a) The infinite series in sigma notation is described by this expression:
[tex]y = \sum \limits_{i=1}^{\infty} \frac{1}{i\cdot (i+2)}[/tex] (1)
b) The explicit formula for the n-th partial sum is represented by the following expression:
[tex]y = \frac{1}{i\cdot (i+2)}[/tex], i ∈ [tex]\mathbb{N}[/tex] (2)
How to derive an expression for a monotonous series
An infinite series is monotonous when it is bounded, that is, when the limit of the infinite series exists. In this case, we have an evidence of monotony in the denominators of the terms of the given series. In two consecutive terms, the latter always have a denominator greater than the former.
a) The series in sigma notation is now described below:
[tex]y = \sum \limits_{i=1}^{\infty} \frac{1}{i\cdot (i+2)}[/tex]
b) The explicit formula for the n-th partial sum is defined by the expression within the sum, which is now presented below:
[tex]y = \frac{1}{i\cdot (i+2)}[/tex], i ∈ [tex]\mathbb{N}[/tex]
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URGENT!! VERY HARD QUESTION. WHAT IS 2+2?? NEED ANSWER RIGHT NOW!!
Answer:
4
Step-by-step explanation:
2+2=4
emergency!!
Write the function f(x)=x² – 25x in the form f(x) = a(x - h)? +k. Identify the vertex.
Answer:
See below
Step-by-step explanation:
Complete the square
[tex]f(x)=x^2-25x\\\\f(x)+(\frac{-25}{2})^2=x^2-25x+(\frac{-25}{2})^2\\\\f(x)+156.25=x^2-25x+156.25\\\\f(x)+156.25=(x-12.5)^2\\\\f(x)=(x-12.5)^2-156.25\\\\f(x)=(x-\frac{25}{2})^2-\frac{625}{156}[/tex]
Identify vertex
[tex](h,k)\rightarrow(-\frac{25}{2},-\frac{625}{156})[/tex]
The volume of a cylinder is 4πx3 cubic units and its height is x units.
Which expression represents the radius of the cylinder, in units?
: 2x, 4x
Expression represents the radius of the cylinder, 2x units.
What is a cylinder?
A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
Given that:
Volume of cylinder =[tex]4\pi x^{3}[/tex]
we know that, Volume of cylinder = [tex]\pi r^{2} h[/tex]
[tex]4\pi x^{3}[/tex]= π * [tex]r^{2}[/tex] *h
[tex]4x^{3} = r^{2}*h[/tex]
[tex]4x^{3} = r^{2}*x[/tex] [since, height=x]
[tex]4x^{2} = r^{2}[/tex]
r= 2x
Hence the radius of the cylinder is 2x units
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This makes zero sense give answer
Answer:
IQR for males: 3
IQR for females: 2
Q1 for males: 5
Q1 for females: 6
the number of females who spend over 6 hours exercising is greater(?) than the number of males who spent 6 hours exercising
Step-by-step explanation:
An equal amount of men and women were randomly selected and asked how many hours per week they spend excercising
How to find IQR?to find IQR you have to identify your median(middle value) of the lower and upper half of the data. These are called quartile 1(Q1) and quartile 3(Q3). You subtract these two (Q3 and Q1) and the IQR is the difference.
Males box plot:
Minimum: 1
Maximum: 10
Q1: 5
Q2: 7
Q3: 8
Subtract Q3 and Q1
8 - 5 = 3
This is the IQR
Females box plot:
Minimum: 4
Maximum: 10
Q1: 6
Q2: 7
Q3: 8
Subtract Q3 and Q1
8 - 6 = 2
IQR =2
the number of females who spend over 6 hours exercising is greater than the number of males who spent 6 hours exercising
It's going 2 by 2 for the paper i couldn't get it all in at a time so the first 2 are one paper and its like that for the next 2 papers but the last paper is the whole paper
it took I'd :safalbista10 10
Natalia makes $17.82 per hour, and is expecting to receive a 10% increase in pay. What can Natalia expect her future hourly rate to be?
help is on the way! :D
Im sorry if im wrong but i could do 17.82x10= 178.20
Find the missing side
Answer:
5^2+7^2= 12^2 so your answer should be 12
Find the area of triangle
Answer:
C- 17 cm
A- 9cm
Step-by-step explanation:
C - because plus 9 and 8 is 17 cm
A - because plus 4 and 5 is 9 cm
What is the length of segment
Answer: square root of 53
Step-by-step explanation:
did the math
Question: Write an equation for this.
You have total 100 coins
that consist of 50 cents
and 10 cents. The total
money is 34 dollar. Find the
number of the 50 cent
coin.
