Use summation formulas to rewrite the expression without the summation notation .
sum i=1 ^ n 2i^ 3 -3i n^ 4
Answers
Factor out 1/n⁴, and distribute the sum over each term:
[tex]\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac1{n^4}\sum_{i=1}^n(2i^3-3i)[/tex]
[tex]\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac2{n^4}\sum_{i=1}^ni^3-\frac3{n^4}\sum_{i=1}^ni[/tex]
Recall the following formulas:
[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]
[tex]\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4[/tex]
So we have
[tex]\displaystyle\sum_{i=1}^n\frac{2i^3-3i}{n^4}=\frac{n^2(n+1)^2}{2n^4}-\frac{3n(n+1)}{2n^4}=\boxed{\dfrac{(n+1)(n^2+n-3)}{2n^3}}[/tex]
Related Questions
A line passes through the point (-8,4) and has a slope of -3/2 .
Write an equation in point-slope form for this line.
Answers
Answer:
y - 4 = [tex]-\frac{3}{2}(x+8)[/tex]
Step-by-step explanation:
Point slope equation of a line passing through (x', y') and slope 'm' is given by,
y - y' = m(x - x')
We have to find the equation of the line which passes through (-8, 4) and slope [tex](-\frac{3}{2})[/tex],
By substituting these values in the equation,
y - 4 = [tex]-\frac{3}{2}(x+8)[/tex]
Therefore, point slope form for the given line is,
y - 4 = [tex]-\frac{3}{2}(x+8)[/tex]
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the distance in 1.5 h. Car B traveled 15 mph faster than Car A.
How fast did Car B travel?
(The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.)
Enter your answer for the box.
Answers
Answer:
Car B traveled half an hour traveled 20 miles in 1.5 h
Step-by-step explanation: If car B traveled 15 mph than add 5 to 15 (.5) and you get 20 miles in 1.5 h.
Answer:
The answer is 60
Step-by-step explanation:
CAUSE I KNOW THE ANSWER HBNAHIDNHAWNDVAW
Which of the following best describes how the y values are changing over each interval?
x
y
1
4
2
8
3
12
4
16
5
20
They are increasing by 4 each time.
They are increasing by 6 each time.
They are being multiplied by 2 each time.
They are being multiplied by 4 each time.
Answers
Answer:
A
Step-by-step explanation:
The equation for the given scenario is y=4x. Therefore, option D is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, (1, 4), (2, 8), (3, 12), (4, 16) and (5, 20).
Now, slope = (8-4)/(2-1)
m=4
Substitute m=4 and (x, y)=(1, 4) in y=mx+c, we get
4=4(1)+c
c=0
Substitute m=4 and c=0 in y=mx+c, we get
y=4x
Therefore, option D is the correct answer.
To learn more about the the equation of a line visit:
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What is the y-intercept of the line whose equation is y = x - 3?
-3
1/2
3
Answers
Answer:
-3
Step-by-step explanation:
y=0-3
y=-3
By definition, the correct answer is the first option: the y-intercept is -3.
A linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point. m is the slope. b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.The ordinate to the origin is the value where the line intersects the axis. Thus, the value of x must be 0 for this to occur.
In this case you know that the form of the linear equation is y=x-3.
Being x=0, then:
y=0-3
y= -3
Finally, the correct answer is the first option: the y-intercept is -3.
Learn more about the equation of a line:
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multiply 3 3/4 how to solve please tell
Answers
Step-by-step explanation:
[tex]3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{9} \\ [/tex]
What word phrase can you use to represent "5x + 2"?
Answers
Answer:
5 times a number plus 2
in the figure below, m || n. drag and drop each label into its corresponding box to show the appropriate angle pair
Answers
Answer/Step-by-step explanation:
A. <1 and <4 => vertical angles.
They share the same vertex/corner and are opposite each other as two straight lines intersect.
B. <3 and <5 => same-side interior angles.
They lie on the same side of the transversal and within the two parallel lines the transversal intercepts.
C. <4 and <5 => Alternate Interior Angles.
These angles lie on either side of the transversal, and within the parallel blinds cut across by the transversal.
D. <3 and <7 => Corresponding Angles.
They are found in the same side of the transversal occupying the same position.
Consider the function: y = - 3x + 6. Interpret the slope of this function using "inputs" and
"outputs".
Answers
Output = values for y
Input x = 1
Output y = 3
Input x = 0
Output y = 6
Therefore the slope of this function is -3
Item 16 Joanne paid $ 28 , 000 for her new car. In addition, she paid $ 1 , 400 in taxes. What was the tax rate Joanne paid on her new car?
Answers
Answer: 20%
Step-by-step explanation:
Help!!
Question 1 Multiple Choice Worth 4 points)
(02.05)
Solve the quadratic equation x? - 8x + 18 = 0 using the quadratic formula. What is the solution when expressed in the form a + bi, where a and b are real numbers?
Answers
Answer:
do u go to il Texas and BTW u look nice
-8x=0-18
-8x/8=-18/8
X= -18/8=-9/4
Question 1. We would like to test the null hypothesis that the treatment (HRT) has no effect on the outcome (CHD), against the alternative hypothesis that the treatment does have an effect. What would be a good test statistic
Answers
Answer:
Pearson's r test or Pearson's t- test
Step-by-step explanation:
The null hypothesis is that there is no effect on the outcome against the claim that there is some effect. The Greek letter rho is used to denote the parameter.This test can also be two tailed or one tailed depending on the direction of the parameter.
This test is used for qualitative variables.
H0: ρ= 0 against Ha : ρ≠0
It is possible to use Pearson's r test to find the t- test and do the calculations.
The slope of the line below is –3. Use the coordinates of the labeled point to find a point-slope equation of the line. (15 points)
Answers
Answer:
C
Step-by-step explanation:
The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. What is the slope of the line that passes through the points?
