calculates the sum of the first 8 terms of an arithmetic progression starting with 3/5 and ending with 1/4

Answers

Answer 1

We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

How to get the sum of the first 8 terms?

In an arithmetic sequence, the difference between any two consecutive terms is a constant.

Here we know that:

[tex]a_1 = 3/5\\a_8 = 1/4[/tex]

There are 7 times the common difference between these two values, so if d is the common difference:

[tex]a_1 + 7*d = a_8\\\\3/5 + 7*d = 1/4\\\\7*d = 1/4 - 3/5 = (5 - 12)/20 = -7/20\\\\d = -1/20[/tex]

Then the sum of the first 8 terms is given by:

[tex]3/5 + (3/5 - 1/20) + (3/5 - 2/20) + ... + (3/5 - 7/20)\\\\8*(3/5) - (1/20)*(1 + 2 + 3+ 4 + 5 + 6 + 7) = 3.4 = 34/10 = 17/5[/tex]

So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

If you want to learn more about arithmetic sequences:

https://brainly.com/question/6561461

#SPJ1


Related Questions

The graph of y= (x + 2)(x-2)(x + 1) is shown.
4
3
2-
D
-6-5-4-3-2-1₁
23 456x
D
76
B
C
Which point is a relative minimum?
OA
OD

Answers

Answer:

Point C

Step-by-step explanation:

At point C, the graph is changing from decreasing to increasing.

If the area of a certain square is 81 square inches or less, which set
describes the domain of the function?
F(s)=s^2

(0,81]
[0, 9]
(0,91
[0,81)

Answers

Answer:

(0, 9]

Step-by-step explanation:

√81 = 9

We must take positive numbers into consideration here.

factoring / gcf ??? (in picture)

got really sick and missed a bunch of school, would really appreciate the help !

Answers

Step-by-step explanation:

hope this will help you....

A motion sensor has a range of 65 meters as shown. The ultrasonic waves sweeping out from the sensor span an angle of 135°.

A figure shows the appendix cone has a range of 65 meters in which waves with an angle of 135 degrees.

What is the approximate area that is within range of the motion sensor? Use the value = 3.14.

Answers

The approximate area that is within range of the motion sensor is 4975 square meters

How to determine the area of the range?

The figure is not given, however the area of the range can be calculated without the figure.

The given parameters are:

Angle, ⊕ = 135°

Radius, r = 65 meters

The area of the range is calculated using the following sector area

[tex]A = \frac{\theta}{360} * \pi r^2[/tex]

This gives

[tex]A = \frac{135}{360} * 3.14 * 65^2[/tex]

Evaluate

A = 4974.9375

Approximate

A = 4975

Hence, the approximate area that is within range of the motion sensor is 4975 square meters

Read more about sector areas at:

https://brainly.com/question/16736105

#SPJ1

Peter and Henry went to the movies Peter bought the two Movie tickets for 7 dollars each. How much did he spend for the movie tickets Henry bought two buckets of popcorn for 5 dollars each. How much did Henry spend on popcorn. What was the total expenditure

Answers

Answer:

tickets: $14

popcorn: $10

total: $24

Step-by-step explanation:

2 movie tickets at $7 each is 2*7 which is $14

2 buckets of popcorn at $5 each is 2*5 which is $10

adding these together we get a total spending of $24

Given f(x) = x² + 4x - 3, find f(-3)
O -3
O -6
O 0
O 18

Answers

Answer:

f(-3) = -6

Step-by-step explanation:

f(x) = x^2 + 4x - 3

f(-3) means to put -3 in place of x and then do the calculation.

f(-3)

= (-3)^2 + 4(-3) - 3

= 9 - 12 - 3

= -3 - 3

= -6

First square -3, its 9. Then multiply -3 and 4, that's -12. Then add everything.

f(-3) = -6

Suppose that 50% of all babies born in a particular hospital are boys. If 6 babies born in the hospital are randomly selected, what is the probability that fewer than 3 of them are boys?

Answers

Using the binomial distribution, it is found that there is a 0.3438 = 34.38% probability that fewer than 3 of them are boys.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

In this problem, the values of the parameters are given as follows:

n = 6, p = 0.5.

