in the school cafeteria 6 people can sit together at 1 table. if 2 tables are placed together end to end in a row 10 people can sit together. if 3 tables are placed together in a row how many can be seated? if 4 tables are placed together in a row how many people can be seated? if 5 tables are placed together in a row how many people can be seated? what patterns do you notice?
write an equation that would help find the number of people seated for any number of tables. show all your mathematical thinking giving 40 points and brainliest plss helpp

We will consider two cases: n is even and n is odd. In this step, you will complete the proof of the first case. Proof. Case 1: n is even Let n be an even integer. By the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`

Since is an integer, `n^3+17n + 1` must be an integer. Since `na +17n – 1` equals times an integer plus `n+ 17n – 1` is 2The solution explains the concept of even integer. Let n be an even integer, and by the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`.Since 2k is an integer, n^3 + 17n + 1 must also be an integer. This is because even times even is even and even times odd is even, which means that (2k + 1) is always odd. The integer n^3 can be written as (n*n*n). Given that n is an even integer, it follows that n*n is even. And since an even number times an even number is always even, it follows that (n*n*n) is even. Since the sum of an even number and an odd number is always odd, adding 1 to n^3 + 17n gives an odd number, and thus an integer, as desired. The equality `na +17n – 1 = 2` is not needed in this proof.

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Answer:

34

Step-by-step explanation:

1/2 multiplied by 68=34

34 is 1 half of 68 .

Here, we have,

given that,

what is 1 half of 68

we know that,

Half of a number can be found by dividing the number by 2.

i.e. we have to find half of 68,

for that, we need to divide 68 by 2

so, we get,

To find half of 68:

68 / 2 = 34

Therefore, half of 68 is 34.

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The conclude that the Y1 and Y2 are not independent.

The joint probability density function for the random variables Y1 and Y2 for a mixture of insecticide isf(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhereTo verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Therefore, we need to find the marginal density functions of Y1 and Y2.Probability Density Function:We know that for a given joint probability density function, the probability density function of Y1 is given by integrating over all possible values of Y2, and vice versa.Mathematically,P(Y1)=∫0∫1f(y1,y2)dy2... (1)P(Y2)=∫0∫1f(y1,y2)dy1... (2)Using equation (1) to calculate P(Y1), we get,  P(Y1)=∫0∫1f(y1,y2)dy2=∫0∫1(2)dy2=2... (3)Similarly, we can use equation (2) to calculate P(Y2) as follows:P(Y2)=∫0∫1f(y1,y2)dy1=∫0∫1(2)dy1=2... (4)Product of marginal density functions:Now we can find the product of marginal density functions as follows:P(Y1)P(Y2)=2×2=4... (5)Thus, to verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Since 2 ≠ 4, Y1 and Y2 are not independent. Hence, we can conclude that the Y1 and Y2 are not independent.

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Answer:

D

Step-by-step explanation:

First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.

Hope this helps.

Answer:

In the example given, 5my × 5ym, you can simplify it using the commutative property of multiplication as follows:

5my × 5ym = 5 × 5 × m × m × y × y

= 25m²y²

So, the answer is 25m²y².

Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

Step-by-step explanation:

Answer:2.4 inches

Step-by-step explanation:

if 6 is for 30 feet, we can use a proportional statement to find what the length of the line will be for a room that is 12 feet.

Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).

In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:

final amount = 5.00 - 5.00 - (5.00 * 0.045)

final amount = 5.00 - 5.00 - 0.225

final amount = 4.775

Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.

(x, y) = (0,0) is the solution of the system of equations.

Simultaneous equations are a set of two or more equations that contain multiple variables, which must be solved at the same time. The solution to the system of equations is the set of values of the variables that satisfy all of the equations in the system simultaneously.

4x - y = 3x + y

4x + 3y = x + 6y

Simplifying the first equation by moving all the y-terms to the left-hand side and all the x-terms to the right-hand side, we get:

4x - 3x = y + y

x = 2y

Substituting this value of x into the second equation, we get:

4(2y) + 3y = (2y) + 6y

8y + 3y = 8y

11y = 0

y = 0

Substituting y = 0 into the equation x = 2y, we get:

x = 2(0)

x = 0

Therefore, the solution to the system of equations is:

x = 0 and y = 0

Hence, (x, y) = (0,0) is the solution of the system of equations.