To solve this question, we need to write out an equation for this and proceed to solve the system of equation. the number of 50 cents coins are 60.
System of EquationThe given data in this problem are
number of coins = 10050 cents = x10 cents = yamount = $34The system of equations can be written as
[tex]x + y= 100...eq(i)\\0.5x + 0.1y = $34..eq(ii)[/tex]
Let's start with equation (i)
[tex]x + y = 100\\\\y = 100 - x[/tex]
Substitute equation (iii) into equation (ii)
[tex]0.5x + 0.1(100 - x) = 34\\0.5x + 10 - 0.1x = 34\\0.4x = 24\\x = 60[/tex]
From the calculations above, the number of 50 cents coins are 60.
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find the value of x
50°
6
X
Not drawn to scale
Answer:
Hence option C is correct...hope this helps you:)
Given the points K(-2;5), L(1,3) and M(-5; 2p). Calculate the value
of p if KL ILM.
How do I solve this question?
The product of the perpendicular lines is a negative one. Then the value of p will be negative 3.75.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Given the points K(-2,5), L(1,3) and M(-5, 2p).
If KL is perpendicular to LM. Then we have
The slope of KL will be
KL = (1+2)/(3-5)
KL = -1.5
The slope of LM will be
LM = (1+6)/(3-2p)
LM = 7/(3-2p)
We know the product of the perpendicular lines is a negative one.
KL x ML = -1
-1.5 x 7/(3-2p) = -1
-10.5 = -3 + 2p
2p = -7.5
p = -3.75
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Find the area of the rhombus
[tex]60cm^{2}[/tex]
Step-by-step explanation:
A=pq/2
shorter diagonal= 8cm
longer diagonal = 15cm
15*8 = 120
120/2 = 60
A = [tex]60cm^{2}[/tex]
Find the sum of 2/3 and it’s additive inverse
Answer:
0
Step-by-step explanation:
2/3 additive inverse is 2/3
-2/3+2/3 is neutral = zero
-2/3+2/3 = 0
The measures of the angles of a triangle are shown in the figure below solve for X
Answer:
29 degrees
Step-by-step explanation:
The interior angles of all triangles equals 180. We know already that we have 101 and 50 degrees. If we add that, we get 151. To find x, we have to simply subtract 151 from 180. If we do this, we get 29. x=29.
Hope this helps!
A municipal trash facility allows a person to throw away a maximum of 40 pounds of trash per week. Last week, 195 people threw away the maximum allowable trash. How many tons of trash did this equal
The total tons of trash that was thrown away by the people is 3.9 tons.
How many tons of thrash was thrown away?The first step is to convert pounds to tons
1 pound = 0.0005 tons
40 x 0.0005 = 0.02 tons
The second step is to multiply 0.02 by 195
0.02 x 195 = 3.9 tons
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One container of lemonade mix weighs 2.33 kilograms. How much will 7 containers weigh?
Answer:
16.31 kg.
Step-by-step explanation:
2.33 * 7
a bicyclist rides 25 miles every 2 hours during race which equation represents the relationship between the number of miles and the number of hours of the bicyclist rides? let x represent the number of hours and let y represent the number of miles?
Answer:
y=12.5x
Step-by-step explanation:
what is the measurement of angle B
Answer:
41 degrees
Step-by-step explanation:
All of the angles must add up to 360 degrees to form a circle. So we have 22 + b + 297 = 360. Solving for b, we get b = 41.
If a right circular cylinder and oblique cylinder both have a height of 12 inches and diameter of 6 inches, do they have the same volume? (Use straight pi equals 3.14)
Group of answer choices
Yes, they both have a volume of 339.12 inches cubed.
No, the right circular cylinder has a volume of 339.12 inches cubed and the oblique cylinder has a volume of 1 comma 356.48 inches cubed.
No, the right circular cylinder has a volume of 1 comma 356.48 inches cubedand the oblique cylinder has a volume of 339.12 inches cubed.
Yes, they both have a volume of 1 comma 356.48 inches cubed.
Answer:
Yes, they both have a volume of 339.12 inches cubed.
Step-by-step explanation:
To calculate the volume of an oblique cylinder is very simple, we must multiply π (Pi = ~ 3.14) by the radius to the power of two and then multiply by the height. In this case the height forms a 90 degree angle from the opposite base to the position of the base, but outside of it.
Volume = π × Radius² × Height
The formula for the volume of a regular cylinder or an oblique cylinder is the same, if we imagine a stack of poker chips (forming a cylinder), even when we tilt the chips to one side (forming an oblique cylinder) the volume remains the same.
Now using this information, we must find the volumes of both cylinders.
