Cuantas permutaciones pueden hacerse con la palabra columna

Answers

Answer 1

There are 720 Permutations that can be made with the word "column."

The number of permutations that can be made with the word "column," we need to consider the arrangement of the letters in the word.

The word "column" has 6 letters. When calculating permutations, we need to consider that the order of the letters matters.

In this case, we have 6 options for the first letter, 5 options for the second letter, 4 options for the third letter, 3 options for the fourth letter, 2 options for the fifth letter, and 1 option for the last letter.

To find the total number of permutations, we multiply the number of options for each letter:

6 * 5 * 4 * 3 * 2 * 1 = 720.

Therefore, there are 720 permutations that can be made with the word "column."

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Related Questions

Write a function inches_to_ft that takes a number of inches x and returns the number of feet. One foot equals 12 inches.

Answers

Answer:

def inch_to_feet (x):

return 1/x

Step-by-step explanation:

Implementating the program Using python 3 :

def - - - > function declaration keyword

inch_to_feet - - > function name

x - - > argument which the function takes

The value returned is a conversion of x which is in inches to feets

1/12 feet = 1 inch

To see the value returned ;

We can run the code :

def inch_to_feet(x):

return (1/12)*x

b = inch_to_feet(12)

print(b)

The code above will print 1.

What is the greatest common factor of 8,16,40

Answers

Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

Solve all 3 Questions. 50 Points + Brainelist ​

Solve all 3 Questions. 50 Points + Brainelist

Answers

Answer:

i)  Using log law:  \(\log_aa=1\)

\(\implies \log_55+1=1+1=2\)

ii) \(\log \left(\dfrac{15}{8}\right)+4 \log 2-\log 3\)

Using log law \(a \log b=\log b^a\):

\(\implies \log \left(\dfrac{15}{8}\right)+\log 2^4-\log 3\)

\(\implies \log \left(\dfrac{15}{8}\right)+\log 16-\log 3\)

Using log law \(\log a-\log b=\log (\frac{a}{b})\):

\(\implies \log \left(\dfrac{15}{8}\right)+\log\left(\dfrac{16}{3}\right)\)

Using log law  \(\log a+\log b=\log(ab)\):

\(\implies \log \left(\dfrac{15}{8}\cdot \dfrac{16}{3}\right)\)

\(\implies \log 10\)

Using log law:  \(\log_aa=1\)

\(\implies \log_{10} 10=1\)

iii) Take log of base 10:

\(\log_{10}(\sqrt{8.357}\times0.895^2)\)

\(\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)\)

Log tables

The characteristic of the logarithm of a number is the exponent of 10 in its scientific notation.

The mantissa is found using the log tables and is always prefixed by a decimal point.

The row is the first two non-zero digits of the number, and the column is the 3rd digit of the number

Use the log tables to find \(\log_{10}(8.357)\):

8.357 = 8.357 × 10⁰

⇒ characteristic = 0

log table:  row 83, column 5 ⇒ mantissa 9217

(as there is a 4th digit) Mean difference 7 = 4

mantissa + mean difference = 9217 + 4 = 9221 ⇒ 0.9221

characteristic + mantissa = 0 + 0.9221 = 0.9221

Therefore, \(\log_{10}(8.357)=0.9221\)

Use the log tables to find \(\log_{10}(0.895)\):

\(0.895 = 8.95\times 10^{-1}\)

⇒ characteristic = -1

log table: row 89, column 5 ⇒ mantissa 9518⇒ 0.9518

characteristic  + mantissa = -1 + 0.9518= -0.0482

Therefore, \(\log_{10}(0.895)=-0.0482\)

Therefore,

\(\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)\)

\(\implies \dfrac12 \cdot 0.9221+2\cdot-0.0482\)

\(\implies 0.36465\)

Therefore,

\(\log_{10}(\sqrt{8.357}\times0.895^2)=0.36465\)

Using \(\log_ab=c \implies a^c=b\)

\(\implies \sqrt{8.357}\times0.895^2=10^{0.36465}\)

\(\implies \sqrt{8.357}\times0.895^2=2.3155\)

pls help i am in k12
Refer to the equation 2x − 6y = 12.

