting 6x.

6x-6x=0.

please help me please i really need help please

Answers

Answer:

x = -22/3 and y = -1

Step-by-step explanation:

First, simplify the equation 12x + 20y = -108 by dividing both sides by 4:

3x + 5y = -27

now, you can subtract the two equations:

3x + 5y = -27

- (3x - 12y = -10)

17y = -17

y = -1

plug y = -1 into the equation 3x - 12y = -10

3x - 12 *(-1) = -10

3x + 12 = -10

3x = -22

x = -22/3

Answer:

-(22/3,-1)

Step-by-step explanation:

HELP IM BEING TIMED ON THIS

Answers

Answer:

im pretty sure its 1

Step-by-step explanation:

Answer:

the answer is (3 4)

Step-by-step explanation:

(10x 18) + (10xs) = how to solve

Answers

Answer:

i dont know dude

Step-by-step explanation:

del puerto de cabo San Lucas México salen dos barcos el barco México 1,navega con una trayectoria de x+y=88;el barco México 2 navega con una trayectoria de 2x + 2y= -176 en que punto se encontrarán los dos barcos?​

Answers

pls in english!!!!!!!?????

1. You have three standard decks of cards in front of you. What is the probability of drawing a heart card from all three decks?
2.12%
9.38%
1.56%
17.31%

Answers

Answer:

1.56%

Step-by-step explanation:

A standard deck of cards has 52 cards, and 13 of these are hearts, as there are 4 suits, and 52/4=13. This means the probability of choosing a heart card from a deck of cards is 1/4, or 25%. Now to find the probability of doing this from 3 decks in a row, we simply cube 1/4 to get 1/64, and in percentage this is ~1.56%.

Answer: 1.56%

Step-by-step explanation: there's really nothing to explain here.

Quiz From Buzz (Acceleration Education)

Hope it helps you!

What value of x and y will make the polygon a parallelogram
105°
V
15x

Answers

Answer

60

Step-by-step explanation:

105+15= 120

180-120=60

I think this is the correct answer but I dont know

map of field: 12 in × 15 in

scale of map: 1 in = 3 ft

What are the dimensions
of the actual field?

Answers

multiply the dimensions by 3 to convert to feet.

12 x 3 = 36 ft.

15 x 3 = 45 ft.

the dimensions are 36 ft. x 45 ft.

Estimate 307‾‾‾‾√ between two consecutive whole numbers. Enter the numbers in the boxes below.

Answers

Answer:

17, 18

Step-by-step explanation:

closest perfect square that is lower than 307 is 289

closest perfect square that is greater than 307 is 324

[tex]\sqrt{289} < \sqrt{307} < \sqrt{324}[/tex]

[tex]17<\sqrt{307} <18[/tex]

Presented below are the financial statements for the Amphlett Corporation, as of year-end 2012 and 2013.
AMPHLETT CORPORATION
Consolidated Balance Sheets
As of Year-End ($ thousands) 2013 2012
Assets
Current
Cash $18,000 $108,000
Marketable securities 240,000 -
Accounts receivable (net) 708,000 528,000
Inventory 720,000 738,000
Total current assets 1,686,000 1,374,000
Noncurrent
Long-term investments 372,000 468,000
Property & equipment 2,160,000 1,320,000
Less: Accumulated depreciation (600,000) (600,000)
Property & equipment (net) 1,560,000 720,000
Intangibles (net) 114,000 126,000
Total noncurrent assets 2,046,000 1,314,000
Total assets $3,732,000 $2,688,000
Liabilities & Shareholders' Equity
Accounts payable $1,080,000 $1,020,000
Short-term bank debt 228,000 -
Total liabilities 1,308,000 1,020,000
Shareholders' equity
Common stock, $10 par value 930,000 810,000
Additional paid-in-capital 456,000 360,000
Retained earnings 1,038,000 498,000
Total shareholders' equity 2,424,000 1,668,000
Total liabilities & shareholders' equity $3,732,000 $2,688,000
AMPHLETT CORPORATION
Consolidated Income Statement
For Year Ended ($ thousands)
2013
2012
Revenues
$1,716,000
$1,440,000
Less: Cost of goods sold
600,000
504,000
Gross margin
1,116,000
936,000
Less: Selling, general & administrative expenses
180,000
144,000
Operating income
936,000
792,000
Gain on sale of investments
84,000
-
Net income before taxes
1,020,000
792,000
Less: Income taxes
60,000
13,200
Net income after taxes
$960,000
$778,800
The footnotes to the Amphlett Corporation's financial statements revealed the following additional information:
Property and equipment costing $540 million was sold for its book value of $240 million.
Long-term investments were sold for $180 million, which included a gain of $84 million.
Required
Using the above financial data for the Amphlett Corporation, prepare the firm's statement of cash flow for 2013 using the indirect method.
Use a negative sign with answers to indicate a decrease in cash.
Amphlett Corporation
Statement of Cash Flows
For Year Ended 2013
(in thousands)
Cash flow From Operations BLANK
Net Income $Answer
Add:
Depression Expense Answer
Amortization expense Answer
Less:
Gain on Sale of Investments Answer
Accounts receivable (net) Answer
Inventory Answer
Accountable Payable Answer
Cash Flow From Operations Answer
Cash Flow for Investing BLANK
Marketable securities Answer
Long-term investments Answer
Purchase of property and equipment Answer
Sale of Property and Equipment Answer
Cash Flow for Investing Answer
Cash From Financing BLANK
Short-term bank debt Answer
Common stock + additional paid in capital Answer
Dividends Paid Answer
Cash From Financing Answer
Decrease in Cash Answer
Cash, beginning of year Answer
Cash, end of year $Answer

