Which of the following show a geometric series? select all that apply. 2 3 4.5 6.75 … 2 2.5 3 3.5 … 6 7 9 12 … 4 8 16 20 … 8 4 2 1 …

One specific example of a rule for the function f such that the series Σα) f(n)/n^2 does not converge is the function f(n) = (-1)^n.

To justify this, we can use the alternating series test, which states that if a series has alternating signs and the absolute values of its terms decrease monotonically to 0, then the series converges. However, if the absolute values of its terms do not decrease monotonically to 0, then the series diverges.

In this case, we have Σα) f(n)/n^2 = Σα) (-1)^n/n^2. The absolute value of each term is 1/n^2, which does decrease monotonically to 0. However, the signs of the terms alternate, meaning that the series does not converge. Therefore, this is a valid example of a rule for the function f such that the series Σα) f(n)/n^2 does not converge.

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The angle in degrees used to indicate the b region is 70.

The total number of students= Sum of the number of students with different grades and the failed ones.

                                          = 50+75+114+98+50

                                          = 387

Now,

The number of students in b region, that is, those who got b's

=75      (given)

We know that,

The sum of all angles due to different grades in the pie chart = 360 degrees.

So the distribution of degrees to b region in the pie chart will be in proportion to the number of students in b region out of total students

Let x degrees be used to indicate the "b" region.

∴ x/360=75/387              (because of the same proportion)

⇒x=75/387×360

⇒x=69.76≅70

Hence, the angle in degrees used to indicate the b region is 70.

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Step-by-step explanation:

we use a function as a kind of recipe or template for an actual calculation (or actual "ingredients").

as long as we don't handle the actual food items or actual numbers, it all stays theoretical. variables have no actual value and represent every possible case with every possible value.

but as soon as we get an actual unit value (like 8 in our case), we can put it in place of the variables (that are really nothing else but placeholders for actual values) and simply caucuses the result.

so,

when the question asks what is f(8), it really means what is the result when x = 8.

therefore,

f(8) = 8 - 7 = 1

that's it. that is the whole thing. no mystery, magic or genius strikes necessary.

Answer:

[tex] \sf \: f(8) = 1[/tex]

Step-by-step explanation:

Given function,

→ f(x) = x - 7

Now we have to,

→ Find the required value of f(8).

We have to use,

→ x = 8

Then the value of f(8) will be,

→ f(x) = x - 7

→ f(8) = 8 - 7

→ [ f(8) = 1 ]

Hence, the value of f(8) is 1.

Answer:

[tex] \frac{7 \sqrt{39} }{5} [/tex]

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]( {11.2})^{2} - { {7} }^{2} = 76.44 > 0[/tex]

The missing side is equal to:

[tex] \sqrt{76.44} = \frac{7 \sqrt{39} }{5} [/tex]

The size of an exterior angle of a regular hexagon is 60 degrees.

In a regular hexagon, all the interior angles are equal and are given by the formula:

Interior angle = (n-2) x 180 / n

where n is the number of sides of the polygon.

For a hexagon, n = 6, so the interior angle is:

Interior angle = (6-2) x 180 / 6 = 120 degrees

An exterior angle is the supplement of an interior angle, which means it is the angle that when added to the interior angle, will equal 180 degrees.

So, exterior angle = 180 - interior angle = 180 - 120 = 60 degrees.

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Using tangents theorem, we can find the value of the missing length,

n = 18.7units.

"To touch" is how the word "tangent" is defined. The same idea is conveyed by the Latin word "tangere". A tangent, in general, is a line that, while never entering the circle, precisely touches it at one point on its circumference. A circle has a number of tangents. They make a straight angle with the radius.

Here in the diagram,

We can see that as per the central angle and tangent theorem,

AB/BC = ED/DC

⇒ 17/10 = n/11

Cross multiplying:

⇒ 17 × 11 = n × 10

⇒ 10n = 187

⇒ n = 187/10

⇒ n = 18.7

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The exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.

