how to express -8+4-2+1 in sigma notation

Answers

Answer 1

It's pretty clear what the pattern is - 2^(k-1) * (-1)^(k-1) would work backwards, but we have to work forwards to get lower in this case, so we could start at -3 (as long as we put the k-1 in absolute value to make sure it's not 1/8), so we could write it as ∑ (k=1, goes to 4) 2^(|k-4|)*(-1)^(k-4)

It doesn't matter for k-4 because 1/-1 and 1/1 are the same thing as -1 and 1 respectively

Related Questions

A geometric sequence has a common ratio of 2/9 and the first term is 729 what is the 8th term?

Answers

This is the concept of sequences and series. The formula for geometric series is given by:
an=ar(n-1)
where;
a=first term
r=common ratio
n=nth term
thus the 8th term will be:
8th=728*(2/9)^(8-1)
=728*(2/9)^7
=128/6561

It takes an older employee 13 hours to shovel the snow from a sidewalk, but a younger employee can shovel the same sidewalk in 10 hours. how long will it take them to clear the walk if they work together?

Answers

Time taken by both of the older employee and younger employee is 5.6 hrs

What is Componendo-dividendo rule?

Componendo-dividendo rule: A theorem based on the topic of proportions permits a faster way to carry out the calculations and cut down the count of expansions required. It is helpful in situations involving equations with fractions or rational functions. The componendo and dividendo rule are used while studying ratios and proportions. If the ratio of any two given numbers is the same as the ratio of the other 2 numbers, then the ratios of the sum total of the numerator and denominator to the difference of the numerator and denominator of the two rational numbers are equal in nature.

Given, older employee needs 13 hours to shovel the snow.

So in 1 hr the older employee will shovel = 1/13

Younger employee needs 10 hours to shovel the snow.

So in 1 hr the younger employee will shovel = 1/10

Now, when they work together

[tex]1/13+1/10 = 1/x \\(10+13)/130 = 1/x \\3/130 = 1/x\\x = 130/23 = 5.6 hrs[/tex]

Hence, the time taken by both of them together is 5.6 hrs

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Final answer:

Two employees working together can clear the sidewalk in approximately 6 hours and 31 minutes. This is determined by finding the individual work rates, combining them, and then taking the reciprocal of the combined rate to find the total time worked together.

Explanation:

To find out how long it will take two employees to shovel snow together, we need to determine their combined work rate. The older employee takes 13 hours, and the younger employee takes 10 hours. First, we calculate each of their work rates per hour by taking the reciprocal of their time.

So, the older employee's work rate is 1/13 sidewalks per hour and the younger employee's 1/10 sidewalks per hour. To find their combined work rate, we add these two rates together:

Combined work rate = (1/13) + (1/10) = (10 + 13) / (13 × 10) = 23/130 sidewalks per hour

Now, to find the total time taken to shovel the sidewalk when working together, we take the reciprocal of the combined work rate:

Time taken working together = 1 / (23/130) = 130/23 hours

To make this more interpretable, we can convert it into a mixed number:

Time taken working together = 5 hours and (130/23 - 5 × 23/23) hours = 5 hours and 35/23 hours

We can convert 35/23 hours into minutes by multiplying by 60:

Additional minutes = (35/23) × 60 minutes = approximately 91 minutes

Therefore, the time taken working together is roughly 5 hours and 91 minutes, which simplifies to 6 hours and 31 minutes.

If the problem is 7+(-5) how many spaces do you move to the right or left

Answers

Start at seven and move 5 spaces to the left.

Addition of a negative is the same as subtraction.

[tex]-2y + y - 3 = 6
[/tex]

Answers

Combine like terms. -2y+y=-y. The equation is now -y-3=6. You need to get the y by itself so add 3 to both sides. The equation is now -y=9. You are solving for y so divide both sides by -1. The equation will be y=-9. The answer is y=-9. Hope this helps! ;)

Can some one please help me with this question answer What is 40%of 320

Answers

40% = 40/100 = 0.4

320 * 0.4 = 128 ← answer

320*0.4=128
Final answer: 128

WILL MAKE BRAINLIEST!!! A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims, that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.

