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The sum of the infinite geometric series is: ²/₅

The formula for the sum of an infinite geometric series is;

[tex]S_{\infty} = \frac{a}{1 - r}[/tex]

where;

a is first term

r is common ratio

The first term is; a = ⁴/₁₅

Common ratio; r = ⁴/₉ ÷ ⁴/₁₅ = ⁵/₃

r = ²⁰/₂₇  ÷  ⁴/₉ = ⁵/₃

Thus;

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ (⁵/₃ - 1)

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ ²/₃

= ²/₅

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Answer:

How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;S_∞ = a/(1 - r)where;a is first termr is common ratioThe first term is; a = 4/15Common ratio; r = (4/9)/(4/15) = 5/3r = (20/27)/(4/9)  = 5/3Thus;S_∞ = (4/15)/((5/3) - 1)S_∞ = (4/15)/(2/3) = 2/5

Answer:

Where is the expression bro

The equation for the logarithmic function that passes through (0,0) and (-5,3) is given as follows:

y = log2(-x + 1)

First we must consider the vertical asymptote of the logarithmic equation, which is given as follows:

x = 1.

As the function is defined for the values to the left of the vertical asymptote, the function was reflected over the y-axis, hence:

y = logb(-x + 1) + d.

When x = -1, y = 1, hence we can have a logarithm of base 2 with a vertical shift of zero, hence:

y = log2(-x + 1)

Which is the logarithmic function for the function graphed in this problem.;

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The two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.

What is combination ?

Combination refers to the number of ways a selection of items can be made from a larger set of items without regard to their arrangement. In other words, combinations are a way to calculate the total number of possible groups of items that can be formed, regardless of the order in which the items are selected. The formula for calculating the number of combinations is nCr, where n is the total number of items and r is the number of items being selected.

According to the question:
Let's start by finding the possible prices of the pie. Since the price must be an exact number of pence, we can convert the price range to pence by multiplying each value by 100:

£1.30 = 130 pence

£2.99 = 299 pence

We know that the price plus the 24% tip must be an exact number of pence. If we let x be the price of the pie in pence, then we can write this as:

x + 0.24x = 1.24x

Since 1.24 is not divisible by 5 (which we'll need for the change), we need to find two values of x that differ by a multiple of 5. One way to do this is to start with the lower bound and add multiples of 5 until we get a valid value:

x = 130: 1.24x = 161.2

x = 135: 1.24x = 167.4

x = 140: 1.24x = 173.6 (valid)

x = 145: 1.24x = 179.8

x = 150: 1.24x = 186.0 (valid)

x = 155: 1.24x = 192.2

x = 160: 1.24x = 198.4

So the possible prices of the pie are 140p and 150p. To find the possible amounts of change, we need to subtract each price from 500p (the value of the £5 note) and express the result as a combination of coins. For example:

Price = 140p, change = 360p = 3 x £1 + 1 x 50p + 1 x 10p

Price = 150p, change = 350p = 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p

Therefore, the two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.

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Hence, in response to the provided question, we can say that Therefore equation there are 600 pupils in the seventh grade.

An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.

Let's call the total number of pupils in the seventh grade "x".

We know that the 12 students in the Environmental Club account for 2% of the seventh-grade students, which means:

12 = 0.02x

To find x, we must isolate it on one side of the equation. This can be accomplished by dividing both sides by 0.02:

12 ÷ 0.02 = x

This boils down to:

600 = x

Therefore there are 600 pupils in the seventh grade.

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As a result, the probability of selecting a 7 and a jack from a regular deck of cards, one at a time and without replacement, is about 0.006 or 0.6%.

Probabilistic theory is a branch of mathematics that evaluates the probability of a certain occurrence or proposition occurring or being true. A danger is a number in the range between 0 and 1, whereas 1 signifies certainty and a probability of around 0 reflects how likely an event seems to be to occur. Probability seems to be a mathematical function for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences between equally as likely possibilities that result in a specific event.

