Find the 54th term of the arithmetic sequence —2,-8,-14, ...

Answers

Answer 1

Answer:

-320

Step-by-step explanation:

You would first create an explicit formula for the provided sequence.

The basic explicit formula for arithmetic sequences is , \(a_{n} = d(n-1) + a_{1}\)where an is the number of the term, d is the number you are adding or subtracting by, n the location of the term, and a1 is the first number.

We would then substitute the values given.

We are trying to solve the value of the 54th term. This makes n = 54. The first number of the sequence is -2, so a1 is -2. Finally, d is -6 because we are subtracting 6 to each number in the sequence.

Therefore, our resulting equation would be\(a_{n} =-6(54-1)-2\) , which equals -320.

Answer 2

Answer:

-320.

Step-by-step explanation:

n54 = a1 + d(54 - 1)

Here a1 = -2 and d = -8 - (-2) = -6.

So 54th term = -2 + -6*53

= -320.


Related Questions

Question 6 of 10
Which of the following is most likely the next step in the series?
A.
B.
C.
D.

Answers

If the series is A B C D then the next one is E

find the surface area ​

find the surface area

Answers

Answer:

70 inches²

Step-by-step explanation:

We can break this shape up into 5 different shapes.

Two triangles, and three rectangles.

The three rectangles will be A = L * W and are all the same size,

A = L * W

A = 3(L * W)

A = 3(10 * 2)

A = 3(20)

A = 30 inches²

Now, we need to find the area for the two triangles. Usually, you would take the base times the height and divide by two, but since we have two triangles of the same size we do not need to divide by two,

A = B * H

A = 10 * 4

A = 40 inches²

Last, we will add the two areas for the triangles and rectangles together,

40 inches² + 30 inches² = 70 inches²

how does hermite interpolation differ from ordinary interpolation? how does a cubic spline interpolant differ from a hermite cubic interpolant?

Answers

it does not use the additional information provided by the second derivative to ensure continuity between the interpolating polynomials, which can result in a less smooth interpolant than a cubic spline.

Hermite interpolation and ordinary interpolation are both methods used to find an approximation of a function based on a given set of data points. However, they differ in the way they approach the problem.

In ordinary interpolation, a unique polynomial of degree n-1 (where n is the number of data points) is constructed that passes through all the given data points. The polynomial is then used to approximate the function between the data points. The drawback of ordinary interpolation is that it can result in a very oscillatory or wiggly interpolant, especially when the data points are unequally spaced.

On the other hand, Hermite interpolation constructs a polynomial of degree 2n-1 that not only passes through all the given data points but also includes the values of the first n-1 derivatives at each data point. This additional information allows Hermite interpolation to produce a smoother interpolant that more accurately represents the behavior of the function.

A cubic spline interpolant is a type of piecewise interpolation where a polynomial of degree 3 is used to approximate the function between each adjacent pair of data points. The splines are connected at the data points such that the function and its first and second derivatives are continuous across the entire range of data points.

In contrast, a Hermite cubic interpolant constructs a single polynomial of degree 3 that passes through all the given data points and includes the values of the first derivative at each data point. Therefore, it does not use the additional information provided by the second derivative to ensure continuity between the interpolating polynomials, which can result in a less smooth interpolant than a cubic spline.

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Let the long-run profit function for a representative firm is given by π i

=p 2
−2p−399, where p is the price of computer. The inverse market demand for computer is given by p=39−0.009q, where q is unit of computers. Suppose technology for producing computers is identical for all firms and all firms face identical input prices. (a) Find the firm's output supply function. (b) Find the market-equilibrium price and the equilibrium number of firms. (c) Find the number of computers sold by each firm in the long run.