Answers

Let's consider the triangle ABC shown in the first diagram below. We name the sides with small letters: a, b, and c. We name the angles by the capital letters A, B, and C. Side a pairs with angle A° which are opposite each other. The same with side b and angle B° and side c and angle C°.

We can use the cosine rule when we know the length of two sides and the angle opposite the side that is unknown. For example, referring to the second diagram, we know the length of side a and side b and we are looking for the length of side c. We also know the angle that is located on the opposite of side c, then to solve this we can use the cosine rule

c² = a² + b² - 2ab(cos(C°))

The third diagram shows a scenario when sine rule can be used. Say we need the length of the side c. We know the length of side a, the size of angle A° and angle C° then we can use the sine rule

[tex] \frac{c}{sin(C)} = \frac{a}{sin(A)} [/tex]

We can also use sine rule if we know length of side b and the size of angle B° instead of side a and angle A°

If a weighted score for a project is based on just two criteria, fit with strategy, weighted 70% and roi, weighted 30%, what would be the weighted score for a project with scores of 80 on fit with strategy and 50 on roi?

Answers

When dealing with weighted averages, we multiply the score of each item by the percentage that it's been weighted and add the scores together. 80/100 X 70/100 = 5600/10000 or 56/100 50/100 x 30/100 = 1500/10000 or 15/100 56 + 15 = 71 and so your grade would be 71%

Final answer:

To calculate the weighted score for a project, apply the weights to the scores for each criterion and sum the results. The calculated weighted score for a project with scores of 80 on 'fit with strategy' (70% weight) and 50 on 'ROI' (30% weight) is 71.

Explanation:

To calculate the weighted score for a project based on the provided criteria, you need to apply the weights to the scores for each criterion and then sum the results. In this case, the criteria are 'fit with strategy' which has a weight of 70% and 'ROI' which has a weight of 30%.

The weighted score for 'fit with strategy' is calculated as follows:
(Score for 'fit with strategy' × Weight of 'fit with strategy') = (80 × 0.7) = 56.

The weighted score for 'ROI' is calculated as follows:
(Score for 'ROI' × Weight of 'ROI') = (50 × 0.3) = 15.

To find the total weighted score for the project, you add these two results together: 56 (from fit with strategy) + 15 (from ROI) = 71.

Therefore, the total weighted score for the project is 71.

What's an equation for "Six more then twice a number is 72?"

Answers

the equation would be:

2x+6 = 72

2n + 6 = 72 <== ur equation

I NEED THIS ANSWER NOWWWW PICTURE ATTACHED

Which system of inequalities is represented by the graph?

y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1

Answers

So first, you need to notice the blue line is y = 2x, and the other one is y = -2x - 1

For the purple area, let's choose a point (1,0), which is in the area.

For y = 2x -> 2 >0, so the inequality will be y ≤2x

For y = -2x - 1 -> -3 < 0, so the inequality will be y ≥ -2x - 1

You can use the similar approach to find other area representations

Explain 2 other ways other than rotating 180 degrees counterclockwise or clockwise, that would allow the point to find it’s way to the same place from its original position. Hint: You may combine transformations.

Answers

check picture 1

Notice that a 180° rotation clockwise or counterclockwise (around the origin) send any point P(a, b) to a point with coordinates (-a, -b).

this means the number values of the respective x and y coordinates are the same, but the signs are different.

for example rotating point P(-3, 17) 180 degrees results in point (3, -17)

check picture 2.

reflecting point P(a, b) with respect to :

the y-axis results in point (-a, b)

the x-axis results in point (a, -b)

for example , consider point P(-3, 17)

reflecting this point with respect to the y axis, results in (3, 17)

reflecting (3, 17) with respect to the x-axis results in (3, -17)

So the effect of reflecting with respect to the y axis, the x axis (the other way around is the same) results in the same point as rotating 180 degrees.

Answer:

1) reflect with respect to the y-axis, then reflect this last point with respect to the x-axis

2) reflect with respect to the x-axis, then reflect this last point with respect to the y-axis

Felicia put $175 into a CD that pays 4% interest, compounded semiannually. According to the rule of 72, approximately how long will it take for her money to double?