The probability that fewer than 3 of them are boys is given by:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.5)^{0}.(0.5)^{6} = 0.0156[/tex]

[tex]P(X = 1) = C_{6,1}.(0.5)^{1}.(0.5)^{5} = 0.0938[/tex]

[tex]P(X = 2) = C_{6,2}.(0.5)^{2}.(0.5)^{4} = 0.2344[/tex]

Then:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0156 + 0.0938 + 0.2344 = 0.3438[/tex]

0.3438 = 34.38% probability that fewer than 3 of them are boys.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

#SPJ1

Cynthia beach wants to buy a rug for a room that is 22 ft wide and 31 ft long.she wants to leave a uniform strip of floor around the rug.she can afford to buy 580 square feet of carpeting.what dimensions should the rug have?

Answers

The dimensions the rug should have is 20 by 29

How to determine the dimension?

The dimension of the rug is given as:

22 ft by 31 ft

The area of the carpet is given as:

Area = 580

Represent the length of the empty space with x.

So, the dimension of the carpet is:

22 - 2x by 31 - 2x

The area is calculated as:

Area = (22 - 2x) * (31 - 2x)

Expand

Area = 682 - 62x - 44x + 4x^2

Evaluate the difference

Area = 682 -106x + 4x^2

Substitute Area = 580

682 -106x + 4x^2 = 580

Subtract 580 from both sides

102 -106x + 4x^2 = 0


Rewrite as:

4x^2 - 106x +102 = 0

Using a graphing calculator, we have:

x = 1 and x = 22.5

Substitute these values in 22 - 2x by 31 - 2x

So, we have:

Length = 22 - 2(1) = 20 or Length = 22 - 2(22.5) = -23

Width = 31 - 2(1) = 29 or Length = 31 - 2(22.5) = -14

The dimensions cannot be negative.

So, we have:

Length = 20 and Width = 29

Hence, the dimensions the rug should have is 20 by 29

Read more about areas at:

https://brainly.com/question/24487155

#SPJ1

Find the surface area of the regular pyramid.

Answers

The surface area of the regular pyramid as given in the task content is; 16m².

What is the surface are of the regular pyramid?

The task content requires that the surface area of the pyramid be determined. This surface area can therefore be evaluated as follows;

Surface area = (2×2) + 4((1/2)×2×3) = 4 + 12 = 16m².

The surface area of the regular pyramid is therefore; 16m².

Read more on pyramids;

https://brainly.com/question/16174451

#SPJ1

Which sentence correctly compares the two numbers 5.395 and 5385 ?
5.395= 5385
5.385 > 5.395
5395< 5.385
5385 < 5.395

Answers

The sentence that correctly compares the two numbers is 5385 > 5.395

What is the correct sentence?

Here are inequality signs and what they mean:
Note that

> means greater than< means less than≥ means greater than or equal to ≤ less than or equal to

5385 is greater than 5.385. Thus, the correct statement is 5385 > 5.395.

To learn more about inequality, please check: https://brainly.com/question/5031619

#SPJ1

Evaluate the expression below when x = 6 and y = 2. 6x2y3

Answers

Answer:

I think that the answer is 432.

Step-by-step explanation:

6x2y3.We have x as 6 and y as 2.So we replace them with their numbers.

We'll have 6*6*2*2*3 which will give us 432. I HOPE THIS HELPS.

I need some help please

Answers

Answer:

HexagonHeptagon

Step-by-step explanation:

The first shape has 6 sides. Hence, it is called a hexagon.

The second shape has 7 sides. Hence, it is called a heptagon.

Given:Polygon 1Polygon 2To find:

The mathematical name for the given 2 polygons.

Solution:

The first polygon has 6 sides with an angle sum of 720°, which means the mathematical name given for this polygon is,

[tex]\large\boxed {Hexagon}[/tex]

The second polygon has 7 sides with an angle sum of 900°, which means the mathematical name given for this polygon is,

[tex]\large\boxed {Heptagon}[/tex]

Hence, the first polygon is a hexagon and the second polygon is a heptagon.

The graph of the absolute value parent function, f(x) = |x, is stretched
orizontally by a factor of 3 to create the graph of g(x). What function is g(X)

Answers

Answer:

g(x) = 1/3 • |x|

Step-by-step explanation:

To stretch a parent function, you multiply by whatever you want to stretch it with. If you multiplied by 3, it would be a vertical stretch... if you multiplied by 1/3, it makes it horizontal.

Hope this helps!

Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?

Answers

The equation that can be used to represent the situation is y = 5.5 + x

How to write and solve equation?