Answers

Answer:

For Year Ended 2013    

(in thousands)    

Cash flow From Operations BLANK    

Net Income   792,000

Add:    

Depression Expense   300,000

Amortization expense   12,000

Less:    

Gain on Sale of Investments    

Accounts receivable (net)   -180,000

Inventory   18,000

Accountable Payable Answer   60,000

Cash Flow From Operations   1,002,000

Cash Flow for Investing    

Marketable securities   -240,000

Long-term investments   96,000

Purchase of property and equipment    -1,380,000

Sale of Property and Equipment    280,000

Cash Flow for Investing    -1,244,000

Cash From Financing    

Short-term bank debt   228,000

Common stock + additional paid in capital   96,000

Dividends Paid   8,000

Cash From Financing   332,000

Decrease in Cash    90,000

Cash, beginning of year   18,000

Cash, end of year   108,000

   108,000

   0

Step-by-step explanation:

Assets    

Current    

Cash  $18,000  $108,000

Marketable securities  240,000  

Accounts receivable (net)  708,000  528,000

Inventory  720,000  738,000

Total current assets  1,686,000  1,374,000

Noncurrent    

Long-term investments  372,000  468,000

Property & equipment  2,160,000  1,320,000

Less: Accumulated depreciation  -600,000  -600,000

Property & equipment (net)  1,560,000  720,000

Intangibles (net)  114,000  126,000

Total noncurrent assets  2,046,000  1,314,000

Total assets  $3,732,000  $2,688,000

Liabilities & Shareholders' Equity    

Accounts payable  $1,080,000  $1,020,000

Short-term bank debt  228,000  

Total liabilities  1,308,000  1,020,000

Shareholders' equity    

Common stock, $10 par value  930,000  810,000

Additional paid-in-capital  456,000  360,000

Retained earnings  1,038,000  498,000

Total shareholders' equity  2,424,000  1,668,000

Total liabilities & shareholders' equity  $3,732,000  $2,688,000

                                                                                                       

AMPHLETT CORPORATION    

Consolidated Income Statement    

For Year Ended ($ thousands)  2013  2012

Revenues  $1,716,000  $1,440,000

Less: Cost of goods sold  600,000  504,000

Gross margin  1,116,000  936,000

Less: Selling, general & administrative expenses  180,000  144,000

Operating income  936,000  792,000

Gain on sale of investments  84,000  

Net income before taxes  852,000  792,000

Less: Income taxes  60,000  13,200

Net income after taxes  $792,000  $778,800

   

For Year Ended 2013    

(in thousands)    

Cash flow From Operations BLANK    

Net Income   792,000

Add:    

Depression Expense   300,000

Amortization expense   12,000

Less:    

Gain on Sale of Investments    

Accounts receivable (net)   -180,000

Inventory   18,000

Accountable Payable Answer   60,000

Cash Flow From Operations   1,002,000

Cash Flow for Investing    

Marketable securities   -240,000

Long-term investments   96,000

Purchase of property and equipment    -1,380,000

Sale of Property and Equipment    280,000

Cash Flow for Investing    -1,244,000

Cash From Financing    

Short-term bank debt   228,000

Common stock + additional paid in capital   96,000

Dividends Paid   8,000

Cash From Financing   332,000

Decrease in Cash    90,000

Cash, beginning of year   18,000

Cash, end of year   108,000

   108,000

   0

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