Answers
Answer:
2 or -2
Step-by-step explanation:
Answer:
the answer is A on edge
Step-by-step explanation:
2
what value should replace the ? in the table
Answers
Answer:
Step-by-step explanation:
16 I think
Answer:
17
Step-by-step explanation:
y=6x-1
m=6
b=-1
Barney earns $24.75 in 3 hours if the amount that Barney earns varies directly with the number of hours, how much would he earn in 20 hours.
Answers
Answer:
$165
Step-by-step explanation:
Divide 24.75 by 3 to get how much Barney(lol) would get in a hour then I got 8.25 so 8.25 x 20 hours = $165
Answer:
165$ in 20 hours
Step-by-step explanation:
Barney earns 24.75 in 3 hours, so 24.75 / 3 is 8.25. This is every hour so you would take 8.25 and multiply it by 20. That gives you 165
14) Centroid R is found in TriangleABC below with BZ = 42, CA = 40 and RY = 16. Determine the
perimeter of Triangle ARZ.
Answers
Answer:
Missing BZ= 42, 40 RY= ARZ
Step-by-step explanation:
Hope it helps!! Please give brainleist
In science class, Graciela noticed that the balance scale showed 2 ounces for a sample of matter and 56.7 grams for the same sample. She has a rock that weighs 708.75 grams but needs to know the weight in ounces. Which proportion could Graciela use to find x, the weight of the rock in ounces?
Answers
Answer:
2/56.7= x/708.75
Step-by-step explanation:
Side lengths and angle measures in similar figures
Answers
Answer:
It looks like they are isosceles triangles meaning that two sides are going to be the same.
PQ=42
GH=21
Quadrilateral ABCD has the following vertices:
.
A(6,8)
B(6,-5)
. C(-5, -10)
D(-5,3)
Is quadrilateral ABCD a rhombus, and why?
Answers
Answer:
no!!
Step-by-step explanation:
because AB is longer than BC
Answer:
No, because AB is longer than BC
Step-by-step explanation:
Khan Academy
Find the values of x and y. Justify your answers by stating the postulates, theorems, or definitions used for each step.
Answers
Answer:
Step-by-step explanation:
10) From the diagram you can see that the diagram at the right hand side is am isosceles triangle. An isosceles triangle is triangle that has its two base angles equal. Hence
x = 75°
Reason: Base angle of an isosceles triangle are equal.
To get y:
First we need to find the third angle of the isosceles triangle. Let's take the angle as p
Since sum of angle in a triangle is 180°, then
p+ 75 +x = 180
p+75+75 = 180
p+150=180
p = 180-150
p = 30°
To get y:
Know that the y + p = 90° (right angled)
y + 30 = 90
y = 90-30
y = 60°
Hence x = 75° and y = 60°
b)Note that the triangle in the middle is an equilateral triangle. The sum of angle in a triangle is 180°
Hence all the angles are 60°
To get x;
Sum of angle on the straight line is expressed as;
40°+60°+x° = 180°
100°+x = 180°
x = 180°-100°
x = 80°
Also since the lines are parallel, the angle at the right corner of the triangle is also 40° (corresponding to that angle at the corner of the first triangle)
To calculate y;
Sum of angle in the triangle at the right is 180° hence;
x+y+40 = 180
80+y+40=180
120+y = 180
y = 180-120
y = 60°
Hence the value of x and y are 80° and 60° respectively.
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Second-degree, with zeros of
-4 and
1, and goes to
- oo as
x-00
Answers
Answer:
Please help me
Step-by-step explanation:
Please!
Which of the following is equal to 2/3
Answers
Answer:
4/6, 8/12,16,24
Step-by-step explanation:
PLEASE HELP BEING TOMED WITH GIVE BRAINLIST
Answers
Answer:
2/3 times 3/4 =1/2
Good Luck!!!
f(x) = -4x4 - 3x2 + 2
Find the end behavior
Answers
Answer:
-20 is the answer :) hoped I helped
-16 - 6 = -22+2
-20 is the answer
You want to purchase a new car in 3 years and you anticipate the cost of the car to be $25,000. You are given an investment plan with a fixed APR of 5.3% if you make regular monthly deposits.
How much should you deposit at the end of each month to reach your goal of $25,000 in 3 years?
a.$642.23
c.$648.62
b.$645.65
d.$649.13
Answers
Answer:
The answer is A: $642.23
Step-by-step explanation:
I just took the test lol
help with the answer plz. help
Answers
Answer:
D because 6 minutes and 60 meters meets on the graph
!!15 points!!Choose the answer that best represents the situation described below.
John takes a job after school to earn money to buy a surfboard. He knows
that the more hours he works, the more money he will make.
A. The amount of money John makes is a function of the number of
hours he works.
B. The number of hours John works is a function of the amount of
money he makes
C. John's job is a function of his interest in surfing.
Answers
Answer:
c is the answer
Step-by-step explanation:
bc
Help me please this is a math TEST if it is correct I will give you lots of points and if it's wrong well no points for you and I am rating it
Answers
Answer:
[tex]12000 \: g = 12 \: kg \\ 120 \: cm = 1200 \: mm \\ 1.2 \: l \: = 1200 \: ml \\1200 \: cm =12 \: m \\ 0.12 \: m = 120 \: mm[/tex]
Olivia picked 482 apples from the orchard's largest apple tree. She divided the apples evenly into 4 baskets. How many apples are in each basket? How many are left over?
Answers
Answer:
120 with 4 left
Step-by-step explanation:
482 divided by 4 is 120.5. so you throw 120 apples in each basket and you have 2 left.
Solve 18x+ 6>12x +18
Answers
6x+6>18
6x>12
x>2