Whole wheat flour = 5.5 cupsWhite flour = x cupsTotal flour = y

The equation:

Total flour = Whole wheat flour + White flour

y = 5.5 + x

Therefore, the equation that can be used to represent the situation is y = 5.5 + x

Learn more about equation:

https://brainly.com/question/13763238

#SPJ1

Answer:

C

Step-by-step explanation:

Express 5 1/2 and 2 1/2 as a ratio of whole numbers​

Answers

Answer:

your answers are 5.5 and 2.5 as they both have a half extra

using the figure below identify 1 pair of the following angle relationships

Answers

Answer:

\begin{gathered}\\1) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\end{gathered}

1)

Alternateinteriorangles:

\begin{gathered} \sf \implies \: 2\: \: and \: \: 7\\\end{gathered}

⟹2and7

\begin{gathered} \sf \implies \: 6\: \: and \: \: 3\\\\\end{gathered}

⟹6and3

\begin{gathered}\\2) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\\\end{gathered}

2)

Alternateinteriorangles:

\begin{gathered} \sf \implies \: 1\: \: and \: \: 8\\\end{gathered}

⟹1and8

\begin{gathered} \sf \implies \: 5\: \: and \: \: 4\\\\\end{gathered}

⟹5and4

\begin{gathered}\\3) \: \: \underline{ \sf{ Corresponding \: angles \: \: : }}\\\end{gathered}

3)

Correspondingangles:

\begin{gathered} \sf \implies \: 3\: \: and \: \: 1\\\end{gathered}

⟹3and1

\begin{gathered} \sf \implies \: 5\: \: and \: \: 7\\\end{gathered}

⟹5and7

\begin{gathered} \sf \implies \: 4\: \: and \: \: 2\\\end{gathered}

⟹4and2

\begin{gathered} \sf \implies \: 6\: \: and \: \: 8\\\\\end{gathered}

⟹6and8

\begin{gathered}\\4) \: \: \underline{ \sf{ Consecutive\: Interior \: angles \: \: : }}\\\end{gathered}

4)

ConsecutiveInteriorangles:

\begin{gathered} \sf \implies \: 2\: \: and \: \: 3\\\end{gathered}

⟹2and3

\begin{gathered} \sf \implies \: 6\: \: and \: \: 7\\\\\end{gathered}

⟹6and7

\begin{gathered}\\5) \: \: \underline{ \sf{ Consecutive\: Exterior \: angles \: \: : }}\\\end{gathered}

5)

ConsecutiveExteriorangles:

\begin{gathered} \sf \implies \: 1\: \: and \: \: 4\\\end{gathered}

⟹1and4

\begin{gathered} \sf \implies \: 5\: \: and \: \: 8\\\\\end{gathered}

⟹5and8

Need your help now please; the assignment is due tonight and this is the last problem I am having trouble with. The red box is the value I keep getting wrong

The region R is bounded by the x-axis, the straight line in the graph and the vertical line x=2.

Answers

The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

What is the volume of the solid (R) on the X-axis?

If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

From the given graph:

The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:

[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]

here:

(x₁, y₁) and (x₂, y₂) are two points on the straight line

Suppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8)  from the graph, we have:

[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]

y = 4x

Now, our region bounded by the three lines are:

y = 0 x = 2y = 4x

Similarly, the change in polar coordinates is:

x = rcosθ, y = rsinθ

where;

x² + y² = r²  and dA = rdrdθ

Therefore;

rsinθ = 0   i.e.  r = 0 or θ = 0rcosθ = 2 i.e.   r  = 2/cosθrsinθ = 4(rcosθ)  ⇒ tan θ = 4;  θ = tan⁻¹ (4)

⇒ r = 0   to   r = 2/cosθ    θ = 0  to    θ = tan⁻¹ (4)

Then:

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

Learn more about the determining the volume of solids bounded by region R here:

https://brainly.com/question/14393123

#SPJ1

Joe went shopping and purchased a pair of pants for $56 and a pair of shoes for $45. The tax in Joe's city is 4%. How much will Joe pay when he checks out ?

Answers

Answer:

$105.04

Step-by-step explanation:

First add $56 plus 45$ and you will get $101, then times $101 and 1.04 together.

Your answer should be $105.04.


Write a doubles fact that can help you find the
sum. Write the sum.
3+4

Answers

Step-by-step explanation:

4 + 4 = 8 is one of the two closest double to 3 + 4

W.K.T(we know that )..

