Find the six first terms of an arithmetic sequence with:
d = 2
Po= 30

Answer:

Step-by-step explanation:

Using algebra to solve this problem

Let x be the number of adult tickets sold and y be the number of student tickets sold. We can set up a system of two equations to represent the information given in the problem:

x + y = 1098 (equation 1) (the total number of tickets sold is 1,098)
5x + 1y = 2366 (equation 2) (the total amount collected is $2,366)

To solve for x and y, we can use substitution or elimination method. Let's use the substitution method.

From equation 1, we can solve for y as follows:

y = 1098 - x

Substituting this expression for y into equation 2, we get:

5x + 1(1098 - x) = 2366

Simplifying and solving for x, we get:

5x + 1098 - x = 2366
4x = 1268
x = 317

So, 317 adult tickets were sold. To find the number of student tickets sold, we can substitute this value for x into equation 1 and solve for y:

317 + y = 1098
y = 1098 - 317
y = 781

Therefore, 781 student tickets were sold.

Answer:

x+y= 1098

5x+1y= 2366

y= 1098 - x

5x+ 1(1098-x) = 2366

5x + 1098 - x = 2366

4x= 1268

x= 317

x+y= 1098

317 + y= 1098

y= 781

So the answer is: 317 adult tickets and 781 student tickets were sold.

Answer:

2 1/4

Step-by-step answer

Answer:

Step-by-step explanation:

Convert these mixed fractions to improper fractions.

3 3/5 = 18/5

-8 1/3 = -25/3

Now, it is easier to multiply them. Multiply the numerators and the denominators.

18  x   25   =   450

5          3           15

Simplify the final answer by dividing 450 ÷ 15, which is 30.

Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

Answer: Total visitors =1500

Step-by-step explanation:

By rounding off each no. nearest to 100 is :

185=200, 349=300, 107=100, 355= 400. 451= 500

By adding round off  no. i.e.200+300+100+400+500= 1500

So total no. of visitors were 1500

Answer:

Step-by-step explanation:

To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:

(24/18) * (2/17) * (34/3)

First, we can simplify the fractions by reducing any common factors in the numerators and denominators:

24/18 = (212)/(29) = 12/9 = 4/3

2/17 = 2/17

34/3 = (2*17)/3 = 34/3

Now we can multiply the simplified fractions:

(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153

The product of the given fractions in lowest terms is 272/153.

Answer:she is correct i dont really get the formula but if -9 - 8 = -17

Step-by-step explanation:

The equations are y = 30x + 13 and y = 28x + 15. And the charge less for cleaning 4 mattresses is $127 given by company B. Then the amount of money saved to clean 7 mattresses is $22.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of mattresses and 'y' be the total cost. Then the equations are given as,

Company A: y = 30x + 13

Company B: y = 28x + 15

The amount for x = 4 is given as,

Company A: y = 30 (4) + 13 = $133

Company B: y = 28 (4) + 15 = $127

The amount for x = 4 is given as,

Company A: y = 30 (7) + 13 = $223

Company B: y = 28 (7) + 15 = $211

Then the amount of money saved is given as,

⇒ $233 - $211

⇒ $22

The amount of money saved to clean 7 mattresses is $22.

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The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.

The given trinomial is x²-8x+16.

Factors of 16           Sum of factors

-1 and -16               -1+(-16)=-17

-2 and -8                  -2+(-8)=-10

-4 and -4                  -4+(-4)=-8

The set of factors would used to factor the trinomial are -4 and -4.

Therefore, option C is the correct answer.

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Using the periodicity of the tangent function we can see that:

tan(-4π/3) = -√3

Ok, we know that the trigonometric functions have a period of 2π, that means that we can rewrite the expression:

tan(-4π/3)

as:

tan(-4π/3 + 2π)

The argument can be rewritten as:

tan(-4π/3 + 2π) = tan(2π/3)

Using a table for the tangent function we can see that it is equal to -√3, that is the value of the tangent.

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Answer:

\(\frac{511\,\,\sqrt{3} }{99}\)  which is an irrational number

Step-by-step explanation:

Recall that the repeating decimal 0.7373737373... can be written in fraction form as: \(\frac{73}{99}\)

Now, let's write the number 147 which is inside the square root in factor form to find if it has some perfect square factors:

\(147=7^2\,3\)

Then, 7 will be able to go outside the root when we compute the final product requested:

\(\frac{73}{99} \,*\,7\,\sqrt{3} =\frac{511\,\,\sqrt{3} }{99}\)

This is an irrational number due to the fact that it is the product of a rational number (quotient between 511 and 99) times the irrational number \(\sqrt{3}\)

Answer:

D

Step-by-step explanation:

In order for a line on a graph to be a function it has to pass the vertical line test.

How you do that for points, multiple X values can't have more than 1 Y value.

A has points (2, -6) and (2, 6), so it doesn't pass the vertical line test because the X value (2) goes to multiple Y values (6 and -6).

B has points (-3, -5) and (-3, -4), so it doesn't pass the vertical line test because the X value (-3) goes to multiple Y values (-3 and -4)

C has points (-8, 9) and (-8, 4), so it doesn't pass the vertical line test because the X value (-8) goes to multiple Y values (4 and 9).

