Answer:
[tex]\sum_{k=0}^{n}2k+1[/tex]
Step-by-step explanation:
Let's take a look at how much is added from one term to the next and see if we can recognize a pattern!
1 to 4: +34 to 9: +59 to 16: +716 to 25: +925 to 36: +11If we start by listing the first number in sequence, 1, we get the familiar list:
1, 3, 5, 7, 9, 11
Of course, this is simply the list of the first six odd numbers. To get the first term, we add the first 1 odd number, to get the second, we add first 2 (1 +3), to get the third, we add the first 3 (1 + 3 + 5), and so on. How do we shorten these sums so we're not writing out dozens of terms as the sequence goes on?
Sigma notation: Summing things upFor situations where we're adding up a lot of numbers that follow a predictable pattern, mathematicians came up with something called summation notation, or sigma notation, coming from the Greek S, Σ, short for "sum". Here's a simple example of a sum expressed in sigma notation:
[tex]\sum_{n=1}^{4}n=1+2+3+4[/tex]
Let's break this down. n acts as our counter. [tex]\sum_{n=1}[/tex] sets it to start counting at 1, and tells us to stop counting at n = 4. The [tex]\sum n[/tex] bit tells us what pattern we'll be following, in this case, each step of the way we'll be adding the value of the counter.
In summationSo how do we express the sum 1 + 3 + 5 + ... in sigma notation? First, we need an expression that describes the pattern algebraically. Ever odd number is 1 away from an even number, so we can either describe our list with the expression [tex]2k+1[/tex] (if we start at k = 0), or [tex]2k-1[/tex] (if we start at k = 1). I'll choose [tex]2k+1[/tex] for this problem.
We want to start counting at k = 0 , and we can choose whatever we want for our stopping point. Let's call that stopping point n, for the nth term in the series. In sigma notation, we can now write this series in the form
[tex]\sum_{k=0}^{n}2k+1[/tex]
Let's test it out for the first few values to see if it works!
n = 0: [2(0) + 1] = 1n = 1: [2{0) + 1] + [2(1)+1] = 1 + 3 = 4n = 2: [2{0) + 1] + [2(1) + 1] + [2(2) + 1] = 1 + 3 + 5 = 9Checks out!
To write the series in summation notation, we have to identify a pattern. After we identify the pattern, we get that the notation is:
[tex]S = \sum_{n = 1}^{\infty} n^2[/tex]
Terms:
The first term is 1, which is also the square of 1, as [tex]1^1 = 1[/tex]The second term is 4, which is also the square of 2, as [tex]2^2 = 2[/tex]The third term is 9, which is also the square of 3, as [tex]3^2 = 9[/tex]The fourth term is 16, which is also the square of 4, as [tex]4^2 = 16[/tex]The fifth term is 25, which is also the square of 5, as [tex]5^2 = 25[/tex]The sixth term is 36, which is also the square of 6, as [tex]6^2 = 36[/tex]From this, we can get a pattern that each term is the square of the index, and the notation is:
[tex]S = \sum_{n = 1}^{\infty} n^2[/tex]
A similar question is found at: https://brainly.com/question/16543477
Find the value of S
1/3 s + 14 = 26
Step-by-step explanation:
1/3 s + 14 = 26
1/3 s = 26 - 14
1/3 s = 12
s = 3 * 12
s = 36 (ANS)
Answer:
S=36
Step-by-step explanation:
You first turn the 14 into 0 by -14. Then you do it on the other side of the equall sign. Then you times 3 with the 1 on top and then times 12 by three. and botta boom botta bang theres your answer
f(n)=10*2^n at n=5
please show step by step on how you got the answer
Answer:320
Step-by-step explanation:PEMDAS. So first you would do the exponent 2^5= 32 (2x2=4 4x2=8 8x2=16 16x2=32)
Then you multiply 10x32 which equals 320
8. The length of the hypotenuse of a right
triangle measures 2.5 inches. If one leg
measures 1.5 inches, what is the length
of the other leg?
Answer:4
Step-by-step explanation:
The formula we want to use for this is leg^2 + leg^2 = Hypotenuse^2
Let’s make x the other leg length since that’s what we are trying to find.
So it should look like this
Equation: 1.5^2 + x^2= 2.5^2
1) lets square them
2.25 + x^2 = 6.25
2) let’s get x^2 by itself so what we will do is subtract 2.25 from both sides
X^2 = 4
3) we need to remove the exponent from x so what we would do is put a radical on 4 and since we need to get four out of the radical, we need two of the same numbers that multiply to get four with is 2 because
2x2=4
4) so ur answer would be 2
X=2
Which is the graph of the equation y = 3x – 5?
Answer:
Step-by-step explanation:
Next time please share the answer choices. Here we have a straight line graph with y-intercept (0, -5) and slope of m = 3. The x-intercept is (5/3, 0).
A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point. The x-intercept is (5/3, 0) and slope is 3.
What is Straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point.
The standard form of a straight line is y=mx+c.
A slope of a line is the change in y coordinate with respect to the change in x coordinate
where m is the slope and c is the y intercept.
Here we have a straight line graph with y-intercept (0, -5)
and slope of m = 3.
The x-intercept is (5/3, 0).
Hence the x-intercept is (5/3, 0) and slope is 3.
To learn more on Straight lines click:
https://brainly.com/question/27560536
#SPJ2
A bag contains yellow marbles and red marbles, 77 in total. The number of yellow marbles is 5 more than 3 times the number of red marbles. How many yellow marbles are there?
Answer:
41
Step-by-step explanation:
yellow marbles=5+ 3r(r is the number of red marbles)
red marbles=3r
3r+3r+5=77
6r=77-5
6r=72
r=72/6=12
yellow marbles = 5 + 3r
5+ 12 x 3
5+ 36
=41
Which of the following is most likely the next step in the series?
Answer:
B. The triangle.
Step-by-step explanation:
Because as the list goes down, the number sides goes down by one.
6000 + 4500 + 58 1500
Answer:
592,000
Step-by-step explanation:
6000 +4500 = 10,500 + 581,500
= 592,00
Have a good day and stay safe!
Jori has 2 gallons of distilled water and uses 7/6 gallon in a science experiment. What fraction of a gallon does she have left?
Answer:
Step-by-step explanation:
6/6 = 1 gallon
12/6 = 2 gallons
12/6 - 7/6 = 5/6
5/6 should be the answer
Based on the spreadsheet below, what is the net cash flow? A 2-column spreadsheet showing Cash Inflows and Cash Outflows. Total Cash inflow is 2,040 dollars and total cash outflow is 1,750 dollars. a. $290 b. $390 c. $1,750 d. $2,040
The net cash flow from the spreadsheet dataset is $290
What is cash flow?The net cash flow is the difference between the total cash inflow and the total cash outflow.
The given parameters are:
Total cash inflow: $2040Total cash outflow: $1750So, we have:
[tex]Net = \$2040 - \$1750[/tex]
Calculate the difference
[tex]Net = \$290[/tex]
Hence, the net cash flow is $290
Read more about cash flows at:
https://brainly.com/question/10295065
rewrite the equation in slope intercept form 7x + 9y = 9
Answer:
y = -7/9 x +1
Step-by-step explanation:
7x + 9y = 9
The slope intercept form is y = mx+b where m is the slope and b is the y intercept
Subtract 7x from each side
7x -7x+ 9y =-7x+ 9
9y = -7x+9
Divide each side by 9
9y/9 = -7/9 x +9/9
y = -7/9 x +1
The slope is -7/9 and the y intercept is 1
Answer:
[tex]y = \frac{7}{9} x + 1[/tex]
Step-by-step explanation:
[tex]7x + 9y = 9 \\ 9y = 9 - 7x \\ y = \frac{9 - 7x}{9} \\ y = \frac{7}{9} x + 1[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!!
PLEASE HELP ME!
Martha has 3 red beads and 5 blue beads. In how many unique ways can they be ordered?
100 points
What is the result of the refraction of the light?
The fish appears fuzzy.
The fish is not where it appears to be.
The fish is where Sam expects it to be.
The fish is able to see Sam more easily.
EXPLAIN YOUR ANSWER
Answer:
Water gives in affect like this to a pencil in water as well. Refraction makes the object seem distorted or further away than you would expect.
Step-by-step explanation:
Which of the following equations match the graph of the circle shown below?
Answer:
The circle in graph as radius = 4 and center O(2, 3)
=> equation of this circle: (x - 2)^2 + (y - 3)^2 = 4^2 = 16
=> Option C is correct
Hope this helps!
:)
How do i solve this?
Answer:
O
Step-by-step explanation:
The graph shows the best-fit regression model for a set of data comparing the number of hours spent hiking and the number of miles traveled in one day.
A graph shows hours labeled 1 to 9 on the horizontal axis and distance (miles) on the vertical axis. A line shows an upward trend.
Which is most likely true of the data set represented by the regression model on the graph?
Answer:
C.Each point in the data set is near the regression line.
Step-by-step explanation:
The most likely true option about the data set is that Each point in the data set is near the regression line.
What is a regression line?
This is the line that shows the behavior of a given group of data. The line is made up of data that are all fitted together when a straight line is drawn.
Hence when we look at the graph, we see a line that is made up of all of the data points contained in the data.
Read more on regression lines here:
https://brainly.com/question/25987747
I need help showing my work plz
equipos, resuelvan los siguientes problemas
hacer paquetes de 6 libretas y paquetes de 6 lápices de co-
ores, los maestros de una escuela se percataron de que habla
mas paquetes de lápices que de libretas, y de que en ambos
casos no sobraba nada. Se sabe que la cantidad original de
bretas está entre 185 y 190, y la de lápices, entre 220 y 225.
¿Cuál será la cantidad original de libretas y lápices de colores?
y
Answer:
186 notebooks; 222 pencils
Step-by-step explanation:
1. Notebooks
The number of notebooks must be between 185 and 190.
To have no notebooks left over, the number of 6-packs must be an integral multiple of six.
The only integral multiple of six between 185 and 190 is 186.
186÷ 6 = 31
So, there are 31 packs containing a total of 186 notebooks.
2. Pencils
The number of pencils must be between 220 and 225.
To have no pencils left over, the number of 6-packs must be an integral multiple of six.
The only integral multiple of six between 220 and 225 is 222.
222÷ 6 = 37
So, there are 37 packs containing a total of 222 pencils.
There were originally 186 notebooks and 222 pencils.
The record high temperature for Massachusetts is 104 degrees Fahrenheit. The record low is -18 degrees Fahrenheit. What is the difference between high and low?
Subtracting Integers question.
S has the coordinates (1,3) and is the midpoint of R and T where the coordinates of R are (4,-7) find the coordinates of T
Step-by-step explanation:
(1-4, 3-(-7))
=(-3,10)
Choosing a career means you also need to think about your ________ ________ .
Answer:
Life Path
Step-by-step explanation:
It's two words, and they are both of equal length. I hope that helps.
What’s the mid point for 0.2 and 0.3
Answer: 0.25
Step-by-step explanation:
Answer:
0.25
Step-by-step explanation:
The midpoint of a number is its halfway or middle.
from 0.20-0.30 the half way would be 0.25
that's because you both either add or subtract 0.05 to get its middle
A parabola intersects the X-axis at X
= 3 and x= 9.
What is the x-coordinate of the parabola's vertex?
Answer:
x = 6
Step-by-step explanation:
The vertex lies on the axis of symmetry which is situated midway between the x- intercepts, thus x- coordinate of vertex is
[tex]x_{vertex}[/tex] = [tex]\frac{3+9}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6
Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out -12 inch squares from each corner. The length of the original piece of cardboard is 24 inch more than the width. If the volume of the box is 1740 inch , determine the dimensions of the original piece of cardboard.
