The sum of the first and second terms of an AP is 4 the tenth term is 19 find the sum of the fifth and sixth terms

Answer:   18<204>18

Step-by-step explanation:

Truncation error for s4 = Sum of the infinite series - s4 = 3 - 0.2187 ≈ 2.7813

The value of s4, which represents the sum of the series with the given expression, is approximately 0.2187. To calculate this, we substitute n = 4 into the expression and perform the necessary calculations.

On the other hand, if the sum of the infinite series is given as 3, we can determine the truncation error for s4. The truncation error is the difference between the sum of the infinite series and the partial sum s4. In this case, the truncation error is approximately 2.7813.

The truncation error indicates the discrepancy between the partial sum and the actual sum of the series. A smaller truncation error suggests that the partial sum is a better approximation of the actual sum. In this scenario, the truncation error is relatively large, indicating that the partial sum s4 deviates significantly from the actual sum of the infinite series.

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It is proved that the if a and b are nonzero integers, a divides b, and a b is odd, then a is odd.

According to the statement

we have to prove that the if a and b are nonzero integers, a divides b, and a b is odd, then a is odd.

And for this proof we use the contradiction

So,

Proof by contradiction is a common proof technique that is based on a very simple principle: something that leads to a contradiction can not be true, and if so, the opposite must be true.

So for this purpose,

Assume a is even, so a = 2k for some integer k. Now let a and b be integers such that a divides b and a + b is odd.

Since a divides b, b = an for integer n, and in turn b = 2nk, which means b is even and hence a + b is also even. But this contradicts our initial assumption, so a must be odd.

So, It is proved that the if a and b are nonzero integers, a divides b, and a b is odd, then a is odd.

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Answer:

Infinite amount of solutions

Step-by-step explanation:

Step 1: Write systems of equations

4x - y = 7

3y - 12x = -21

Step 2: Rewrite

-y = 7 - 4x

y = 4x - 7

Step 3: Solve for x

Here we see that we would have infinite amount of solutions.

Answer: infinite solutions. Just took the quiz

Step-by-step explanation:

The product of a number and 14 plus 10 is written in an algebraic expression as 4x + 10.

Given the phrase in the question;

"The product of a number and 14 plus 10"

Translation

Let the number be represented by 'x'

The product of a number and 14 ⇒ x × 14 = 4x

Plus 10 ⇒ + 10

Now lets combine the terms.

4x + 10

Therefore, the product of a number and 14 plus 10 is written in an algebraic expression as 4x + 10.

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The answer of the given question based on the Simple interest is , the tuition at the University of Georgia in 2028 will be approximately $13,442.61.

To calculate the tuition at the University of Georgia in 2028, we need to consider the annual increase of 1.5%.

First, let's find the tuition for the next year (2022). We can do this by multiplying the current tuition by (1 + 1.5%) or (1 + 0.015).

Tuition in 2022 = $12,080 * (1 + 0.015) = $12,273.20

Now, let's find the tuition for the following year (2023) using the same formula:

Tuition in 2023 = $12,273.20 * (1 + 0.015) = $12,466.95

We can repeat this process for each year until we reach 2028:

Tuition in 2024 = $12,466.95 * (1 + 0.015) = $12,661.16
Tuition in 2025 = $12,661.16 * (1 + 0.015) = $12,855.79
Tuition in 2026 = $12,855.79 * (1 + 0.015) = $13,050.90
Tuition in 2027 = $13,050.90 * (1 + 0.015) = $13,246.48

Finally, to find the tuition in 2028, we use the same formula one more time:

Tuition in 2028 = $13,246.48 * (1 + 0.015) = $13,442.61

Therefore, the tuition at the University of Georgia in 2028 will be approximately $13,442.61.

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Pulling the arms inward will result in an increase in the angular speed due to the conservation of angular momentum principle.

When a student with outstretched arms stands on a rotating platform, they have a certain amount of angular momentum. Angular momentum is the product of rotational inertia and angular velocity and is conserved in the absence of external torques. As the student pulls their arms inward, the rotational inertia decreases because the mass is closer to the axis of rotation.

According to the conservation of angular momentum principle, when the rotational inertia decreases, the angular velocity must increase to keep the angular momentum constant. This is analogous to the ice skater pulling their arms inward to spin faster. By reducing the moment of inertia, they increase their rotational speed.

