In conclusion, the series ∑ (n = 0 to ∞) 2^n * 9^n * n! diverges and does not have a finite sum.
To find the sum of the series ∑ (n = 0 to ∞) 2^n * 9^n * n!, we can start by analyzing the terms of the series.
Let's consider the nth term of the series:
Tn = 2^n * 9^n * n!
We notice that the term involves the exponential growth of 2^n and 9^n, as well as the factorial n! term. This suggests that the series may diverge since both exponential and factorial growth tend to increase rapidly.
To confirm this, let's examine the ratio of consecutive terms:
R = Tn+1 / Tn
R = (2^(n+1) * 9^(n+1) * (n+1)!) / (2^n * 9^n * n!)
Simplifying the expression, we get:
R = (2 * 9 * (n+1)) / n!
As n approaches infinity, this ratio does not tend to zero, indicating that the terms of the series do not converge to zero. Therefore, the series diverges, and we cannot find a finite sum for it.
To know more about series,
https://brainly.com/question/31966672
#SPJ11
you friend buys 8 boxes for 88$ find the unit rate of the cost of one box
Answer: $11
Step-by-step explanation:
88/8 = 11
(7.2×10−1)×(4×10−7) how do i solve this
Answer:
Step-by-step explanation:
To solve the expression (7.2×10^(-1))×(4×10^(-7)), you can multiply the numerical values and combine the exponents.
First, multiply the numerical values:
7.2 × 4 = 28.8
Next, add the exponents of 10:
10^(-1) × 10^(-7) = 10^(-1-7) = 10^(-8)
Putting it all together, the expression simplifies to:
28.8 × 10^(-8)
This is the final answer in scientific notation.
n △abc, b=51∘, b=35, and a=36. what are the two possible values for angle a to the nearest tenth of a degree? select both correct answers.
Thus, the two possible values for angle A are 67.4° and 112.6° to the nearest tenth of a degree.
In △ABC, you have given B = 51°, b = 35, and a = 36. To find the two possible values for angle A, we can use the Law of Sines.
The Law of Sines states: (sinA)/a = (sinB)/b
Plugging in the given values, we get:
(sinA)/36 = (sin51°)/35
Now, solve for sinA:
sinA = 36 * (sin51°)/35 ≈ 0.923
Since sinA = 0.923, we can find the two possible values for angle A using the inverse sine function:
1. A = arcsin(0.923) ≈ 67.4°
2. A = 180° - arcsin(0.923) ≈ 112.6°
So, the two possible values for angle A are 67.4° and 112.6° to the nearest tenth of a degree.
Know more about the Law of Sines
https://brainly.com/question/30401249
#SPJ11
all the students in the 6th grade either purchased their lunch or brought their lunch from home on monday.how many students are in the sixth grade if
The total number of students in the sixth grade is equal to 250.
Percent of students purchased their lunch = 24%
Number of students brought their lunch from home = 190
Let us call the total number of students in the 6th grade 'x'.
We know that all students either purchased their lunch or brought their lunch from home,
x = students who purchased their lunch + students who brought their lunch from home
24% of the students purchased their lunch, so the number of students who purchased their lunch is 0.24x.
And we know that 190 students brought their lunch from home.
Substituting these values into the equation above, we get,
x = 0.24x + 190
Solving for x, we can start by subtracting 0.24x from both sides,
⇒ 0.76x = 190
Then we divide both sides by 0.76 to isolate x,
x = 250
Therefore, there are 250 students in the 6th grade.
Learn more about students here
brainly.com/question/28468566
#SPJ4
The above question is incomplete, the complete question is:
All students in the 6th grade either purchased their lunch or brought their lunch from home on Monday.• 24% of the students purchased their lunch.• 190 students brought their lunch from home. How many students are in the 6th grade?
What additional information must be known to prove the triangles are similar by SAS?
An additional information that must be known to prove the triangles are similar by SAS include the following: C. ∠G ≅ ∠R.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆DFG is congruent to ∆PQR when the angles G (∠G) and (∠R) are congruent.
