Find all values of x for which the series converges. (enter your answer using interval notation. ) [infinity] (4x)n n = 1

The amount paid to the man in the first year given the total he received in four years is $3,700.

= (x + 1000)

= (x + 1500)

Total payment = first year + second year + third year + fourth year

x + (x + 500) + (x + 1000) + (x + 1500) = 17,800

x + x + 500 + x + 1000 + x + 1500 = 17800

4x + 3000 = 17,800

4x = 17,800 - 3000

4x = 14,800

x = 14,800/4

x = $3,700

Therefore, $3,700 was paid to the man in the first year.

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In (A) statistics class Wilson's students earn a higher ratio of a's to b's.

To find the higher ratio:

Given -

As we can observe that 3:5 < 11:15.

Therefore, in (A) statistics class Wilson's students earn a higher ratio of a's to b's.

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Answer:

  12% loss

Step-by-step explanation:

The selling price is the sum of the cost price and the markup. Here, the markup (profit) is expressed as a percentage of the cost price.

The relation between selling price and cost price is ...

  selling price = cost price + cost price × markup fraction

  selling price = cost price × (1 + markup fraction)

Then the original cost price is ...

  cost price = (selling price) / (1 + markup fraction)

  cost price = #1.35 / (1 +8%) = #1.25

After the change in selling price, we can find the markup fraction (profit rate) to be ...

  1 + markup fraction = (selling price)/(cost price)

  markup fraction = (selling price)/(cost price) -1

  markup fraction = #1.10/1.25 -1 = 0.88 -1 = -0.12

The trader has a 12% loss when selling the oranges at #1.10.

The average view of the dress code is that this dress is not good

For Rashad's sample to be a random sample gotten from the population, the following must be considered.

To do this, we simply create a bar graph.

The response would go into the x-axis, while the number of people would go into the y-axis

See attachment for bar graph

The average view of the dress code is that this dress is not good

It is considered the average view of the dress code because it is the opinion with the most frequency

The number of students that do not like the dress as:

210 + 206 + 770 = 1186

Their percentage is

Percentage = 1186/(210 + 206 + 770 + 358)

Percentage = 77%

This means that

Yes, the dress will change

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The missing value in the table is 12.4

From the question, we are to determine the missing value in the table

From the given information,

The chart shows conversion between kilometers and miles

The given table is

Kilometers           Miles

2                            1.2

7                            4.2

20                          ?

30                          18

NOTE: 1 kilometer ≈ 0.62 miles

Then, 20 kilometer ≈ 20×0.62 miles

20 kilometer ≈ 12.4 miles

Hence, the missing value in the table is 12.4

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The inequality to describe the possible temperature in Bismarck, North Dakota given that t represent temperature is t < 4°F

The inequality signs are;

Let

So

t < 4°F in Bismarck, North Dakota

This means, temperature in Bismarck, North Dakota is less than 4°F

Therefore, t < 4°F is the inequality to represent temperature in Bismarck, North Dakota.

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Answer:

416 people

Step-by-step explanation:

The way you get the answer is by adding up the number of people from the sample, which gives you 175 people. After finding that you take the number of people who like pretzels (26) and divide it by 175, giving you 0.16 or 16%.
This means 16% of people will like pretzels, so you apply this to the actual number of people coming, 2600, and find 16% of 2600 (0.16 x 2600) which is 416 people. I hope this makes sense :)

All the parts of the questions about the given histogram have been answered below.

(A) The distribution of minting year:

According to the histogram, the distribution of minting years is 1900-1910 and 1940-2020.

(B) The median:

Add the two middle numbers together and divide them by two to get the median.

10 + 15 / 2 = 12.5

So, the median is somewhere between 10-15.

(C) The range:
The range is computed by subtracting the lowest and highest values.

25 - 0 = 25

So, the range is 25.

(D) The potential outliers:

According to the histogram, the potential outliers are 1910-1940.

Therefore, all the parts of the questions have been answered.

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Answer:

Step-by-step explanation:

I got it right on khan

The measure of the complement  is 25°.

If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

Given that, [tex]A_{1}[/tex] = 115°

sum of two angles  [tex]A_{1}+A_{2} = 180[/tex]°

                                  [tex]A_{2} = 180- A_{1}[/tex]

                                  [tex]A_{2} = 180- 115[/tex]

                                  [tex]A_{2} = 65[/tex]°

Since,  [tex]A_{1}[/tex] and  [tex]A_{2}[/tex] are supplementary angles.

