How many 2/3 -cup servings are in 6 cups of cereal?

suppose we want to choose 6 letters without replacement from 13 distinct letters. A) how many ways can this be done if order doe

kiruha [24]

Answer: A) 1716 B) 1235520

Step-by-step explanation:

If order doesn't matter , then we use combinations, where the number of combinations of selecting r things from n is given by :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

If order matters , then we use permutations, where the number of permutations of selecting r things from n is given by :-

$^nP_r=\dfrac{n!}{(n-r)!}$

Given, Total distinct letters = 13

To choose = 6 letters

A) Number of ways to choose (if order does not matter)= $^{13}C_6$

$=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= $$1716$

B) Number of ways to choose (if order matters)= $^{13}P_6$

$=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= $$1235520$

Hence, A) 1716 B) 1235520

5 0

4 years ago

If the diagonal of the sandbox measures 14 feet, which best describes the shape of the sandbox? a rectangle, because angle c is

LenKa [72]

The shape which describe the shape of the sandbox is "A quadrilateral, because angle c and angle x are acute."

<h3>What is Quadrilateral?</h3>

A quadrilateral is a four-sided polygon, having four edges and four corners.

Here, Diagonal = 14 ft.

Length = 12 ft.

Width = 8 ft.

14² = 196, 12² = 144, 8² = 64

8² + 12² ≠ 14²

so it is not a rectangle.

Now, 14² < 12² + 8²

this condition does not occur in rectangle, so it will be a quadrilateral and here sum of square of two adjacent side is greater than the square of third side (Diagonal). So that is an acute angle.

From this situation we can conclude that:

Thus, the shape which describe the shape of the sandbox is "A quadrilateral, because angle c and angle x are acute."

Learn more about Quadrilateral from:

brainly.com/question/13805601

#SPJ1

8 0

2 years ago

Identify the asymptotes of y= (1/x) -5

elena55 [62]

$\bf y=\cfrac{1}{x}-5\implies y=\cfrac{1-5x}{x}\implies y=\cfrac{-5x+1}{x}$

to find the vertical asymptotes, is simply check what makes the denominator to 0 whilst not zeroing out the numerator, clearly is just x = 0, thus that is the vertical asymptote.

now, for the horizontal asymptote, notice, the degree of the numerator is the same degree of the denominator, thus the horizontal asymptote is at at the fraction whose value is from the coefficients of the leading terms,

$\bf y=\cfrac{1}{x}-5\implies y=\cfrac{1-5x}{x}\implies y=\cfrac{-5x+1}{x}\stackrel{\stackrel{horizontal}{asymptote}}{\implies }\cfrac{-5}{1}
\\\\\\
-5\qquad thus\qquad y=-5$

6 0

3 years ago

Kevin says it will take him less than 1 hour to play soccer, and practice piano because these tasks will take a total of 8/12 ho

OverLord2011 [107]

no, because if you multiply 8x2 it will be 16 and it will be more than a whole hour

it will be 16/12

so it will be more

8 0

4 years ago

Select the decimal that is equivalent to 28/30

bonufazy [111]

The answer is 0.93333333333333.

Fraction to Decimal Conversion

(Math | General | Fraction to Decimal Conversion)

Fraction to Decimal Conversion Tables

Important Note: any span of numbers that is underlined signifies that those numbers are repeated. For example, 0.09 signifies 0.090909....

Only fractions in lowest terms are listed. For instance, to find 2/8, first simplify it to 1/4 then search for it in the table below.

fraction = decimal

1/1 = 1

1/2 = 0.5

1/3 = 0.3 2/3 = 0.6

1/4 = 0.25 3/4 = 0.75

1/5 = 0.2 2/5 = 0.4 3/5 = 0.6 4/5 = 0.8

1/6 = 0.16 5/6 = 0.83

1/7 = 0.142857 2/7 = 0.285714 3/7 = 0.428571 4/7 = 0.571428

5/7 = 0.714285 6/7 = 0.857142

1/8 = 0.125 3/8 = 0.375 5/8 = 0.625 7/8 = 0.875

1/9 = 0.1 2/9 = 0.2 4/9 = 0.4 5/9 = 0.5

7/9 = 0.7 8/9 = 0.8

1/10 = 0.1 3/10 = 0.3 7/10 = 0.7 9/10 = 0.9

1/11 = 0.09 2/11 = 0.18 3/11 = 0.27 4/11 = 0.36

5/11 = 0.45 6/11 = 0.54 7/11 = 0.63

8/11 = 0.72 9/11 = 0.81 10/11 = 0.90

1/12 = 0.083 5/12 = 0.416 7/12 = 0.583 11/12 = 0.916

1/16 = 0.0625 3/16 = 0.1875 5/16 = 0.3125 7/16 = 0.4375

11/16 = 0.6875 13/16 = 0.8125 15/16 = 0.9375

1/32 = 0.03125 3/32 = 0.09375 5/32 = 0.15625 7/32 = 0.21875

9/32 = 0.28125 11/32 = 0.34375 13/32 = 0.40625

15/32 = 0.46875 17/32 = 0.53125 19/32 = 0.59375

21/32 = 0.65625 23/32 = 0.71875 25/32 = 0.78125

27/32 = 0.84375 29/32 = 0.90625 31/32 = 0.96875

Need to convert a repeating decimal to a fraction? Follow these examples:

Note the following pattern for repeating decimals:

0.22222222... = 2/9

0.54545454... = 54/99

0.298298298... = 298/999

Division by 9's causes the repeating pattern.

Note the pattern if zeros precede the repeating decimal:

0.022222222... = 2/90

0.00054545454... = 54/99000

0.00298298298... = 298/99900

Adding zero's to the denominator adds zero's before the repeating decimal.

To convert a decimal that begins with a non-repeating part, such as 0.21456456456456456..., to a fraction, write it as the sum of the non-repeating part and the repeating part.

0.21 + 0.00456456456456456...

Next, convert each of these decimals to fractions. The first decimal has a divisor of power ten. The second decimal (which repeats) is converted according to the pattern given above.

21/100 + 456/99900

Now add these fraction by expressing both with a common divisor

20979/99900 + 456/99900

and add.

21435/99900

Finally simplify it to lowest terms

1429/6660

and check on your calculator or with long division.

= 0.2145645645...

3 0

3 years ago

Read 2 more answers