Read more on triangle here: brainly.com/question/22891315
#SPJ1
can yall help me with this
Answer:
D
Step-by-step explanation:
Usr the equation they gave you and plug in the number given for x and y.
y=2x+4
4=2(0)+4. 4=0+4. 4=4
8=2(2)+4. 8=4+4. 8=8
12=2(4)+4. 12=8+4. 12=12
16=2(6)+4. 16=12+4. 16=16
If you did that method with the other options they don't equal each other such as option B for example
0=2(0)+4. 0=0+4. 0=4
4=2(2)+4. 4=4+4. 4=8
These don't equal each other .
The coordinates of the vertices of parallelogram CDEH are C(5,5), D(2,5) and H(8,1). What are the coordinates for E?
The coordinates for E from the parallelogram CDEH are (5, 1).
We know that diagonals of parallelograms bisect each other. Therefore coordinates of the midpoint of CE and DH will be the same.
Here, (x, y) = [(2+8)/2, (5+1)/2]
= (5, 3)
Let the coordinates of E be (a, b)
Now, (5, 3) = [(5+a)/2, (5+b)/2]
(5+a)/2 =5 and (5+b)/2 = 3
5+a=10 and 5+b=6
a=10-5 b=6-5
a=5 b=1
Therefore, the coordinates for E from the parallelogram CDEH are (5, 1).
Learn more about the parallelogram here:
https://brainly.com/question/19187448.
#SPJ1
if the area of a rectangle is 12n12-30n6 168n3 and the length of a rectangle is 6n3, what is the width
The width of the rectangle is 2n^9 - 5n^3 + 28.
To find the width of the rectangle, we need to use the formula for the area of a rectangle:
Area = Length x Width
We are given that the area of the rectangle is:
12n^12 - 30n^6 + 168n^3
And we know that the length of the rectangle is:
6n³
So we can plug these values into the formula and solve for the width:
Area = Length x Width
12n^12 - 30n^6 + 168n^3 = 6n^3 x Width
Dividing both sides by 6n^3:
2n^9 - 5n^3 + 28 = Width
Therefore, the width of the rectangle is 2n^9 - 5n^3 + 28.
Know more about the rectangle here:
https://brainly.com/question/25292087
#SPJ11
What is the value of d? The picture is below, help me ASAP
Answer:
D = 5
Step-by-step explanation:
The line from center of the circle perpendicularly biscets chord. Hence, you can form a right-angled triangle with the radius as the hypotenuse (See picture)
So now you use Pythagoras theorem to solve for d:
a^2 +b^2 =c^2
12^2 +b^2 = 13^2
b^2 = 13^2 - 12^2
b = [tex]\sqrt{13^{2}-12^{2} }[/tex]
b= 5
Hence, d = 5
find the arc length of the curve x = a(θ − sin θ), y = a(1 − cos θ) from 0 to 2π.
The arc length of the curve x = a(θ − sin θ), y = a(1 − cos θ) from 0 to 2π is 8a.
To find the arc length of the given curve, we need to use the formula:
L = ∫ [a to b] √[1 + (dy/dx)²] dx
Here, a = 0 and b = 2π, and the given parametric equations are:
x = a(θ − sin θ), y = a(1 − cos θ)
So, we need to find dx/dθ and dy/dθ and then substitute these in the above formula. On solving and simplifying, we get L = 8a as the final answer.
You can learn more about arc length at
https://brainly.com/question/2005046
#SPJ11
find the laplace transform of f(t)=2 t36−2sin(5t) 2e−3t f(s)=
After taking the Laplace transform, we obtain f(s) = (72/s^38) - (20/(s^2 + 25)) * (2/(s + 3)). The Laplace transform of the function f(t) = 2t^36 - 2sin(5t) * 2e^(-3t) can be found by applying the linearity and derivative properties of the Laplace transform.