The probability of selecting a 7 and a jack from a regular deck of cards, one at a time and without replacement, is as follows:

As a result, the odds of selecting a jack from the remaining cards are 4/51.

The product of these probabilities is the likelihood of selecting a 7 and a jack in sequence:

P(7) = P(7) x P(jack|7 not picked) = 4/52 x 4/51

When we simplify this expression, we get:

P(Jack and 7) = 16/2652

As a result, the likelihood of selecting a 7 and a jack from a regular deck of cards, one at a time and without replacement, is about 0.006 or 0.6%.

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In this the point (-2,3) on the graph of f multiplied by the corresponding point (-2,2) on the graph of g yields the product (-2,6), which is equal to -8.

A coordinate plane is a two-dimensional surface composed of two number lines, one horizontal (x-axis) and one vertical (y-axis). It is used to graph points, lines, and other shapes. Each point is identified by a pair of numbers which indicate its position along the x and y axes. The x and y axes intersect at the origin and divide the plane into four quadrants.

The graph of fg can be found by first graphing both f and g on the same coordinate plane. From there, the graph of fg can be found by taking each point on the graph of f and multiplying it by the corresponding point on the graph of g. In this example, the point (x,y) on the graph of f is multiplied by the corresponding point (x,y) on the graph of g to form a new point (x,yz). This new point is then placed on the graph of fg.

Using the graphs of f and g provided, we can determine that (fg)(-2) = -8. To find this, first locate the point (-2,3) on the graph of f. Then, locate the corresponding point (-2,2) on the graph of g. The product of these two points is (-2,6). This means that (fg)(-2) = -8.

In summary, to find (fg)(-2) using the graphs of f and g, first graph both f and g on the same coordinate plane. Then, take each point on the graph of f and multiply it by the corresponding point on the graph of g. In this example, the point (-2,3) on the graph of f multiplied by the corresponding point (-2,2) on the graph of g yields the product (-2,6), which is equal to -8.

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Answer:

Step-by-step explanation:

To find the expected difference in height between a child 49 months of age and a child 16 months of age, we need to first find the average height of each child and then find the difference between them.

For a child who is 49 months old, the average height can be found by substituting x = 49 in the given equation:

y1 = 2.9sqrt(49) + 20.1 = 42.7 inches

For a child who is 16 months old, the average height can be found by substituting x = 16 in the given equation:

y2 = 2.9sqrt(16) + 20.1 = 28.9 inches

Therefore, the expected difference in height between the two children would be:

y1 - y2 = 42.7 - 28.9 = 13.8 inches

So we can expect the child who is 49 months old to be, on average, 13.8 inches taller than the child who is 16 months old.

The set of values that is greater than the quadratic function with zeros -5 and -13 and includes the point (-9, -32) is: y > 2(x+5)(x+13)

A quadratic function is a type of function in mathematics that can be represented by a quadratic equation, which is a polynomial equation of the second degree. It is an equation, for example, y = ax2 + bx + c, where a, b, and c are constants and x is the variable, that involves a variable raised to the power of two.

The factored form of the quadratic function with zeros -5 and -13 is as follows:

f(x) = a(x + 5)(x + 13)

where a is a constant.

Substituting the given point (-9, -32) into the quadratic function, we get:

-32 = a(-9 + 5)(-9 + 13)

-32 = -16a

a = 2

So, the quadratic function in factored form is:

f(x) = 2(x + 5)(x + 13)

we need to find the range of values that satisfy this inequality:

y > a(x + 5)(x + 13)

Therefore, the set of values that is greater than the quadratic function with zeros -5 and -13 and includes the point (-9, -32) is: y > 2(x+5)(x+13)

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Answer:

The percentage rate of change of a function f(t) is given by:

(Δf / f) x 100

where Δf is the change in f and f is the original value of the function.

To find the largest value of t such that the percentage rate of change equals 100, we need to find the value of t for which:

(Δf / f) x 100 = 100

Simplifying, we get:

Δf / f = 1

This means that the change in f is equal to the original value of f.

