Determine whether the series converges or diverges...

The vectors having length of 10 units are,

-6 + 8i , 10 ,  10i , -10 , -10i , 3 + 9i , -3 + 9i

We have to find the seven complex numbers that have the length of 10 units.

So, the vectors having length of 10 units are,

1) -6 + 8i

2) 10

3) 10i

4) -10

5) -10i

6) 3 + 9i

7) -3 + 9i

Hence, the vectors having length of 10 units are,

-6 + 8i , 10 ,  10i , -10 , -10i , 3 + 9i , -3 + 9i

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The average rate of change of the height as a function of time from 1 to 2 is 96

Rate of change

Rate of change defines the ratio that compares the change in values of the y variables to the change in values of the x variables.

Given,

The height (in feet) of a falling object with an initial velocity of 48 feet per second launched straight upward from the ground is given by h(t) = 16t² + 48t where is time (in seconds).

Here we need to find the average rate of change of the height as a function of time from 1 to 2.

In order to find the average rate of change we need to find the value for the time 1 and time 2.

For, that we have to apply the value on the function,

First, we have to apply the value of t as 1, then we get the value of the function as,

h(1) = 16(1)² + 48(1)

h(1) = 16 + 48

h(1) = 64

Now, we have to apply the value of t as 2, then we get,

h(2) = 16(2)² + 48(2)

h(2) = (16 x 4) + 96

h(2) = 64 + 96

h(2) = 160

Therefore, the average rate of change is,

=> rate of change = (160 -64) / 2 - 1

=> rate of change = 96

Therefore, the average rate of change from 1 to 2 is 96.

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The reflection of (-2, -2) and (-1, 1) are

preimage    image

(-2, -2)         (-4, -2)

(-1, 1)             (-5, 1)

Reflection is one of the movements in transformation that involve creation of mirror image

Transformation rule for reflection over x-axis at origin (0, 0)) is

(x, y) → (x, -y)

Transformation rule for reflection over line y-axis at origin (0, 0)) is

(x, y) → (-x, y)

The reflection to be done is over line x = -3

However, reflection over line x = -3 which is (-3, 0) is  done as follows

from -2 to -3 = -2 - -3 = 1 unit

reflecting 1 unit over x = -3

-3 - 1 = -4

(-4, -2)

(-2, -2) ⇒ (-2 - -3, -2) ⇒ (1, -2) ⇒ (-3 - 1, -2) → (-4, -2)

from -1 to -3 = -1 - -3 = 2 units

reflecting 2 units over x = -3

-3 - 2 = -5

(-5, 1)

(-1, 1) ⇒ (-1 - -3, 1) ⇒ (2, 1) ⇒ (-3 - 2, 1) → (-5, 1)

The calculation is simply saying put

(-2, -2) this point is just before the reflection line, the image will formed at the point just after the reflection line -3 which is -4 hence (-4, -2)

(-1, 1) this point is a line before the reflection line, the mirror image will be formed skipping a line (-4) to get to -5 hence the point  (-5, 1)

the y coordinate is constant for both situations

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Answer:

A. TPR

B. NM

C. 6

Step-by-step explanation:

1. The triangle NKM matches up with TPR. We also already knew KMN= PRT. So, it was just a matter of aligning the order.

2.  If you flip PRT then TR will match with NM

3. 4x-3=21

4x-3+3=21+3

Simplify: 4x=24

4x/4=24/4

x=6

AS per the combination method, Mr. Walters receive both payments in the same month in the 6th time.

Combination method:

A way of adding equations together in such a way that the variables are set aside, one by one is called as combination.

Given,

Mr. Walters receives a dividend every 5 months and a royalty check every 6 months. He received both payments in May 2019.

Here we need to find the next time he would receive both payments in the same month.

While looking into the given question we have identified he following things,

Dividend payment = 5 months

Royalty payment = 6 months

Both payment received = May 2019.

So, according to the combination method,

The value of n = 6 and the value of x = 5

So, the next time he would receive both payments in the same month is

=> 6 C 5 = 6! / 5! (6 - 5)!

Which results the value as 6.

Therefore, on 6th time from this payment he will receive both in the same month.

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Answer: 30 kids are in the math class

Step-by-step explanation: A simple way to solve this question is by knowing divisors. Since 24 is only 80% of X, then look for common divisors betweet 24 and 80% (4) If 6 is 20%, then 30 is 100%

Answer:

m = 37

Step-by-step explanation:

The interior and corresponding exterior angle of a triangle are always supplementary.

Therefore, we can set the sum of the two given angle measures to 180°:

[tex](2m-12) \textdegree + (3m+7) \textdegree = 180 \textdegree[/tex]

and solve algebraically for m.