To find the Laplace transform of f(t) = 2t^36 - 2sin(5t) * 2e^(-3t), we can apply the linearity property of the Laplace transform.
The Laplace transform of 2t^36 can be found using the derivative property of the Laplace transform. Taking the derivative of t^36, we get 36t^35. Then, applying the Laplace transform to 36t^35, we obtain (36!/s^37).
The Laplace transform of 2sin(5t) can be directly found using the standard Laplace transform table. The transform of sin(5t) is 5/(s^2 + 25).
The Laplace transform of 2e^(-3t) can also be found using the standard Laplace transform table. The transform of e^(-at) is 1/(s + a).
Now, using the linearity property of the Laplace transform, we can combine the transforms of each term:
f(s) = (72/s^37) - (20/(s^2 + 25)) * (2/(s + 3)).
Thus, the Laplace transform of f(t) is f(s) = (72/s^37) - (40/(s^2 + 25)(s + 3)).
Learn more about linearity property here:
brainly.com/question/28007778
#SPJ11
if f(x) = f(g(x)), where f(−4) = 9, f ′(−4) = 3, f ′(5) = 3, g(5) = −4, and g ′(5) = 4, find f ′(5). f '(5) =
The chain rule states that if a function is composed of two functions, say f(x) and g(x), then its derivative can be computed as f′(g(x))g′(x). Using this rule and the given information, we can find f′(5) as follows.
First, we know that f(5) = f(g(5)) by definition. Since g(5) = −4, we can write this as f(5) = f(−4). Taking the derivative of both sides with respect to x, we get f′(5) = f′(−4)g′(5). We know f′(−4) = 3 and g′(5) = 4 from the given information, so we can substitute these values into the equation to obtain f′(5) = 3(4) = 12. Therefore, the derivative of the function f(x) at x = 5, denoted by f′(5), is equal to 12. This means that the slope of the tangent line to the graph of f(x) at x = 5 is 12. The chain rule is a powerful tool for computing derivatives of composite functions, and it is widely used in calculus and its applications.
Learn more about tangent line here: brainly.com/question/31402614
#SPJ11
PLEASE HELP FAST
For questions 5,6 add or subtract the polynomials
(m²-m+3)+(m-1)
A. M²-M-2
B.M²-2
C.M²+2
D.M²+M+2
6.( 7X²-X-2)- (-6X³+3)
A.6X³+7X²-X-5
B.-6X³+7X²-X+1
C-X³-X-5
D.X²-X+1
Answer:
m^2-2 and -6x^3+7x^2-x+1
non-rivalry and non-excludability apply to group of answer choices private goods public goods goods produced by monopolies natural resources
Non-rivalry and non-excludability apply to public goods. Public goods are goods or services that are non-excludable,
meaning that it is impossible or impractical to exclude people from using them, and non-rivalrous, meaning that consumption of the good by one individual does not diminish its availability to others.
Examples of public goods include national defense, clean air and water, and scientific research. Because of their non-excludable and non-rivalrous nature, public goods often suffer from under-provision in a market economy.
Private goods, on the other hand, are both rivalrous and excludable. This means that only one person can consume the good at a time, and individuals can be prevented from consuming the good if they do not pay for it.
Goods produced by monopolies and natural resources can be either private or public goods depending on their excludability and rivalrousness.
To know more about time click here
brainly.com/question/30823895
#SPJ11
1. In a board game where players are directed to move the game pieces forward or backward on each turn, Peter had many gains and losses of spaces moved. This list represents his moves in order: gain of 5 spaces, loss of 2 spaces, gain of 12 spaces, gain of 7 spaces, loss of 10 spaces. What is the overall gain or loss from all moves? Show all work
A)36
B)16
C)12
D)-2
The overall gain or loss from Peter's moves is 12.
The correct option is C.
To find the overall gain or loss from Peter's moves, we need to consider the direction and magnitude of each move. A positive value represents a gain or moving forward, while a negative value represents a loss or moving backward.