To solve the quadratic equation 2x² - 9x + 1 = 0 using the quadratic formula, we first need to identify the values of a, b, and c. From the given equation, we can see that a = 2, b = -9, and c = 1.

The quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-9) ± √((-9)² - 4(2)(1))) / 2(2)
x = (9 ± √(81 - 8)) / 4
x = (9 ± √73) / 4

So, the exact solutions to the equation 2x² - 9x + 1 = 0 are (9 + √73) / 4 and (9 - √73) / 4.

As for the answer choices, it's possible that the answer key has simplified the solution further. However, your answer is correct and provides the exact solutions to the equation.

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Answer:a=40

Step-by-step explanation:

angles on a straight line add to 180. This means that the missing angle that isn't a is 40. Angles in a triangle add to 180 so a=40

Monica's claim is incorrect. Even though her interest rate is higher, she will earn less interest, $10.20, after one year than Paul because her initial deposit is lower.

Paul will earn more interest of $13.20 because he deposited more money, even though his interest rate is slightly lower.

To determine who will earn more interest in one year, we shall calculate the interest earned by each person using the simple interest formula.

The formula for simple interest is:

I = P * r * t

where:

I = the interest earned

P = the principal (the amount deposited)

r = the interest rate (as a decimal)

t =s the time (in years)

For Monica, we are given:

P = $300

r = 0.034 (the interest rate is 3.4%)

t = 1 (the interest earned in one year)

Plugging these values, we have:

I = 300 * 0.034 * 1 = $10.20

So, Monica will earn $10.20 in interest after one year.

For Paul, we are given:

P = $400

r = 0.033 (interest rate = 3.3%)

t = 1 (interest earned in one year)

Plugging the values, we get:

I = 400 * 0.033 * 1 = $13.20

So, Paul will earn $13.20 in interest after one year.

Therefore, Monica's claim is incorrect. Monica will earn $10.20 in interest after one year while Paul will earn $13.20 in interest after one year.

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a) It will take approximately 16.85 years for the rabbit population to double.

b) It will take approximately 37.28 years for the rabbit population to reach 1000.

The formula for calculating the population of rabbits in x years, starting with 100 rabbits and a natural growth rate of 4% per year, is given by:

f(x) = 100(1.04)ˣ

(a) To find out how long it will take for the rabbit population to double, we need to solve the following equation:

100(1.04)ˣ = 200

Dividing both sides by 100, we get:

(1.04)ˣ = 2

Taking the logarithm of both sides with base 1.04, we get:

x = log₁.₀₄ 2

Using a calculator, we get:

x ≈ 16.85

(b) To find out how long it will take for the rabbit population to reach 1000, we need to solve the following equation:

100(1.04)ˣ = 1000

Dividing both sides by 100, we get:

(1.04)ˣ = 10

Taking the logarithm of both sides with base 1.04, we get:

x = log₁.₀₄ 10

Using a calculator, we get:

x ≈ 37.28

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The approximate height of the tall oak tree is 60.0 feet.

To find the height of the tree, follow these steps:

1. Convert the distance between you and the mirror from inches to feet: 36 inches = 3 feet.
2. Create a proportion using similar triangles, where the height of the tree (h) divided by the distance from the tree to the mirror (24 feet) equals your eye height (5 feet) divided by the distance from your eyes to the mirror (3 feet).
3. Set up the proportion: h / 24 = 5 / 3.
4. Solve for h: h = (5 / 3) * 24.
5. Calculate h: h = 40 feet (height of tree above your eye level).
6. Add your eye height (5 feet) to the height of the tree above your eye level: 40 + 5 = 60 feet.
7. Round the answer to the nearest tenth: 60.0 feet.

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To determine the values of A and B, we can use the following system of equations: 1. 5A = -15 2. -2A + B = 10 This system of equations can be used to find the values of A and B.