So, we need to solve the equation:

f(t + Δt) - f(t) = f(t)

where Δt is the change in t.

Substituting the given function, we get:

[1 - 2(t + Δt) + 4(t + Δt)^2] - [1 - 2t + 4t^2] = 1 - 2t + 4t^2

Simplifying, we get:

-8tΔt + 8Δt^2 = 1

Since we are interested in the largest value of t, we can assume that Δt is a small positive number, such that Δt << t.

Ignoring the term Δt^2, we get:

-8tΔt = 1

Solving for Δt, we get:

Δt = -1 / (8t)

Substituting this value of Δt back into the equation -8tΔt + 8Δt^2 = 1, we get:

-8t(-1 / (8t)) + 8(-1 / (8t))^2 = 1

Simplifying, we get:

1 / t^2 = 1

Solving for t, we get:

t = 1

Therefore, the largest value of t such that the percentage rate of change equals 100 is t = 1.

Answer:

154%

Step-by-step explanation:

First, we need to calculate the increase in size of the privately owned farm:

increase = new value - old value

increase = 432 - 170

increase = 262

Next, we can use the formula to calculate the percent increase:

percent increase = (262 / 170) x 100%

percent increase = 1.54 x 100%

percent increase = 154%

Therefore, the percent increase in the size of privately owned farms in the country is 154%.

The volume of the resulting block of wood is 576 in³. The correct option is the second option 576 in³

From the question, we are to determine the volume of the resulting block of wood.

From the given information,

The dimensions of the block of wood is 10 in. by 10 in. by 6 in.

First, we will calculate the original volume of the block of wood.

The original block of wood has a volume of

V = 10 x 10 x 6

V = 600 in³

Now, we will determine the volume og the hole that was cut through

The dimensions of the hole is 2 in. by 2 in. by 6 in.

Volume of the hole = 2 x 2 x 6

Volume of the hole = 24 in³

The resulting block would have a volume of

Volume of resulting block = 600 - 24

Volume of resulting block = 576 in³

Hence, the volume is 576 in³.

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Best answer for the statement are Linear, Nonlinear.

A linear function is a type of mathematical function that has the following form:

f(x) = mx + b

where "m" and "b" are constants. "m" represents the slope of the line, or the rate at which the function changes .

Linear functions have a constant rate of change and when graphed form a straight line. Nonlinear functions do not have a constant rate of change, can be graphed with one or more curves or a "v-shape".

Therefore, the best answer to complete the sentence is:

Linear functions have a constant rate of change and when graphed form a straight line. Nonlinear functions do not have a constant rate of change, can be graphed with one or more curves or a "v-shape".

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Answer:

in absolute value you consider both the positive and negative side of the expression in the absolute bar.

Answer:

To multiply polynomials, you can follow these steps:

Distribute each term of the first polynomial to each term of the second polynomial.

Combine like terms.

Simplify the resulting expression.

Here is an example:

(2x + 3)(x - 4)

Distribute:

2x(x - 4) + 3(x - 4)

Combine like terms:

2x^2 - 8x + 3x - 12

Simplify:

2x^2 - 5x - 12

So, (2x + 3)(x - 4) = 2x^2 - 5x - 12.

Step-by-step explanation:

Answer: It looks like it could be III I'm not sure thought I hope it was right

Step-by-step explanation:

1) The system of inequalities that models this scenario will be:

6x + 3y ≤ 24

6x + 3y ≥ 4

2)
i) the solution for y is y ≤ 5 - 2x.
ii) the solution for y is y ≥ 3 - x.

3) The graph is attached accordingly.

a)
Let's use the variables x and y to represent the number of Mickey pretzels and Mickey bars, respectively, that Mrs. Tobie can buy. We want to ensure that at least four children get one snack each, so the inequality for the total number of snacks should be greater than or equal to 4.