4 is 1 more than 3 this means ;

4 + 4 will be 1 more than 3 + 4

4 + 4 = 8 ,so finding 1 Less ;

3 + 4 = 7

here is the answer hope It helped U

please mark as BRAINLIEST

Which graph shows the solution to the following system of inequalities x+y>4

Answers

The solution to this system of inequalities x + y>4  , x + y <3 is Option A

The complete question is

Which graph shows the solution to this system of inequalities? x + y>4 x + y <3

The image are attached with the answer.

What are Inequality ?

When an expression is equated with another expression by an Inequality operator (< , >  < etc) then the mathematical statement formed is called Inequality.

The inequalities are

x+y>4

x + y <3

After plotting both the inequalities in the graph the following graph that is attached with the answer is obtained.

Therefore the correct answer is Option A

To know more about Inequalities

https://brainly.com/question/20383699

#SPJ1

What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common?

A.)Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.

B.)Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).

C.) Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.

D.) Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.

Answers

The key features are (1) both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.

How to determine the key features

The functions are given as:

f(x) = 4 - x

[tex]g(x) = -\sqrt{x - 4}[/tex]

Using a graphing calculator:

The domain of g(x) is [4,∞)The range of g(x) is (-∞,0]The domain of f(x) is (-∞,∞) The range of f(x) is (-∞,∞) Both functions have positive values for their domains

By comparing the above highlights, the true statement between functions g(x) and f(x) is option (1)

Read more about function domain and range at:

brainly.com/question/10197594

#SPJ1

Answer:

B.)Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).

Step-by-step explanation:

b is correct


Please show work and thank you

Answers

Answer: [tex]\sqrt{109} \text{ m }[/tex]

Step-by-step explanation:

If we let the length of the ladder be [tex]x[/tex], as shown in the diagram, this means that by the Pythagorean theorem, [tex]x=\sqrt{10^{2}+3^{2}}=\boxed{\sqrt{109}}[/tex] m.

calculate time if distance is 53km and speed is 60km/hour?

Answers

60km / 60min (1h)
53km / 53min

=53 minutes

Which graph represents the function f(x) = |x + 3|?

On a coordinate plane, an absolute value graph has a vertex at (0, 3).
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
On a coordinate plane, an absolute value graph has a vertex at (3, 0).

Answers

Answer:

Graph of Modulus

The graph of a modulus or absolute value function is in a form of a 'V' shape whose vertex depends upon the coordinates. The equation for the graph is given as,

where,

(a, b) are the coordinates of the vertex of 'v' in the form of (x, y),

And h shows how wider or lean will be the function, for h=0, it is a straight line, while for a negative value the graph will face downwards and opposite for a positive value.

Given to us

y = |x-3|

On the coordinate plane

The graph will be in the shape of a 'V' whose vertex will lay at the coordinates (3, 0). As the value of a is 1 the graph will face upwards. As shown below on the graph.

Learn more about Modulus:

brainly.com/question/18106342

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

edge 23

heIp??

everyone??

Brainliest = Good Answer/Solution​

Answers

Given : Radius = 6 cm

To Find = Diameter, Area

Solution :

Diameter = 2 × Radius

Diameter = 2 × 6cm

Diameter = 12 cm

Area = 2πr

[tex]area \: = 2 \times \frac{22}{7} \times 6cm[/tex]

[tex]area \: = \frac{264}{7} [/tex]

[tex]area \: = 37.7 \: cm[/tex]

____________________________________

2. Given : Diameter = 8 DM

( 1dm = 10 cm

8dm = 8 × 10 = 80cm )

To find : Radius , area

Solution :

[tex]raduis \: = \frac{1}{2} \times diameter[/tex]

[tex]radius \: = \frac{1}{2} \times 80cm[/tex]

[tex]radius \: = 40 \: cm \: or \: 4dm[/tex]

Area = 2πr

[tex]area \: = 2 \times \frac{22}{7} \times 40[/tex]

[tex]area \: = \frac{1760}{7} [/tex]

[tex]area \: = 251.4cm \: \: \: or \: 25.14dm[/tex]

____________________________________

3. Given : Radius = 2.5m

To find : Diameter , Area

Solution :

Diameter = 2 × radius

Diameter = 2 × 2.5m

Diameter = 5m

Area = 2πr

Area = 2 × 22/7 × 5m

Area = 220/7

Area = 31.4m

what are the missing values

Answers

Answer:

The answer is on the image, which is color coordinated with the how i got it

Karen runs for 45 minutes every day. Which unit best describes the distance Karen runs for each day?
A. 50 kilometers
B. 5 kilometers
C. 50 meters
D. 50 centimeters
! URGENT !