In this case, Peter had a gain of 5 spaces, followed by a loss of 2 spaces, a gain of 12 spaces, a gain of 7 spaces, and finally a loss of 10 spaces. When we add up these individual gains and losses, we find that the total sum is 12.
This means that, overall, Peter gained a net total of 12 spaces from all his moves. It indicates that he moved forward more than he moved backward. The positive value suggests a net gain in terms of spaces on the game board.
Therefore, the answer C) 12 represents the overall gain or loss from Peter's moves.
To learn more about subtraction;
https://brainly.com/question/2346316
#SPJ1
What is the area on the object above
A.102
B.166
C.204
D.126
Answer
D. 126 inches squared
Step-by-step explanation:
8 x 17 = 136
2 x 5 = 10
136-10= 126
The half-life of a radioactive isotope Is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 190 grams of a radioactive isotope, how much will be left after 5 half-lives?
The amount of the substance that will be left after 5 half life is 5.94 grams
What is radioactive decay?Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation.
The time required for half of the original population of radioactive atoms to decay is called the half-life.
Half life = 1/2
5 half life = 1/2 × 1/2 × 1/2 × 1/2 × 1/2
= 1/32
This means 1/32 of tht original mass will be left after 5 half life.
Therefore;
The mass of the substance left = 190 × 1/32
= 5.94 grams
therefore 5.94g of the mass of the substance will be left.
learn more about radioactive decay from
https://brainly.com/question/9932896
#SPJ1
ANSWER THIS QUESTION FAST AND YOU GET A LOT OF POINTS PS THIS IS A STEPS QUESTIONS
Emma, erin, and eden complete the problem to the right
A. who completed the problem correctly
B. what did the other two did wrong in their awnsers
i belive yall can do this :)
The correct one is Eden, the exponents should be added.
The mistakes are that Erin multiplies the exponents and Emma multiplies the bases.
Who completed the problem correctly?Remember that when we have the product of two powers with the same base, we just need to add the exponents, so:
[tex]x^n*x^m = x^{n + m}[/tex]
With that in mind, we can see that the one who did the operation correctly is Eden, because:
[tex]6^2*6^5 = 6^{2 + 5} = 6^7[/tex]
The mistake for Erin is that she multiplied the exponents, while the problem for Emma is that she also multiplied the bases.
Learn more about exponents:
https://brainly.com/question/847241
#SPJ1
50 POINTS PLEASE HELP SOON
The bag contains 20 marbles. There are 5 green marbles, 9 red marbles, and 6 blue marbles. What is the probability of randomly selecting a marble that is NOT red? Simplify your fraction if possible.
A. P(not red) = 9/20
B. P(not red) = 3/10
C. P(not red) = 11/20
The probability of randomly selecting a marble that is NOT red is C. P(not red) = 11/20.
There are 9 red marbles out of a total of 20 marbles. Thus, the probability of selecting a red marble is 9/20.
To find the probability of selecting a marble that is NOT red, we can subtract the probability of selecting a red marble from 1 (since the probability of selecting any marble must be 1).
P(not red) = 1 - P(red) = 1 - 9/20 = 11/20
Therefore, the probability of randomly selecting a marble that is NOT red is C. P(not red) = 11/20.
for such more question on probability
https://brainly.com/question/13604758
#SPJ11
The graph shows the distribution of the amount of time
(in minutes) people spend watching TV shows on a
popular streaming service. The distribution is
approximately Normal, with a mean of 71 minutes and a
standard deviation of 15 minutes.
Streaming TV
What percentage of people spend between 41 and 56
minutes watching TV shows on this streaming service?