Answers

(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

To find the firm's output supply function, we need to maximize the firm's profit function, which is given by π = p^2 - 2p - 399. In the long run, firms will produce where marginal cost equals marginal revenue. Marginal revenue can be obtained by differentiating the inverse market demand function with respect to q, and marginal cost is equal to the derivative of the profit function with respect to q. Equating the two, we get:

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

To find the market-equilibrium price and the equilibrium number of firms, we need to find the intersection point of the market demand and supply. Substituting the output supply function into the inverse market demand function, we have:

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

Since each firm sells 70 computers in the long run, and there are 10 firms, the total number of computers sold by each firm is:

70 * 10 = 700

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Find the diameter and circumference

6.2 mi

PLS HELP I NEED AN ANSWER PLS

Find the diameter and circumference 6.2 mi PLS HELP I NEED AN ANSWER PLS

Answers

Answer:

diameter: 2.4 mi

circumference = 38.96 mi

Step-by-step explanation:

d=2r=2·6.2=12.4

C=2πr=2·π·6.2≈38.95575

how do i write a composition of transformations that maps a polygon onto another polygon that are congruent

Answers

Answer:A conductor is mapping a trip and records the distance the train travels over certain time intervals. time (hours) Distance (miles) 0.5 22.5 1 45 1.5 67.545 The train travels at a constant speed. What is its speed in miles per hour?

Step-by-step explanation:

do not uses this site i got all my answers wrong going here

#1 Shane bought 4 shirts for $17 and 4 pants. He spent a total of $71.
How much did each pant cost?


#2 Julie has 4 more apples than Sam. Julie and Sam have a total of 30
apples. Find the number of apples Julie has


Help me out please

Answers

Each pant cost $13.50 because 71-17=54 and 54/4=13.5. Julie has 17 apples.

Solve: 7×-4=-8×+8
hurry!​

Answers

The answer to your question is X=4/5




Answer:

x = 4/5

FILLER FILLER FILLER

Applied (Word) Problems NoteSheet
Consecutive Integers
Consecutive numbers (or more properly, consecutive integers) are integers nrand ngsuch that
/h - nl = I, i.e., IJlfollows immediately after 17,.
Given two consecutive numbers, one must be even and one must be odd. Since the sum of an
even number and an odd number is always odd, the sum of two consecutive numbers (and, in
fact, of any number of consecutive numbers) is always odd.
Consecutive integers are integers that follow each other in order. They have a difference of 1
between every two numbers.
If n is an integer, then n, n+1, and n+2 wi II be consecutive integers.
Examples:
1,2,3,4,5
-3,-2,-1,0,1,2
1004, 1005, 1006

Answers

The concept of consecutive integers is explained as follows:

Consecutive numbers, or consecutive integers, are integers that follow each other in order. The difference between any two consecutive numbers is always 1. For example, the consecutive numbers starting from 1 would be 1, 2, 3, 4, 5, and so on. Similarly, the consecutive numbers starting from -3 would be -3, -2, -1, 0, 1, 2, and so on.

It is important to note that if we have a consecutive sequence of integers, one number will be even, and the next number will be odd. This is because the parity (evenness or oddness) alternates as we move through consecutive integers.

Furthermore, the sum of two consecutive numbers (and, in fact, the sum of any number of consecutive numbers) is always an odd number. This is because when we add an even number to an odd number, the result is always an odd number.

To generate a sequence of consecutive integers, we can start with any integer n and then use n, n+1, n+2, and so on to obtain consecutive integers. For example, if n is an integer, then n, n+1, and n+2 will be consecutive integers.

Here are some examples of consecutive integers:

- Starting from 1: 1, 2, 3, 4, 5, ...

- Starting from -3: -3, -2, -1, 0, 1, 2, ...

- Starting from 1004: 1004, 1005, 1006, 1007, ...

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Find the measure of the indicator arc

Find the measure of the indicator arc

Answers

Answer:

m(WXY) = 224°

Step-by-step explanation:

Measure of inscribed angle = ½ the measure of intercepted arc

Therefore:

m<C = ½*m(WXY)

112° = ½*m(WXY) (substitution)

Multiply both sides by 2

2*112° = m(WXY)

224° = m(WXY)

m(WXY) = 224°

f(x) = x^2 - 3x+ 5 g(x) = 2x^2 - 4x - 11 what is h(x) = f(x) + g(x)

Answers

Hey there! :)

Answer:

h(x) = 3x² - 7x - 6

Step-by-step explanation:

Calculate h(x) by adding the two polynomials:

h(x) = f(x) + g(x):

h(x) = x² - 3x + 5 + 2x² - 4x - 11

Combine like terms:

h(x) = 3x² - 7x - 6

Answer:

\(\huge\boxed{(f+g)(x)=3x^2-7x-6}\)

Step-by-step explanation:

\(f(x)=x^2-3x+5\\\\g(x)=2x^2-4x-11\\\\(f+g)(x)=f(x)+g(x)\\\\\text{substitute}\\\\(f+g)(x)=(x^2-3x+5)+(2x^2-4x-11)\\\\(f+g)(x)=x^2-3x+5+2x^2-4x-11\\\\\text{combine like terms}\\\\(f+g)(x)=(x^2+2x^2)+(-3x-4x)+(5-11)\\\\(f+g)(x)=3x^2-7x-6\)

In two weeks, your class collected more than 380 cans of food for the annual food drive. In the first week, 145 cans were collected. How many cans c of food were collected in the second week? Write and solve an inequality.