Also, Mrs. Tobie has a budget of S24, so the cost of the snacks should be less than or equal to S24. Putting these together, we get:

6x + 3y ≤ 24 (budget constraint)

6x + 3y ≥ 4 (at least four snacks)

So the system of inequalities that models this scenario is:

6x + 3y ≤ 24

6x + 3y ≥ 4

b)

To solve for y in each inequality, we need to isolate y on one side of the inequality sign.

For the first inequality, we have:

x + y ≥ 3

Subtracting x from both sides, we get:

y ≥ 3 - x

So the solution for y is y ≥ 3 - x.

For the second inequality, we have:

6x + 3y ≤ 15

Dividing both sides by 3, we get:

2x + y ≤ 5

Subtracting 2x from both sides, we get:

y ≤ 5 - 2x

So the solution for y is y ≤ 5 - 2x.

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Answer: y = 4/3x -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

b-y=55

Answer: 9·9 -36 +4.

Step-by-step explanation: 9x² -12x +4 for x=3. 9·3² -12·3 +4 = 9·9 -36 +4.

The width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.

The region contained inside the rectangle's perimeter is referred to as the area of the rectangle. In other terms, the area of a rectangle is the whole area that a rectangle encloses. Depending on the provided dimensions, this may be determined using the area of rectangle formula and a number of other techniques.

Let us suppose the width = x.

Then, length is given as:

l = x + 7

The area of the rectangle is:

A = lw

Substituting the values:

A = (x + 7)x

The perimeter of the rectangle is:

P = 2(l + w)

P = 2(x + 7 + x)

P = 2(2x + 7)

P = 4x + 14

Also, we have:

A = 2P

Substituting the values of area and perimeter:

4x + 14 = (x + 7)x

Simplifying the expression:

x^2 + 7x = 8x + 30

x^2 - x - 30 = 0

(x-6)(x+5) = 0

Since, width cannot be negative value we have:

x = 6.

l = 7 + 6 = 13 inches.

Hence, the width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.

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Answer:

Step-by-step explanation:

(9/4 * 8/7) - (3/8*4/1) =

(72/28) - (12/8)

18/7 - 3/2

36/14 - 21/14

15/14 = 1 1/14

Using the information shown on the auger shell. The value of x is found as 16.

Fractions and ratios can both be stated as reciprocals of one another. Similar rules apply to proportions, which are just the equivalence of two ratios.

For the given values in question:

8.8 mm

11 mm

20 mm

Value of x.

Using proportion of the numbers:

8.8 / 11 = x / 20

x = 8.8*20 / 11

x = 16

Thus, using the information shown on the auger shell.  The value of x is found as 16.

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Answer: 9.60

Step-by-step explanation:

Labeled price = $ 12

Discount = 20% of labeled price = 12 x 20%

= 12 x 2 / 10 = 24 / 10 = $ 2.4

Sale price = Labeled price - Discount.

Sale price = $ 12 - $ 2.40 = $ 9.60

Thus the sale price of the case of soda is 9.60 $

The image after the reflection over the line x = 2 is (11, -3)

Here we have the point T which has coordinates (-7,  -3), and we apply a refletion across the line x = 2.

This reflection will only chane the value of x in our point, such that the initial value x = -7

Is at the same distance of the line x = 2 than the final x-value

The distance between these values is:

d = |-7 - 2| = 9

Then the new x-value will be:

x = 2 + 9 = 11

Thus, the image after the reflection is (11, -3)

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According to the given conditions, the equation of the ellipse is [tex]{\frac{(x+1)^2}{25}+(y+5)^2=1}$.[/tex]

An equation is a mathematical statement that shows the equality between two expressions. In other words, it is a way to describe a relationship between two or more variables or quantities.

The center of the ellipse is (-1,-5), which means that the center of the ellipse is shifted from the origin. We can find the equation of the ellipse using the standard form equation:

[tex]$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$[/tex]

where (h,k) is the center of the ellipse, and a and b are the lengths of the semi-major and semi-minor axes, respectively.