Therefore, the correct answer is that pulling the arms inward will result in an increase in the angular speed due to the conservation of angular momentum principle. The conservation of energy principle does not directly affect the angular speed in this scenario.

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Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

4

Step-by-step explanation:

9-5=4

The correct standard form for the given LP model is option C: Max(Z) = 3x1 + 2x2, subject to the constraints 11x1 + 3x2 - 5 <= 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70, with x1, x2 >= 0. This option aligns with the original objective function and constraints of the LP model.

To convert the LP model into standard form, we need to rewrite the constraints with the variables on the left-hand side and constants on the right-hand side, with inequality signs (<= or >=) consistent throughout. Additionally, we introduce slack or surplus variables to transform any non-standard constraints.

In option C, the constraints are correctly transformed as 11x1 + 3x2 - 5 = 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70. These constraints are consistent with the original model. The objective function remains the same, Max(Z) = 3x1 + 2x2.

Option A has incorrect signs in the transformed constraints, and option B introduces surplus variables (+5) instead of slack variables (-5), resulting in an incorrect standard form. Option D includes a non-standard term with a dollar sign, which is inconsistent with linear programming conventions.

Therefore, option C is the correct standard form, adhering to the original LP model's objective function and constraints.

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At time t, the position of a particle moving in the xy-plane is defined by its x-coordinate and y-coordinate. The x-coordinate represents the position of the particle along the x-axis, while the y-coordinate represents its position along the y-axis.

Together, these coordinates give us a point in the plane that represents the particle's position at time t.

To find the position of the particle at any given time t, we need to know its velocity and initial position. The velocity of the particle is the rate at which it is changing its position with respect to time. If we know the velocity, we can use it to determine how the particle's position is changing at each moment in time.

The initial position of the particle is the position it was at when we started measuring its motion. If we know the initial position and the velocity, we can use them to determine the position of the particle at any time t.

In summary, the position of a particle moving in the xy-plane at time t is defined by its x-coordinate and y-coordinate. To determine the position at any given time, we need to know the particle's initial position and velocity. By combining these factors, we can find the particle's position at any time during its motion.

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Answer:

example lang po

Flagpole height is 50 ft.

Explanation:

This is a ratio problem

height of object

length of shadow

Let the height of the flagpole be

x

⇒

6

3

=

x

25

x

=

6

×

25

3

=

50

f

t

Answer:

The total number of winners is 17.

Step-by-step explanation:

Let's assume that the number of winners is "x". Then the number of participants who did not win is "45 - x".

The amount of money awarded to the winners is 1000x rupees.

The amount of money awarded to the participants who did not win is 200(45 - x) rupees.

According to the question, the total amount of prize money distributed is 22600 rupees. So we can write:

\(\sf\implies 1000x + 200(45 - x) = 22600 \)

Simplifying this equation:

\(\sf\implies 1000x + 9000 - 200x = 22600 \)

\(\sf\implies 800x = 13600 \)

\(\sf\implies x = 17 \)

Therefore, the total number of winners is 17.

Hope it helps!

The area of the square increasing with  56 cm²/s

Area or A = x²

where x represents one side of the square

The rate at which each side is increasing or dx/dt = 4 cm/s.

The area of the square is 49cm²

A = x²

x = √A

x = √49 = 7

Each side of the square or x = 7cm

We are trying to find the rate the area is changing, so dA/dt

A=x²

Take the derivative of the area equation with respect to time

dA/dt= 2x * dx/dt

Now plug in the values given to solve for dA/dt: x = 7 cm and dx/dt= 4 cm/s

2 (7) * (4) = 56 cm²/s

Therefore, the area of the square increasing with  56 cm²/s

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In regression analysis, the independent variable is typically plotted on the x-axis.

The x-axis represents the independent variable or predictor variable, which is the variable that is believed to influence or have an impact on the dependent variable. This variable is typically plotted horizontally on the graph.

For example, let's say we are studying the relationship between the amount of study time and exam scores. In this case, the independent variable would be the amount of study time, which could be measured in hours.

By plotting the amount of study time on the x-axis, we can visually analyze how it relates to the dependent variable, which is the exam scores, typically plotted on the y-axis. This helps us understand the nature and strength of the relationship between the two variables.