145 + c < 380; c < 235


c + 145 > 380; c > 525


c − 145 ≥ 380; c ≥ 525


145 + c > 380; c > 235

Answers

Answer:

Step-by-step explanation:

145+c>380 subtract 145 from each side

c>235 so the answer is

145+c>380; c>235

B = P + Prz solve for r

Answers

Answer:

(B-P) / Pz  = r

Step-by-step explanation:

B = P + Prz

Subtract P from each side

B-P = P -PPrz

B-P = Prz

Divide each side by Pz

(B-P) / Pr  = Prz/Pz

(B-P) / Pz  = r

Helen has a set of number cards numbered 1 thru 10. If Helena randomly draws two cards from the deck, what is the probability that she will draw an even number and then a five?

A. 6/10
B. 5/10
C. 1/9
D. 5/90

Answers

It’s B because it is

pls help asap if you can!!!

pls help asap if you can!!!

Answers

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

How to determine the statement

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Same-Side interior angles (consecutive angles) are supplementary. Each diagonal of a parallelogram separates it into two congruent triangles.The diagonals of a parallelogram bisect each other.

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Find the number of standard deviations from the mean. Round your answer to two decimal places. Mario's weekly poker winnings have a mean of $353 and a standard deviation of $67. Last week he won $185. How many standard deviations from the mean is that?

1.25 standard deviations below the mean
1.25 standard deviations above the mean
2.51 standard deviations below the mean
2.51 standard deviations above the mean

Answers

The answer is: 2.51 standard deviations below the mean. Therefore, the long answer is: Mario's winnings last week equation were 2.51 standard deviations below the mean of his weekly poker winnings, which have a mean of $353 and a standard deviation of $67.

To find the number of standard deviations from the mean, we need to use the formula:
z = (x - μ) / σ
where z is the number of standard deviations, x is the observed value, μ is the mean, and σ is the standard deviation.
In this case, x = 185, μ = 353, and σ = 67. Substituting these values into the formula, we get:
z = (185 - 353) / 67
z = -2.51


This means that Mario's winnings last week were 2.51 standard deviations below the mean.
Your question is: How many standard deviations from the mean is Mario's last week winnings of $185, given a mean of $353 and a standard deviation of $67.
To find the number of standard deviations from the mean, you need to use the following formula:
(Number of standard deviations) = (Value - Mean) / Standard deviation
So, Mario's last week winnings of $185 are 2.51 standard deviations below the mean.

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What are the Examples of Adding Fractions with Unlike Denominators

Answers

2/3 + 1/4 = 11/12

Fractions are very important in many areas such as math, physics, engineering, chemistry and many more, understanding how to add fractions with unlike denominators is a fundamental skill that will help you in many aspects of your life.

Adding fractions with unlike denominators can be a bit tricky, but with the right understanding and techniques, it's definitely doable.

When we add fractions with unlike denominators, we need to first find a common denominator. A common denominator is a number that is a multiple of both denominators. Once we have a common denominator, we can add the fractions as usual by adding the numerators and keeping the denominator the same.

Here are a few examples of adding fractions with unlike denominators:

2/3 + 1/4

We can find a common denominator by finding the least common multiple (LCM) of 3 and 4. The LCM of 3 and 4 is 12.

So, we can convert 2/3 to 8/12 by multiplying the numerator and denominator by 4.

We can convert 1/4 to 3/12 by multiplying the numerator and denominator by 3.

Now we can add the fractions by adding the numerators: 8/12 + 3/12 =

1/5 + 2/7

We can find a common denominator by finding the least common multiple (LCM) of 5 and 7. The LCM of 5 and 7 is 35.

So, we can convert 1/5 to 7/35 by multiplying the numerator and denominator by 7.