[tex]2m-12 + 3m+7 = 180[/tex]

[tex](2m + 3m) + (-12+7) = 180[/tex]

[tex]5m-12+7 = 180[/tex]

[tex]5m - 5 = 180[/tex]

[tex]5m = 185[/tex]

[tex]m=37[/tex]

The value of m is 37.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.

Given:

m ∠Z = (2m − 12)° and exterior angle ∠Z =(3m + 7)°.

int. m <Z + ext. <Z= 180

2m - 12 + 3m + 7 = 180

5m - 5 = 180

5m = 185

m = 185/ 5

m = 37

Hence, the value of m is 37.

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For the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :

N(x) = 26,000 - 100x where  x ≥ 200.

As given in the function,

Number of passengers carried by airlines per month = 6,000

Price of ticket of each passenger = $200

For each $1 increase in the ticket price lose of 100 passengers

Let N(x) be the function representing the number of passengers

And x represents the price of the ticket where  x ≥ 200.

Required function to represent the number of passengers is given by :

N(x) = 6,000 -100 ( x -200)

⇒ N(x) = 6,000 -100x + 20,000

⇒ N(x) = 26,000 -100x where  x ≥ 200

Therefore, for the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :

N(x) = 26,000 - 100x where  x ≥ 200.

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The correct option is option (B) .

In other words Histograms , Pareto charts and scatter plots have a common thing that they are all visual tools to display data.

Histogram :

It show continuous data in ordered rectangular columns. There are usually no gaps between columns.

Scatterplot :

A scatterplot is an x-y plot that shows the relationship between two variables. Used to plot data points on vertical and horizontal axes.

Pareto Chart :

A Pareto chart is a common tool used by manufacturers to analyze quality and defect data, providing a quick visual representation of the frequency and cumulative percentage of occurrences of a particular problem.

Hence , all of three have a common thing that is they visualize tools to represent the data

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The required speed is 45 mph in each direction.

What is speed?

The definition of speed is a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.

We know that distance=rate*time

d=rt

45=rt

45=(r+30)(t-2)

rt=(r+30)(t-2)    

This shows,

rt=rt+30t-2r-60

0=30t-2r-60

if 45=rt, then r=45/t

substitute in the equation

0=30t-2(45/t)-60

multiply both sides by t

0=30t²-90-60t

on solving this quadratic equation, we get  t= 3 s, t=-1 s

consider positive value

t=3 hours

45=rt

45=r*3

r=45/3 =15 mph to new site

r+30=15+30=45 mph returning

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The minimum length that you can buy is 7.68 foot and the greatest length that you can buy is 8.32 foot

The length of the planks that lumber stores sell = 8 foot

The error tolerance of the plank = 4%

Then the 4% of the length 8 is

= 8 × (4/100)

Divide the terms

= 8 × 0.04

Multiply the terms

= 0.32

Therefore the error tolerance will be ±0.32

The minimum length that you can buy = 8 - 0.32

= 7.68 foot

The greatest length that you can buy = 8 + 0.32

= 8.32 foot

Hence, the minimum length that you can buy is 7.68 foot and the greatest length that you can buy is 8.32 foot

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Since the congruent angle is a right angle and it is not included, the two congruent sides of the triangles must include their hypotenuses and one of their legs.The triangles would be congruent by the hypotenuse leg theorem, which states that if the hypotenuse and one leg of a right triangle is congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.Answer:hypotenuse leg theorem

Anlges on the same side of the transversal add up to 180 degrees.

What is Transversal?

A transversal is a line in geometry that connects two lines in the same plane at two separate places. Transversals help determine if two or more lines in the Euclidean plane are parallel.

Solution:

Using the property of Lineaar Pair Angle the Interior Angles on the same side of the Transversal add up to 180 degrees.

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There are 420 arrangements for seven-digit numbers that can be formed with the digits of 2201213 by permutation.

The term permutation is simply the process of arrangement or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.

We can apply the formula for permutation;

[tex]p(n,r) = \frac{n!}{(n - r)!}[/tex]

where n = total number of object and r = number of objects selected.

Total number of digits = 7

number of the digit 2 = 3

number of the digit 1 = 2

number of the digit 0 = 1

number of the digit 3 = 1

so the permutation for the digits 2201213 is calculated as;

7!/(3! × 2! × 1! × 1!)