O 13.5%
34%
47.5%
95%
The percentage of people that spend between 41 and 56 minutes watching TV shows on this streaming service is: 13.5%
How to find the p-value from z-score?The formula for the z-score here is:
z = (x' - μ)/σ
where:
x' is sample mean
μ is population mean
σ is standard deviation
Thus, for:
σ = 15
μ = 71
x' = 41, we have:
z = (41 - 71)/15
z = -30/5
z = -6
for:
σ = 15
μ = 71
x' = 56, we have:
z = (56 - 71)/15
z = -15/5
z = -3
From online p-value from 2 z-scores calculator, we have the p-value as:
P(-6 < z < -3) = 0.135
Read more about P-value from Z-score at: https://brainly.com/question/25638875
#SPJ1
if you use 100 degrees celsius for the temperature of steam in your calculations, how much error do you introdcue if it is actuallly 99
If the actual temperature of steam is 99 °C and is assumed to be 100 °C in calculations, the error introduced can be significant depending on the specific calculations being performed.
Similarly, if the actual temperature of steam is 101 °C and is assumed to be 100 °C, the error introduced can also be significant.
The amount of error introduced when assuming the temperature of steam to be 100 °C instead of the actual temperature of 99 °C or 101 °C depends on the specific calculations being performed.
Similarly, in industrial processes, assuming an incorrect temperature of steam could result in inefficiencies or even safety hazards. Therefore, the difference between the actual temperature of steam and the assumed temperature of 100 °C should not be considered negligible in many cases.
In conclusion, the error introduced by assuming a temperature of 100 °C instead of the actual temperature of steam depends on the specific calculations being performed and can be significant in some cases. It is always best to use accurate and precise measurements in scientific and engineering calculations to minimize the potential for error.
Learn more about temperature here:
brainly.com/question/4658134
#SPJ11
Complete Question:
1. If you use 100 °C for the temperature of steam in your calculations, how much error do you introduce if it is actually 99 °C or 101 °C? Is this difference negligible?
Someone help I’ll give so many points
Answer:
Angles 4 and 8 do not equal 180 degrees (supplementary), therefore letter A is the answer.
Step-by-step explanation:
Looking at the other angles they all equal 180 degrees except for A which would appear to equal more than 180.
I WILL GIVE YOU BRAINLIEST IF YOU ARE SERIOUSLY LEGIT AND IS CORRECT FOR THIS ANSWER!!!!!!
Answer:
$1,134 + $926 + $562 + $333 + $55 + $130
+ $1,500 + $313 = $4,953
Find the length of the missing side length=3 , width =4
The length of the missing side of the right triangle is given as follows:
x = 5.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The sides for this problem are given as follows:
3 and 4.
Hence the hypotenuse is given as follows:
x² = 3² + 4²
x² = 25.
x = 5.
Missing InformationThe missing side is the hypotenuse.
More can be learned about the Pythagorean Theorem at brainly.com/question/30203256
#SPJ1
find h(x, y) = g(f(x, y)). g(t) = t2 t , f(x, y) = 7x 6y − 42
Therefore, h(x, y) = 49x^3 - 294x^2y + 441xy^2 - 252x^2 + 252xy - 588y^2 + 294x - 252y - 1764.
To find h(x, y) = g(f(x, y)), we first need to evaluate f(x, y) and then use the result as input for g(t).
Starting with f(x, y), we have:
f(x, y) = 7x - 6y - 42
Next, we need to use this as input for g(t), which is defined as:
g(t) = t^2*t
Substituting f(x, y) for t, we get:
g(f(x, y)) = (7x - 6y - 42)^2*(7x - 6y - 42)
Simplifying this expression, we can expand the square and get:
h(x, y) = 49x^3 - 294x^2y + 441xy^2 - 252x^2 + 252xy - 588y^2 + 294x - 252y - 1764
Therefore, h(x, y) = 49x^3 - 294x^2y + 441xy^2 - 252x^2 + 252xy - 588y^2 + 294x - 252y - 1764.
To know more about evaluate visit:
https://brainly.com/question/12837686
#SPJ11
Alexa drew a square that has a perimeter of 20 inches.
How long is one side of her square?
Answer:
5 in.