We can convert 2/7 to 10/35 by multiplying the numerator and denominator by 5.

So, we can convert 3/4 to 9/12 by multiplying the numerator and denominator by 3.

We can convert 1/3 to 4/12 by multiplying the numerator and denominator by 4.

Now we can add the fractions by adding the numerators: 9/12 + 4/12 = 13/12

So, 3/4 + 1/3 = 13/12

It's important to note that when adding fractions, it's also important to simplify the final result if possible.

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find the x and y intercepts of the graph -6x + 4y = 32 state your answers as while numbers or as improper fractions in simplest form

Answers

Answer:

x intercept = -5.33

y intercept = 8

Step-by-step explanation:

The given equation is ,

⇒ -6x + 4y = 32 ,

The standard form of the Intercept form is ,

⇒ x/a + y/b = 1 , where

a is x interceptb is y intercept .

• Converting the equation :-

⇒ 2( -3x + 2y ) = 32

⇒ -3x + 2y = 16

⇒ -3x + 2y / 16 = 1

⇒ (-3x)/16 + 2y/16 = 1

⇒ -3x/16 + y/8 = 1

Convert -3x/16 in x/a form

⇒ x/-5.33 + y/8 = 1 .

Therefore ,

x intercept = -5.33 y intercept = 8
find the x and y intercepts of the graph -6x + 4y = 32 state your answers as while numbers or as improper

thirty students at eastside high school took the sat on the same saturday. their raw scores are given next. 1,450 1,620 1,800 1,740 1,650 1,710 1,900 1,910 1,950 1,820 1,800 2,010 1,780 1,840 1,490 1,590 2,350 2,260 1,870 1,530 1,620 1,480 2,390 1,640 1,830 1,950 2,000 1,830 1,980 2,100 picture click here for the excel data file consider a frequency distribution of the data that groups the data in classes of 1,400 up to 1,600, 1,600 up to 1,800, 1,800 up to 2,000, and so on. how many students scored at least 1,800 but less than 2,000?

Answers

The frequency of scores falling into this interval is 11. Therefore, 11 students scored at least 1,800 but less than 2,000.

A frequency distribution is a way to organize and present data by grouping it into intervals or classes and showing how many observations fall into each interval.

In this case, the data given represents the raw scores of thirty students who took the SAT on the same Saturday.

To create a frequency distribution, we can group the data into classes of 1,400 up to 1,600, 1,600 up to 1,800, 1,800 up to 2,000, and so on.

To create this frequency distribution, we can use the Excel data file provided and create a histogram. The histogram will show the frequency of scores falling into each class or interval.

The interval 1,800 up to 2,000 will contain the scores 1,800, 1,810, 1,820, 1,830, 1,840, 1,870, 1,900, 1,910, 1,950, 1,950, 1,980, and 2,000.

To find how many students scored at least 1,800 but less than 2,000, we need to add up the frequencies in this interval.


In conclusion, creating a frequency distribution helps to organize and summarize data. By grouping the data into intervals or classes, we can better understand the distribution of the data and answer questions related to it.

In this case, we were able to determine how many students scored at least 1,800 but less than 2,000 by using the frequency distribution created.

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Melanie and noah are baking a birthday cake for franceca. The recipe call for 3/4 meauring cup and noah ha a 1/8 meauring cup. Which cup hould they ue

Answers

They should use 6 cup of Noah's measuring cup

What are algebraic operations?

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Recipe call = 3/4Noah's cup = 1/8Number of cup = ?

Calculating the number of cup the should use:

Number of cup = Recipe call / Noah's cup

Number of cup = (3/4) / (1/8)

Number of cup = 3*8 / 4*1

Number of cup = 24/4

Number of cup = 6

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Correctly written question:

Melanie and Noah are baking a birthday cake for Francesca. The recipe call for 3/4 measuring cup and Noah has a 1/8 measuring cup. Which cup should they use?

Urgent What is the image of (-8,2) after a reflection over the y-axis?

Answers

Answer:

(8, 2 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 8, 2 ) → (8, 2 )

Answer:

the answer is (8,2)

Step-by-step explanation:

hope it helps

Cory has only dimes in his piggy bank. A dime is worth 10 cents. Which could be the value of the money in Cory's piggy bank?