(7 × 6 × 5 × 4 × 3!)/(2 × 3!) {cancel out 3! with 3! and 4 with 2}

7 × 6 × 5 × 2

420 arrangements

Hence, by permutation, we can say that there are 420 arrangement for which seven-digit numbers can be formed with the digits of 2201213

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Step-by-step explanation:

any particular result with 2 dice has a probability of

1/6 × 1/6 = 1/36

a 3 on one die or both simply means at least one 3.

so, if all the 36 different outcomes we are looking at

3 1

3 2

3 3

3 4

3 5

3 6

1 3

2 3

4 3

5 3

6 3

the 3 3 combination can be counted only once !

so, we have 11 desired outcomes out of the possible 36.

so, the probability of getting at least one 3 is

11/36

the sum of at least 10 means the corresponding cases

4 6

5 5

5 6

6 4

6 5

6 6

in this case we don't need to turn this around, because it would be exactly the same outcomes again, and we don't want to count them twice.

so, we have 6 desired outcomes of the 36.

the probability of that is

6/36 = 1/6

Among the equations and inequality the true expression is 1 / 3 × 9 = 3.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Therefore, let's check the inequality that is true.

Hence,

1 / 4 × 28  > 8

28 / 4 > 8

7 > 8 (false)

1 / 6 × 48 < 5

48 / 6 < 5

8 < 5 (False)

1 / 3 × 9 = 3

9 / 3 = 3

3 = 3(True)

1 / 5 × 25 = 125

25 / 5 = 125

5 ≠ 125(False)

1 / 6 × 24 > 9

24 / 6 > 9

4 > 9 (False)

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Banerjee Company is  liable for FUTA tax this year and the net FUTA tax for the year is $528.60.

a. Yes. Banerjee Company liable for FUTA tax this year.

b. FUTA tax

FUTA tax =0.6%

Hence,

Net FUTA tax = (Wages paid  × tax rate ) +(Taxable wages × Tax rate)

Net FUTA tax = ($23,400 × 0.6%) + ($64,700 ×0.6%)

Net FUTA tax = $140.40 + $388.30

Net FUTA tax =$528.60

Therefore $528.60 is the Net FUTA tax.

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If Cassidy sells all of the popcorn, his profit would be equal to $208.00.

Mathematically, the slope-intercept form of a line can be modeled by using this linear function:

y = mx + b

Where:

In order to determine Cassidy’s profit, we would have to calculate the cost of the containers of popcorn by using this mathematical expression:

Note: the price tag for a container of popcorn is one dollar and fifty cents.

Cost of containers = revenue - total profit

Cost of containers = 1.50(15) - 5.50

Cost of containers = 22.5 - 5.50

Cost of containers = $17.00

Therefore, the linear function which models Cassidy’s profit is given by:

y = 1.50x - 17

If Cassidy sells all of the popcorn, his profit is given by:

Cassidy’s profit, y = 1.50x - 17

Cassidy’s profit, y = 1.50(150) - 17

Cassidy’s profit, y = 225 - 17

Cassidy’s profit, y = $208.00

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Complete Question:

Cassidy is selling popcorn for a fundraiser sale at the price shown.

A photo of a container of popcorn is shown. The price tag reads one dollar and fifty cents.

He purchases a total of 150 containers of popcorn to sell. After he sells 15 containers, he will make a total profit, after his upfront costs, of $5.50. Cassidy’s profit, after upfront costs, can be modeled by a linear function in the form y=mx+b.

What is Cassidy’s profit if he sells all of the popcorn?

HInt: Substitute 150 for x to find the profit if all the popcorn is sold.

Answer:

y = 1/2 x + 3/2

Step-by-step explanation:

A perpendicular slope is the opposite reciprocal, so it is 1/2

2 = 1/2(1) + b  To solve for b  

2 = 1/2 + b  Subtract 1/2 from both sides

1 1/2 = b

y = 1/2 x + 3/2

Answer:

m∠1 = 126°

m∠2 = 154°

Step-by-step explanation:

First, find the measure of angle that is supplementary to ∠1. (I will call it ∠A)

We know that the measures of the interior angles of a triangle add to 180°.

Therefore,

m∠A + 96° + 30° = 180°

m∠A + 96° = 150°

m∠A = 54°

From this value, we can solve for m∠1, since it is supplementary to ∠A:

m∠A + m∠1 = 180°

54° + m∠1 = 180°

m∠1 = 126°

To solve for ∠2, we must first solve for the adjacent supplementary angle that I have named ∠B.

First, the measures of the interior angles of a triangle add to 180°:

28° + m∠1 + m∠B = 180°

28° + 126° + m∠B = 180°

m∠B = 26°

Finally, we can solve for m∠2 because it is supplementary to ∠B.

m∠B + m∠2 = 180°

26° + m∠2 = 180°

m∠2 = 154°

Answer:

[tex]y = x^2 - 2x -1[/tex]

Step-by-step explanation:

General Form of a parabola :

[tex]y = a (x - h)^2 + k[/tex]

Solving :

h and k refer to the point of the vertex. In this case, it's (1, -2), so :

[tex]y = a(x - 1)^2 - 2[/tex]

Plug in values for x and y. In this case, they're (0, -1), so :

[tex]-1 = a(0 - 1)^2 - 2\\-1 =a(1) - 2\\1 = a[/tex]

Plug in all values :

[tex]y = ( x - 1)^2 -2[/tex]

Further simplifying :

[tex]y = ( x - 1 )^2 - 2 \\y = (x^2-2x + 1) - 2\\y = x^2 - 2x -1[/tex]

The answer is -9.