Step-by-step explanation:
For a square:
perimeter = 4 × side
20 in. = 4 × side
side = 20 in. / 4
side = 5 in.
need to find m angel S
The measure of the angle S is 60 degrees
How to determine the angleTo determine the angle, we need to know the six different trigonometric identities in mathematics;
These trigonometric identities are;
sinecosinetangentcotangentsecantcosecantWe also have that these identities have their ratios, we have that;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
Adjacent = 2√3
Hypotenuse= 4√3
Then,
cos S = 2√3/4√3
Divide the values
cos S = 0. 5
find the inverse
S = 60 degrees
Learn about trigonometric identities at: https://brainly.com/question/22591162
#SPJ1
how do you find the height of a pyramid if the base and volume are given?
formula: 1/3Bh (B=Base H=Height)
The height of the pyramid from the base and the volume is h = 3V/B
Finding the height of the pyramid from the base and the volumeFrom the question, we have the following parameters that can be used in our computation:
Volume and base area are known
This means that we make the height the subject of the formula
The volume of a pyramid is calculated as
V = 1/3Bh
Where
B Base area
h - height
So, we have
h = 3V/B
By making the height the subject of the formula
Hence, the height of the pyramid from the base and the volume is h = 3V/B
Read more about volume at
https://brainly.com/question/463363
#SPJ1
for the following relation ∼ on r × r, determine whether it is an equivalence relation. (x1,y1) ∼ (x2,y2) ⇔ (x1)2 (y1 )2 = (x2)2 (y2 )2
The relation ∼ on R × R, given by (x1,y1) ∼ (x2,y2) ⇔ (x1)²(y1)² = (x2)²(y2)², is an equivalence relation.
To show that the given relation is an equivalence relation, we need to prove that it satisfies the three conditions of reflexivity, symmetry, and transitivity.
Reflexivity: For any (x,y) in R × R, we have (x)²(y)² = (x)²(y)², which implies that (x,y) ∼ (x,y).
Symmetry: If (x1,y1) ∼ (x2,y2), then (x1)²(y1)² = (x2)²(y2)². This implies that (x2)²(y2)² = (x1)²(y1)², and hence (x2,y2) ∼ (x1,y1).
Transitivity: If (x1,y1) ∼ (x2,y2) and (x2,y2) ∼ (x3,y3), then (x1)²(y1)² = (x2)²(y2)² and (x2)²(y2)² = (x3)²(y3)². Multiplying these equations, we get (x1)²(y1)² = (x3)²(y3)², which implies that (x1,y1) ∼ (x3,y3).
Since the given relation satisfies all three conditions, it is an equivalence relation.
To learn more about equivalence relation : brainly.com/question/30766579
#SPJ11
Find an equation of the set of all points equidistant from the points A(-1, 4, 2) and B(4, 1, -1). Describe the set. .a line perpendicular to AB .a cube with diagonal AB .a plane perpendicular to AB .a sphere with diameter AB
Therefore, the equation of the set of all points equidistant from A and B is 5x - 3y - 3z = 0. This represents a plane perpendicular to the line segment AB.
The set of all points equidistant from points A(-1, 4, 2) and B(4, 1, -1) forms a plane perpendicular to AB.
To find the equation of this plane, we can use the midpoint formula to find the coordinates of the midpoint M between A and B, and then use the vector AB as the normal vector for the plane.
Midpoint M:
M = ((-1 + 4) / 2, (4 + 1) / 2, (2 - 1) / 2) = (1.5, 2.5, 0.5)
Vector AB:
AB = B - A = (4 - (-1), 1 - 4, -1 - 2) = (5, -3, -3)
Now, we can write the equation of the plane in point-normal form:
(x - 1.5, y - 2.5, z - 0.5) · (5, -3, -3) = 0
Expanding the dot product, we get:
5(x - 1.5) - 3(y - 2.5) - 3(z - 0.5) = 0
Simplifying:
5x - 7.5 - 3y + 7.5 - 3z + 1.5 = 0
5x - 3y - 3z = 0
To know more about plane perpendicular,
https://brainly.com/question/14705166
#SPJ11