If the nth partial sum of a series n = 1 as it approaches infinity an is sn = 6 - n5^-n, find an and n = 1 as it approaches infinity an.

The length of the rectangle is 15.9 inches. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often known as "arithmetic operations," can be used to explain any real number. Operations like quotient, product, sum, and difference come after operations like division, multiplication, addition, and subtraction in mathematics.

We are given that the perimeter of a rectangle is 42.4 inches and the length is three times its width.

Let the width be 'x'.

So, length will be 3x.

From this, we get

⇒ Perimeter = 2 (length + width)

⇒ 42.4 = 2 (3x + x)

⇒ 42.4 = 2 (4x)                             (Using addition operation)

⇒ 42.4 = 8x                                  (Using multiplication operation)                

⇒ x = 5.3                                      (Using division operation)

So,

⇒ Length = 3 * 5.3

⇒ Length = 15.9 inches

Hence, the length of the rectangle is 15.9 inches.

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Answer:

When we have a set of points, we can find the distance between them using the formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where d is the distance, x1 and x2 are one point and y1 and y2 are another point.

OB:

Thus, for OB, we can allow O(6, 6) to be our x1 and x2 point and we can allow B(9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(6-9)^2+(6-6)^2} \\d=\sqrt{(-3)^2+(0)^2} \\d=\sqrt{(-9)} \\d=3[/tex]

Thus, the first part/step in the equation is your subtraction expression to find the length of OB.

AB:

For AB, we can allow A(9, 10) to be our x1 and x2 point and we can allow B (9, 6) to be our y1 and y2 point:

[tex]d=\sqrt{(9-9)^2+(10-6)^2}\\ d=\sqrt{(0)^2+(4)^2}\\ d=\sqrt{16}\\ d=4[/tex]

The first part/step is your subtraction expression for the length of AB.

Answer:

[tex] \frac{w}{3} [/tex]

Answer: $702.39

Step-by-step explanation: To find the total cost of the laptop with sales tax included, we need to add the sales tax to the listed price.

First, we need to calculate the amount of sales tax.

Sales tax = 9.75% of 639.99

Sales tax = 0.0975 x 639.99

Sales tax = 62.40

Now we can find the total cost of the laptop with sales tax included:

Total cost = listed price + sales tax

Total cost = 639.99 + 62.40

Total cost = 702.39

Therefore, the total cost of the laptop with sales tax included is $702.39.

Answer:

189.1034.

Step-by-step explanation:

The result of the expression is approximately 189.1035.

To calculate the expression 192 - 84 ÷ (71 + 16) x 3, follow the order of operations, which is commonly remembered by the acronym PEMDAS:

Parentheses: Perform the operation within the parentheses first.

71 + 16 = 87

Division: Perform the division.

84 ÷ 87 ≈ 0.9655 (rounded to four decimal places)

Multiplication: Perform the multiplication.

0.9655 * 3 ≈ 2.8965 (rounded to four decimal places)

Subtraction: Finally, perform the subtraction.

192 - 2.8965 ≈ 189.1035 (rounded to four decimal places)

The result of the expression is approximately 189.1035.

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If the room is 12'x20' with 8' ceilings and the tile costs $4.75 per square foot,  the total cost is $1140.

To calculate the cost of replacing the tile in the kitchen, we need to first calculate the total area of the floor.

Area of the floor = Length x Width = 12 ft x 20 ft = 240 sq ft

Since we know the cost per square foot of tile, we can now multiply the total area of the floor by the cost per square foot to find the total cost:

Total cost = Area of the floor x Cost per square foot

Total cost = 240 sq ft x $4.75/sq ft

Total cost = $1140

Therefore, it will cost $1140 to replace the tile in the kitchen, assuming there are no additional costs such as labor or materials for removing the old tile.

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Answer:

-2a⁴ b⁶ c³

Step-by-step explanation:

2a² b c³ (-a² b⁵)

determine the signs for multiplication or division

-2a²bc³a²b⁵

multiply the monomials

-2a⁴b⁶c³

(then done)

Answer:

11 dimes and nickels.