Answers

Answer:

It depends on how many dimes are in the piggy bank. It could be any answer that didn't have a 5 in the tenths place. For example, it couldn't be a number like $1.05 because any whole number multiplied by 10 would end in a 0

a witness to a hit-and-run accident tells the police that the license plate of the car in the accident, which contains three letters followed by three digits, starts with the letters as and contains both the digits 1 and 2. how many different license plates can fit this description?

Answers

There are 140 different license plates that can fit the description provided by the witness of a hit-and-run accident. There are 1,689,660 different license plates that can fit the given description.

To find the number of different license plates that match the given description, we need to consider the available options for each position in the license plate.

The first position is fixed with the letters "as". Since there are no restrictions on these letters, they can be any two letters of the alphabet, resulting in 26 × 26 = 676 possible combinations.

The second position can be filled with any letter of the alphabet except "s" (since it is already used in the first position). This gives us 26 - 1 = 25 options.

Similarly, the third position can also have 25 options, as we need to exclude the letter "s" and the letter used in the second position.

For the fourth position (the first digit), there are 10 options (0-9).

The fifth position can be either 1 or 2, giving us 2 options.

Finally, the sixth position (the second digit) can also be filled with any of the remaining 10 options.

To find the total number of combinations, we multiply the options for each position: 676 × 25 × 25 × 10 × 2 × 10 = 1,690,000.

However, we need to exclude the cases where the digits 1 and 2 are not present together. So, we subtract the cases where the first digit is not 1 or 2 (8 options) and the cases where the second digit is not 1 or 2 (9 options): 1,690,000 - (8 × 2 × 10) - (10 × 9 × 2) = 1,690,000 - 160 - 180 = 1,689,660.

Therefore, there are 1,689,660 different license plates that can fit the given description.

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Could someone help me find the length of each segment and which statements are true?

Could someone help me find the length of each segment and which statements are true?

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true

Simplify (−7b)(−16b).
112b
−112b
112b^2
−112b^2

Answers

Answer:

112b^2

Step-by-step explanation:

When you multiply two negative numbers, the outcome will always become positive.

7bx16b= 112b^2

Answer:

112b^2

Step-by-step explanation:

1. What is the role of humans/technology in the introduction of invasive species?

Answers

Answer:

Invasive species are primarily spread by human activities, often unintentionally. People, and the goods we use, travel around the world very quickly, and they often carry uninvited species with them. Ships can carry aquatic organisms in their ballast water, while smaller boats may carry them on their propellers.

Step-by-step explanation: hope i helped mark brainlist plz

The stochastic variables X and Y describe the outcome of two tosses with a dice. Let Z =X+Y be the sum of the results. How do you calculate P (X|Z=z) (probability of X given Z) and P (Z|X=x) probability of Z given X?

Answers

To calculate the probability of X given Z (P(X|Z=z)), you can use Bayes' theorem. Bayes' theorem states:

P(X|Z=z) = (P(Z=z|X) * P(X)) / P(Z=z)

Here's how you can calculate P(X|Z=z) step by step:

1. Calculate P(Z=z): This is the probability of the sum of the results being z. To calculate this, you would need to consider all possible combinations of X and Y that result in Z=z and sum up their probabilities. Since X and Y are outcomes of a fair dice toss, each has a probability of 1/6. For example, if z=7, the possible combinations are (X=1, Y=6), (X=2, Y=5), (X=3, Y=4), (X=4, Y=3), (X=5, Y=2), and (X=6, Y=1). Summing up their probabilities, P(Z=7) = (1/6) * (1/6) + (1/6) * (1/6) + (1/6) * (1/6) + (1/6) * (1/6) + (1/6) * (1/6) + (1/6) * (1/6) = 1/6.

2. Calculate P(Z=z|X): This is the probability of Z being z given that X takes a particular value. Since the outcomes of Y are independent of X, P(Z=z|X) would be the same as the probability of Y being z-X. For example, if x=3, then P(Z=7|X=3) would be the same as the probability of Y being 7-3=4. Since Y is also a fair dice toss, the probability would be 1/6.

3. Calculate P(X): This is the probability of X taking a particular value. Since X is the outcome of a fair dice toss, each value has a probability of 1/6.

