Find the sum of the first 100

Find The Sum Of The First 100

Answers

Answer 1

The terms of an arithmetic sequence are generated by adding a fixed term [tex]r[/tex] every time.

So, we start with [tex]a_1=15[/tex], and we continue with [tex]a_2=15+r[/tex], [tex]a_3=15+2r[/tex] and so on.

As you can see, the general rule is [tex]a_n = 15+(n-1)r[/tex]

With this information, we can derive [tex]r[/tex], knowing that

[tex]a_{100} = 307 = 15+99r \iff 99r = 292 \iff r = \dfrac{292}{99}[/tex]

So, the sum of the first 100 terms is

[tex][tex]\displaystyle \sum_{i=0}^{99} 15+i\dfrac{292}{99} = \displaystyle \sum_{i=0}^{99} 15 + \displaystyle \dfrac{292}{99}\sum_{i=0}^{99} i = (15\cdot 99) + \dfrac{292}{99}\dfrac{99\cdot 100}{2} = 1485 + \dfrac{490342}{99}[/tex]


Related Questions

Gia went to the movies with her 7-year old daughter and her 70-year-old mother. Movie tickets are half-priced for children under 12 years old, and there is a 25% discount for senior citizens. If Gia's $8.00 ticket was the regular retail price, what percent of the full retail price did Gia pay for the three tickets?




A.60% B.66.6% C.70% D.75% ​

Answers

Answer:

D. 75%

Step-by-step explanation:

Percent of full retail price = 8+(1/2)(8)+(3/4)(8)/24

This simplifies to 0.75, which is equivalent to 75 percent.

$24 is full retail price so by dividing the amount Gia paid by it, you can find the percent of the full retail price.

Final answer:

Gia paid 75% of the full retail price for the three movie tickets.

Explanation:

To calculate the percent of the full retail price that Gia paid for the three tickets, we need to determine the total amount Gia paid and the full retail price for the three tickets.

Gia's $8.00 ticket is the regular retail price, so she paid the full price for her ticket. Her daughter's ticket is half-priced, which is $8.00 divided by 2, equaling $4.00. Her mother's ticket has a 25% discount, so she paid 75% of the full price, which is $8.00 multiplied by 0.75, equaling $6.00.

The total amount Gia paid is $8.00 + $4.00 + $6.00 = $18.00. The full retail price for the three tickets is $8.00 + $8.00 + $8.00 = $24.00. Therefore, Gia paid $18.00/$24.00 = 0.75, which is 75%, of the full retail price.

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Which best describes the graphs of the line that passes through (0,2) and (6,4) and the line that passes through (2,1) and (5,7)?

Answers

Answer:

The line which has slope 1/3 is a shallow line.

The line which has slope 2 is a steep line.

Both are increasing.

Step-by-step explanation:

Compare the lines by finding the slope between each pair of points.

Using the slope formula, substitute the points.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{4-2}{6-0} = \frac{2}{6} = \frac{1}{3}[/tex]

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{7-1}{5-2} = \frac{6}{3} = 2[/tex]

The line which has slope 1/3 is a shallow line.

The line which has slope 2 is a steep line.

I don’t know how to do this

Answers

the domain, is the values for "x", namely the values used up over the x-axis.

the arrowheads on the lines, indicate the graph continues, upwards and to the sides, so it keeps on going to infinity.

however, let's notice that the values between -3 and 5, are not used up, those are not part of the graph, and therefore, are not part of the domain, however -3 and 5 ARE part of it, whilst all numbers between them are not.

using interval notation

( -∞ , -3 ]  ∪ [ 5 , +∞ )

it's notable that the ∞ signs have a parentheses, reason being, is a number we never touch because we don't know what the last number is :).

Which of the following points is a solution to the system of inequalities?

6x-2y < 10 6x + 3y > 15

(?,?)

Answers

Answer:

See attached picture.

Step-by-step explanation:

If you graph the system, you will find a region of solutions which are shaded. The point must be within the darkest shaded portion where each equation overlaps. This means it is a solution to both. Choose a point form your list in this region.

See attached picture.

Answer: ITS (0,5)

Step-by-step explanation:

i just did the algebra nation!!!

all real numbers between -4 and 6​

Answers

Final answer:

The real numbers between -4 and 6 are -3, -2, -1, 0, 1, 2, 3, 4, and 5.

