given the series 1+2+3+4+5+6+...+5000. Write the series in sigma notation if all the powers of 4 are removed from the series.​

Answers

Answer 1

We have 4⁶ = 4096 and 4⁷ = 16,384, which is to say that the given sum only contains the first six powers of 4.

Now,

[tex]\displaystyle 1+2+3+\cdots+5000 = \sum_{k=1}^{5000}k[/tex]

and you subtract the sum of the first six powers of 4 to get the sum S that you want,

[tex]\displaystyle S = \boxed{\sum_{k=1}^{5000}k - \sum_{k=1}^64^k}[/tex]


Related Questions

In the figure, triangles ABC and DEF are congruent.
Find the measure of DF.
a. 13m
b. 12m
c. 7m
d. 13.928m

Answers

It’s d hope it helps

In Riverview Middle school, 20 percent of the students participate in an after school club for every 100 students how many are in an afterschool club

Answers

Answer:

What is the diferentes between and red bolos celos ?

Step-by-step explanation:

20

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

A department store mails a customer satisfaction survey to people who make credit card purchases at the store. This month, 3521 people made credit card purchases. Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form. Identify the population and the sample.

Answers

Answer:

The population is the population of 3521 people who made credit card purchases.

The sample is the 172 people who returned the survey form.

Step-by-step explanation:

Department mails customers satisfactions forms to those who make credit cards purchase at the store, totaling 3521 people. Thus, the population is the population of 3521 people who made credit card purchases.

Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form.

Thus the sample, that is, those from whom the data will be taken and expanded to the rest of the population, is the 172 people who returned the survey form.

The population is all 3521 people who made credit card purchases.

The sample is the 172 people who returned the survey form.

What are the zeroes of f(x) = x2 - X - 2?
x= -2,1
x = 2, -1
x= -2, -1
x = 2,1

Answers

Answer:

x=2    x=-1

Step-by-step explanation:

f(x) = x^2 - X - 2

0= x^2 -x-2

Factor

0 =(x-2)(x+1)

Using the zero product property

x-2 =0   x+1 =0

x=2    x=-1

Answer:

x=2, -1

Step-by-step explanation:

Hi there!

We want to find the zeros of this function: f(x)=x²-x-2

The zeros are the values of x that will make f(x)=0

So that means in order to find the zeros, set f(x) as 0

In that case,

x²-x-2=0

Now let's solve the quadratic equation

We can do it by factoring

-x is the sum of two numbers, while -2 is the product of those two same numbers

Now think: which two numbers add up to -1, but multiply to get -2?

Those numbers are -2 and 1

Now factor the polynomial by FOIL:

(x-2)(x+1)=0

Split and solve

x-2=0

x=2

x+1=0

x=-1

The zeros are x=2, -1

Hope this helps!

Find RS. Can anyone help?

Answers

The segment XT splits the trapezoid exactly in half. The average of RS and Q will give us XT because of the properties of a trapezoid.

We find the area of a trapezoid by averaging the bases as well.

RS + Q / 2 = XT

RS + 26 / 2 = 22

RS + 26 = 44

RS = 18

Hope this helps!

Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x Question 7 options: A) (–4, 0) and (0, 0) B) (0, 0) C) (–4, 0) and (4, 0) D) (0, 0) and (4, 0)

Answers

Answer:

Hello,

Answer A (-4,0) and (0,0)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y&=&x^2+4x\\y+x^2&=&-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\y&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\x^2+4x&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}2*x^2+8*x&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}x(x+4)&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\[/tex]

[tex]\left\{\begin{array}{ccc}x&=&0 \\y&=&0\\\end{array} \right. \ or\ \left\{\begin{array}{ccc}x&=&-4 \\y&=&0\\\end{array} \right.[/tex]

Match each set of vertices with the type of triangle they form.
A(2, 0), B(3, 2), C(5, 1)
obtuse scalene triangle
A(4, 2), B(6, 2), C(5, 3.73)
isosceles right triangle
A(-5, 2), B(-4, 4), C(-2, 2)
right triangle
A(-3, 1), B(-3, 4), C(-1, 1)
acute scalene triangle
A(-4, 2), B(-2, 4), C(-1, 4)

Answers

9514 1404 393

Answer:

rightacuteobtuserightobtuse

Step-by-step explanation:

When the same problem is repeated, I like to solve it using a spreadsheet. That way, the formulas only need to be entered once, and the arithmetic is (almost) guaranteed to be done correctly.

