Does the following series converge or diverge?
Σ
n=1
4
8√n +7³√n
O The series diverges.
O The series converges.

The function that has a minimum and is transformed to the right and down from the parent function is; g(x) = 8(x² - 3²) - 5

By inspection, only Functions B) and D) have a minimum.

For the first function in option B, we have:

g(x) = 4(x²- 6x + 9) + 1

This can be simplified to;

g(x) = 4( x - 3 )² + 1

Thus, we can say that this first function is transformed to the right and up from the parent function.

For the second function in option D, we have;

g(x) = 8(x² - 6x + 9 ) - 5

The function can be simplified to get;

g(x) = 8( x - 3 )² - 5

Thus, we can say that it is transformed to the right and down.

The function that has a minimum and is transformed to the right and down from the parent function is D

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Answer: option D

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to begin by making each fraction have  the same common denominator. The LCF (least common factor) is 77. So, knowing this, we can now multiply the fractions that need to have a denominator of 77.

1. 5/7*11/11=55/77

2. 9/11 * 7/7 =63/77

Now we can add

55/77 + 63/77 + 21/77 = 139/77 or 1.805194805

Answer:

mLx = 144

mLy=154

Step-by-step explanation:

180-36=144

x=144

180-62=118

36+118=154

180-154=26

180-26=154

y=154

Answer:

154 degrees

Step-by-step explanation:

you can find measure of angle y, since it is the supplement of angle a, so

measure of angle y = 180 - measure of angle a, which is 144 degrees

you can find the measure of angle x, by finding its complement.

Looking at the center triangle, we see that it is formed from angle a, the supplement of angle b, and the supplement of angle x, so the equation is 180 = 36 + 180 - 62 + supplement of angle x

so, the supplement of angle x is 26 degrees, so x is 154 degrees

Answer:

  |-3| = 3 and -|-4| = -4

Step-by-step explanation:

The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.

|-3| = 3 (true) and -|-4| = -4 (true)   ⇒ this statement is true

|-3| = 3 (true) and |-4| = -4 (false)   ⇒ this statement is false

-|3| = 3 (false) and |4| = 4 (true)   ⇒ this statement is false

|-3| = 3 (true) and -|4| = 4 (false)   ⇒ this statement is false

__

Additional comment

A compound "and" statement is only true if all of the parts of it are true.

Answer:

5,526

Step-by-step explanation:

Mean of scores = Total Value of Scores / Number of Values

= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]

= 5,526

Answer:5526

Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers

Using relations in a right triangle, it is found that the length of AC is of 14 cm.

The relations in a right triangle are given as follows:

Researching this problem on the internet, we have that:

Hence the hypotenuse is found as follows:

sin(A) = 48/h

0.96 = 48/h

h = 48/0.96

h = 50 cm.

The length of side AC is the other leg of the triangle, found using the Pythagorean Theorem, hence:

[tex]x^2 + 48^2 = 50^2[/tex]

[tex]x^2 = \sqrt{50^2 - 48^2}[/tex]

x = 14 cm.

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The count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.

In the question, we are given that there are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills.

We are asked to find the count of each denomination, given there was altogether $115 in the bag.

We assume the number of $1-bills in the bag to be x.

Total amount in x bills of $1 =  x * $1 = $x.

Given that there are 5 fewer $5-bills than $1-bills in the bag, number of $5-bills in the bag = x - 5.

Total amount in (x - 5) bills of $5 = (x - 5) * $5 = $5(x - 5).

Given that there are half as many $10-bills as $5-bills in the bag, number of $10-bills in the bag = (x - 5)/2.

Total amount in (x - 5)/2 bills of $10 = (x - 5)/2 * $10 = $5(x - 5).

Thus, the total amount in the bag = $x + $5(x - 5) + $5(x - 5).

But, the total amount in the bag = $115.

Thus, we get an equation:

$x + $5(x - 5) + $5(x - 5) = $115,

or, x + 5x - 25 + 5x - 25 = 115,

or, 11x = 115 + 50,

or, 11x = 165,

or, x = 165/11,

or, x = 15.

Thus, number of $1-bills = x = 15.

The number of $5-bills = x - 5 = 15 - 5 = 10.

The number of $10-bills = (x - 5)/2 = (15 - 5)/2 = 10/2 = 5.

Thus, the count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.

The provided question is incomplete. The complete question is:

There are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills. If there is $115 altogether, find the number of each type of bill in the wallet."

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The value |x−9|≤9 is equivalent to [18,0] in interval notation.

According to the statement

We have given that the distance of 9 from the number 9. and we have to find the all value of x between it.