-2 -(+7) = -2 -7

-2 -7 = -9

The library’s December record is 29442  

Mathematical operations are Operators which emphasize particular actions like adding, subtracting, adding multiple times, dividing, etc.

There are 4 basic operations in mathematics as given below.  

1. Addition  =>  (+)

2. Subtraction  => (-)

3. Division  => (÷)

4. Multiplication  =>  (x)  

Here we have

In 2017 the library was able to record 4907 borrowed books  

By December of the same year, the library has 6 times its January record.  

[ Here we use Multiplication to find the December record ]

The December record = 6 times of January record

⇒ 6 × January record

⇒ 6 × 4907    

⇒ 29442

Therefore,

The library’s December record is 29442

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Answer:

-28 meters

Step-by-step explanation:

The speed of the submarine = (-3.5) per minute

Since it's descending, we know the answer will be negative.

The distance covered by the submarine is 8 minutes = (-3.5) x 8 = -28 meters.

Answer:

28

Step-by-step explanation:

-3.5*8

well, we know the price is $18, now, if we jack it up by 70%, well, what's 70% of 18?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 18}}{\left( \cfrac{70}{100} \right)18}\implies 12.6~\hfill \underset{price}{\stackrel{18~~ + ~~12.6}{\text{\LARGE 30.60}}}[/tex]

Answer: 6,001 milliliters

Step-by-step explanation: 6 Liter translates to 6,000 milliliters, which is 1 less than 6,001 milliliters.

Answer:

I believe 6 liters is more.

Sorry I don't have the answer but I can rule out 2.

Step-by-step explanation:

4,2 and 2,0 are not going to be correct because I got them wrong on a quiz I had 2 attempts to take.

So its either 1,-3 or -1,-5.

Hope this helps you.

Answers in bold

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

Explanation:

Always start with what is given. The last statement is the thing we want to prove.

Complementary angles add to 90 degrees. They form a right angle.

When "definition of congruence" is mentioned, we go from two angles being congruent to having them be of the same measure. It's a slight change of notation.

Vertical angles form whenever we cross two lines to form an X shape. The vertical angles are opposite one another, and always congruent.

The substitution property is the idea of replacing one thing with something it is equivalent to. In other words, we plug in the item.

Notice on line 2, if we replace "angle 1" with "angle 4" (valid because the two angles are congruent), and then replace "angle 2" with "angle 3", then we get the result on line 7.

Answer:

1. Given.

2. Definition of complementary angles.

3. Given.

4. Definition of congruent angles.

5. Vertical Angles Theorem.

6. Definition of congruent angles.

7. Substitution Property of Equality.

8. Definition of complementary angles.

Step-by-step explanation:

Statement 1

∠1 and ∠2 are complementary.

Reason:  Given.

Statement 2

m∠1 + m∠2 = 90°

Reason:  Definition of complementary angles.

Complementary angles are two angles that sum to 90°.  Therefore, if ∠1 and ∠2 are complementary, then their measures must sum to 90°.

Statement 3

∠1 ≅ ∠4

Reason:  Given.

Statement 4

m∠1 = m∠4

Reason:  Definition of congruent angles.

Congruent angles are angles with exactly the same measure.  As angle 1 is congruent to angle 4, then their measures are equal.

Statement 5

∠2 ≅ ∠3

Reason:  Vertical Angles Theorem.

Vertical angles are always congruent.  

Statement 6

m∠2 = m∠3

Reason:  Definition of congruent angles.

Congruent angles are angles with exactly the same measure.  As angle 2 is congruent to angle 3, then their measures are equal.

Statement 7

m∠4 + m∠3 = 90°

Reason:  Substitution Property of Equality.

For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.

As m∠2 = m∠3 and m∠1 = m∠4, replacing them in m∠1 + m∠2 = 90° gives m∠4 + m∠3 = 90°.

Statement 1

∠3 and ∠4 are complementary.

Reason:  Definition of complementary angles.

Complementary angles are two angles whose sum is 90°.  Therefore, if the sum of m∠4 and m∠3 is 90°, this means that ∠4 and ∠3 must be complementary.

The area of the irregular shape is 288 sq. units

Given,

We have to estimate the area of the irregular shape;

Here,

The shape can be broken down into a trapezoid, a rectangle, and a triangle

The total area = 76.5 + 140 + 71.5 = 288 sq. units

Therefore,

The area of the irregular shape is 288 sq. units

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