Answers

The compound interest is given by:
A=p(1+r/100)^n
where;
A=amount
p=principle
r=rate
n=time
therefore the time taken for Felicia's money to double will be:
350=175(1+4/100)^n
350/175=1.04^n
2=1.04^n
therefore introducing natural longs we get:
ln2=nln1.04
n=(ln2)/(ln1.04)
n=17.7 years
The answer is 17.7 years

Answer:

the answer is 18 years

Step-by-step explanation:

i just did this on 12/8/18 good luck to cheaters

The graph shows the location of Jacob's, Kent's, and Hakim's houses. Each unit on the graph represents 1 kilometer. A coordinate plane is shown. Hakims house is located at negative 3, 1, Jacobs house is located at 1, 5, and Kents house is located at 1, 1. Line segments connect the points to form a right triangle.

Answers

The distance between any two points is:

d^2=(x2-x1)^2+(y2-y1)^2 so in this case we have:

d^2=(5-1)^2+(1-3)^2, d^2=(1-5)^2+(1-1)^2, d^2=(1-3)^2+(1-1)^2

d^2=(16+4), d^2=16, d^2=4

So the total distance or perimeter, p, is:

p=√20+√16+√4

p=√20+4+2

p=6+√20 km (exact)

p≈10.47 km (to nearest hundredth of a kilometer)

Answer:

14 km

Step-by-step explanation:

I did FLVS

the price of a television decreased from 1000.00 to 800.00.what is the percent of decrease.

Answers

Percentage change = 100((New Value - Original Value) / Original Value)
So....
100((800 - 1000) / 1000)
= 100(-1/5) = -20%
Considering the question asks what is the percentage 'decrease' and thus has mentioned that the price is decreasing, you should just give the answer as 20%. If it was not mentioned that the value increases or decreases, it would be correct to put it as -20%

Answer:

The decrease is 20%

Step-by-step explanation:

Identify the standard form of the equation by completing the square

Answers

[tex]4 x^{2} -9 y^{2} -8x-36y-68=0[/tex]

[tex]4 x^{2} -8x-(9 y^{2} +36y)-68=0[/tex]

[tex](2x)^{2} -2*(2x)*2-((3y)^{2} +2*(3y)*6)-68=0[/tex]

add and subtract 2^ to the x-expression and 6^ to the second expression to complete the square.

[tex][(2x)^{2} -2*(2x)*2+4]-4-((3y)^{2} +2*(3y)*6+36-36)-68=0[/tex]

[tex](2x-2)^{2} -4-((3y+6)^{2} -36)-68=0[/tex]

[tex](2x-2)^{2} -(3y+6)^{2} -4+36-68=0[/tex]

[tex](2x-2)^{2} -(3y+6)^{2} -36=0[/tex]

[tex](2x-2)^{2} -(3y+6)^{2} = 6^{2} [/tex]

divide by 6 squared

[tex]( \frac{2x-2 }{6} )^{2} -( \frac{3y+6}{6} )^{2} =1[/tex]

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

[tex] \frac{ (x-1)^{2} }{9} - \frac{(y+2)^{2}}{4} =1[/tex]

Answer: A

Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π? (?

Answers

consider the function [tex]f(x)=-4cos(x- \frac{ \pi }{2})[/tex]

the x-intercepts of the graph of f, are the zeros of f, that is the solutions of f(x)=0.

so we solve

[tex]-4cos(x- \frac{ \pi }{2})=0[/tex]

[tex]cos(x- \frac{ \pi }{2})=0[/tex]

at this point we ask ourselves, keeping the unit circle in mind, "cosine of what is 0?"