C also has the points (8, -5) and (8, 1), and this has the same problem as all of the other problems.

D has {(-3, 5), (6, 10), (5, 2) , (-6, -5), and (3, 9)} which every X value has exactly 1 Y value.

Therefore, D is the correct answer.

Answer:

5x(−7yz+4y+3)

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

1)

So we have:

\(\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2\)

This can be interpreted as:

"There exists a natural number x and an integer y such that x² is equal to y²."

2)

So we want even numbers are in the set of integers.

\(\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}\)

This is interpreted as:

"The set of even numbers (2n such that n is an integer) is in the set of integers"

The constant of proportionality in the equation is 5/4

The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.

The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In the problem, y = 5/4x

The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values

The term helps in relating x to y

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Answer:

y = -5/2x + -4 (or) y = -5/2x - 4

Step-by-step explanation:

Your slope is -5/2, so all you have to do is take the point (-2, 1) and use the slope to find a second point of (0, -4) which is coincidentally the y-intercept. Then you just plug the data into the equation y = mx+b. You do that and you get the answer of y = -5/2x+-4

Mark would need 15 new clients.

In the year 2000, it was estimate that the population of the world was 6, 082, 966, 429 people.

Based on data provided by the table give, the global population in the year 2000 was estimated to be around 6, 082, 966, 429 individuals. This remarkable figure, serving as a testament to the expansive tapestry of humanity, reflects the vastness and intricacy of our interconnected world during that period.

Within the context of demographic analysis, the United Nations diligently compiled and analyzed extensive data to derive this population estimate for statistical reasons.

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The full question is:

In the year 2000 the world population was

The first linear equation passes through (2,4) and (1,1).

Using two point form the equation can be determined as,

The second linear equation passes through (2,-2) and (-1,-5).

Using two point form the equation can be determined as,

The system of equation can be solved graphically as,

Thus, (-1,-5) is the required solution.

Answer:

x = 15

Step-by-step explanation:

Similar triangles and proportional side lengths.

10/4 = x/6

5/2 = x/6

2x = 5 * 6

2x = 30

x = 15

The volume of the rectangular sandwich box of Austin is given by the equation V = 468 cm³

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangular box be represented as V

Now , the equation will be

The length of the sandwich box = 13 cm

The width of the sandwich box = 12 cm

The height of the sandwich box = 3 cm

And , volume of the rectangular box V = Length x Width x Height

Substituting the values in the equation , we get

Volume of the rectangular box V = 13 x 12 x 3

On simplifying the equation , we get

Volume of the rectangular box V = 468 cm³

Hence , the volume of rectangular box is 468 cm³

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Answer:

\(\dfrac{a^6}{144b^8}\)

Step-by-step explanation:

a) They did not use the exponent rule: \((a \cdot b)^n=a^nb^n\) correctly.

They added the exponents rather than multiplied them.

b) Correct solution:

\((12a^{-3}b^4)^{-2}\)

Apply exponent rule:  \(a^{-b}=\dfrac{1}{a^b}\)

\(\implies \dfrac{1}{(12a^{-3}b^4)^2}\)

Apply exponent rule: \((a \cdot b)^n=a^nb^n\)

\(\implies \dfrac{1}{12^2a^{(-3\times2)}b^{(4 \times2)}}\)

\(\implies \dfrac{1}{144a^{-6}b^8}\)

Apply exponent rule:  \(\dfrac{1}{a^{-b}}=a^b\)

\(\implies \dfrac{a^6}{144b^8}\)

The unit digits multiplies by 2 is 9 less than three times the tens digits, and reversing the digits is 45 more than the original number indicates;

The tens digit is the digit in the tens place value of a number.

Let x and y represent the digits in the two digit number, where;

x = The tens digit (The digit in the tens place value)

y = The units digit

The specified two digit number, can therefore be expressed as; 10·x + y

2·y - 9 = 3·x...(1)

Part of the possible question, includes;

The value obtained by reversing the digits is 45 more than the original number, therefore, we get;

10·y + x  = 10·x + y...(2)
The question is a word problem question, therefore;

y = (3·x + 9)/2

10 × ((3·x + 9)/2) + x = 45 + 10·x + ((3·x + 9)/2)

16·x + 45 = 45 + (23·x + 9)/2

16·x = (23·x + 9)/2

32·x = 23·x + 9

32·x - 23·x = 9

9·x = 9

x = 9/9 = 1

x = 1

y = (3 × 1 + 9)/2 = 6

y = 6

The original number is therefore; 1 × 10 + 6 = 16

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Ending Inventory Cost and Cost of Goods Sold using different inventory methods:

FIFO Method:

Ending Inventory Cost: $11,920

Cost of Goods Sold: $15,068

LIFO Method:

Ending Inventory Cost: $11,996

Cost of Goods Sold: $15,123

Weighted Average Cost Method:

Ending Inventory Cost: $11,974

Cost of Goods Sold: $15,087

Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.

This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.

Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.

This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.

Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.

Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.

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Answer: x=−5/24

Step-by-step explanation: hope this help

Answer:

-42.

Because you subtract to the 2. -2, multiply by 3, -6. Then multiplying by 7. And getting -42.

Answer:

their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster