A1=12−12,a2=23−13,a3=34−14,a4=45−15,a5=56−16. a1=12−12,a2=23−13,a3=34−14,a4=45−15,a5=56−16.
a.find an explicit formula for anan: .
b.determine whether the sequence is convergent or divergent: . (enter "convergent" or "divergent" as appropriate.)
c.if it converges, find limn→∞an=limn→∞an= .

Answers

Answer 1
[tex]a_1=12-12=(1\times12-0)-(12+0)[/tex]
[tex]a_2=23-13=(2\times12-1)-(12+1)[/tex]
[tex]a_3=34-14=(3\times12-2)-(12+2)[/tex]
[tex]a_4=45-15=(4\times12-3)-(12+3)[/tex]
[tex]a_5=56-16=(5\times12-4)-(12+4)[/tex]

Clearly, the general for the [tex]n[/tex]-th term is

[tex]a_n=(12n-(n-1))-(12+n-1)=10n-10[/tex]

(Aside: given the simple pattern, it's curious why the terms would be given the way they are. It's easier to divine [tex]10n-10[/tex] from [tex]a_1=0,a_2=10,a_3=20,\ldots[/tex], but that's just my opinion.)

The sequence does not converge. As [tex]n\to\infty[/tex], so does [tex]a_n\to\infty[/tex].

Related Questions

What is the volume of the right rectangular prism 8L 10W 3

Answers

volume is L x W x H

8 x 10 x 3 = 240 cubic units

25 if answered please help

Answers

a line = 180 degrees
 so z = 180 - 124

z = 56

Kevin needs to convert 620 millimeters per minute to meters per hour. Which conversion factors should he use?













Answers

Try this option:
1 meter=1000 mm; 1 hour=60 min. From another side: 1 mm=0.001 m. and 1 min=1/60 h.
Using this rule:
620 mm/h=0.06*620 m/h=37.2 meters per hour.

answer: 0.06

What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve

B.x=-3 sqrt5 and x= -1 is the correct answer

Answers

So what are exactly are you asking

The correct answer is gonna be B. Or x = -3√5 and x = -1

Identify if the expressions below are polynomials or not for each of them.

Answers

The polynomials can´t contain:
 
 -Variables in the exponents of the terms.
 -Variables in the denominator.
 - Negative exponents.
 -Fractionals exponents.
 -The variables cant be as radicals.
 
 Therefore:
 
 a) It is a polynomial (The variable is under a radical)
 b) It is not a polynomial.
 c) It is a polynomial.
 d) It is not a polynomial. (It has a variable in the denominator).
 e) It is a polynomial.
 f) It is not a polynomial.  (It has a variable in the denominator).

Determine the simple interest. the rate is an annual rate. Assume 360 days in a year. p= $460 r= 2.75% t= 3.25 years

Answers

I=P*R*T  460(.0275)(3.25)=41.11
The simple interest formula is i = prt, where i equals interest, p = principal, r = interest rate, and t = time. Your principal is $460, your rate is 2.75%, and your time is 3.25 years. Since 2.75% = 0.0275, the equation becomes i = 460*0.0275*3.25 which equals $41.11 rounded. Hope this helps! :) have a nice day. 

a net has two equilateral triangles and three rectangles what solid figure could this make

Answers

it would make a triangular prism. 

i hope im right

Please Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

With which one and I can’t see the questions either

The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation and Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.

Answers

Helena is correct in saying that the point-slope form will generate the equation. The point-slope form is written as:


y-y₁ = m(x-x₁), where,
m = (y₂-y₁)/(x₂-x₁) is the slope of the line
(x₁,y₁) and (x₂,y₂) are the coordinates of the two points


On the other hand, the slope-intercept form is written as:


y = mx + b, where,
m is the slope of the line
b is the y-intercept


In this case, since only two points were given, the y-intercept of the line is not readily known. Thus, it is only through the point-slope form that the equation of the line can be determined. This is because it only requires the substitution of the x and y-coordinates of the points in the equation. 
The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation and Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.

Sample Response: Both are correct. Using either form will result in the same equation. The slope-intercept form uses slope and a point to find the y-intercept. Point-slope form uses the slope and a point to solve for y to generate the equation.