In the unit circle, from 0 to 2π radians,

cos 90° = cos (π/2) rad = 0

and

cos 270° = cos (3π/2) rad = 0

this means that

i)
[tex]x- \frac{ \pi }{2}= \frac{ \pi }{2}[/tex]

[tex]x= \pi [/tex]

and

ii)
[tex]x- \frac{ \pi }{2}= 3\frac{ \pi }{2} [/tex]

[tex]x=3\frac{ \pi }{2} +\frac{ \pi }{2}=2 \pi [/tex]

ii) also, check that [tex]f(0)=-4cos(0- \frac{ \pi }{2})=-4cos(-\frac{ \pi }{2})[/tex] is also 0, because cos (-pi/2)= cos (-90°)=cos 270°=0

Answer:

x=0, x=π, and x=2π

In a horse race, how many different finishes among the first 33 places are possible if 20 horses20 horses are running? (exclude ties)

Answers

To solve this problem, let us break this down one by one.

There are 20 possible horses that could win in first place. Therefore this means that for each of these possibilities, there are now 19 horses that could come in second. So meaning there are 20 x 19 possible combinations for the first 2 places.

20 x 19 = 380. And for each of those combinations, there are also 18 possible horses that could come in the third place. So

20 x 19 x 18 = 6,840

There are 6,840 possible horse combinations for the first 3 places in the race.

Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a downward sloped line crossing the y axis at two that ends at the open point 2, 1.3, a closed point at 2, -1, and an upward sloped line starting at the open point 2, 4. Find = limit as x approaches two from the right of f of x..

Answers

Answer: The right hand limit is 4

-------------------------------

Start on the right side of the value x = 2. In other words, start at some value larger than 2, say x = 4. Starting at x = 4, move closer to x = 2. Move as close as you can. The closer x gets to 2, the closer y gets to 4. You'll never actually get to x = 2 or y = 4 because of the hole. However, the right-hand limiting value is 4 assuming you can keep getting closer and closer.

Note: if you approach x = 2 from the left side, you arrive at a different y value So this suggests that overall, the limit at x = 2 doesn't exist. But the right hand limit (RHL) does exist as described above.

Solve the equation using square roots. x^2-15=34

Answers

Hello there!

First, let's take a look at our equation.
[tex] x^{2} [/tex] - 15 = 34
We need to isolate x^2 to completely square root both sides properly, so let's do so.
Add 15 to both sides to isolate [tex] x^{2} [/tex].

We are now left with:
[tex] x^{2} [/tex] = 49
Now, square root both sides.
[tex] \sqrt{x^2} [/tex] = x
[tex] \sqrt{49} [/tex] = 7

We are now left with the solution:
x = 7

I hope this helps!

X^2-15=34 add 15 to both sides
X^2=49 square both sides
X=7

"It was you who awoke me last summer out of a life-long stupid dream" write the conclusion for this quote

Answers

The person that "awoke [the author]" helped change the authors life around and helped him find the purpose for his life

hope this helps

How to divide fractions with whole numbers

Answers

To divide fractions with whole numbers, write the whole number as a fraction, then it should be more solveable

To divide fraction with whole number write the whole number as a fraction like write 2 as 2/1.

Hope this helps.

Find the area of a rectangular almond orchard that is 200 yards long and 100 yards wide.
300 square yards
2100 square yards
2000 square yards
20000 square yards

Answers

A = L * W
A = 200 * 100
A = 20,000 square yards

In a restaurant there are 3 choices for appetizers, 6 choices for entrees, and 4 choices for desserts. How many different meal choices are there if you were to have 1 appetizer, 1 entree, and 1 dessert?
24
72
13
18

Answers

The correct answer is B. 72 because you can multiply 3*6*4 to represent every combination possible.

What is the answer to

-18= 117/p-9

Answers

-18 = 117/(p-9)
(p-9)(-18) = 117
p-9 = 117/-18
p = (117/-18) +9
p = 2.5

Hey there!

So here are the steps you need to follow to get the answer!

-18 = 117/(p - 9)
-18(p - 9) = 117 -----> multiply "(p - 9)" on both sides
-18p + 162 = 117 ------> distribute the "-18"
-18p = -45 ------> subtract "162" on both sides
p = 2.5 ------> divide "-18" on both sides

I hope this helps! :D

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Angie baked 100 cookies and 20 brownies. She wants to split them into equal groups for the big sale. Each group must have the same number of cookies and brownies, with none left over. What is the greatest number of groups she can make? Angie baked 100 cookies and 20 brownies. She wants to split them into equal groups for the big sale. Each group must have the same number of cookies and brownies, with none left over. What is the greatest number of groups she can make? Angie baked 100 cookies and 20 brownies. She wants to split them into equal groups for the big sale. Each group must have the same number of cookies and brownies, with none left over. What is the greatest number of groups she can make?