Explanation:

The question asks for all real numbers between -4 and 6. In this case, the numbers between -4 and 6 are -3, -2, -1, 0, 1, 2, 3, 4, and 5.

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G(x)= 3/4x+6
What is the value of g(12)?

Answers

Answer:

G(12) = 15

Step-by-step explanation:

When doing g(x) equations, all you do is substitute the value inside the parentheses to x in the equation.

So you get 3/4(12) + 6.

Then simplify to get g(12) = 15

How many solutions does the equation 4p + 7 = 3 + 4 + 4p have?

Answers

4p + 7 = 3 + 4 + 4p

subtract 4p on both sides

7=7

since the equation equals it is infinite many solutions or...

all real numbers

Answer:

Infinite solutions!!

Step-by-step explanation:

4p + 7 = 3 + 4 + 4p

7 = 3 + 4

7 = 7

What is the value of b?
Answer options: 100, 55, 110, 90

Answers

Well according to my calculations its 110.

What are the perpendicular sides???

Answers

Answer:

For triangle VZX, VZ and ZX are perpendicular to each other.

This is because, perpendicular sides intersect to make a right angle.

Hope this helps,

A.W.E.S.W.A.N.

In the diagram, AB CD. If m<3=115, what is m<6=?

55°

65°

75°

115°

Answers

Answer:

65°

Step-by-step explanation:

<3 + <6 = 180  because they are same side interior angles

115 + <6 = 180

Subtract 115 from each side

115-115 +<6 = 180 -115

<6 = 65

If the perimeter of the regular octagon is 48in what’s is the area ? ( round it to the nearest tenths)

Answers

Answer:

The area of the octagon is [tex]173.8\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of a regular octagon is equal to the area of eight isosceles triangle

The base of each isosceles triangle is equal to the length side of the regular octagon

The vertex angle of each isosceles triangle is equal to

[tex]360\°/8=45\°[/tex]

The area of each isosceles triangle is equal to

[tex]A=\frac{1}{2}bh[/tex]

where

b is the length side of the regular octagon

h is the height of each isosceles triangle

Find the length side of the regular octagon b

The perimeter of a octagon is equal to

[tex]P=8b[/tex]

[tex]P=48\ in[/tex]

so

[tex]48=8b[/tex]

[tex]b=6\ in[/tex]

Find the height of each isosceles triangle h

[tex]tan(45\°/2)=(b/2)/h[/tex]

[tex]h=(b/2)/tan(45\°/2)[/tex]

substitute the values

[tex]h=(6/2)/tan(22.5\°)=7.24\ in[/tex]

Find the area of the octagon

[tex]A=8[\frac{1}{2}bh][/tex]

[tex]A=8[\frac{1}{2}(6)(7.24)]=173.8\ in^{2}[/tex]

15 points and show steps


Solve for x. Write the smaller solution first, and the larger solution second. -2x^2-9=-107

Answers

Answer:

x = -7 and x = 7

Step-by-step explanation:

[tex]-2x^2-9=-107\qquad\text{add 9 to both sides}\\\\-2x^2-9+9=-107+9\\\\-2x^2=-98\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x^2}{-2}=\dfrac{-98}{-2}\\\\x^2=49\to x=\pm\sqrt{49}\\\\x=-7\ \vee\ x=7[/tex]

the figure is cute into 12 equal pieces shade 3/4 of the figure

Answers

Shade in 9 boxes

12÷4= 3 (This is 1 fourth)

3×3=9 (This is 3 fourths)

From the said figure, 9 out of the 12 pieces of the figure are shaded

What proportion should  be shaded?

The figure is cut into 12 equal pieces, and 3/4 of the figure is shaded. To find out how many pieces are shaded, we need to calculate 3/4 of 12.

To do this, we can multiply 3/4 by 12:

3/4 * 12 = 36/4 = 9.

So, 9 out of the 12 pieces are shaded.

To visualize this, imagine a circle divided into 12 equal slices. If you shade 3/4 of the circle, you will shade 9 out of the 12 slices.