So, in summary, the independent variable is plotted on the x-axis in regression analysis.

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Joaquin will need 1 and two fifths cups to make his famous chocolate chip cookies for his friend's birthday party

To solve this problem we will use a rule of three with the problem information:

5 people-------- 1/4 cup of butter

28 people -------- x

Applying the rule of three we get:

x = ( 28 people * 1/4 cup of butter) / 5 people

x = 1,4 cup of butter

x = 1 + 2/5 cup of butter = 1 and two fifths cups

It describes the proportionality of 3 known data and an unknown data. When you have more than 3 known facts that are involved in the proportionality, it is known as a compound rule. The rule of three is also known as a direct proportions.

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Answer:

z≥-10

Step-by-step explanation

it just is, trust.

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

Given data;

Here, we present the dataset from the United Nations, which contains information on the number of kilowatt-hours of wind energy generated globally. The data set provides statistics on the US for 25 years, from 1990 to 2014, in millions of kilowatt-hours.

The linear equation for the first 11 years of data, from 1990 to 2000, must be determined.

To determine how much the actual value and anticipated value for the year 2001 differ in Quantity, we must first forecast the value for the year 2001 using our fitted equation with y-intercept.

It will be written as y = m(x) + c.

where,

The dependent variable is y. (in our example is quantity)

The independent variable is x. (in our example is the year)

'm' is equal to the slope of the variable X.

'C' is a constant.

The fitted equation is provided as follows:

Quantity = 186.87 (year) - 369274.72

Now that the value for the year 2001 has been provided,

Quantity = -1868.87 -369274.72 

Quantity = 4652.15

The value that the linear equation predicts for the year 2001 is 4652.15.

The precise figure for 2001 is 6806.

For the year 2001, the discrepancy between the actual and anticipated values is

6806 - 4652.15 = 2173.85

The distinction is 2173.85.

(2173.85/6806)*100 is the percentage difference.

As a result, the difference between the actual value and the forecasted value for the year 2001 is 31.94%.

Hence,

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

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Answer: $ 10,988.25

Step-by-step explanation:

Hi, to answer this question, first we have to multiply the original number of students scheduled to go to the trip (420) by the added students’ percentage (15%) in decimal form (divided by 100)

420 x (15/100) = 420 x 0.15 = 63 students added

Adding the number of extra students to the original number:

420+63 = 483 students (total number of students)

Finally, we have to multiply the result by the cost of each admission ticket (22.75)

483 x 22.75 = $ 10,988.25  

Answer:

\(x=18,\:y=6\)

Step-by-step explanation:

Solve by substitution

\(\begin{bmatrix}x+y=24\\ 75x+60y=1710\end{bmatrix}\)

\(\mathrm{Substitute\:}x=24-y\)

\(\begin{bmatrix}75\left(24-y\right)+60y=1710\end{bmatrix}\)

\(\begin{bmatrix}1800-15y=1710\end{bmatrix}\)

\(\mathrm{For\:}x=24-y\)

\(\mathrm{Substitute\:}y=6\)

\(x=24-6\)

\(x=18\)

\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)

\(x=18,\:y=6\)

Toy Cars=6 and total spending by Mr.Lee=$156

Step-by-step explanation:

Let us first consider

Number of Airplanes=A Cars=C and Trains=T

Now how to start with the problem ? Just start reading it step by step. First statements says that The number of airplanes is 2/3 of The number of cars.

Now how to convert it into an mathematical expression?

here the word "=" is of most important, The number of airplanes "is" whenever you encountered "is" just place a "="

so the first statement can be converted into mathematical expression as,

A=2/3*C  (The number of airplanes is 2/3 of The number of cars.)

Now as per the second condition we can write it in mathematical form as,

C=3/5*T (The number of cars is 3/5 the number of trains).

and the third condition as,

C=3/5*T (The number of cars is 3/5 the number of trains).

Now , we have expressed the statements in mathematical expressions. we have three expressions.

Now It is also given that total number of Toys=20 so we can write it as,

A+C+T=20. ............(1)

Till now we have expressed everything in the question in mathematical form.

now for solving such type of question we need to express the expression giving total in a single entity, expressed it in terms of Airplanes,Cars or Trains,

here we are expressing it in terms of Cars so we can rewrite it (1) as,

2/3*C+C+5/3*C=20 (A=2/3*C and C=3/5*T so T=5/3*C)

by solving this we will get C=6

Total number of car toys, answer of first part

now put this value of C in expression 1,

2/3*C+C+T=20

so the value of T will be 10. T=10

and the total is toys are 20 so 20-10+6=4

Means Airplanes are 4.