Find the equation of the line having a slope of 4 and a y-intercept of (0,3)

Answers

notice, (0, 3), means x = 0, y = 3, namely the y-intercept

[tex]\bf y=\stackrel{slope}{4}x\stackrel{y-intercept}{+3}\qquad \impliedby \textit{slope-intercept form}[/tex]

reason why that form is called like so.

This a fraction problem, can u solve it
3 1/2 - 2 5/9

Answers

The answer is 7/18
or 0.39 in decimal
3 1/2 - 2 5/9 = 17/18

LCM of 9 and 2 is 18

Then, you change it to an improper question
3 1/2 = 7/2 = 63/18
2 5/9 = 23/9 = 46/18

63/18 - 46/18 = 17/18

Hope this helps! ;)

Help needed and explain!!

Answers

First calm down listen to the steps

1. Since there are 4 triangle so you will need to find the area and the formula is base(height)1/2 but you should probably check the formula just to make sure

2.Then you will find the area of the square which is length times width

3.Add all 5 areas together and the answer should be labeled in squared

hope that helped

2 1/4 was subtracted twice from a number; then 1/8 was subtracted three times and 2/3 was subtracted twice. The resulting number is 3 11/24 . Find the number

Answers

I would say its 9 2/3 (Hope this helped for the answer)

Answer:

9 2/3

Step-by-step explanation:

mr.kiniston jogged how many miles

Answers

The answer is letter G.
Start by takingvthe original number of minures amd dividing by miles walked. all 3 wxamples cone out as 7. Now, you can make a graph. image above. He jogs 6 miles in 35 minutes, 6 miles in r2 minutes, and 7 miles in 49 minutes. If you need help, just comment and I can help as much as I can.

If a ship sailed due south from Iceland to Antarctica, it would sail through an angel of rotation of about 140° around Earths center. Find this measure in radians. Then , using 3960 miles for earth radius, find how far the ship would travel.

Answers

Final answer:

To convert the angle in degrees to radians, multiply the angle by π and divide by 180. The ship would travel approximately 3081.23 miles.

Explanation:

To find the measure in radians, we need to convert the given angle from degrees to radians. There are 2π radians in a full circle, which is equal to 360°. Therefore, to convert 140° to radians, we can use the formula: radians = (degrees × π) / 180. Substituting the given angle, we get: radians = (140 × π) / 180 = (7π / 9) radians.

Next, to find how far the ship would travel, we need to calculate the arc length. The formula for the arc length of a circle is: arc length = radius × angle in radians. Given that the radius of Earth is 3960 miles and the angle of rotation is (7π / 9) radians, we can calculate the arc length as follows: arc length = 3960 × (7π / 9) ≈ 3081.23 miles.

Learn more about Conversion of angles to radians here:

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Find the area of a sector with a central angle of 2pi/15 and a radius of 18.8 m

Answers

we know that
[Area of a circumference]=pi*r²
for r=18.8 m
Area=pi*18.8²=1109.80 m²

if the area for 2pi radians (full circumference) is --------------> 1109.80 m²
                  for 2pi/15----------------------------------> X
X=(2pi/15)*1109.80/2pi----------> 73.99 

the answer is 73.99 m²

Answer:

74.02 square meters.

Step-by-step explanation:

We are asked to find the area of sector of circle, whose central angle is [tex]\frac{2\pi}{15}[/tex].

We will use area of sector formula to solve our given problem.

[tex]\text{Area of sector}=\frac{\theta}{2\pi}\times \pi r^2[/tex], where, r represents radius of circle.

Upon substituting our given values in above formula, we will get:

[tex]\text{Area of sector}=\frac{\frac{2\pi}{15}}{2\pi}\times \pi (18.8)^2[/tex]

Using fraction rule [tex]\frac{\frac{a}{b}}{c}=\frac{a}{bc}[/tex], we will get:

[tex]\text{Area of sector}=\frac{2\pi}{15\times 2\pi}\times \pi (18.8)^2[/tex]  

[tex]\text{Area of sector}=\frac{1}{15}\times \pi \times 353.44[/tex]  

[tex]\text{Area of sector}=23.5626666\times \pi[/tex]  

[tex]\text{Area of sector}=74.0243004\approx 74.02[/tex]  

Therefore, the area of given sector of circle is 74.02 square meters.