Answers

Answer:

your mom fat as he'll that way you are adopted

Determine whether the relation represents a function. State the domain and range of the relation.
{(-2,-9).(-4,-4). (1,5), (5, -7)}

Answers

Answer:

It is a functionDomain: {-4, -2, 1, 5}Range: {-9, -7, -4, 5}

Step-by-step explanation:

A function is defined so that for each input (known as the domain), there is no more than one output (known as the range).

y-intercept: 4
-: x-intercepts: -2, 5, 7
-: Relative maximum at (0,4)
-: Relative maximum at (6, -3)
-: As → −∞, → −∞
-: As → ∞, →

Answers

The attached figure represents the sketch of the graph

The missing part of the question

The complete question requires that we sketch the graph that follows the given parameters

How to sketch the graph?

The given parameters are:

y-intercept: 4x-intercepts: -2, 5, 7Relative maximum at (0,4)Relative maximum at (6, -3)As x → −∞, y → −∞As x → ∞, y → ∞

To start with, we plot the points on an empty coordinate plane.

Next, we connect the points using a rough curve

Lastly, the points are labelled

See attachment for the sketch of the graph

Read more about graphs at:

https://brainly.com/question/4025726

#SPJ1


Which is equivalent to 64 1/4

Answers

Answer:

4*64=256

256+1=256

there fore 64 1/4 is equivalent to 257/4

Other Questions
vehicle A has a final sale price of $25,000 at 5% interest and financing up to 60 months and vehicle B has a final sale price of $29,000 at 4% interest and financing up to 60 monthshow do I solve this and do I have enough information to answer the question and what step would take to solve the problem and how do I calculate the results Please tell me the following correct answers if I am wrong. Multiple Choice jack sets of shops at twenty past nine.he arrives at the shop 35 minutes later.draw the times on the clock face? RATIONAL EXPONENTS pls help what do i do?? Solve the compound inequality for x and identify the graph of its solution.x+7 > 3 and x-5-1O A. Solution: x < -4 or x 41 2 3 4 5OB. Solution: x>-4 and x 412 3 4 5OC. Solution: x>-4 and x 4++-5 -4 -3 -2 -1123 4 5OD. Solution: x-4 and x < 41 2 3 45-5 -4 -3 -2 -1 0-5 -4 -3 -2 -1 00-5 -4 -3 -2 -1 0 As religious leader Greg Boyle notes, Abject poverty, political instability, torture, and other abuses push thousands across our border. There is not a deterrent imaginable that equals the conditions that force their migration.How does this quote help the author develop the claim that border walls will not discourage immigration?Choose 1 answer:A: It establishes some of the conditions that might force people to flee their home countries.B: It asks the reader to consider the moral and religious factors that might force people to leave their homes.C: It explains the ways that border walls and border security act as deterrents to migration.D: It provides details on a study that outlines how many people risk their lives to cross borders in search of better lives. When the restaurant wanted to raise its reviews from two stars to three stars, the chef worked with his sous chefs to improve on his original recipe for pork tacos that later became the restaurant's star menu item. The chef was a Give three ways that photosynthesis and respiration are dependent on one another. Which best indicates pen pressure in handwriting analysis?The height-to-width ratio is uniform. The capital letters and lowercase letters are connected. The letters are either above, below, or on a baseline. The downstrokes and upstrokes are an even width . Which is the correct rhyme scheme? Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. tan(/5) which element have 6 valence electrons? Find the present value, using the future value formula and a calculator. Future value is $6,000 in two years at 9.5% simple interest. Round your answer to the nearest cent (two decimal places). Enter only the number without $ sign. Answer quickly please What is the molecular weight of one mole of HCO3? What is the digital revolution and how did it change society? 9. Which point is on the graph of 2x - 16y=-8?OA (-4,0)O B. (0,2)Oc. (0,4)O D.D. (1.0) Please select the letter from the list that best fits the definition ere what are the trends in the global job market? A spinner is divided into five colored sections that are not of equal size: red, blue,green, yellow, and purple. The spinner is spun several times, and the results arerecorded below:Spinner ResultsColor FrequencyRed4Blue3Green20Yellow14Purple 16Based on these results, express the probability that the next spin will land on red as apercent to the nearest whole number.