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Based on the picture, we can use the Pythagorean theorem to find MBC. Therefore, MBC is equal to  [tex]7[/tex]√2.

Theorem of Linear Pairs Two angles are supplementary if they create a linear pair. Additional theorem, Two angles are congruent if they are supplements of the same angle.

Theorem of congruent complements an of thes., but it will be the first of a series of events that will result in a new set of rules and the.

First, we can find AB:

AB = √(AD² + BD²)

= √ [tex](3^2 + 4^2)[/tex]

= √[tex](9 + 16)[/tex]

= √ [tex]25[/tex]

[tex]= 5[/tex]

Next, we can find AC:

AC = √(AD² + CD²)

= √[tex](3^2 + 8^2)[/tex]

= √ [tex](9 + 64)[/tex]

= √[tex]73[/tex]

Finally, we can find BC:

[tex]BC = √(AB^2 + AC^2)[/tex]

= √(5² + (√73)²)

= √(25 + 73)

= √98

= 7√2

Therefore, m Bc is = 7√2

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a. The joint distribution of the numbers of black, white, and red balls in the sample is given by P(x, y, z) = nCx * nCy * nCz / (p + q + r)Cn, where x is the number of black balls, y is the number of white balls, z is the number of red balls, and n is the total number of balls chosen.

b. The joint distribution of the numbers of black and white balls in the sample is given by P(x, y) = nCx * nCy / (p + q)Cn, where x is the number of black balls, y is the number of white balls, and n is the total number of balls chosen.

c. The marginal distribution of the number of white balls in the sample is given by P(y) = nCy / qCn, where y is the number of white balls, and n is the total number of balls chosen.

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The answer of the given factor and multiplication term for the positive integers are 3.

Positive, negative, and zero digit whole numbers are all included in the category of integers. They can be stated without any fractional or decimal components and are a subset of the real numbers. On a number line, integers can be visualized as positive numbers to the right of zero and negative numbers to the left.

In mathematics, a multiplication term is a mathematical expression that involves the multiplication of two or more factors. The factors can be numbers, variables, or a combination of both. Multiplication terms are commonly represented using the multiplication symbol "×" or the dot "." symbol.

For example, in the expression 2x × 3y, the multiplication term is 2x × 3y, which involves the multiplication of the factors 2x and 3y.

If you want to find the smallest possible value of the given term we have that,The smallest factor of 15 is 1.

The smallest multiple of 3 is 3so, the smallest answer is 1x3 = 3.

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Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.

The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.

The ratio of seniors bringing a bag lunch= 78/104 or 0.75,

while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.

This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.

Further, the difference between the proportions is

0.75-0.65 = 0.1,

which is a large enough difference to be considered significant.

The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.

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0.05723 is 0.05223 greater than 0.005.

"Greater than" is a comparison term used to indicate that one quantity or value is larger or more than another quantity or value. It is represented mathematically by the symbol ">".

"Lesser than" is a comparison term used to indicate that one quantity or value is smaller or less than another quantity or value. It is represented mathematically by the symbol "<".

In the given question,

To find out how much greater 0.05723 is than 0.005, we can subtract 0.005 from 0.05723:0.05723 - 0.005 = 0.05223

Therefore, 0.05723 is 0.05223 greater than 0.005.

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Answer: 100:3

Step-by-step explanation:

Answer:

the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.

Step-by-step explanation:

The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.

The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.

To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.

So the ratio can be expressed as:

2,250/75,000

To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:

2,250/75,000 = 3/100

Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Stefanie bought total 10 erasers.

Equation:

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal.

According to the Question:

The number of erasers bought by Stefanie:

Let we denote the number of erasers bought by her by x (an unknown variable)

Then we will have:

Total amount before tax = cost of one package of pencil + cost of  erasers

   $4.25 = $1.75 + X × $0.25

⇒ 4.25 = 1.75 + 0.25x

Now,

we will perform subtraction by 1.75 and division by 0.25 on both sides.

4.25 = 1.75 + 0.25x

Subtracting 1.75 both side:

   4.25 -1.75 = 0.25x

⇒ 2.5 = 0.25x

Dividing by 0.25 on both sides:

   2.5/0.25 = 0.25x/0.25

⇒ x = 10

Thus, Stefanie bought total 10 erasers.

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The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.

The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.

z + 3x4 = 15 + 3x4

= 15 + 12

= 27

Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).