Therefore, 9 out of the 12 pieces of the figure are shaded

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consider the function f(x)=15x^2+60-19 Part A: Write the function in vertex form. Part B: Name the vertex for the function

Answers

Answer:

Part A) The function written in vertex form is [tex]f(x)=15(x+2)^{2}-79[/tex]

Part B) The vertex of the function is the point [tex](-2,-79)[/tex]

Step-by-step explanation:

Part A) Write the function in vertex form

we know that

The equation of a vertical parabola in vertex form is equal to

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

where

(h,k) is the vertex of the parabola

In this problem we have

[tex]f(x)=15x^{2}+60x-19[/tex]

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)+19=15x^{2}+60x[/tex]

Factor the leading coefficient

[tex]f(x)+19=15(x^{2}+4x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]f(x)+19+60=15(x^{2}+4x+4)[/tex]

[tex]f(x)+79=15(x^{2}+4x+4)[/tex]

Rewrite as perfect squares

[tex]f(x)+79=15(x+2)^{2}[/tex]

[tex]f(x)=15(x+2)^{2}-79[/tex] -----> function in vertex form

Part B) Name the vertex for the function

we have

[tex]f(x)=15(x+2)^{2}-79[/tex]

The vertex of the function is the point [tex](-2,-79)[/tex]

The parabola open upward, so the vertex is a minimum

see the attached figure to better understand the problem

which is an equation of the given line in standard form (-3, -1 ) (1/2, 2)​

Answers

Answer:

6x - 7y = -11

Step-by-step explanation:

To write the equation of a line when given two points, calculate the slope and substitute it into the point slope form of a line. From this form of the equation, you can simplify and convert to the standard form.

First, find the slope using the formula.

[tex]m = \frac{y_2-y_1}{x_2-x_1} =\frac{2--1}{\frac{1}{2} --3} =\frac{3}{\frac{7}{2}} = \frac{6}{7}/tex]

Substitute m = 6/7 and the point (-3,-1) into the point slope form [tex](y-y_1) = m(x-x_1)[/tex].

[tex]y--1=\frac{6}{7}(x--3)\\y + 1 = \frac{6}{7}(x+3)\\7y + 7 = 6(x + 3)\\7y + 7 = 6x + 18\\-6x + 7y + 7 = 18\\-6x + 7y = 11\\6x - 7y = -11[/tex]

To convert to standard form, multiply the equation by 7. This means each term is multiplied by 7 to clear the denominator. Then multiply using the distributive property. You will now need to move terms across the equal sign. Begin by subtracting 6x from both sides. Then subtract 7 from both side. Lastly, multiply the equation by -1 since the leading coefficient in standard form cannot be negative.

If the side lengths of a cube are 14 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?

1) 14³

2) 3¹⁴

3) 14 ⋅ 3

4) 14 ⋅ 14 ⋅ 14

Answers

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

This will make sense once you see the formula:

volume = length x width x height

As it is a cube, all lengths are the same

Substitute the values in:

volume = 14 x 14 x 14

Exponents are when you multiply a value by itself

For example, 2 x 2 can be written as [tex]2^{2}[/tex]

In this case, the answer would be option 1. [tex]14^{3}[/tex]

Hope This Helps You!

Good Luck (:

Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ

Answer:

14 x 14 x 14

Step-by-step explanation:

Can you guys please help me out

Answers

A. ability to access cash value

hope this helps!!

What is the rate of change of this function?

Answers

Answer:

50 miles per day

Step-by-step explanation:

Answer:

Step-by-step explanation:

35 per day

Which other congruency statements are true?

Answers

ans 4th. ∆dcj =∆yam

ray and hunter sell newspapers after school. ray earns $11 more than hunter. if ray earns $25,how much money does hunter earn?

Answers

Answer:

$14

Step-by-step explanation:

This should be simple, if ray earns $11 more, than hunter earns $25-$11, or $14

To find out how much Hunter earns, we subtract the $11 that Ray earns extra from Ray's total earning of $25, resulting in Hunter earning $14.

The student has asked a question regarding how much Hunter earns if Ray earns $25 which is $11 more than Hunter. To solve this, we subtract $11 from Ray's earnings to find Hunter's earnings:

Ray's earnings = $25Hunter's earnings = Ray's earnings - $11Hunter's earnings = $25 - $11Hunter's earnings = $14

Therefore, Hunter earns $14.