So, For find all x value we use absolute value inequalities.

distance of 9 from number 9.

So, when we draw the number line

we see that the number will become

The distance from x to 9 can be represented using an absolute value symbol, |x−9|.

Write the values of x that satisfy the condition as an absolute value inequality.

So, it become

|x−9|≤9

Now write two inequalities then it become

x−9≤9 and x−9≥−9

x≤18  and x≥0

So, The solution set is x≤18 and x≥0,

then the solution set is an interval including all real numbers between and including 18 and 0.

So |x−9|≤9 is equivalent to [18,0] in interval notation.

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The material-handling cost per wall mirror under activity-based costing is $280

What is activity-based costing?

Activity-based costing involves absorbing overheads based on cost drivers which directly impact the incurrence of the overhead, in this case, material moves determine the amount of material-handling costs to be incurred, hence, material-handing overheads would be absorbed into the two products based on material moves, which is the appropriate cost driver.

There 25 materials move in both divisions (i.e. 7+18=25)

Material-handling cost per material move=Budgeted material-handling costs /total material moves

Budgeted material-handling costs =$30,000

Material-handling cost per material move=$30,000/25

Material-handling cost per material move=$1,200

Total material-handing costs for wall mirror=number of material moves for wall mirror*Material-handling cost per material move

Total material-handing costs for wall mirror=7*$120

Total material-handing costs for wall mirror=$8,400

material-handling cost per wall mirror=Total material-handing costs for wall mirror/number of wall mirrors

material-handling cost per wall mirror=$8,400/30

material-handling cost per wall mirror=$280

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Answer:

Step-by-step explanation:

9.05737

The length of the radius of the cone to the nearest foot is 5 feet.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The surface area of a cone is 216π sq units and the height of the cone is  (5/3) times of the radius.

∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.

∴ πrl = 216π.

√{(34/9)r³ = 216.

1.9r³ = 216.

r³ = 113.7.

r = 4.8 feet Or 5 feet.

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From all the steps below, we have been able to prove that; 1 - cot23° = 2/(1 - cot22°).

We want to prove that  1 - cot23° = 2/(1 - cot22°).

We will prove it using the trigonometric expression

cot(22° + 23°) = cot45°

Using trigonometric identities, we can rewrite as;

(cot22° cot23° - 1)/(cot22° + cot23°) = 1

Cross multiply to get;

cot22° cot23° - 1 = cot22° + cot23°

Rearrange to get;

cot22° cot23° - 1 - cot22° - cot23° =0

⇒ cot22° cot23° - 1 - cot22° - cot23° + 2 =2

⇒ cot22° cot23° + 1 - cot22° - cot23° =2

⇒ cot22° cot23° - cot22° - cot23° + 1 = 2

⇒ cot22° (cot23° - 1) - 1 (cot23° - 1) = 2

⇒ (cot22° - 1) (cot23° - 1) = 2

Divide both sides by  (cot23° - 1) to get;

cot23° - 1 = 2/(cot22° - 1)

⇒ 1 - cot23° = 2/(1 - cot22°).

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The solution to the equation is 0.07, 0.17, 0.27, 0.38........

The trigonometry equation is given as:

tan(30x - 90°) = -x³

We start by splitting the trigonometry equation as follows, by creating two different equations

y = tan(30x - 90°)

y = -x³

Next, we plot the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³

From the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³, we have the x coordinate of the point of intersection to be:

x = 0.07, 0.17, 0.27, 0.38........

Hence, the solution to the trigonometry equation is 0.07, 0.17, 0.27, 0.38........ .

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The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).

In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:

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The magnitude of -1-5i is √26.

Given the complex expression; -1 - 5i

To find the magnitude, we use the formula;

| a+bi | = √[ a² + b² ]

| a+bi | = √[ a² + b² ]

| -1-5i | = √[ (-1)² + (-5)² ]

| -1-5i | = √[ 1 + 25 ]

| -1-5i | = √26

Therefore, the magnitude of -1-5i is √26.

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(infinity -1/2]u [-1/2 -1/2] u [1/2 infinity)

Answer: 9

Step-by-step explanation: it is what it is

15-6=9 omg i never knew

Based on the number of periods for the simple discount note to reach maturity and the discount rate, the proceeds are $7,598.74.

You can solve for the discounted price as:

= Maturity value x discount rate x number of periods

Solving gives:

= 7,700 x (6% / 365) x 80

= $101.26

The proceeds can then be found by subtracting the discounted price from the maturity price.