For the oblique cylinder:
Given
Using the formula,
The volume would be 339.29 m³
Now solving for the other cylinder:
V=πr²h=π·32·12≈339.29201
Rounded, the answer would be 33.29 m³
This therefore proves that they both have the same volume.
Find the area of a triangle whose sides are 35 cm, 45 cm and 50 cm.
Answer:To find out the Area of a scalene triangle whose three sides are given, first find out the half perimeter
s = (a+b+c)/2
where a, b, and c are the length of the three sides of a triangle
s = (35 + 45 + 50) / 2
= 130 / 2
= 65 cm
Area of scalene triangle is given by
A = sqrt (s (s - a) (s - b) (s - c))
= sqrt (65 * (65 - 35) ( 65 - 45) (65 - 50))
= sqrt (65 * 30 * 20 * 15)
= sqrt (585000)
= 764.853 sq cm
Step-by-step explanation:
Patricia has a circular swimming pool. The diameter of the pool is 15 feet. What is the area of the swimming pool.
Answer:
The area of the pool is 176.71
Step-by-step explanation:
The formula for a triangle is Area= Pi r (radius) sq.
In this problem, you need to remember that radius is half the diameter.
STEP 1: Divide the diameter in half.
STEP 2: Multiply your answer by itself. (example: if your answer was 8, you would multiply by 8)
STEP 3: Multiply the answer by 3.14 (or Pi)
STEP 4: You just found the area of a circle, GREAT JOB!
diameter= 15 feet
to find:the area of the circular swimming pool.
solution:[tex]a = \frac{1}{4} \pi {d}^{2} [/tex]
[tex]a = \frac{1}{5} \times \pi \times {15}^{2} [/tex]
[tex]a = 176.71459 \: {ft}^{2} [/tex]
[tex]a = 176.71 \: {ft}^{2} [/tex]
therefore, the area of the circular swimming pool is 176.71 square feets.
Find the value of x in the parallelogram below.
Answer:
102
Step-by-step explanation:
78 and x are adjacent angles.
Sum of adjacent angles is 180 in a parallelogram.
78 + x = 180
x = 180 - 78
x = 102
Answer:
102°
Step-by-step explanation:
A parallelogram is a special type of quadrilateral that has both the pair of opposite sides parallel and equal.78+x= 180( adjacent angles in a parallelogram)
x=180-78=102°
P is a rectangle with length 80 cm and width x cm.
q is a rectangle with width y cm.
p
the length of q is 25% more than the length of p.
the area of q is 20% less than the area of p.
work out the ratio x:y
give your answer in its simplest form.
x cm
80 cm
:
q
y cm
The ratio of x and y will be equal to x:y = 25:16
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
We know that
The length of Q is 25% more than the length of p
length Q=1.25 x 80--------> 100 cm
The area of Q is 20% less than the area of p
Area Q=100 x y
Area P=80 x x
100 x y=0.80 x [80 x x]---------> 100 x y = 64 x x-------> x/y=100/64--> 25/16
Therefore the ratio of x and y will be equal to x:y = 25:16
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Answer:
25:16
Step-by-step explanation:
What is the image point df (-2, -3) after a translation right 2 units and up 4 units?
Answer:
(0, 1)
Step-by-step explanation:
right 2 units: add 2 to x
up 4 units: add 4 to y
Answer: (0, 1)
What is the slope of the line segment?
у
15
12
9
6
3
0
1 2 3 4 5
0-3
O_1
له |
3
0 1
3
3
Indigo needs to order some new supplies for the restaurant where she works. The restaurant needs at least 430 knives. There are currently 269 knives. If each set on sale contains 18 knives, what is the minimum number of sets of knives Indigo should buy?
The minimum number of sets of knives Indigo should buy is 9.
What is Inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Here, Let the minimum number of sets be x.
restaurant needs at least 430 knives
currently restaurant have 269 knives
each set contains 18 knives.
According to question,
18x + 269 ≥ 430
18x ≥ 161
x ≥ 161/18
x ≥ 8.94
Thus, the minimum number of sets of knives Indigo should buy is 9.
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How do I solve this!! Quick and urgent (23. Is the number for the equation)
Answer:
Independent: Time
Dependent: Views
Step-by-step explanation:
Independent variables are the things that are purposefully altered.
Dependent variables are the things that change in response to the independent variables being changed.
As the hours increase, so do the views. The views will change as time goes by. A change in the number of views does not affect the time passed. Therefore, time is the independent variable and the number of views is the dependent variable.
Consider the following shape. Find the value of x. Round your answer to two decimal places.
Answer: 7.81
Step-by-step explanation:
f(x) = x + 3
g(x) = 7x +4
What does (f+g) (x)equal?
To obtain credit, provide your answer with no spaces. Example answer: 42x+9