Answer:
29 feet in length, 5 feet in width and 12 feet in height
Step-by-step explanation:
We have that for the volume of a quadrangular prism is:
V = l * w * h
Ie length times width times height
In this case, the height is determined by the squares that you put in each corner, taking into account that a square has all the same sides, the height is 12 inches. h = 12
they tell us that the length is 24 inches more than the width, that is, l = 24 + w
replacing we have:
1740 = (24 + w) * w * 12
1740 = 12 * w ^ 2 + 288 * w
12 * w ^ 2 + 288 * w - 1740 = 0
if we calculate the root, we have w = 5 or w = -29
only works when w = 5
Thus:
l = 24 + 5
l = 29
which means that the dimensions are:
29 feet in length, 5 feet in width and 12 feet in height
29 feet in length, 5 feet in width and 12 feet in height
The calculation is as follows;
The volume of a quadrangular prism is:
[tex]V = l \times w \times h[/tex]
The length is 24 inches more than the width,
So l = 24 + w
Now
[tex]1740 = (24 + w) \times w \times 12\\\\1740 = 12 \times w ^ 2 + 288 \times w\\\\12 \times w ^ 2 + 288 \times w - 1740 = 0[/tex]
if we calculate the root, we have w = 5 or w = -29
only works when w = 5
So,
l = 24 + 5
l = 29
Learn more: https://brainly.com/question/13981855?referrer=searchResults
Anthony starts each week at the animal shelter with a new 5.5-ounce bag of dog treats. Last week, he used One-half a bag of treats. This week, he used 1 whole bag. How many more ounces of treats did Anthony use this week than last week?
Which statements are true? Check all that apply.
1.Anthony used more treats this week than last week
.
2.This is a part-whole problem.
3.To find out how many treats Anthony used last week, multiply 5.5 × 1/2
.
4.Anthony used more than 5.5 ounces of treats last week.
5.The answer will be written in this form: “Anthony used ____ ounces of treats all together in both weeks.”
mutily question awnser also i will give brainlest if u awnser
Answer:
Anthony used 2.75 more ounces then last week for a total of 8.25 ounces both weeks.
Answer:
The Correct answers are A and C on EDG.
Step-by-step explanation:
A restless point moved from point 12 to the left at the speed of 5/6 units per minute. Where will it be in 10.2 minutes?
Answer:
78 is the anwser to this problem
Answer:
Actually the answer is 3.5
Step-by-step explanation:
how to escape out my residential will mark brainlist
Answer:
make whole in wall and destroy securitie
Step-by-step explanation:
Answer:
do your program and leave
Step-by-step explanation: Be their for several months (6 months-least amount of time 1 year, 3 months, and 5 days or more- most amount of time) do programming (literally everything the staff + what your therapist say or need you to do). Don't do anything to get on precautions (which includes sleeping in the common area and showering with a foot in the door). And lastly respect everyone. No need for laser-beams or hurting security just do anything and everything you need to do to leave that place and never do anything to go back b/c in the end no one belongs in a place like that. I know from experience.
Hope this helped!
The solids are similar. Find the surface area S of the red solid.
Answer:
756 m²
Step-by-step explanation:
The surface area is the function of 2 dimensions.
Scale factor is
6/4 = 1.5Surface are for the bigger solid will be 1.5*1.5 times the area of the smaller one
S = 336*1.5*1.5 = 756 m²Which of the following is true of (1, 4) and (1, −7)?
More information is needed to determine the relationship between the two points.
The points lie on a diagonal line.
The points lie on a vertical line.
The points lie on a horizontal line.
Answer:
The points lie on a vertical line.
Step-by-step explanation:
The x-values in the given two points are the same. If they were graphed and then connected, it would form a vertical line.
[see graph]
So, the points would lie on a vertical line.
25 POINTS PLEASE HELP
Identify the zeros of the quadratic function.
A)
x = 2 and x = 5
C)
x = -2 and x = -5
B)y = 2 and y = 5
D )y = -2 and y = -5
Answer:
- 2 and - 5
Step-by-step explanation:
as those are the points where the parabola intersects
f(x) = -2/3x+ 2; find f(-3)
Answer:
Step-by-step explanation:
f(-3) = -2/3(-3) + 2
2 + 2 = 4