Solving for the proceeds gives:

= 7,700 - 101.26

= $7,598.74

Based on the simple discount note period, the maturity value, and the discount rate, the proceeds can be found to be $7,598.74.

In conclusion, the proceeds are $7,598.74.

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Answer:

index of m is -2

Step-by-step explanation:

any number or letter to the negatIve power(index) is the same as 1 divided by that number or letter to the positive index.

for example, 10^-2 = 1/10^2 and X^-4 is the same as 1/X^4.

The value of x from the given circle is 4

The intersecting chords theorem is a statement in geometry that describes a relation of the four line segments created by two intersecting chords within a circle.

It states that the products of the lengths of the line segments on each chord are equal.

According to the theorem;

x * 3 = 2 * (4 + 2)

3x = 2(6)

3x = 12

Divide both sides by 3

3x/3 = 12/3

x =4

Hence the value of x from the given circle is 4

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Answer: square of 459 is 210681

According to John Locke, Experience is how we acquire basic knowledge.

What explains why, in many of the problems, historical data is used is; Information changes rapidly.

1) John Locke's theory simply means that all knowledge comes exclusively through experience. He argues that at birth the mind is a tabula rasa, that humans fill with ideas as they experience the world through the five senses.

Thus, the missing word in the question is "Experience".

2) The reason why historical data is used in may problems is because Information changes rapidly. The information being circulated currently may be different from that circulated 100 years ago.

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Answer: 55.2 in

Step-by-step explanation:

1ft = 12 in

41.4/9 = 4.6 ft

4.6 x 12 = 55.2 in

The length of the vine wounded to the tree is 21 feet.

Circumference is the perimeter of a circular object. Therefore,

circumference = 2πr

where

The circumference of the tree is 3 feet. A vine was wound around 7 times .

The length of the vine can be calculated as follows:

Therefore,

circumference = 3 ft

length of the vine = 7 × 3

length of the vine = 21 feet

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First of all, we would calculate the predetermined overhead rate by using this formula:

Predetermined overhead rate = Manufacturing overhead/Direct material costs

Predetermined overhead rate = $2,342,400/$1,464,000

Predetermined overhead rate = 1.6 per DM $.

Next, we would calculate the overhead applied by using this formula:

Overhead applied = Job × DM cost

For job 0701, we have:

Overhead applied = 76,000 × 1.6

Overhead applied = $121,600.

For job 0702, we have:

Overhead applied = 104,000 × 1.6

Overhead applied = $166,400.

For job 0703, we have:

Overhead applied = 135,000 × 1.6

Overhead applied = $216,000.

For job 0704, we have:

Overhead applied = 67,000 × 1.6

Overhead applied = $107,200.

For the overapplied manufacturing overhead for year 1:

Less applied overhead = $1,630,000 × 1.6

Less applied overhead = $2,608,000.

Overapplied manufacturing overhead = Actual overhead cost - Less applied overhead

Overapplied manufacturing overhead = $2,480,000 - $2,608,000

Overapplied manufacturing overhead = $128,000.

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2 angles that have the same angle measure are congruent.

Given that the two angles have the same angle measure.

Congruence is a term reserved for geometry. Two metrics are congruent when you can perfectly map to each other by mirroring, rotating, and translating without distortion.

We know that two shapes or objects are congruent if they have the same shape and the same size. For two angles to be congruent, they must coincide when they are overlapped. This is only possible if the two angles are equal.

Therefore, if two angles have the same measure, then they are said to be congruent.

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Answer:

GC and GD

Step-by-step explanation:

The only points on plane L are: J, C, G, D

GC and GD

The company's inventory turnover ratio, based on the financial data, equals 10 times.

The inventory turnover ratio measures the number of times the company sells and replaces its inventory over a given period.

The formula for calculating the Inventory Turnover Ratio is the Cost of Goods Sold divided by the Average Inventory.

The Average Inventory is the mean of the beginning and ending inventories.

Sales revenue = $60,000

Cost of goods sold = $20,000

Beginning inventory = $1,600

Ending inventory = $2,400

Average inventory = $2,000 ($1,600 + $2,400)/2

Inventory turnover ratio = 10x ($20,000/$2,000)

Thus, the company sells and replaces its inventory over a period of 10 times.

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Step-by-step explanation:

5)f(g(8))

from the table g(8)=4

f(4) =4 from the table

7)g(f(5))

from the table f(5)=0

g(0)=9 from the table

9)f(f(4))

from the table f(4)=4

f(4)=4 from the table

Answer:

x - 2, x - 3

Step-by-step explanation:

3x² - 5x + 2

x² - 5x + 6

(x - 3)(x - 2)

length = x - 2

width = x - 3