A "form factor" computed from side lengths can be used to determine the type of triangle. Where 'c' is the long side, that factor can be computed as ...

  f = a² +b² -c²

and interpreted as follows:

f = 0, right trianglef > 0, acute trianglef < 0, obtuse triangle

(The sign of f matches the sign of the cosine of the largest angle computed using the law of cosines.)

Of course, a right triangle can also be identified by looking at the slopes of the sides of the triangle. If any pair of slopes has a product that is -1, or if any pair is 0 and "undefined", then the triangle will be a right triangle.

__

The attached spreadsheet is designed to accommodate a number of different problem requirements. It shows both side lengths and slopes, and it shows the "form factor" as described above. The final classification is shown at far right.

rectangle a is dilated to form rectangle b. what is the scale factor used .​

Answers

Answer:

5

Step-by-step explanation:

The scale factor is 5. Answered by Gauthmath

The length and the width of rectangle a are expanded 5 times respectively.

What is a scale factor?

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

According to the question

Rectangle a is dilated to form rectangle b.

By division operation, the ratio

[tex]\frac{20}{4} =\frac{30}{6} =5[/tex]

The length and the width of rectangle a are expanded 5 times respectively.

Find out more information about scale factor here

brainly.com/question/2839518

#SPJ2

By which number should (2/5)^-3 be multiplied to get (1/2)^4 as a product ?​

Answers

Answer:

[tex]\frac{2}{5}^{-3}[/tex]×[tex]x=\frac{1}{2}^{4}[/tex]

[tex]x=\frac{2}{5} ^{3} \\[/tex]×[tex]\frac{1}{2}^{4}[/tex]

(negative in the exponent means reciprocal of the fraction)

x= [tex]\frac{1}{250}[/tex]

Brainliest please

Find the interval in which f(x) = 3x2 - 2x is decreasing.

Answers

Answer:

Option (3)

Step-by-step explanation:

Given function is,

f(x) = 3x² - 2x

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

     = [tex]3(x^{2} -\frac{2}{3}x+\frac{1}{9}-\frac{1}{9})[/tex]

     = [tex]3(x^{2}-\frac{2}{3}x+\frac{1}{9})-\frac{1}{3}[/tex]

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

Vertex of the parabola → [tex](\frac{1}{3},-\frac{1}{3})[/tex]

Here, leading coefficient is positive (+3),

Therefore, parabola will open upwards.

In a parabola opening upwards function decreases from negative infinity to the x value of the vertex.

Function will decrease in the interval (-∞, [tex]\frac{1}{3}[/tex]).

Option (3) will be the answer.

A town recently dismissed 8 employees in order to meet their new budget reductions. The town had 9 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that at least 7 employees were over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answers

Answer:

The probability that at least 7 employees were over 50 is 0.0073%.

Step-by-step explanation:

Given that a town recently dismissed 8 employees in order to meet their new budget reductions, and the town had 9 employees over 50 years of age and 16 under 50, if the dismissed employees were selected at random, to determine what is the probability that at least 7 employees were over 50, the following calculation must be performed:

9/25 x 8/24 x 7/23 x 6/22 x 5/21 x 4/20 x 3/19 = X

0.36 x 0.33 x 0.304 x 0.272 x 0.238 x 0.2 x 0.157 = X

0.000073 = X

100X = 0.0073

Therefore, the probability that at least 7 employees were over 50 is 0.0073%.