Now the cost for each toy is.

A=$12,C=$8 and T=1/2 A i.e T=$6.

So the total cost would be,

4*12+6*8+10*6=$156

$156 answer of second part

I Hope this will help you to solve such kind of Problems.

The number of arrangements of letters in REPETITION with the first E occurring before the first T is 362,880 - 40,320 = 322,560

To find the number of arrangements of letters in the word REPETITION where the first E occurs before the first T, we can approach the problem by breaking it down into simpler steps.

Step 1: We need to determine the total number of arrangements of the letters in REPETITION. Since there are 9 letters in the word, the total number of arrangements can be calculated using the formula for permutations of n objects taken r at a time, which is n!/(n-r)!. In this case, we have n=9 and r=9, so the total number of arrangements is 9! = 362,880.

Step 2: We need to count the number of arrangements where the first E occurs before the first T. To do this, we can first fix the positions of the first E and T in the word. There are 9 possible positions for the first letter, 8 remaining positions for the second letter, and so on, down to 1 possible position for the ninth letter. This gives us a total of 9x8x7x6x5x4x3x2x1 = 362,880 possible arrangements of the letters in REPETITION.

However, we want to exclude the arrangements where the first T appears before the first E. To do this, we can fix the position of the first T and count the number of arrangements of the remaining letters. There are 8 possible positions for the first T, and then 7 remaining positions for the second letter, and so on, down to 1 possible position for the eighth letter. This gives us a total of 8x7x6x5x4x3x2x1 = 40,320 arrangements where the first T appears before the first E.

Therefore, the number of arrangements of letters in REPETITION with the first E occurring before the first T is 362,880 - 40,320 = 322,560.

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Answer:

2

Step-by-step explanation:

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

Answer:

y=2

Step-by-step explanation:

6y-2 (y + 1) = 3(y-2) + 6

6y-2y-2 = 3y-6+6 *simplify*

4y-2 = 3y *minus 4y on both sides*

-2 = -y *swich the sign for both*

2=y or y=2

Answer:

i dont know if its a typo but here

Step-by-step explanation:

Answer:

-6.5y - 1.1x

Step-by-step explanation:

Rearrange the problem to where like terms are closer together:

11.7y+5.2y + 1.2x + x - 3.3x

Simplify by adding the like terms and your final answer will be -6.5y -1.1x

The solution that we have here is a combination question not a permutation.

You can order pizza with:  1, 2, 3, 4 toppings for $10.

The ways to do the ordering are

In total there would be  3060+816+153+18=4047 ways of ordering for the pizza.

3. Given 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 and there are no restrictions, we would have

2¹⁸ ways of ordering = 262144 ways

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Answer: y=4x+9

Step-by-step explanation:

M= 1+11/-2+5= 12/3= 4

y=mx+b

1=4(-2)+b

1=-8+b

b=9

y=4x+9

The vector equation of the line tangent to the graph of r(t) at the point P0(-1, 2) is (-1 + 2t)i + (2 + √3t)j.

For the vector equation of the line tangent to the graph of r(t) at the point P0(-1, 2), we need to find the derivative of r(t) with respect to t and evaluate it at t = t0.

We have:

r(t) = (2t - 1)i + (√3t + 4)j

P0(-1, 2)

To find the derivative of r(t), we differentiate each component with respect to t:

r'(t) = (2)i + (√3)j

Now, let's evaluate r'(t) at t = t0. Since P0 is the point on the curve, we can substitute t = t0 = -1 into r'(t):

r'(-1) = (2)i + (√3)j

Therefore, the vector equation of the line tangent to the graph of r(t) at the point P0(-1, 2) is:

r(t) = P0 + t * r'(-1)

Substituting the values:

r(t) = (-1)i + 2j + t * [(2)i + (√3)j]

Simplifying, we get:

r(t) = (-1 + 2t)i + (2 + √3t)j

So, the vector equation of the line tangent to the graph of r(t) at the point P0(-1, 2) is (-1 + 2t)i + (2 + √3t)j.

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