Decide if the measurements determine no triangle, a unique triangle, or more than one triangle.

ITEMBANK:
3 cm, 4 cm, 11 cm

3 cm, 5 cm, 15 cm

30°, 40°, 110°

6 cm, 7 cm, 12 cm

60°, 60°, 60°

8 cm, 90°, 45 °

Options: No triangle, Unique triangle, or More than one triangle

Answers

1) No triangle
2) No triangle
3) More than 1 triangle
4) 1 triangle
5) More than 1 triangle
6) Either 1 or more than 1 triangle

Explanation:
1)  The sum of the two smaller sides is not greater than the third side, so these will not form a triangle.
2) The sum of the two smaller sides is not greater than the third side, so these will not form a triangle.
3) The angles add up to 180, so this will make more than one triangle (there is no information given about the sides, so the triangles would be similar but not necessarily congruent)
4) The sum of the two smaller sides is greater than the third side, so one triangle is formed
5) The angles add up to 180, so this will make more than one triangle (there is no information given about the sides, so the triangles would be similar but not necessarily congruent)
6) Depending on whether the side is between the two given angles, either 1 triangle or more than 1 triangle could be formed.

Answer:

1.)No Triangle

2.)No Triangle

3.)More Than One Triangle

4.)Unique Triangle

5.)More Than One Triangle

6.)Unique Triangle

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total 21499
. The variable costs will be $12
per book. The publisher will sell the finished product to bookstores at a price of 22.75
per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answers

The publisher makes (22.75 -12.00) = 10.75 per book, so to cover the 21,499 fixed cost, must sell
.. 21,499/10.75 = 1999.9
books

Sales revenue will equal production costs when the publisher produces and sells 2000 books.

-5.8c+4.2-3.1+1.4c combine like terms to create an equivalent expression

Answers

Answer:

The equivalent expression to the given expression is:

                    [tex]-4.4c+1.1[/tex]

Step-by-step explanation:

We are given an algebraic equation in terms of the variable c as follows:

                          [tex]-5.8c+4.2-3.1+1.4c[/tex]

Now, we will first combine the like term i.e. the terms with the same variable term and the constant terms are combined altogether i.e. the expression is given as follows:

        [tex]-5.8c+4.2-3.1+1.4c=-5.8c+1.4c+4.2-3.1[/tex]

On simplifying this expression we get :

                  [tex]-5.8c+4.2-3.1+1.4c=-4.4c+1.1[/tex]

Final answer:

To combine like terms in the expression -5.8c + 4.2 - 3.1 + 1.4c, we add the coefficients of the terms with 'c' and separately combine the constant terms. The simplified expression is -4.4c + 1.1.

Explanation:

To combine like terms and create an equivalent expression for -5.8c + 4.2 - 3.1 + 1.4c, we must identify and combine terms that have the same variable to the same power, which in this case are the terms with 'c' and the constant terms without variables.

Combining like terms with 'c':

-5.8c + 1.4c = -4.4c

Combining constant terms:

4.2 - 3.1 = 1.1

Equivalent Expression:

The equivalent expression by combining like terms is -4.4c + 1.1.

Jason buys a pizza for $15.59 . He also buys 6 sodas. Each soda costs the same amount. He spends $23.33 on the pizza and the sodas. Jason finds the cost of each soda by calculating (23.33 − 15.59) ÷ 6 .

Answers

Final answer:

Jason found that each soda costs $1.29 by calculating (23.33 - 15.59) ÷ 6.

Explanation:

Jason spends $23.33 on the pizza and the sodas, and the total cost of the pizza is $15.59. Let's find out the total cost of the sodas by subtracting the cost of the pizza from the total amount spent. So, $23.33 - $15.59 = $7.74.

Now, to find the cost of each soda, we need to divide the total cost of the sodas by the number of sodas purchased. In this case, there were 6 sodas, so $7.74 ÷ 6 = $1.29.

Therefore, Jason found that each soda costs $1.29 by calculating (23.33 - 15.59) ÷ 6.

Cost of each soda (x) is approximately $1.29.

Jason buys a pizza for $15.59.

The cost of the pizza is $15.59.

He also buys 6 sodas:

The total cost of the pizza and sodas is $23.33.

Each soda costs the same amount:

Let's denote the cost of each soda as x.