Find the value of the variable leave answer in simplest radical form

Answers

X is 7 and y is 7 square root of 3.

Answer:

x = 7 and y = 7√3

Step-by-step explanation:

Let's review, and then apply, the definition of "cosine."

cos Ф = adjacent side / hypotenuse.

Here, x is the adjacent side, Ф is the angle and is 60°, and 14 represents the length of the hypotenuse.  cos Ф = adjacent side / hypotenuse becomes:

adjacent side = hypotenuse * cos Ф.

Here, Ф = 60° and cos Ф = cos 60° = 1/2.  Therefore,

in this case, x = 14(1/2), or 7.

Applying the definition of sine:

sin Ф = opp / hyp.  In this case, sin Ф = sin 60° = y/14, so that

y = 14 sin 60°, or y = 14(√3 / 2) = 7√3.

In summary, x = 7 and y = 7√3.

A rectangular note card has an area of 28 square inches. Its perimeter is 22 inches. What are the dimensions of the note card?

Answers

Answer: 4 inches x 7 inches

Step-by-step explanation: Knowing that the formula for the area is length times width, 4 x 7 = 28 square inches. The perimeter of the rectangle with 2 sides that are 4 inches and 2 sides that are 7 inches is 22 inches. (2 x 4) + (2x7) = 8 + 14 = 22 inches.

The dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.

Let l be the length of the rectangular note card and w be its width.

Since the area of the rectangular note card is 28 square inches, we have that

lw = 28 (1)(the area of a rectangle).

Also, the perimeter of the rectangular note card is 22 inches. We have that

2(l + w) = 22 (2) (perimeter of a rectangle)

So, l + w = 11 (3)

From (3), l = 11 - w.

Substituting l into (1), we have

(11 - w)w = 28

11w - w² = 28

re-arranging, we have

w² - 11w + 28 = 0

Factorizing, we have

w² - 7w - 4w + 28 = 0

w(w - 7)- 4(w - 7) = 0

(w - 7)(w - 4) = 0

w - 7 = 0 or w - 4 = 0

w = 7 or w = 4

Since l = 11 - w,

substituting w = 7 into l, we have

l = 11 - 7 = 4 inches

substituting w = 4 into l, we have

l = 11 - 4 = 7 inches.

So, we have l = 4 and w =  7 or l = 7 and w = 4

So, the dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.

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The points (4,1) and (x,-6) lie on the same line. If the slope of the line is 1, what is the value of x?


*show work + explain*

urgent!!!

Answers

Answer:

x = -3

Step-by-step explanation:

Substitute the values m = 1 and from the points into the slope formula. Then solve for x.

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\1 = \frac{1--6}{4-x}\\\\1 = \frac{7}{4-x}\\\\4-x = 7\\\\-3 = x[/tex]

An estimated three out of every 25 men are left-handed what percent of the men are left-handed?

Answers

Answer:

12%

Step-by-step explanation:

3/25 x 100 = 12

Answer:12%

Step-by-step explanation:

3/25 * 100 ☺

Which statement describes what these four powers have in common?

Answers

Answer:

"All the powers have a value of 1 because the exponent is 0"

Step-by-step explanation:

To answer this, we need to recall the property that "ANYTHING to the power 0 is ALWAYS equal to 1" (except 0^0).

Here, we see that the base of all of the 4 choices are integers (and NOT ZERO) and all of them are raised to 0th power. So all of them are EQUAL TO 1.

Hence, the correct answer is "All the powers have a value of 1 because the exponent is 0"

Answer:

All the powers have a value of 1 because the exponent is 0

Step-by-step explanation:

When John bought his new computer, he purchased an online computer help. Service.
The help service has a yearly fee of $25.50 and a $10.50 charge for each help session a person uses. If John can only spend $170 for the computer help his year, what is the maximum number of help seccion he can use this year?

Answers

Final answer:

John can afford a maximum of 13 help sessions with his $170 budget for the year, after accounting for the $25.50 annual fee and the $10.50 per session charge.