Write the equation in Slope Intercept Form.






Find the x-intercept and the y-intercept?





Create a table of values for 4 points. You can include the intercepts. Show your work.


X

Y

Answers

Answer:

(Hope this helps can I pls have brainlist (crown)☺️)

Step-by-step explanation:

To find the x-intercept, substitute in  0  for  y yand solve for  x . To find the y-intercept, substitute in  0  for  x and solve for  y .

x-intercept(s):  ( 6 , 0 )

y-intercept(s):  ( 0 , − 2 )

Use the slope-intercept form  y = m x + b to find the slope  m and y-intercept  b .

Slope: \(\frac{1}{3}\)

graph in pic

(Credit: M a t h w a y)

pls help i am in k12Refer to the equation 2x 6y = 12.Write the equation in Slope Intercept Form.Find

AAAAAAAAA help please​

AAAAAAAAA help please

Answers

The answer is the first one BC ~ CD
Ok done. Thank to me:>

A boy walks 5km due north and then 4km due east. Find the bearing of his current position from the starting point, how far is the boy now from the starting point

Answers

He will be 9km away from the point

Calc II Question

Sketch the region enclosed by the given curves and find its area.
Y = lxl , y = x^2 - 2

Answers

Answer:

\(\displaystyle A=\frac{20}{3}\)

Step-by-step explanation:

\(\displaystyle A=\int^2_{-2}(|x|-(x^2-2))\,dx\\\\A=2\int^2_0(x-(x^2-2))\,dx\\\\A=2\int^2_0(-x^2+x+2)\,dx\\\\A=2\biggr(-\frac{x^3}{3}+\frac{x^2}{2}+2x\biggr)\biggr|^2_0\\\\A=2\biggr(-\frac{2^3}{3}+\frac{2^2}{2}+2(2)\biggr)\\\\A=2\biggr(-\frac{8}{3}+2+4\biggr)\\\\A=2\biggr(-\frac{8}{3}+6\biggr)\\\\A=2\biggr(\frac{10}{3}\biggr)\\\\A=\frac{20}{3}\)

Bounds depend on whether you use -x or +x instead of |x|, but you double regardless. See the attached graph for a visual.

Calc II QuestionSketch the region enclosed by the given curves and find its area.Y = lxl , y = x^2 -

Out of the 25 families that Tod delivered magazines to on
Friday, 10 families were home and the rest were away. How is
the fraction of magazines that were delivered to families who
were home written as a decimal?

Out of the 25 families that Tod delivered magazines to onFriday, 10 families were home and the rest were

Answers

The fraction of magazines that were delivered to families who were home written as a decimal is 0.4

Difference between fraction and decimal?

There are just two ways to represent numbers: fractions and decimals. In comparison to decimals, where the whole number part and the fractional part are connected by a decimal point, such as in the case of 0.5, fractions are expressed as p/q, where q0. Decimals and fractions show the link between parts and wholes. We use 1 to represent the entire in fractions and decimals. To comprehend the relationship between fractions and decimals, let's look at some instances. Think of a six-slice, full-thin crust pizza. Your mother gave you three slices, or half of it, which is written as 1/2 in fractional form and as 0.5 in decimal form.

Total number of families = 25

Number of families in home = 10

Then, number of families away = 25 - 10 = 15

Fraction of magazines that were delivered to families who were home

= Number of families in home/ Total number of families

= 10 / 25

= 0.4

Hence, the fraction of magazines that were delivered to families who

were home written as a decimal is 0.4

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order 0.76 grams of med each pill contains 0.02 grams of med how many pill will the patient need​

Answers

Answer:

38 pills

Step-by-step explanation:

To find the number of pills, you need to divide the weight of each pill by the total weight needed.