He spends $23.33 on the pizza and the sodas.

The total cost can be expressed as the sum of the cost of the pizza and the cost of the sodas:

15.59+6x=23.33.

Now, Jason finds the cost of each soda by calculating (23.33 − 15.59) ÷ 6.

This expression represents the cost of each soda.

Let's calculate it:

[tex]\frac{7.74}{6} \approx 1.29[/tex]

So, Jason finds that each soda costs approximately $1.29.

Jenny used her credit card to buy a refrigerator with a base cost of $824. The refrigerator consumed an average of $0.09 in electricity every day. Jenny made regular monthly payments for three and a half years, at which point the refrigerator was paid off. Over the eight years that Jenny had the refrigerator, it needed repairs three times, costing $68.75 each time. If Jenny’s credit card has an APR of 10.54%, compounded monthly, and sales tax in Jenny’s area is 7.13%, what was the lifetime cost of Jenny’s refrigerator? Assume that Jenny made no other purchases with her credit card, and round all dollar values to the nearest cent. (Remember that leap year occurs every four years.) a. $1,528.47 b. $1,622.46 c. $1,779.63 d. $1,457.91

Answers

I think the answer is A) $1,528.47.

The lifetime cost of Jenny's refrigerator is A. $1,528.47.

What is lifetime cost?

Lifetime cost is the total expenses relating to the purchase of a good, like a car, a home, or a refrigerator from the purchase date to the end of the asset's lifespan.

We can calculate the lifetime cost by using an online finance calculator to determine the total payment, including interests, for the asset and then adding up other expenses like repairs and electricity costs.

Data and Calculations:

Base cost of refrigerator = $824

Sales tax = 7.13%

Total cost of refrigerator, including sales tax (loan amount) = $882.75 ($824 x 1.0713)

Average daily electricity consumption = $0.09

Total electricity cost = $262.98 ($0.09 x 8 years x 365 days + $0.09 x 2 leap year days)

Payment period for credit purchase = 3 1/2 years

Total repairs cost = $206.25 ($68.75 x 3)

Period of possessing the refrigerator = 8 years

APR = 10.54% compounded monthly

From an online finance calculator:

Monthly Payment = $25.22

Total Payment = $1,059.24 ($25.22 x 12 x 3.5)

Total Interest for 3 1/2 years = $176.49 ($1,059.24 - $882.75)

Lifetime cost of Jenny's refrigerator = Total loan payment + Electricity cost + Repairs cost)

= $1,528.47 ($1,059.24 + $262.98 + $206.25)

Thus, the lifetime cost of Jenny's refrigerator is A. $1,528.47.

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Twelve ounces of Brand X costs $1.14. Sixteen ounces of Brand Y costs $1.28. Brand X costs how much more per ounce than Brand Y.

Answers

"Per" means "divided by", so "cost per ounce" means "cost"/"ounces".

The difference in cost per ounce is
.. (1.14/12) -(1.28/16) = .095 -.08 = 0.015

Brand X costs 1.5¢ more per ounce than Brand Y.

alex originally paid $5200 for her car 1 year ago. the value of her car now is $4,420. what is the percent of decrease in the value of her car?

Answers

the answer is 15%
hope it helps
please mark as brainliest

graph
[tex]y = - \frac{x}{2} + 1[/tex]

Answers

One way, and probably the fastest way to graph, [tex]y = - \frac{x}{2} + 1[/tex] would be to plug in x values and plot the y value you get with the corresponding x value.

You only need two points because it's a linear graph. You already know one point, the y intercept, because your equation is in point slope form and b = 1, so 1 is the y intercept. 

Tom wanted to compare what proceeds he would receive with a simple interest note versus a simple discount note. Both had the same terms: $18,235 at 10% for 2 years. Use ordinary interest as needed.

a. Calculate the simple interest note proceeds.
b. Calculate the simple discount note proceeds.