Which of the statements is true for the two division problems below? A: (x^2-3x-18)/(x-6) B. (x^3-x^2-5x-3)/(x^2+2x+1)

Answers

Answer:

B is the right statement

Answer:

add the answer choices

Step-by-step explanation:

one month is what percentage of a year given that there are 7 days in a week, and 12 months in a year

Answers

Answer:

it should be 8.333333%

Step-by-step explanation:

The answer is 8.3% or 8.4% when rounding. If you were to round to the nearest it would be 8.0% since 8.3 is closer to 8.0 not 9.0.

A map has a scale in which 1.25 inches represents 250 miles.

How many miles does 1 inch represent?

Answers

Answer:  200 miles

Work Shown:

(1.25 inches)/(250 miles) = (1 inch)/(x miles)

(1.25)/(250) = 1/x

1.25x = 250*1 ..... cross multiplication

1.25x = 250

x = 250/(1.25)

x = 200 miles

While planning a hiking trip, you examine a map of the trail you are going on hike. The scale on the map shows that 2 inches represents 5 miles.

If the trail measures 12 inches on the map, how long is the trail?

Answers

Answer:

30 miles

Step-by-step explanation:

Given that :

Scale = 2 inches represents 5 miles

This means that 2 inches in the map equals to 5 miles on ground ;

Hence, if the trail measures 12 inches on the map, the length on ground will be ; x

2 inches = 5 miles

12 inches = x miles

Cross multiply :

2x = (12 * 5)

2x = 60

x = 60 / 2

x = 30 miles

Consider the function z(x,y) describing the paraboloid \[z = (2x - y)^2 - 2y^2 - 3y.\]Archimedes and Brahmagupta are playing a game. Archimedes first chooses $x.$ Afterwards, Brahmagupta chooses $y.$ Archimedes wishes to minimize $z$ while Brahmagupta wishes to maximize $z.$ Assuming that Brahmagupta will play optimally, what value of $x$ should Archimedes choose?

Answers

Answer: -3/8

Step-by-step explanation:

Expanding z we get  

z = 4x^2 - 4xy + y^2 - 2y^2 - 3y

  = -y^2 - (4x + 3) y + 4x^2.

After Archimedes chooses x, Brahmagupta will choose

y=-(4x+3/2) in order to maximize z

Then  

z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2

z=8x^2+6x+9/4

To minimize this expression, Archimedes should choose x=-3/8

Bobby wants to bring popsicles to a summer barbecue. He decides to try a new recipe for pineapple-orange popsicles, so he makes a small batch with 1 cup of pineapple juice and 3 cups of orange juice to taste. He likes the combination, so he uses 3 cups of pineapple juice and 7 cups of orange juice to make a larger batch for the barbecue. Which batch of popsicles tastes more like oranges?

Answers

Answer:The first would taste more like oranges

Step-by-step explanation:

Mr Gardner is making 6 treat bags. He has 185 chocolate-covered raisins to share evenly among the treat bags.

Answers

Answer:

✎There will be 30 Chocolate-Covered raisins in each bag.

✎ And 5 Remaining.

Step-by-step explanation:

Take 185 and divide it by 6 and you should get 30 per bag with a remainder of 5 :)

A) 30 chocolate covered raisins will be in each bag.

B) 5 chocolate covered raisins will be left over

See the photo attached to see the long division.

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

Which of the binomials below is a factor of this trinomial?
x^2+8x+16

Answers

Answer:  x+4

This is because the given expression factors to (x+4)(x+4), which condenses to (x+4)^2.

To factor, think of two numbers that A) multiply to 16, and B) add to 8. Those values would be 4 and 4

4+4 = 8

4*4 = 16

So that's how we end up with (x+4)(x+4). You can use the FOIL rule to expand that out and get x^2+8x+16 again to help verify you have the correct factorization.

The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars) t years after 1995.

400t + 5750


Use this expression to predict what the total average credit card debt will be in the year 2025.