0.76 grams / 0.02 grams = 38 pills

Find two numbers that the quotient 3,382/6 is between

Answers

The most appropriate choice for division will be given by

Quotient of \(\frac{3382}{6}\) is between 563 and 564

What is division?

The process of dividing a certain number into equal parts is called division

The answer obtained after division is called quotient and the other part is the remainder. The number which is divided is called the dividend and the number by which the dividend is divided is called divisor.

General rule of division

Divisor x Quotient + Remainder = Dividend

Here,

Quotient of \(\frac{3382}{6}\) = 563

563 is between 562 and 564

So, quotient of \(\frac{3382}{6}\) is between 563 and 564

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11 of 3011 of 30 Questions





















Question
A baker makes peanut butter cookies and chocolate chip cookies.

She needs 2 cups of flour and 34
cup of butter to make one batch of peanut butter cookies.
She needs 3 cups of flour and 1 cup of butter to make one batch of chocolate chip cookies.
If the baker has 26 cups of flour and 9 cups of butter, how many batches of each type of cookie can she make?

Answers

The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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please help i only have 2 minutes left​

please help i only have 2 minutes left

Answers

Answer:

30mm 2.5cm 20cm 1m

Step-by-step explanation:

Add 34+(−212) using the number line. Select the location on the number line to plot the sum.

Answers

Answer:

Answer is explained below in the explanation section.

Step-by-step explanation:

Solution:

For this question, we need to have a number line, we can not make the number line here. As it will be very long. Instead, I have attached a number line from -11 to +11 for your understanding and explained it below. Please refer to the attachment below for the number line.

Number Line:

A number line is a line which contains all the numbers from negative infinity to positive infinity divided by a single number zero. It has two sides, left hand side and right hand side. A side left to zero contains all the negative numbers and a side right to 0 contains, all the positive numbers.

So,

We are asked to add 34 in (-212), we will get 178 but with the negative sign, and it will lie on the left hand side of the number line.

SO,

34 + (-212) = 34 - 212 = -178

Hence,

Our sum which is 178 will lie on the left hand side of the number line.

Add 34+(212) using the number line. Select the location on the number line to plot the sum.

Using long division what is the quotient of this expression

3x^4-2x^3-x-4
———————-
X^2+2

Answers

3x² - 2x -6 is quotient in polynomial after long division .

What in mathematics is a polynomial?

Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video.A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It is made up of indeterminates (also known as variables) and coefficients. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.

\(\frac{3x^{4} - 2x^{3} - x - 4 }{x^{2} + 2}\)  

after long division we get quotient -  3x² - 2x -6 .

Divide using long division: standard \(3x^{2} + \frac{3x + 8 }{x^{2} + 2} - 2x - 6\)

quotient - 3x² - 2x -6

remainder - 3x + 8

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Answer:

see image

Step-by-step explanation:

Plato/Edmentum

Using long division what is the quotient of this expression 3x^4-2x^3-x-4- X^2+2

Gavin and Eric each ate 1/4 of a pizza. Megan ate 1/3 of what was left. How much pizza did Megan eat?
A) 1/2
B) 1/3
C) 1/6
D) 1/7

Answers

If Gavin and Eric each eat 1/4 of a pizza, they eat 1/4 + 1/4 = 1/2 in total. Megan eats 1/3 of a 1/2, so first make the denominator the same. The LCM of 3 and 2 is 6. Megan is eating 1/3 of 3/6, so Megan eats 1/6. The answer is C.

Match each term with its notation.

___________ The number of treatment conditions
___________ The number of scores in each treatment.
___________ The total number of scores in the entire study.
___________ The sum of the scores for each treatment condition.
___________ The sum of all of the scores in the research study.
___________ The F-ratio

1. n
2. F
3. G
4. N
5. k
6. T

Answers

Answer:

_k_ The number of treatment conditions

_n_ The number of scores in each treatment.

_N_ The total number of scores in the entire study.

_T_ The sum of the scores for each treatment condition.

_G_ The sum of all of the scores in the research study.