Step-by-step explanation:

22 total coins divided by 2 equals 11 for each.

the number 2 represents the dimes and nickels, 22 for the total amount of coins, and 11 for the answer.

Answer:15 nickels  and  7 dimes.

Step-by-step explanation:

The work done on an object if a force of 4 x − x^2 is applied from x = 0 to 3 is 9J

Work Done serves as the quantity of energy which is been moved by the  force  so that a particular energy can move  howver the relation between Work and Energy can be seen as a direct one.

Give that force= 4 x − x^2  from x = 0 to 3

Work done by force , F= ∫(4 x − x^2 )dx                  (0-3)

F= (4x^2/2 - x^3/3)

=[2x^2 -x^3/3]

= [2*3^2 -3^3/3 - 2*0^2 -0^3/3]

18 -9= 9

9J

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The selling prices of the sculpture, painting, and photograph were 166.5 million, 107.0 million, and 57.6 million respectively.

Let's call the selling prices of the sculpture, painting, and photograph as S, P, and Ph respectively.

From the first sentence, we know that:

S + P + Ph = 308.0 million

From the second sentence, we know that:

P = Ph + 49.4 million

And from the third sentence, we know that:

P + Ph = S + 24.4 million

Now we can substitute the second equation into the third equation:

(Ph + 49.4 million) + Ph = S + 24.4 million

Simplifying:

2Ph + 49.4 million = S + 24.4 million

2Ph = S - 25 million

Substituting this into the first equation:

S + P + Ph = 308.0 million

S + (Ph + 49.4 million) + Ph = 308.0 million

2Ph + S = 258.6 million

Now we can substitute the equation we derived earlier:

S + 2Ph - 49.4 million = 258.6 million

S + 2Ph = 308.0 million

Substituting 2Ph = S - 25 million:

S + S - 25 million = 308.0 million

2S = 333.0 million

S = 166.5 million

Now we can use this value to find P and Ph:

P = Ph + 49.4 million

P + Ph = S + 24.4 million

Substituting S = 166.5 million in both equations:

P + Ph = 190.9 million

P = Ph + 49.4 million

Solving these two equations simultaneously:

Ph = 57.6 million

P = 107.0 million

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The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

An example is the expression x + y, which combines the terms x and y with an addition operator.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.

A number is [tex]6[/tex] more than half of the other number, which is x. This statement is represented by the mathematical equation [tex]\frac{x}{2} +6[/tex]. Mathematical expressions are used to solve complicated puzzles.

According to the problem,

The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

This is because it incorrectly adds [tex]1p to 0.035p[/tex], which would result in an overestimation of the population growth.

The correct way to calculate next year's population with a growth rate of [tex]3.5[/tex]% is to multiply the current population (p) by [tex]1[/tex] + [tex]0.035[/tex], as shown in the other three expressions: [tex]3.5p, 1.035p, (1+0.035)p[/tex].

Therefore,the expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

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There are four significant digits in the number 9.15 x 10⁴.

The digits that provide the number with useful information are known as the important digits.

As they add to the value of the number in this instance, the numbers 9, 1, and 5 are all important.

The exponent, 4, just instructs us on how many places to relocate the decimal point, therefore it has no bearing on the number of significant digits.

Therefore, the number 9.15 x 10⁴ has four significant digits.

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Answer:

2

Step-by-step explanation:

The numerical coefficient is the number that is multiplied to a variable.

Example.

2x^2 + 7y^3

The numerical coefficients would be 2 and 7.

So for your problem it would be 2 since 2 is the number being multiplied to x and y.

========================================================

Work Shown:

[tex]d_1 = \text{ one of the diagonals} = 10\\\\d_2 = \text{ the other diagonal}= \text{x}\\\\A = \text{ area of the rhombus} = 20\\\\A = \frac{d_1*d_2}{2}\\\\20 = \frac{10\text{x}}{2}\\\\20*2 = 10\text{x}\\\\40 = 10\text{x}\\\\\text{x} = 40/10\\\\\text{x} = 4[/tex]

The other diagonal is 4 miles long.