Now,

Complementary angles add to 90, so the complement of [tex]A_{2}[/tex]  is 90 - [tex]A_{2}[/tex] .

Then,

90-65

= 25°

Hence,  The measure of the complement  is 25°.

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Answer:

landline

hshdjdh

dbbdhdhdh

bdbdhdhdhe

Answer:

Router

Step-by-step explanation:

Hope this helps

Answer:

$0.32

Step-by-step explanation:

8 ounces is 1/16 of a gallon so

5.12*(1/16) = 0.32

Answer:

32 cents (0.32 dollars)

Step-by-step explanation:

One gallon contains 128 ounces

Calculate the cost of each ounce:

[tex]\frac{5.12}{128} =0.04[/tex]

costs 4 cents an ounce

Calculate the cost of 8 ounces:

[tex](8)(4)=32[/tex]

Hope this helps

The vertices T<4, 1> (DEF) are D' = (5, 4), E' = (6, -3) and F' = (1, 2)

The vertices of the triangle are given as:

D(1, 3), E(2, -4), and F(-3, 1).

The transformation represented by T<4, 1> (DEF) is:

(x,y) = (x + 4, y + 1)

So, we have;

D' = (1 + 4, 3 + 1)

D' = (5, 4)

E' = (2 + 4, -4 + 1)

E' = (6, -3)

F' = (-3 + 4, 1 + 1)

F' = (1, 2)

Hence, the vertices T<4, 1> (DEF) are D' = (5, 4), E' = (6, -3) and F' = (1, 2)

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If there was just one of each animal, the outcome would be that of 1 cow and 1 dog.

Option(B) is correct.

The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function.

If you own two cats worth $100 each and a cow worth $2,500. One dog, though, is worth $7000.

Cost of 1 cow = $2500

Cost of 2 cats = $100

Thus, cost of 1 cat = $100/2 = $50

Cost of 1 dog = $7000

If there was only 1 of each animal, total cost = $(2500+50+7000) = $9550.

This outcome resembles the situation of having 1 cow and 1 dog.

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Answer:

[tex]h = \frac{2A}{b+c}[/tex]

Step-by-step explanation:

Original Equation:

[tex]A = \frac{1}{2} (b+c)h[/tex]

Divide both sides by height

[tex]\frac{A}{h} = \frac{1}{2}(b+c)[/tex]

Raise both sides to the exponent -1 :

[tex](\frac{A}{h})^{-1} = (\frac{1}{2}(b+c))^{-1}[/tex]

Rewrite using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = (\frac{b}{a})^{x}[/tex]

[tex]\frac{h}{A} = \frac{1}{\frac{1}{2}(b+c)}\\[/tex]

Multiply 1/2 by (b+c)

[tex]\frac{h}{A} = \frac{1}{\frac{b+c}{2}}\\[/tex]

Keep, change, flip

[tex]\frac{h}{A} = \frac{1}{1} * \frac{2}{b+c} = \frac{2}{b+c}[/tex]

Multiply both sides by A

[tex]h = \frac{2A}{b+c}[/tex]

Also I forgot to mention but the exponent (-1) can be ignored after you flip it, since: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex], but since in our case the exponent is 1, and [tex]a^1 = a[/tex], so there's really no need to write out the distribution part, since we just get the same fraction, after flipping it.

Answer:

a = 12

x = 5.714

Step-by-step explanation:

sf = 15 / 9

20 / (15 / 9) = 12

a = 12

sf = 21 / 6

20 / (21 / 6)

x = 5.714

Answer: 8 Oranges

Step-by-step explanation:

Given information

3 Oranges = $1.23

Total cost = $3.28

Determine the unit price of an orange

Unit price = Cost ÷ Number of Oranges

Unit price = 1.23 ÷ 3

Unit price = $0.41 / orange

Determine the number of oranges bought

Number of orange × Unit price = Total cost

N × (0.41) = (3.28)

Divide 0.41 on both sides

N = 3.28 ÷ 0.41

[tex]\Large\boxed{Number~of~oranges=8}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Option (1)

Step-by-step explanation:

We need a recursive formula.

The common ratio is 2.

So, the answer is option 1.

The match of solutions with the exponential expressions is

1) [tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}=2[/tex]

2) [tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)=1/2[/tex]

3) [tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} =2[/tex]

4) [tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}=1[/tex]

The base will be multiplied by itself a certain number of times, as indicated by the exponent (also known as a power or degree).

Formulae for solving exponents are referred to as exponents formulas. The exponent of a number is written as [tex]x^{n}[/tex], which means that x has been multiplied by itself n times.