_F_ The F-ratio

Step-by-step explanation:

These notations are ANOVA (Analysis of variance) notations, where

k is the number of treatment conditions

n is the number of scores in the treatment

N is the total number of scores in the entire study

T is the sum of scores for a specific treatment

G is the sum of all scores in the study

and F is the F-ratio.

Now, for the question, we will match each term with its notation

_k_ The number of treatment conditions

_n_ The number of scores in each treatment.

_N_ The total number of scores in the entire study.

_T_ The sum of the scores for each treatment condition.

_G_ The sum of all of the scores in the research study.

_F_ The F-ratio

Given two planes how do I find the vector equation?

Given two planes how do I find the vector equation?

Answers

The vector equation for the intersection of the two planes is given by:

9i + 36j - 24k.

What is the vector equation for the intersection of two planes?

Suppose that we have two planes, defined as follows:

ax + by + cz = K1. (K1 constant).dx + ey + fz = K2. (K2 constant).

The vector equation for the intersection between these two places is given by the determinant of the following matrix:

\(\left[\begin{array}{ccc}i&j&k\\a&b&c\\d&e&f\end{array}\right]\)

For this problem, the planes are:

6y + 9z = 39.4x + 3y + 6z = 10.

Hence the matrix of which we have to find the determinant is:

\(\left[\begin{array}{ccc}i&j&k\\0&6&9\\4&3&6\end{array}\right]\)

The determinant of the 3 x 3 matrix is given by:

D = i x  6 x 6 + j x 9 x 4 + k x 0 x 3 - (k x 6 x 4 + j x 0 x 6 + i x 9 x 3).

D = 36i + 36j - (24k + 27i)

D = 36i + 36j - 24k - 27i

D = 9i + 36j - 24k.

Which is the vector equation.

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Can someone help me

Can someone help me

Answers

Answer:

It's 2 units to the right & 5 units down.

There are six girls and ten boys in a class. Three of the girls and four of the boys wear glasses.
a The teacher chooses one person at random. What is the probability that the teacher chooses:

Answers

The probability that the teacher chooses a girl with glasses is 3/16, and the probability that the teacher chooses a boy with glasses is 1/4.

Let's calculate the probability that the teacher chooses a student with glasses.
a) A girl with glasses: There are 6 girls in the class, and 3 of them wear glasses. There are a total of 16 students (6 girls + 10 boys).
Probability = (Number of girls with glasses) / (Total number of students)
Probability = 3 girls with glasses / 16 total students
Probability = 3/16
b) A boy with glasses: There are 10 boys in the class, and 4 of them wear glasses.
Probability = (Number of boys with glasses) / (Total number of students)
Probability = 4 boys with glasses / 16 total students
Probability = 1/4
So, the probability that the teacher chooses a girl with glasses is 3/16, and the probability that the teacher chooses a boy with glasses is 1/4.

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In what quadrant does the angle whose measure is (15pi)/4 terminate?

Answers

Answer:

Quadrant IV

Step-by-step explanation:

15π/4 is the same angle as 15π/4 − 2π = 7π/4.  Which terminates in the fourth quadrant.

Laura orders 50 m² of concrete paving slabs. The slabs cost £16.75 per m². How much do the slabs cost in total

Answers

Answer:

£837.5

Step-by-step explanation:

Cost of slabs =  £16.75 / m²

Ordered amount = 50 m²

Total cost:

£16.75*50 = £837.5

Total cost of slabs is  £837.5

Combine like terms to create an equivalent expression: 6.7+3.5x+3.3-4.7x

Combine like terms to create an equivalent expression: 6.7+3.5x+3.3-4.7x

Answers

Step-by-step explanation:

....djdjbeoehehoeebdnskeje

Combine like terms to create an equivalent expression: 6.7+3.5x+3.3-4.7x

How to find the area of the shape on the right

How to find the area of the shape on the right

Answers

Answer:

19 units²

Step-by-step explanation:

First, divide the shape into two triangles, find the area of those triangles, and then add the areas together.