Answers

stop copying the question, it's confusing

so 100 cookies and 20 brownies
what is the greatest number you can divide them both by?

find the GCF
factor them
100=2*2*5*5
20=2*2*5
so the GCF is the common group to both or 2*2*5 or 20

100/20=5
20/20=1

there are 20 groups, each wit 5 cookies and 1 brownie

20 groups

Lukas graphed the system of equations shown. 2x + 3y = 2 y = x + 3 What is the solution to the system of equations? (–2, 2) (0, 0.67) (0, 3) (1, 0)

Answers

The closest answer that I could find would be (-2, 2). The answer to the system is (-1.4, 1.6)

The solution to the given system of linear equations is (-1.4, 1.6).

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are 2x+3y=2 -----(i) and y=x+3 -----(ii)

Substitute, equation (ii) in equation (i), we get

2x+3(x+3)=2

2x+3x+9=2

5x=-7

x=-7/5

x=-1.4

Substitute x=-1.4 in equation (ii), we get

2(-1.4)+3y=2

-2.8+3y=2

3y=2+2.8

3y=4.8/3

y=1.6

So, the solution is (-1.4, 1.6)

Therefore, the solution to the given system of linear equations is (-1.4, 1.6).

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What is the factorization of the polynomial below?

x^3-4x^2+45x

Answers

The method of factorization is used to find the roots of a given polynomial. Roots are the solutions of the function. Graphically, these roots are where the curve passes the x-axis. The first step to do is to find the common factor of the equation. That would be x. So you place it outside of the parenthesis.

x³-4x²+45x = x(x² - 4x + 45)

If you solve the quadratic equation inside the parenthesis using the quadratic formula, the roots are imaginary. Therefore, the quadratic equation is already a prime polynomial.

The final answer is x(x² - 4x + 45).

Hope This Helps You!(

What is the graph of x = -5?

Answers

hello:
the graph is the line parralle of axis- y passing by the point : (-5 , 0 )

3/5x+19−3/20x−7/35x+19−3/20x−7 simplified is

Answers

Final answer:

To simplify the expression, combine like terms and then simplify to get (1/4)x+24.

Explanation:

To simplify the expression, 3/5x+19−3/20x−7/35x+19−3/20x−7, we can combine like terms and then simplify:

Combine 3/5x−3/20x−7/35x to get (3/5−3/20−7/35)x = (12/20−3/20−4/20)x = (5/20)x = (1/4)x.Combine 19+19 to get 38.Combine −7−7 to get −14.Combine the results: (1/4)x+38−14 = (1/4)x+24.

So, the simplified expression is (1/4)x+24.

A card is drawn from a standard deck of 52 cards. what is the probability that it is a heart? type in your answer to two decimal places!

Answers

There are 13 hearts in a deck, so 13/52 which is just 1/4 which is 0.25

4 suits in a deck
1 suit is a heart

so the probablity is 1 out of 4 or 25% or 0.25

Find an equation for the nth term of the arithmetic sequence.

a15 = -53, a16 = -5

A) an = -725 - 48(n - 1)
B) an = -725 + 48(n + 1)
C) an = -725 + 48(n - 1)
D) an = -725 - 48(n + 1)

Answers

an=a1+d(n-1)

every term increases by d amount

so [tex]a_n+d=a_{n+1}[/tex]
therefor
[tex]a_{15}+d=a_{15+1}=a_{16}[/tex]

-53+d=-5
add 53 both sides
d=48

alright
an=a1+d(n-1)
an=a1+48(n-1)
use a15=-53
a15=-53=a1+48(15-1)
-53=a1+48(14)
-53=a1+672
minus 672 both sides
-725=a1

the equation is
an=-725+48(n-1)
answer is C

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