Answer: In the year 2025, the total average credit card debt for a U.S. household will be ------------ dollars.

Answers

Answer:

In 2025, t=30. so D=418*30+6000 = 18540

(2/3)^x-1=27/8, find x. Please add a step-by-step explanation.

[tex]( \frac{2}{3} ) {x - 1 = \frac{27}{8} }^{?} [/tex]

Answers

so basically after doing all the algebra, you will have to use the log function to solve. rearranging things and you will get the log expression that I obtained, then solve it using the change of base formula.

You throw two four-sided dice. Let the random variable X represent the maximum value of the two dice. Compute E(X). Round your answer to three decimal places.

Answers

Answer:

E(X)=3.125

Step-by-step explanation:

We are given that two four sided dice.

Then , the sample space

{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

Total number of outcomes=16

Let the random variable X represent the maximum value of the two dice

Outcomes                            X                                 P(X)

(1,1)                                          1                                 1/16

(1,2),(2,1),(2,2)                                   2                        3/16

(1,3),(2,3),(3,1),(3,2),(3,3)                    3                           5/16  

(1,4),(3,4) ,(2,4),(4,1),(4,2),(4,3),(4,4)    4                            7/16

Using the probability formula

[tex]P(E)=\frac{Favorable\;outcomes}{Total\;number\;of\;outcomes}[/tex]

Now,

[tex]E(X)=\sum_{i=1}^{n}x_iP(x_i)[/tex]

[tex]E(x)=1(1/16)+2(3/16)+3(5/16)+4(7/16)[/tex]

[tex]E(x)=\frac{1+6+15+28}{16}[/tex]

[tex]E(x)=\frac{50}{16}=3.125[/tex]

Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^4, y=1 and the y-axis and whose cross-sections perpendicular to the x axis are semicircles.

Answers

The base of the solid - call it B - is the set of points

B = {(x, y) : 0 ≤ x ≤ 1 and x ⁴ ≤ y ≤ 1}

Recall the area of a circle with radius r is πr ²; in terms of the diameter d = 2r, the area is π (d/2)² = π/4 d ². Then the area of a semicircle with the same diamater is half of this, π/8 d ².

Cross sections of the solid in question are semicircles arranged perpendicular to the x-axis, which means the diameters of each cross section corresponds to the vertical distance between y = x ⁴ and y = 1 for any given values of x between 0 and 1. So d = 1 - x ⁴, which makes the area of each cross section come out to π/8 (1 - x ⁴)².

Split up the solid into very thin cross sections with "base" area π/8 (1 - x ⁴)² and thickness ∆x. Take the sum of these half-cylinders' volumes, then let ∆x converge to 0. In short, we get the total volume by integrating,

[tex]\displaystyle \int_0^1\frac\pi8(1-x^4)^2\,\mathrm dx = \frac\pi8\int_0^1(1-2x^4+x^8)\,\mathrm dx = \boxed{\frac{4\pi}{45}}[/tex]

Our soccer team lost 9 games this season. That was 3/8 of all they played. How many games did they play this season?​

Answers

Answer:

15

Step-by-step explanation:

3/8 = 9

9÷3= 3

the remainder of 3/8 is 5/8 so

5x3=15

For a two-tailed test with a sample size of 20 and a .20 level of significance, the t value is _____. Selected Answer: d. 1.328

Answers

Answer:

1.328

Step-by-step explanation:

Given :

Sample size, n = 20.

Degree of freedom, df = n - 1

df = 20 - 1 = 19

α = 0.2

Using the T-distribution calculator :

Since it is two - tailed:

Tα/2 ; 19 = T0.2/2 ; 19 = T0.1, 19 = 1.3277 = 1.328

Using a t-distribution calculator, it is found that the t-value is of t = 1.328.

How to find the critical value of the t-distribution?

In a calculator, these following inputs are needed:

The number of degrees of freedom, which is one less than the sample size.The level of significance.Whether the test is one-tailed or two-tailed.