Explanation:

To find the maximum number of help sessions John can use within his budget, we need to set up a simple algebraic equation. The total cost for the online help service consists of an annual fee plus the charge per help session. The equation to represent this situation will be:

Total Cost = Annual Fee + (Charge per Session × Number of Sessions)

We know the Annual Fee is $25.50, the Charge per Session is $10.50, and John's budget, or the Total Cost, is $170.

Let's denote the Number of Sessions as 'x'. The equation therefore becomes:

$170 = $25.50 + ($10.50 × x)

Subtracting the annual fee from both sides gives us:

$170 - $25.50 = $10.50 × x

$144.50 = $10.50 × x

Dividing both sides by $10.50 gives us the number of sessions John can afford:

x = $144.50 / $10.50

x = 13.7619...

Since John can't have a fraction of a session, we round down to the nearest whole number. John can afford a maximum of 13 help sessions within his budget of $170 for the year.

A bag contains 6 red and 10 black
marbles. If you pick a marble from the
bag, what is the probability that the
marble will be black?


plz help ​

Answers

Answer:10/16 (can simplify I think)

Step-by-step explanation: First you do 10+6 to find out the total of all the marbles which is 16. There are 10 blacks so you do 10/16 AS you wanna find out the probability of getting the black.

Answer:

62.5%

Step-by-step explanation:

First you add up all the marbles and then divide 100 into the sum of all of the marbles and then you times it by the black marbles to find the percent

100/(6+10)*10=%

Use elimination to find the solution to the system of equations.

Answers

Answer:  option B.

Step-by-step explanation:

You can apply the elimination method:

- Multiply the first equation by -7 and the second equation by 3.

- Add both equations to cancel out the variable y.

- Solve for x

[tex]\left \{ {{(-7)9x+3y=(-39)(-7)} \atop {(3)(4x+7y)=(-57)(3)}} \right.\\\\\left \{ {{-63x-21y=273} \atop {12x+21y=-171}} \right.\\-------\\-51x=102\\x=-2[/tex]

- Substitute x=-2 into any of the original equations ans solve for y. Then:

[tex]9(-2)+3y=-39\\-18+3y=-39\\3y=-21\\y=-7[/tex]

Hello!

The answer is:

B.

[tex]x=-2\\y=-7[/tex]

Why?

Solving the system of equations by elimination, we have:

[tex]\left \{ {{9x+3y=-39} \atop {4x+7y=-57}} \right.[/tex]

Then, multiplying the second equation by [tex]-\frac{9}{4}[/tex]

So,

[tex]\left \{ {{9x+3y=-39} \atop {4x*(-\frac{9}{4}) +7y*(-\frac{9}{4}) =-57*(-\frac{9}{4})}} \right\\\\\left \{ {{9x+3y=-39} \atop {-9x-\frac{63}{4}y=\frac{513}{4} }} \right\\\\-\frac{51}{4}y=\frac{357}{4}\\\\y=\frac{357}{4}*(-\frac{4}{51})=-\frac{1428}{204}=-7[/tex]

Then, substituting y=-7 into the first equation (also, we could substitute it into the first equation) we have:

[tex]9x+3(-7)=-39\\9x-21=-39\\9x=-39+21\\9x=-18\\x=\frac{-18}{9}=-2[/tex]

So, the solutions for the system of equations are:

[tex]x=-2\\y=-7[/tex]

Have a nice day!

arduino language is based on__ programming language.

Answers

Answer: Normally C/C++

Step-by-step explanation:

Final answer:

The Arduino platform uses a language that is based on the C++ programming language. Despite some simplifications and extensions to better interact with Arduino hardware, those who are familiar with C++ will find similarities in Arduino.

Explanation:

The Arduino language is based on the C++ programming language. Although the materials provided mention Python, Scheme, and Modula-3, none of these are directly related to the Arduino language. The Arduino language includes many functions and libraries common in C++, which means that if you are familiar with C++, you will find it easier to understand and use Arduino.

However, note that Arduino is also slightly different from standard C++ as it includes some simplifications and extensions to make it easier to work with the Arduino hardware.

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Can you help me with 5. 6. 7. 8. Please!!!!

Answers

Answer:

8,if it broke some tiny thing from that it will fail but if it not broke it will be heavy then the broke one. the one that do not broke is the heavy one.

Step-by-step explanation:

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