To review the equation used in writing a partial fraction decomposition, we start with a fraction that has a denominator that can be factored into linear or quadratic factors. The partial fraction decomposition separates the fraction into a sum of simpler fractions, each with a single linear or quadratic factor in the denominator.

The equation you provided for partial fraction decomposition is:

StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction

This equation shows that the original fraction can be decomposed into two simpler fractions, one with a linear factor of (5x - 2) in the denominator (A/(5x - 2)), and one with a quadratic factor of (5x - 2)² in the denominator (B/(5x - 2)²).

To determine the values of A and B, we need to solve for them using a system of equations. In this case, we can use the coefficients of x in the numerator of each fraction to create the following system of equations:

5A = -15
-2A + B = 10

We get the first equation by setting the numerator of the first fraction (A/(5x - 2)) equal to -15x + 10, and the second equation by setting the numerator of the second fraction (B/(5x - 2)²) equal to -15x + 10 and subtracting the first equation from it.

Solving this system of equations gives us:

A = -3
B = 5

Therefore, the partial fraction decomposition of the original fraction is:

StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction -3 Over 5 x minus 2 EndFraction + StartFraction 5 Over (5 x minus 2) squared EndFraction

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Answer:

a^4 - b^4

Step-by-step explanation:

a(a - b) + b(a - b) + (a - b)^2  -->  Given

a^2 - ab + b(a - b) + (a - b)^2  -->  Distributive Property

a^2 - ab + ba - b^2 + (a - b)^2  -->  Distributive Property

a^2 - ab + ba - b^2 + a^2 - b^2  -->  Distributive Property

a^4 - ab + ba - b^2 - b^2  -->  Combine Like Terms

a^4 + 0 - b^2 - b^2  -->  Combine Like Terms (a * b = b * a)

a^4 - b^4 -->  Combine Like Terms

The value of the variable is 9

It is important to note that  inequalities are described as non- equal comparison of numbers or expressions.

The signs of inequalities represents;

From the information given, we have that;

7x - 1  is less than or equal to 62

This is represented as;

7x - 1≤ 62

collect the like terms, we have;

7x ≤ 62 + 1

Add the values

7x ≤ 63

Divide both sides by the coefficient, we get;

x ≤ 63/7

x ≤ 9

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The interest is $2,659.23 and the total value is  $8,959.23.

What is compound interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Here the given principal P = $6300

Number of years = 8

Rate of interest = 4.5% = 4.5/100 = 0.045

Now using compound interest formula then,

=> Amount = [tex]P(1+r)^{t}[/tex]

=> Amount = 6300[tex](1+0.045)^8[/tex]

=> Amount = [tex]6300(1.045)^8[/tex]

=> Amount = $8,959.23

Then Interest = Amount - Principal

=> Interest = $8,959.23 - $6300 = $2,659.23.

Hence the interest is $2,659.23 and the total value is  $8,959.23.

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Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.

Total number of students is 22.

To find the percentage of students who collected between 49 and 98 kilograms of newspapers, we first need to count the number of students who collected within this range. From the given data, we can see that the following students collected between 49 and 98 kilograms of newspapers

87, 64, 90, 76, 60, 55, 57, 75, 56, 88

Percentage of students = (number of students in range / total number of students) x 100

= (10 / 22) x 100

= 45.45%

Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.

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The volume of the cylinder is approximately 1024π cubic meters.

We are given the base area of the cylinder as 64π square meters, which means that the radius of the cylinder is 8 meters (since the area of a circle is given by πr^2). We are also given that the height of the cylinder is twice the radius, which means that the height is 16 meters.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. Substituting the given values, we get V = π(8^2)(16) = 1024π cubic meters. Therefore, the volume of the cylinder is approximately 1024π cubic meters.

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Answer:

[tex]3217.0 m ^{3}[/tex]

Step-by-step explanation:

You must begin to brake 234643.2 feet from the intersection.

In Mathematics and Science, stopping distance can be defined as a measure of the distance between the time when a brake is applied by a driver to stop a vehicle that is in motion and the time when the vehicle comes to a complete stop (halt).