Since the minor axis has length 2, we know that b=1. We also know that the vertex on the minor axis is (5,-5), which means that the semi-major axis has length 5. Therefore, a=5.

Substituting these values into the standard form equation, we get:

Simplifying, we get:

[tex]$\frac{(x+1)^2}{25}+(y+5)^2=1$[/tex]

Therefore, according to the given conditions, the equation of the ellipse is [tex]{\frac{(x+1)^2}{25}+(y+5)^2=1}$.[/tex]

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It is also important to communicate effectively with any individuals involved in the procedure to ensure that everyone is on the same page and working towards the same goal.

The procedure can refer to a variety of things depending on the context. If you are referring to a medical procedure, it is important to first consult with a healthcare professional to determine the specific procedure that is needed.

If you are referring to a legal or administrative procedure, it is important to review the guidelines and protocols set forth by the governing body or organization.

In general, the procedure typically involves a set of steps or instructions that must be followed in order to achieve a specific outcome. These steps may include gathering information, completing forms, submitting documents, or performing specific tasks.

It is important to carefully follow each step of the procedure to ensure that the desired outcome is achieved.

If you need a procedure completed by 12pm today, it is important to prioritize your tasks and ensure that you have all necessary resources and information available. Depending on the specific procedure, you may need to work quickly and efficiently in order to meet the deadline.

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Answer:

To determine the flexible budget for the Cutting Department, we need to use the information provided to adjust the original budget for the actual level of production.

First, we need to calculate the variable cost per hour of production:

Variable cost per hour = Direct labor / Hours of production

Variable cost per hour = $37,260 / 4,140 hours

Variable cost per hour = $9

Next, we can use this variable cost per hour to calculate the flexible budget for the actual level of production:

Flexible budget = (Variable cost per hour x Actual hours of production) + Fixed costs

Flexible budget = ($9 x 4,500 hours) + $43,370

Flexible budget = $40,500 + $43,370

Flexible budget = $83,870

Therefore, the flexible budget for the Cutting Department, based on the actual level of production of 4,500 hours, is $83,870.

In response to the question, we may say that  205 adults and 130 kids equation respectively attended the concert, for a total of 205 adults and 130 kids.

The equals symbol (=), which indicates equivalence, connects two statements in a mathematical equation. An algebraic equation's mathematical assertion proves the equality of two mathematical propositions. The equal sign, for instance, places a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. Use a mathematical formula to understand how the two sentences on opposite sides of a letter relate to one another. Usually, the logo corresponds to the particular programmed. An example would be 2x - 4 = 2.

Assume that "x" represents the proportion of adults who attended the performance and "y" represents the proportion of children.

The problem statement informs us that:

x + y = 335 —-(1) (1) (There are 335 persons present in all.)

The total amount of money gathered is $675 (2.5x + 1.25y).

1.25x + 1.25y = 418.75 —-(3) (3)

2.5x - 1.25x = 675 - 418.75

1.25x = 256.25

x = 205

205 + y = 335

y = 130

205 adults and 130 kids respectively attended the concert, for a total of 205 adults and 130 kids.

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Answer:

See below.

Step-by-step explanation:

For this problem, we are asked to find x, the hypotenuse.

There are a few ways to find the hypotenuse, but an easy way is to use the Pythagorean Theorem.

Represented as;

[tex]a^2 + b^2 = c^2\\(Short \ Leg)^2 + (Long \ Leg)^2 = (Hypotenuse)^2.[/tex]

We have 2 given values, the short leg and the long leg. We can begin solving for the hypotenuse.

Substitute:

[tex]40^2+42^2=c^2[/tex]

[tex]3364 = c^2[/tex]

Square Root the Equation:

[tex]\sqrt{3364} = \sqrt{c^2}[/tex]

[tex]c = 58.[/tex]

The Hypotenuse is 58. Our final answer is Letter D.