Answers

a) Simple interest note proceeds are equal to the face value: $18,235.

b) Simple discount note proceeds are the face value less the inerest due,
.. $18,235(1 -0.10*2) = $14,588.

a seed company planted a floral mosaic of a national flags.the perimeter of the flag is 560 feet determine the flags length and width if the length is 40 feet greater that width.write three situation to which you could apply the resulting system of equations

Answers

Let
x------------> the flags length
y------------> the flags width
P----------> perimeter

we know that
p=2x+2y------> 2x+2y=560----------> equation 1
and
x=y+40-------------> equation 2
 substitute 2 in 1
2*(y+40)+2y=560-----------> 2y+80+2y=560--------> 4y=480------> y=120
x=y+40-------> 120+40----------> x=160

the answer is 
the flags length is 160 ft
the flags width is 120 ft

Part 2) Write three situation to which you could apply the resulting system of equations

 1) It can be used when considering the relationship between the price of a product and the quantities of the product that people want to buy at a certain price.

 2) It can be used to determine the speed, distance and time duration when traveling by car, and you want to know the values ​​of the unknown variables in your trips.

3) It can be used to determine the most convenient loan option to buy a car or a house when considering the duration of the loan.

Assuming that a sample (n = 504) has a sample standard deviation of 2.26, what is the upper bound of a 95% confidence interval if the sample mean is 2.96?

Answers

The upper bound would be 3.16.

We find the standard error by dividing the standard deviation by the square root of the sample size:

[tex]\frac{\sigma}{\sqrt{n}}=\frac{2.26}{\sqrt{504}}=\frac{2.26}{22.45}=0.10[/tex]

To calculate the margin of error, we multiply the standard error by 2:
0.1(2) = 0.2

For the upper bound, we add this to the mean:
2.96+0.2 = 3.16

The upper bound of a 95% confidence interval if the sample mean is 2.96 is 3.16.and this can be determined by using the formula of standard error and margin of error.

Given :

Assuming that a sample (n = 504) has a sample standard deviation of 2.26.95% confidence interval.The sample mean is 2.96.

First, evaluate the standard error by using the below formula:

[tex]\rm SE = \dfrac{\sigma}{\sqrt{n} }[/tex]

Now, put the values of n and [tex]\sigma[/tex] in the above equation in order to determine the standard error.

[tex]\rm SE = \dfrac{2.26}{\sqrt{506} }[/tex]

SE = 0.10

In order to determine the margin of error multiplies the standard error by 2.

ME = 0.1 [tex]\times[/tex] 2

ME = 0.20

Now, add the margin of error and the sample mean in order to evaluate the upper bound.

= 2.96 + 0.20b

= 3.16

The upper bound of a 95% confidence interval if the sample mean is 2.96 is 3.16.

For more information, refer to the link given below:

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A circle has a circumference of 361π. What is the diameter of the circle?

Answers

361pi divided by 3.14 = 114.91 which is the diameter

The formula to find circumference of circle is given by

[tex] C = 2\pi r [/tex]

Where r is radius of circle and pi =3.14

We are given Circumference here as 361π

Plugging the value in the formula :

[tex] 361\pi = 2\pi r [/tex]

r=361/2 = 180.5

radius of circle is 180.5.

We know that Diameter is double of radius.

So diameter = 2*180.5 = 361

Answer : diameter of circle is 361.

Which of the following illustrates the product rule for Logarithmic equations?

Answers

We are given Logarithmic equations.

We need to find the equation which illustrates the product rule.

We know, the product rule of Logarithms is:

[tex]log_b (mn) = log_b(m) + log_b(n)[/tex].

According to the product rule of Logarithms, we need to separate logs by plus sign.

In the given options only 4th option logs are separated by plus sign.

[tex]log_2(4x) = log_2\ 4+log_2\ x[/tex].

Therefore, correct option is 4th option.

Answer:

Its D

Step-by-step explanation:

Took test

write the expression in complete factored form q^2(p+1)+3(p+1)

Answers

first expand the brackets which will give you
[tex]pq {}^{2} + q { }^{2} + 3p \: + 3[/tex]
then factor them
[tex](q {}^{2} + 3)(p + 1)[/tex]