The calculated area of each piece is 1/12 acre

If Barry buys a plot of land that measures 1/4 acre, then the total area of the land is 1/4 acre.

If he divides the land into 3 equal pieces, then each piece will have 1/3 of the total area.

So the area of each piece will be:

Area of each piece = (1/3) x (1/4) acre

Multiplying the fractions, we get:

Area of each piece = 1/12 acre

Therefore, each piece of land will have an area of 1/12 acre.

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Using the tests for symmetry, the following are symmetric with respect to y-axis:

A graph is symmetric with respect to the y-axis if replacing x with -x produces an equivalent equation.

A graph is symmetric with respect to the x-axis if replacing y with -y produces an equivalent equation.

A graph is symmetric with respect to the origin if replacing x with -x and y with -y produces an equivalent equation.

(a) symmetric with respect to the y-axis:

y = 7x - 4 (no)

y = - x + 7 (yes)

y = - 7x² (yes)

y = 6x² - 9 (no)

x = 1/4 × y² (no)

x = - y² + 9 (yes)

y = - 1/6 × x³ (no)

y = x³ - 1 (no)

y = √(x) (no)

y = √(x) - 6 (no)

Therefore, the graphs that are symmetric with respect to the y-axis are:

y = - x + 7

y = - 7x²

x = - y² + 9

None of the graphs are symmetric with respect to the x-axis or the origin.

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Answer:

F

Step-by-step explanation:

First, find the answer to (180 /5 + 4 x 12 - 10) which is 74.

Next, start with solving the possible answers.

Lastly, once you have solves determine which answer is the same, which is F.

The value -5°C represents the temperature outside as measured by the digital thermometer in Olivia's car.

In this context, the value -5 represents the temperature outside in Celsius degrees.

The minus sign indicates that the temperature is below freezing point. The Celsius scale is a temperature scale that uses the freezing point of water (0°C) and the boiling point of water (100°C) at standard atmospheric pressure as its reference points.

Thus, a temperature of -5°C means that it is five degrees Celsius below the freezing point of water.

The negative sign indicates that the temperature is below zero degrees Celsius, which is the freezing point of water.

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Applewood Farmstand sold 102 pieces of apples over the weekend.

Graph is a data structure which consists of nodes (vertices) that are connected with each other. Graphs are used to represent relationships between different objects, such as networks, social connections, and pathways. Graphs are useful for representing data as they can provide a visual representation that is easy to interpret, and can be used to analyse patterns in the data. Graphs can also be used to represent problems such as shortest path problems, and can be used to solve problems such as finding the most efficient route between two points.

The graph shows that apples accounted for 32% of the total fruit sales. To find the exact number of apples sold, we can calculate the following:

Apples = (320 pieces of fruit) x (0.32)

Apples = 102 pieces

Therefore, Applewood Farmstand sold 102 pieces of apples over the weekend.

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The maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

To find the maximum value of z = 4x + y subject to the given constraints, we can use linear programming.

Graph the constraints:

First, we will graph the constraints to visualize the feasible region.

The constraint x + y ≤ 50 represents the region below the line x + y = 50:

The constraint 3x + y ≤ 90 represents the region below the line 3x + y = 90:

The feasible region is the shaded region that satisfies both constraints:

Identify the corner points of the feasible region:

The feasible region has four corner points: (0, 0), (0, 50), (30, 20), and (45, 0).

Evaluate z at each corner point:

z(0, 0) = 4(0) + 0 = 0

z(0, 50) = 4(0) + 50 = 50

z(30, 20) = 4(30) + 20 = 140

z(45, 0) = 4(45) + 0 = 180

Compare the values of z at the corner points:

The largest value of z is 180, which occurs at the corner point (45, 0).

Therefore, the maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

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B) The domain for #1 and #2 is  ≥ -7 and the domain for #3 is -∞ ≤  ≤ ∞.