Big Triangle:

1/2bh

1/2 6(5)

1/2 30

15

Little Triangle

1/2bh

1/2 2(4)

1/2 8

4

Total Area:

15 + 4 = 19 units squared

Are they like terms? 3y & 3x

Answers

Answer:

no

Step-by-step explanation:

Answer:

No because they dont have the same variables

Step-by-step explanation:

In Exercises 33–36, determine if the specified linear transforma- tion is (a) one-to-one and (b) onto. Justify each answer. 14. Let T : R2 R2 be a linear transformation with standard matrix A = aaz], where a, and a, are shown in the figure. Using the figure, draw the image of under the transformation T. [-] 1 |

Answers

If values prοvided then transfοrmatiοn οf vectοrs can be determined.

What is vectοr?

In mathematics, a vectοr is a mathematical οbject that represents a quantity with bοth a magnitude and a directiοn. Vectοrs can be used tο represent physical quantities such as velοcity, fοrce, and acceleratiοn, as well as mοre abstract cοncepts such as cοlοr, sοund, and temperature.

Withοut seeing the figure οr the values οf a1, a2, and a3, it is nοt pοssible tο determine whether the specified linear transfοrmatiοn T : R2 → R2 is οne-tο-οne and οntο.

Hοwever, in general:

A linear transfοrmatiοn T : Rn → Rm is οne-tο-οne if and οnly if its kernel (i.e., the set οf vectοrs that are mapped tο the zerο vectοr) is trivial, meaning that the οnly vectοr that maps tο the zerο vectοr is the zerο vectοr itself.

A linear transfοrmatiοn T : Rn → Rm is οntο if and οnly if its range (i.e., the set οf all vectοrs that can be οbtained by applying T tο sοme vectοr in Rn) is equal tο Rm.

Tο determine whether a linear transfοrmatiοn is οne-tο-οne οr οntο, we can examine its prοperties and characteristics, such as its kernel, range, rank, and determinant. We can alsο use geοmetric intuitiοn and visualizatiοn tο understand hοw the transfοrmatiοn maps pοints and vectοrs in Rn tο Rm.

If yοu prοvide mοre infοrmatiοn abοut the values οf a1, a2, and a3 and the figure that shοws the standard matrix A, it can help yοu determine whether the transfοrmatiοn is οne-tο-οne and οntο and draw the image οf the vectοr [-1, 1] under the transfοrmatiοn T.

Therefοre, if values prοvided then transfοrmatiοn οf vectοrs can be determined.

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Complete question -

In Exercises 33–36, determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer. 14. Let T : R2 R2 be a linear transformation with standard matrix A = aaz], where a, and a, are shown in the figure. Using the figure, draw the image of under the transformation T. [-] 1

In Exercises 3336, determine if the specified linear transforma- tion is (a) one-to-one and (b) onto.

A game is played with a single fair die. A player wins $20 if a 2 turns up, $40 if a 4 turns up, and loses $30 if a 6 turns up. If any other face turns up, there is no winning. Find the expected sum of money the player can win.$3$4$5$6.50

Answers

Given that a game is played with a single fair die. A player wins $20 if a 2 turns up, $40 if a 4 turns up, and loses $30 if a 6 turns up. If any other face turns up, there is no winning

To Determine: The expected sum of money the player can win

Solution:

Let X be the the random variable giving the amount of money won on any toss of the die

The possible amounts won when the die turns up 1,2, 3, 4, 5, and 6 are:

X1, X2, X3, X4, X5, and X6 respectively.

While the probabilities of these are P(X1), P(X2), P(X3), P(X4), P(X5), and P(X6).