In this problem, inputting the data given in a calculator, it is found that the t-value is of t = 1.328.

More can be learned about the t-distribution at https://brainly.com/question/13873630

Choose the correct solution for the given equation x^2-6x=40

Answers

Answer:

10,-4

Step-by-step explanation:

not sure where the options are but if you were to solve this equation first bring everything to one side.

x^2 - 6x - 40 = 0

factor it

(x-10)(x+4) = 0

set each part to 0

x-10 = 0 and x+4 = 0

solutions are 10 and -4

PLEASE HELP ANSWER THISS!!! I NEED THIS PLEASE!!! AND NO LINKS EITHER PLSS!!

Answers

It doesn't change because to add fractions, you need a common denominator. To find it, they multiplied 1/3 by 2 to make 2/6, to add to the 3/6.

Translate To An Algebraic Expression:

S% of 1/r

Answers

Answer:

S/100r

Step-by-step explanation:

S% of 1/r = (1/r x S) : 100

(1/r x S) : 100

S/r : 100

S/100r

S/100r







Have a great day! Stay safe. Hope it helped

Find the missing pieces of the triangle round to the nearest tenth ​

Answers

Answer:

8√3

Step-by-step explanation:

Missing side,

√(19²-13³)

= 8√3

Answered by GAUTHMATH

what is the radius of a circle in it in if the area is 36m²?
A.0.339 m
B.3.39 m
C.78.5 m²
D.339 m

Answers

Answer:

B. 3.39 m

Step-by-step explanation:

r² = A/π

= 36/3.14

= 11.465

r = √11.465 = 3.39

Other Questions
A survey is created to measure dietary habits. The survey asks questions about each meal and snack consumed for each day of the week. The survey seems like a good representation of measuring dietary habits. This survey would be considered to have high ______ validity. Are there possible risks/harms that the genetic engineering process can cause to the public? How could this be prevented/minimized? How would humans benefit from this process? ason Kimble's study of the Archaea in Snowy River in Fort Stanton Cave showed that Archaea play an important role in __________. PLEASE HELP QUICK 30 POINTS !!!!!!Ryan wants to make a triangular deck. He wants each side to be a different length.Select three lengths he could use to make a triangle:Side 1:Side 2:Side 3::: 3 feet:: 10 feet.: 20 feet:: 25 feet:: 60 feet A wind turbine has blades 50m in diameter and an overall height (to the highest point) of 125m. If it has four blades instead of three, create four equations modelling the height of a point on the tip for each of the four blades. 15. What is the solution to k+(-12) = 42? (1 point)k=-54k=-30k= 30k=54 HELP ME WITH THIS PLEASE PLEASE SHOW ME THE FORMULA FOR LETTER C what is x in 8 ^ (x - 1 ) = 16 ?Please help. What is the area of this triangle three hardware priorities for a CAD workstation are a multicore processor, maximum RAM, and a high-end video card. How do each of these components meet the specific demands of this type of computer system simplify 2^x+4-2^x/5*2^xstep by step Find the expected value of the winningsfrom a game that has the followingpayout probability distribution:Payout ($) 0 581015Probability 0.5 0.2 0.15 0.1 0.05Expected Value = [?] How do you write 50% as a fraction? What do viking want Light of wavelength 530.00 nm is incident normally on a diffraction grating, and the firstorder maximum is observed to be 33.0 from the normal. How many slits per millimeter are marked on the grating? what is the full form of xpyt how can I achieve my goals easily He has called together legislative bodies at places unusual, uncomfortable, and distant. . . .He has dissolved Representative Houses repeatedly. . . . He has plundered our seas, ravaged our Coasts, burnt our towns, and destroyed the lives of our people.1 Select the true statement about triangle ABC.A. cos A = cos CB. cos A = sin C C. cos A = sin BD. cos A = tan C What is the range of f(x) = x - 2, if the domain is {3, 1, 2)?