The answer is (p+1) (q^2+3) 
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The probability that a bakery has demand for 2 3 4 or 5 birthday cakes on any given day are 0.32, 0.24, 0.25 and 0.19 respectively. construct a probability distribution for this data Which term BEST applies to president richard nixons foreign policy of improving relations with the soviet union? (SELECT ALL THAT APPLY) WILL REPORTSelect the items that were part of the Missouri Compromise. A.Texas was admitted as a slave state.B Missouri was admitted as a slave state. Maine was admitted as a free state. C.The slave trade was abolished in the north.D. The tariff compromise of 1833 was passed.E. No slavery was allowed north of 36 30'. VERY EASY! HELP ME RIGHT NOW! DUE TOMORROW To make money, one must work.Para ganar dinero, ___________ trabajar.fill in blank What is the sum of 2 numbers is 100 and their difference is 6? what mechanical layer lies below the lithosphere Can someone check my answers?1. Simplify the sum or difference. sqrt 5 + 6 sqrt 5A) 6 sqrt 5B) 30C) 6 sqrt 10D) 7 sqrt 52. Simplify the sum or difference.4 sqrt 2 - 7 sqrt 2A) negative sqrt 6B) -3 sqrt 2C) -11 sqrt 2D) 11 sqrt 23. Simplify the sum or difference.3 sqrt 7 - sqrt 63A) -2 sqrt 7B) -6 sqrt 7C) -4 sqrt 3D) 04. Simplify the sum or difference.-6 sqrt 10 + 5 sqrt 90A) 9 sqrt 10B) -9 sqrt 10C) -39 sqrt 10D) -105. Simplify the product.sqrt 6 (sqrt 2 + sqrt 3)A) sqrt 8 + 3B) sqrt 30C) 2 sqrt 3 + 3 sqrt 2D) 4 sqrt 2 + 3 7 cakes cost 5.60 , what would be the cost of:10 cakes5 cakes12 cakes A ________ is a small, lightweight, power-conserving, computing device that is capable of wireless access. The process of producing recombinant dna involves taking a gene from one organism and attaching it to the dna from another organism. write and an analogy that describes this process. Selena is buying an audio system for her car. She can choose among 3 types of stereos, 4 kinds of speakers, and 2 kinds of amplifiers. Which describes how Selena can show her options? What is the percentage of the total students chose skateboarding?A.) 10%B.) 20% C.) 30%D.) none of these The firing of a Revolutionary War cannon is used to open the local Fourth of July festivities. The muzzle of the cannon barrel is 6 feet above ground level. The height of the cannon ball being fired from the Revolutionary War cannon as a function of elapsed time is modeled by the function h(t) = 16t2 + 75t + 6, where h(t) is the height of the cannon ball in feet, and t is the elapsed time since firing in seconds. Determine at approximately what elapsed time(s) the cannon ball will be at a height of 55 feet. Two cities are 124 miles apart from each other. The cities are 4cm on a map, what is the Scale factor? Plastics are artificial substances. However, the materials needed to produce plastics are often crude oil. Which is a reasonable conclusion based on this fact?A. Plastics require oil and therefore will be lighter than any other material B. Plastics require oil and therefore must be more costly to use than other materialC. Plastics require oil and therefore are renewable resourcesD. Plastics require oil and therefore are nonrenewable resource Read this excerpt from Canto XIX of the Inferno: And [Pope Nicholas III] cried, "Are you already standing there, Are you already standing there, Boniface? By several years the record lied to me! "Are you so quickly glutted with the wealth Which did not make you fear to take by guile The lovely lady and then lay her waste?" I acted like a person who's left standing -- Not comprehending what's been said to him -- Half-mocked and at a loss to make an answer. Then Virgil spoke up, "Tell him right away, 'I am not he, I'm not the one you think!'" And I replied as I had been instructed.What is most likely Dante's purpose for including this scene?A. To show the audience that he believed Boniface deserved to be in Hell as well.B. To show the audiences that even popes are human and capable of mistakes.C. To emphasize Dante's need to impress Virgil with his knowledge of sinners.D. To emphasize that Pope Nicholas III should not be in Hell. What is the distance between the points (9, 32) and (9, 17) in the coordinate plane? what is meaning of microbes,remeber the word micro means small Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 ($1). Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 1 P(xi) What is Miguels expected value from playing the game? answer= $2 Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? answer= $2 What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation. A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue. Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give 1 point. Let X = the points you have after one spin. Fill out the missing values in the table. Xi P(xi) If you take one spin, what is your expected value? What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. Xi 3 0 P(xi) 0.30 0.70 Xi 2 0 P(xi) 0.48 0.52 What is the expected value for each choice? Should he pass the ball or take the shot himself? Explain. Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values. If Claires initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?