Note that the probability of any face turning up in a fair die is

\(P(a\text{ face turn up in a fair die)=}\frac{1}{6}\)

So,

\(\begin{gathered} P(X_1)=\frac{1}{6};P(X_2)=\frac{1}{6};P(X_3)=\frac{1}{6} \\ P(X_4)=\frac{1}{6};P(X_5)=\frac{1}{6};P(X_6)=\frac{1}{6} \end{gathered}\)

The expected sum of money the player can win is

\(E(X)=n_1P(X_1)+n_2P(X_2)+n_3P(X_3)+n_4P(X_4)+n_5P(X_5)+n_6P(X_6)\)\(\begin{gathered} n_1=n_3=n_5=0(\text{Given)} \\ n_2=\text{ \$20;} \\ n_4=\text{ \$40} \\ n_6=-\text{ \$30} \end{gathered}\)\(E(X)=0(\frac{1}{6})+20(\frac{1}{6})+0(\frac{1}{6})+40(\frac{1}{6})+0(\frac{1}{6})+(-30)(\frac{1}{6})\)\(\begin{gathered} E(X)=0+\frac{20}{6}+0+\frac{40}{6}+0-\frac{30}{6} \\ E(X)=\frac{20+40-30}{6} \\ E(X)=\frac{60-30}{6} \\ E(X)=\frac{30}{6} \\ E(X)=5 \end{gathered}\)

Hence, the expected sum of money the player can win is $5

Find the domain of the function using interval notation:f(x) = -2x(x - 3)(x - 6)

Answers

ANSWER

\((-\infty,\infty)\)

EXPLANATION

We want to find the domain of the function using interval notation:

\(f(x)=-2x(x-3)(x-6)\)

The domain of a function is the set of all input values of a function i.e. the set of all x values for which a function is valid.

For the given function, all real values of x satisfy the equation.

This implies that the domain of the function is:

\((-\infty,\infty)\)

That is the answer.

If 1/2 x 10 = 8 - x, then x = ?

Answers

Answer:

3

Step-by-step explanation:

1/2 x 10 is 5

8 - 3 is 5

1/2 x 10 = 8 - 3

Answer:

3

Step-by-step explanation:

1/2 * 10 = 5

8-5=3

A large restaurant chain is curious what proportion of their customers in a given day are new customers. They

are thinking of taking a sample of either n = 50 or nº= 100 customers and building a one-sample z interval for

a proportion using the data from the sample.

Answers

Answer:

It is a false statement

The correct statement is -The margin of error from the smaller sample will be \(\sqrt{2}\)  times the margin of error from the larger sample.

Step-by-step explanation:

P.S - The exact question is -

Given - A large restaurant chain is curious what proportion of their

            customers in a given day are new customers. They  are thinking  

            of taking a sample of either n = 50 or nº= 100 customers and

            building a one-sample z interval for  a proportion using the data

            from the sample.

To find - The margin of error from the smaller sample will be 2 times

               the margin of error from the larger sample.

Proof -

We know that

E ∝ \(\frac{1}{\sqrt{n} }\)

For smaller margin, E₁ = \(\frac{1}{\sqrt{50} }\)

For larger margin , E₂ = \(\frac{1}{\sqrt{100} }\)

Now,

\(\frac{E_{1} }{E_{2} } = \frac{\sqrt{100} }{\sqrt{50} } = \sqrt{\frac{100}{50} } = \sqrt{2}\\\)

⇒E₁ = \(\sqrt{2}\) E₂

⇒The margin of error from the smaller sample will be \(\sqrt{2}\)  times the margin of error from the larger sample.

So,

It is a false statement.

A large restaurant chain is curious what proportion of their customers in a given day are new customers.

Your friend was bored one day and started making patterns using Cheerios from a new box he had opened. He laid the Cheerios on the table as such:
Based on the two images above and the information about the box, answer the following questions.
A) Identify and label the variable
B) Make a table for up to 8-figure patterns
C) Write an equation to represent the nth term of the sequence.
D) If the pattern continues, what figure number will have 20 whole Cheerios in it?
E) Is it reasonable to think this pattern would continue forever? If not, explain.
F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

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Your friend was bored one day and started making patterns using Cheerios from a new box he had opened.
Your friend was bored one day and started making patterns using Cheerios from a new box he had opened.
Your friend was bored one day and started making patterns using Cheerios from a new box he had opened.

Answers

A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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