1. [tex](f + g)(x) = f(x) + g(x)[/tex]

The domain of [tex](f + g)(x)[/tex] is the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for [tex]x > = -7[/tex] (since we can't take the square root of a negative number), the domain of [tex](f + g)(x)[/tex] is [tex]x > = -7[/tex].

2. [tex](f - g)(x) = f(x) - g(x)[/tex]

The domain of [tex](f - g)(x)[/tex] is also the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for[tex]x > = -7[/tex], the domain of [tex](f - g)(x)[/tex] is also [tex]x > = -7[/tex].

3. [tex](fg)(x) - > (f(g(x))[/tex]

The domain of [tex]f(g(x))[/tex] is the set of all values of  [tex]x[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex]. Since the domain of [tex]f[/tex] is all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex]  is defined only for [tex]x > = -7[/tex], the domain of [tex]f(g(x))[/tex] is [tex]x > = -7[/tex].

Therefore, the correct answer is option:

B) The domain for 1) and 2) is [tex]> = -7[/tex] and the domain for 3) is -∞ ≤ [tex]x[/tex] ≤ ∞.

The value of 'x' in the given figure is 14.73.

The given figure is a Right-angled triangle.

According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of squares of the adjacent side and the opposite side.

In the given figure,

Hypotenuse is 19.

The adjacent side is 12.

The opposite side is x.

Now, we have to find the value of x.

According to the theorem,

19² = 12²+x²

361 = 144+x²

x² = 361 - 144

x² = 217

x = √217

x = 14.73

Therefore, the value of 'x' in the given figure is 14.73.

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A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.

To find the cost per pound of hamburger, we need to divide the total cost by the weight in pounds.

For the 2-pound package

Cost per pound = Total cost / Weight in pounds

Cost per pound = $7.00 / 2 lbs

Cost per pound = $3.50 per pound

For the 3-pound package

Cost per pound = Total cost / Weight in pounds

Cost per pound = $10.50 / 3 lbs

Cost per pound = $3.50 per pound

Therefore, the cost per pound of hamburger is the same for both packages, at $3.50 per pound.

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g°f = -9 So, the correct answer is (B) -9.To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

what is function ?

In mathematics, a function is a relation between two sets, called the domain and the range, that assigns to each element of the domain exactly one element of the range.

In the given question,

To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

Step 1: Apply f to -3

f(x) = 3x + 7

f(-3) = 3(-3) + 7 = -2

Step 2: Apply g to the result of f(-3)

g(x) = 2x - 5

g(-2) = 2(-2) - 5 = -9

Therefore, g°f = -9.

So, the correct answer is (B) -9.

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Answer:

$98 a month

Step-by-step explanation:

1,176 divided by 12

The linear inequalities in the given graph  is y ≥ x/2 -1 and  y< -1/2x -3.

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These quantities may be numerical, algebraic, or a combination of the two.

Here, we have,

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.

we have,

In the given graph, the area above solid line,

points, (-2 , -2) , (0 , -1)

slope = 1/2

so,  y ≥ x/2 -1

The area below dashed line ,

points, (-2 ,-2) , (0 ,-3)

slope= -1/2

so, y< -1/2x -3.

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Using the conversion factor we know that we will spend 180.69€ on memorabilia items.

A conversion factor is a number that is used to multiply or divide one set of units into another.

If a conversion is required, it must be done using the correct conversion factor to get an identical value.

A fraction that is equal to "1" is a conversion factor.  

The numerator and denominator are the same amounts, but they are expressed in different units.  It is used to change a number's unit of measurement.  

By multiplying the initial number by the fraction that is equal to "1," you can change the units without changing the original number's value.

So, in the given situation:

$200 = euros?

We know that:
$1 = 0.90€

Then,

$200 = 180.69€

Therefore, using the conversion factor we know that we will spend 180.69€ on memorabilia items.

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Answer:

a. Plot the points on the graphing calculator, then generate a logarithmic regression equation.

y = 34.17860108 - 5.682632245ln(x)

b. Setting this equation equal to 10, we have x = 70.44 mph

c. If x = 75 mph, then y = 9.64.