Based on the information provided above, the speed of this car is represented by the following equation;

s = √(30fd)

Where:

By substituting the given parameters, we have:

20 = √(30(0.3)d)

400 = 9d

d = 400/9

d = 44.44

Conversion:

1 mile = 5,280 feet.

44.44 miles = 234643.2 feet.

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The fractions, decimals, and percent equivalencies that are correct are:

b. 3/8 = 0.375 = 37.5%

c. 24% = 0.24 = 6/25

e.  24/30 = 80% = 0.8

A fraction is a part of a whole.

The number is represented mathematically as a quotient, where the numerator and denominator are split.

In a simple fraction both the numerator and denominator are integers.

In a complex fraction, a fraction appears in the numerator or denominator.

In a proper fraction, the numerator is less than the denominator.

A decimal is a fraction that contains a decimal point.

A percentage is a value out of 100 parts.

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The fair price for annual premiums for the policy holders to pay is $288.42

To determine the fair price for annual premiums, we need to take into account the company's expenses and desired profit. The company's total expenses can be calculated as the sum of the claims paid, marketing expenses, and labor expenses:

Total expenses = Claims paid + Marketing expenses + Labor expenses

Total expenses = $38000 + $1750 + $6000

Total expenses = $45750

To calculate the fair price for annual premiums, we need to add the desired profit to the total expenses and divide by the number of policy holders:

Fair price = (Total expenses + Desired profit) / Number of policy holders

Fair price = ($45750 + 20% of $45750) / 190

Fair price = ($45750 + $9150) / 190

Fair price = $54900 / 190

Fair price = $288.42

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The measure of angle x is: x = (3/5)(180 - z) = (3/5)(180 - 90) = 36 degrees

And the measure of angle y is:y = (2/5)(180 - z) = (2/5)(180 - 90) = 24 degrees

Since lines lll, mmm, and nnn are parallel to each other and ppp is a transversal, we can use the angle properties of parallel lines to find the relationship between angle x and angle y.

From the given information, we have:  2x = 3y

Simplifying this equation, we get:  x = (3/2)y

Now, we can use this relationship to find the measures of angles x and y in terms of a common variable. Let's use z as the common variable.

x + y + z = 180 (angles on a straight line)

Substituting x = (3/2)y, we get:  (3/2)y + y + z = 180

Simplifying this equation, we get: (5/2)y + z = 180

Now, we can express y in terms of z:

(5/2)y = 180 - z

y = (2/5)(180 - z)

Similarly, we can express x in terms of z:

x = (3/2)y = (3/2)(2/5)(180 - z) = (3/5)(180 - z)

Now, we can use the relationship between angle x and angle y to find the measure of angle x in terms of z: 2x = 3y

2[(3/5)(180 - z)] = 3[(2/5)(180 - z)]

Simplifying this equation, we get: (6/5)z = 108

z = (5/6)(108) = 90

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Answer:

Set your calculator to degree mode.

Use the Law of Cosines.

x^2 = 18^2 + 15^2 - 2(18)(15)(cos 105°)

x^2 = 688.7623

x = 26.2 cm

The charitable group has collected $126 to packages of food and clothing to the tornado-affected area

To represent the situation where a charitable group is shipping food and clothing packages to an area devastated by tornadoes, we can use the following inequality:

Let F be the number of food packages and C be the number of clothing packages. The shipping cost for food packages is $18 per package and for clothing packages is $14 per package.

They have collected $126 for shipping costs. The inequality representing this situation is:
18F + 14C ≤ 126

This inequality indicates that the total cost of shipping food packages (18F) plus the total cost of shipping clothing packages (14C) should be less than or equal to the available budget ($126).

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If a person places $81200 in an investment account earning an annual rate of 3. 6%, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.

To solve this problem using the formula V = Pent, we need to plug in the given values.