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____The given question is incomplete , the complete question is given below:

Evaluate the expression, where z = 15

z + 3x4

A. 27

B. 32

C. 56

D. 1,304

Answer:

Step-by-step explanation:

Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:

999n = 727272

To solve for "n", we divide both sides by 999:

n = 727272/999

Using a calculator or long division, we get:

n ≈ 728.56

Therefore, each pizza has approximately 728 slices.

The volume of pyramid is 3.5 cm³.

To find the volume of a pyramid with a square base, where the area of the base is 4.6 cm² and the height of the pyramid is 2.3 cm, we can use the following formula:

V = (1/3)B*h

Where V is the volume of the pyramid, B is the area of the base, and h is the height of the pyramid. Substitute the given values into the formula and solve:

V = (1/3)(4.6)(2.3)V = 3.53 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is 3.5 cm³. Therefore, the volume of pyramid is 3.5 cm³.

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The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a p-value of 1-∝.

So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]

Now, find M as such

[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ

In which is the standard deviation of the population and n is the size of the sample.

[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.

The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.

So the correct answer is:

(91331.94, 113352.06)

Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.

Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.

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Complete Question:

A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices

A). (89869.82, 114814.18)

B). (90292.73, 114391.27)

C). (91331.94, 113352.06)

D). (90371.37, 114312.63)

The final value in cell D2 using the following formula:

price - price× discount = $ 101.19

Take the original price. Multiply that by the discount percentage and divide the result by 100. Subtract the result from the original price. this is your final price

According to the Question:

The final value in cell D2 using the following formula:

(price - price) × discount.

Given that:

Price = $114.99

Discount = 12%

By the above formula:

(price - price) × discount.

= ($114.99 - $114.99) × 12%

= $101.19

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Answer:

Area: 391.92 ft²

Perimeter: 84.4 ft

Step-by-step explanation:

Area of rectangle = L × W

We Take

13.8 × 28.4 = 391.92 ft²

Find the Perimeter of the Rectangle

We Take

28.4 + 13.8 + 28.4 + 13.8 = 84.4 ft

So, Area: 391.92 ft²

     Perimeter: 84.4 ft

Answer:

Area = 391.92 square feet

Perimeter = 84.4 feet

Step-by-step explanation:

The area of a rectangle is the product of its width and length.

The perimeter of a rectangle is twice the sum of its width and length.

Given the width of the rectangle is 28.4 feet and its length is 13.8 feet:

[tex]\begin{aligned}\textsf{Area of the rectangle}&=\sf width \times length\\&=28.4 \times 13.8\\&=391.92 \sf \;\;square\;feet\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=\sf 2(width +length)\\&=2(28.4 +13.8)\\&=2(42.2)\\&=84.4 \sf \;\;feet\end{aligned}[/tex]

Answer:

Were sorry! Answer is not available right now check in later.

Step-by-step explanation:

Answer: 2540

Step-by-step explanation: 1350-80=1270. 1270/0.5=2540

Answer:

y-intercept is (0,3) and the slope is 3

Step-by-step explanation:

Answer: the slope is 3x while 3 is the y-intercept.

Step-by-step explanation:

Answer:

Perpendicular.

Step-by-step explanation:

To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form

y = 2/3x - 4 ==> slope = 2/3

y = -3/2x - 7 ==> slope = -3/2

Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1

(2/3) * (-3/2) = -1

Since the product of the slopes is -1, the two lines are perpendicular.

Therefore, the answer is: perpendicular.

If an access code for a car's security system consist of six digits and the  first digit cannot be zero and the last digit must be even, then the number of different codes available are 4,500,000

Since the first digit cannot be zero, we have 9 choices for the first digit. For each of these 9 choices, there are 10 possibilities for the second digit (0-9).

Similarly, there are 10 possibilities for the third digit, 10 for the fourth digit, 10 for the fifth digit, and 5 (0, 2, 4, 6, 8) for the last digit.

Therefore, the total number of possible access codes is:

9 x 10 x 10 x 10 x 10 x 5 = 4,500,000

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In conclusion  the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.  The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Why it is?

The expression for how much money Elena saves after selling p pens is:

Total money saved = 5 + (1.5)p

The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Solving the equation:

5 + (1.5)p = 20

(1.5)p = 15

p = 10

We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.

If Elena wants to have some money left over, we can write the inequality:

5 + (1.5)p > 20

Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.

To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:

5 + (1.5)p > 20

(1.5)p > 15

p > 10

Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.

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