[tex]x^{n}(x^{m})=x^{n+m} \\\frac{x^{n} }{x^{m} }=x^{n-m} \\(x^{n} )^{m} =x^{nm} \\((x)(y))^{n}=x^{n}(y^{n} \\x^{0}=1[/tex]

1) the solution of the first expression will be

[tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}[/tex]

[tex](2^3) (3^{-6} ) (5^2) (3^4) / (3^{-2}) (10^2)= (2.2^2.5^2) (3^{-6}.3^4) / (3{^-2}) (10^2)= (2)(10^2) (3^{-2}) / (3^{-2}) (10^2)\\=2[/tex]

2)The solution of the second expression will be

[tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)[/tex]

Any  number with power zero is 1.

So,

[tex](3^3) (1^2) (3^{-3}) (2^{-3}) (2^2)= (2^{(-3+2)})=2^-1\\= 1/2[/tex]

3) The solution of third expression will be

[tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} \\= \frac{(12^7) (2^{-3}) (5^{-3}) (5^2)}{(12^7) (5^{-1}) (2^{-4})} =\frac{(2^-3) (5^{(-3+2)})}{(5^{-1}) (2^{-4})} = \frac{(2^{-3}) (5^{-1})}{(5^{-1}) (2^{-}4)} = \frac{1}{(2^{-1})} = 2[/tex]

4) The solution to the forth expression will be

[tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}\\=2^{0}\\ =1[/tex]

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Answer:

The person above litteraly gave you the answer just reread the first equations and then you will figure it out

Step-by-step explanation:

Answer:

Create a table.

Plug values into the equation to complete the table.

Use the table to plot points on the graph.

Draw lines through the points on your graph.

The graph should look linear because there is an x that doesn't have a power greater than or less than 1.

Using the proportionality theorem, the measurements are: c. E = 22 and F = 55.

If two transversals intersect three or more parallel lines, they divide the lines in such a way that the smaller segments are proportional to each other or have ratios that are equal to each other.

Given the following:

A = 36,

B = 24,

C = 60

D = 33.

Since all lines are parallel, then:

A/D = B/E = C/F

Find the measure of E using the ratio, A/D = B/E:

36/33 = 24/E

Cross multiply

E = (24 × 33)/36

E = 22

Find the measure of F using the ratio, A/D = C/F:

36/33 = 60/F

Cross multiply

F = (60 × 33)/36

F = 55

The answer is: c. E = 22 and F = 55.

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I assume the given series is

[tex]\displaystyle 2 + \frac4{2^2} + \frac8{3^2} + \frac{16}{4^2} + \cdots = \frac{2^1}{1^2} + \frac{2^2}{2^2} + \frac{2^3}{3^2} + \frac{2^4}{4^2} + \cdots = \sum_{n=1}^\infty \frac{2^n}{n^2}[/tex]

By the ratio test, the series diverges, since

[tex]\displaystyle \lim_{n\to\infty} \left|\frac{2^{n+1}}{(n+1)^2} \cdot \frac{n^2}{2^n}\right| = 2 \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = 2 > 1[/tex]

Answer: (-5, -5)

Step-by-step explanation:

(-4, 0)

Here, -4 is our x value and 0 is our y value

The x value moves horizontal (left and right) while the y value moves vertical (up and down)

If we move 1 unit left, we change x by -1 so, -4 -1 = -5

If we move 5 units down, we change y by -5 so, 0 -5 = -5

Therefore,

our new endpoint is: (-5, -5)

Answer:

The answer is 1

Step-by-step explanation:

Formula for finding the slope: [tex]\frac{y2-y1}{x2-x1}[/tex]

Take y2 and y1 from (4,4) (1,1)

Take x2 and x1 from (4,4) (1,1)

[tex]\frac{y2-y1}{x2-x1} = \frac{4-1}{4-1} = \frac{3}{3} = 1[/tex]

This is how the answer is 1

Hope it helps :)

The sum of the complex number in standard form is 8 + 3i

Complex numbers are square roots of negative numbers. The square root of -1 for example is equal to "i" as shown;

√-1 = i

The complex number is written as x + iy. Given the expression

(9 + 6i) − (1 + 3i)

Expand to have:

9 + 6i − 1 - 3i

Collect the like terms

9-1 + 6i - 3i

Group into real and imaginary parts

(9-1) + (6i-3i)

8 + 3i

Hence the sum of the complex number in standard form is 8 + 3i

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Answer:

(f ￮ g)(11) = - 1

Step-by-step explanation:

evaluate g(11) then substitute the result obtained into f(x)

g(11) = 11 - 7 = 4 , then

f(4) = [tex]\sqrt{4}[/tex] - 3 = 2 - 3 = - 1

The equation of the circumference of a circle in terms of [tex]\pi[/tex] is [tex]2\pi r[/tex] or [tex]\pi d[/tex].