Plug in the calculated values into Bayes' theorem:

P(X|Z=z) = (P(Z=z|X) * P(X)) / P(Z=z)

P(X|Z=z) = (1/6 * 1/6) / (1/6)

Simplifying, P(X|Z=z) = 1/6

Therefore, for any value of z, the probability of X taking any specific value is 1/6.

To calculate the probability of Z given X (P(Z|X=x)), you can use the fact that X and Y are independent tosses. In this case, since X=x is known, the probability of Z being z is simply the probability of Y being z-x. Since Y is also a fair dice toss, each value has a probability of 1/6. Therefore, P(Z|X=x) = 1/6 for any value of z.

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a group of 268 students are surveyed about their ability to speak mandarin, korean, and japanese. there are 37 students who do not speak any of the three languages surveyed. mandarin is spoken by 174 of the students, japanese is spoken by 139 of the students, and korean is spoken by 112 of the students. the survey results also reflect that 102 students speak both mandarin and japanese, 81 students speak both mandarin and korean, and 71 students speak both japanese and korean. how many students speak all three languages?

Answers

There are 99 students who speak all three languages: Mandarin, Japanese, and Korean. The minimum number of students who speak all three languages is 99.

The method used to solve this problem is based on set theory, which is a branch of mathematics that deals with the study of sets, their properties, and their relationships with one another. Specifically, the principle of inclusion-exclusion, which is used in this problem, is a counting technique that is often used in combinatorics and probability theory, which are also branches of mathematics.

Let X be the number of students who speak all three languages.

Then we have:

Number of students who speak only Mandarin = 174 - 102 - 81 - X = -9 - X (since there cannot be a negative number of students)

Number of students who speak only Japanese = 139 - 102 - 71 - X = -34 - X (since there cannot be a negative number of students)

Number of students who speak only Korean = 112 - 81 - 71 - X = -40 - X (since there cannot be a negative number of students)

Number of students who speak only one language = -9 - X + (-34 - X) + (-40 - X) = -83 - 3X (since there cannot be a negative number of students)

Total number of students who speak at least one language = 268 - 37 = 231

Therefore, the number of students who speak all three languages is:

Total number of students who speak at least one language - Number of students who speak only one language - Number of students who do not speak any of the three languages

= 231 - (-83 - 3X) - 37

= 297 + 3X

Since the number of students who speak all three languages cannot be negative, we have:

297 + 3X ≥ 0

3X ≥ -297

X ≥ -99

Therefore, the minimum number of students who speak all three languages is 99.

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Find the area of trapezium whose parallel side are 10 and 12 cm. And height is 7 cm

Answers

Answer:

77 cm²

Step-by-step explanation:

We know that

Area of trapezium = ½ (a + b) × h

Area = ½ × (10 + 12) × 7

Area = ½ × 22 × 7

Area = 11 × 7

Area = 77 cm²

Given :

Length of parallel sides = 10 cm and 12 cm

Height = 7 cm

What To Find :

Area of trapezium

Formula Using :

\(\begin{gathered} {\underline{\boxed{ \rm {\red{Area \: of \: trapezium \: = \: \frac{1}{2} \: \times \: (a \: + \: b) \: \times \:Height }}}}}\end{gathered}\)

Where ,

a and b is Parallel sides

Solution :

\( \begin{cases} \large\bf\purple{ \implies} \rm \:Area \: of \: trapezium \: = \: \frac{1}{2} \: \times \: (10 \: + \: 12) \: \times \:7 \\ \\ \large\bf\purple{ \implies} \rm \:Area \: of \: trapezium \: = \: \frac{1}{2} \: \times \: 22\: \times \:7 \\ \\ \large\bf\purple{ \implies} \rm \:Area \: of \: trapezium \: = \: \frac{1}{ \cancel2} \: \times \: \cancel{22} \: ^{11} \: \times \:7 \\ \\ \large\bf\purple{ \implies} \rm \:Area \: of \: trapezium \: = \:11 \: \times \: 7 \\ \\ \large\bf\purple{ \implies} \rm \:Area \: of \: trapezium \: = \:77 \: {cm}^{2} \end{cases}\)

Look at the image below. Identify the coordinates for point X, so that the ratio of AX : XB = 5 : 4

Answers

The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

How to determine the coordinates of point X?

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Look at the image below. Identify the coordinates for point X, so that the ratio of AX : XB = 5 : 4
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