P = $81200 (the principal initially invested)
r = 0.036 (the annual interest rate, expressed as a decimal)
t = 13 years

Using the formula V = Pent, we get:

V = $81200e^(0.036*13)

Using a calculator, we can evaluate e^(0.036*13) to be approximately 1.5498.

So V = $81200*1.5498 = $125689.60

Therefore, the amount of money in the account after 13 years is approximately $125689.60 to the nearest cent.

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Answer:

C - 136

Step-by-step explanation:

Something important to remember here is that whenever you replace a variable with something else, that something else needs to go in parentheses.

3(7)² - 2(7) + 3

Following PEMDAS, you need to take care of that exponent before anything else. While parentheses are included as coming first, that is referring to operations within parentheses, which we don't have here.

3(49) - 2(7) + 3

Multiplication is the next step...

147 - 14 + 3

And finally, addition and subtraction.

147 - 11

136

Answer:

136

Step-by-step explanation:

Since the question stated that x= 7 you simply substitute all x in the expression with 7 and it would look something like this

3 (7)^2 - 2 (7) +3

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A function that can be used to find y, the mass of the substance in grams remaining after x hours is [tex]P(x) = 963(0.63)^x[/tex]

In Mathematics and Statistics, a population or substance that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or substance that decreases by r percent per unit of time is an exponential equation of this form:

[tex]P(x) = I(1 - r)^x[/tex]

Where:

By substituting given parameters into the , we have the following:

[tex]P(x) = I(1 - r)^x\\\\P(x) = 963(1 - 0.27)^x\\\\P(x) = 963(0.63)^x[/tex]

In conclusion, we can reasonably infer and logically deduce that the decay rate is equal to 63%.

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We can predict that around 50 of the additional 80 neighbors will feel safe in the neighborhood.

To make a prediction about the number of neighbors who will feel safe, we need to know the proportion of the initial 40 neighbors who felt safe. Let's say that 25 of the 40 neighbors surveyed felt safe.

Then, we can estimate the proportion of the larger group of 120 neighbors (the initial 40 plus the additional 80) who will feel safe as follows:

proportion feeling safe = number feeling safe / total number surveyed

proportion feeling safe = 25 / 40

proportion feeling safe = 0.625

We can use this proportion to estimate the number of the 80 additional neighbors who will feel safe:

number feeling safe = proportion feeling safe x total number surveyed

number feeling safe = 0.625 x 80

number feeling safe ≈ 50

So based on the information given, we can predict that around 50 of the additional 80 neighbors will feel safe in the neighborhood.

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The statement "The harmonic series: 1+1/2+1/3+1/4+... diverges, but when its terms are squared the resulting series converges." is True.

The harmonic series is defined as the sum of the reciprocals of the natural numbers: Σ(1/n) for n = 1 to ∞. This series is known to diverge, meaning that its sum tends to infinity as more terms are added.

However, when the terms of the harmonic series are squared, we get a new series called the p-series, with p=2: Σ(1/n^2) for n = 1 to ∞. The p-series converges if p > 1, which is true for p=2. Thus, the series Σ(1/n^2) converges to a finite sum.

In conclusion, the given statement is true, as the harmonic series diverges, but its squared terms result in a convergent series.

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The decision of how to divide a whole into fractional parts and where to begin and end a number scale depends on the context and purpose.

when dividing a whole into fraction parts, the decision of how to divide it depends on the context and the specific problem being solved. For example, if a pizza needs to be divided among 4 people, it would make sense to divide it into 4 equal parts or fourths. If a recipe calls for 1/3 cup of flour, then the whole cup would be divided into 3 equal parts or thirds.

Regarding number scales, they can begin and end at different points depending on the context and purpose. For example, a temperature scale could start at 0 degrees and end at 100 degrees for Celsius, or start at 32 degrees and end at 212 degrees for Fahrenheit.

A financial scale could start at negative numbers for debts and end at positive numbers for assets. In general, number scales are designed to provide a clear and consistent way of measuring and comparing quantities in a particular context.

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