The circumference for a circle with diameter 10 is [tex]10\pi[/tex].

The circumference for a circle with diameter 19 is [tex]19\pi[/tex].

The circumference for a circle with diameter 30 is [tex]30\pi[/tex].

The circumference for a circle with diameter 16 is [tex]16\pi[/tex].

Relatively easy, right?

The equation of the area of a circle in terms of [tex]\pi[/tex] is [tex]\pi r^2[/tex].

The area of a circle with radius 5 is [tex]25\pi[/tex].

The area of a circle with radius 9.5 is [tex]90.25\pi[/tex].

The area of a circle with radius 15 is [tex]225\pi[/tex].

The area of a circle with radius 8 is [tex]64\pi[/tex].

Hope this helped!

(By the way, I don't know why you're using hard formulas for trying to find the radius or diameter. The diameter is simply twice the radius, and the radius is simply half the diameter.)

Answer:

Circumference = 10[tex]\pi[/tex], 19[tex]\pi[/tex], 30[tex]\pi[/tex], 16[tex]\pi[/tex]

Area = 25[tex]\pi[/tex], 90.25[tex]\pi[/tex], 225[tex]\pi[/tex], 64[tex]\pi[/tex]

Step-by-step explanation:

For the first row we have the radius which is 5, the diameter is 10. The formula for circumference is 2[tex]\pi[/tex]r. So for this one its gonna be 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]

radius = 5

diameter = 10

circumference = 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]5^{2}[/tex] or 25[tex]\pi[/tex]

for the second row

radius = 9.5

diameter = 19

circumference = 2[tex]\pi[/tex]9.5 or 19[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]9.5^{2}[/tex] or 90.25[tex]\pi[/tex]

for the third row

radius = 15

diameter = 30

circumference = 2[tex]\pi[/tex]15 or 30[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]15^{2}[/tex] or 225[tex]\pi[/tex]

for the fourth row

radius = 8

diameter = 16

circumference = 2[tex]\pi[/tex]8 or 16[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]8^{2}[/tex] or 64[tex]\pi[/tex]

Answer:

6/10

Step-by-step explanation:

3/6 = 0.5

6/10 = 0.6

0.6>0.5

Then

6/10 is greater than 3/6

Six different sized rectangles that have an area of 64 square units:

1) 64 units x 1 unit
2) 32 units x 2 units

3) 16 units x 4 units

4) 40 units x 1.4 units

5) 20 units x 3.2 unit

6) 10 units x 6.4 units

For given question,

Let l be the length of the rectangle and w be the width of the rectangle.

We know that, the area of a rectangle is equal to

A = l × w

Here, A = 64 square units

So, we get an equation

l × w = 64                     ...............................(1)

let's assume different values of l to get the different values of w.

Case 1) For l = 64 units

substitute in the equation 1

⇒ 64 × w = 64

⇒ w = 64/64

⇒ w = 1 units

The dimensions of the rectangle are 64 units x 1 unit

See the draw in the attached figure 1

Case 2) For l = 32 units

substitute in the equation 1

⇒ 32 × w = 64

⇒ w = 64/32

⇒ w = 2 units

The dimensions of the rectangle are 32 units x 2 unit

See the draw in the attached figure 2

Case 3) For l = 16 units

substitute in the equation 1

⇒ 16 × w = 64

⇒ w = 64/16

⇒ w = 4 units

The dimensions of the rectangle are 16 units x 4 unit

See the draw in the attached figure 3

Case 4) For l = 40 units

substitute in the equation 1

⇒ 40 × w = 64

⇒ w = 64/40

⇒ w = 1.4 units

The dimensions of the rectangle are 40 units x 1.4 unit

See the draw in the attached figure 4

Case 5) For l = 20 units

substitute in the equation 1

⇒ 20 × w = 64

⇒ w = 64/20

⇒ w = 3.2 units

The dimensions of the rectangle are 20 units x 3.2 unit

See the draw in the attached figure 5

Case 6) For l = 10 units

substitute in the equation 1

⇒ 10 × w = 64

⇒ w = 64/10

⇒ w = 6.4 units

The dimensions of the rectangle are 10 units x 6.4 unit

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