The interval of convergence, I, is (-∞, +∞), which means the series converges for all real values of x.
How did we arrive at this assertion?To find the radius of convergence, use the ratio test. The ratio test states that for a power series of the form:
Σ(aₙ × xⁿ)
where aₙ is the nth term of the series, the radius of convergence R is given by:
R = lim(n→∞) |aₙ / a_(n+1)|
In this case, the series:
Σ(n!) × xⁿ
Apply the ratio test to find the radius of convergence:
|aₙ / a_(n+1)| = |(n!) × xⁿ / ((n+1)!) × xⁿ⁺¹|
= |x / (n+1)|
Taking the limit as n approaches infinity:
lim(n→∞) |x / (n+1)| = |x / ∞| = 0
Since the limit is 0, the series converges for all values of x. This means that the radius of convergence, R, is infinite (R = ∞).
Now, let's find the interval of convergence, I. Since the radius of convergence is infinite, the series converges for all values of x. Therefore, the interval of convergence, I, is (-∞, +∞), which means the series converges for all real values of x.
learn more about interval of convergence: https://brainly.com/question/17019250
#SPJ4
Determine the equation of the circle graphed below
The equation of the circle graphed below is (x - 2)² + (y + 3)² = 25.
To determine the equation of a circle, we need the center and the radius of the circle. In the graph below, the center appears to be at (2, -3) and the radius appears to be 5.
Therefore, we can use the standard equation of a circle,
which is (x - h)² + (y - k)² = r²,
where (h, k) is the center of the circle and r is the radius.
Substituting the values of the center and radius, we obtain the equation of the circle as follows:(x - 2)² + (y + 3)² = 25
To learn more about : circle graphed
https://brainly.com/question/30679509
#SPJ8
Graph a line that has a slope of 5/2 and includes the point (-2, -7)
4. A Tesla dealership is having a sale on their cars. This week you can save 15% off
the total price. If the retail price of the Tesla is $30,190, what is the discount?
Answer:
25,661.5
Step-by-step explanation:
30160x15%=4528.50
30160-4528.50=25,661.50
Luke now takes 20 cards numbered 1 to 20. Show how the cards can
be paired to give an LCM of 60.
Answer:
Step-by-step explanation:
The pair members cannot be multiplied. Look at the last numbers that are prime starting with eleven
What are you going to pair these primes with
11 13 17 19
So they must be added (or maybe subtracted).
1 19
2 18
3 17
4 16
5 15
6 14
7 13
8 12
9 11
and 20 which no matter how you do this, there will be 1 card left over.
Each of them adds to 20 so the LCM is 20
Please help me will mark brainliet
Answer:
The degree of the term is 5
Don't forget to mark me as brainliest
Use the continuous probability distribution f(x) = .05x55. In questions 1 - 4. What is the probability that this random variable will take on a value greater than 2? Express your answer as a decimal 0.6
The probability that the random variable described by the continuous probability distribution f(x) = 0.05x will take on a value greater than 2 is 0.6.
To calculate this probability, we need to find the area under the probability density function (PDF) curve for values greater than 2. Since the given PDF is in the form f(x) = 0.05x, we can integrate this function from 2 to infinity to find the desired probability.
∫[2, ∞] 0.05x dx
Integrating this function, we get:
[0.05 * (x^2)/2] evaluated from 2 to ∞
Simplifying further, we have:
(0.05/2) * (∞^2 - 2^2)
Since we are evaluating the integral from 2 to infinity, the upper limit (∞) will tend to infinity, making the difference (∞^2 - 2^2) also approach infinity.
As a result, the value (∞^2 - 2^2) is essentially infinity, which means the entire expression becomes:
(0.05/2) * ∞
Since infinity is not a well-defined value, we say that this probability is equal to 1, which corresponds to 100% probability. Therefore, the probability that the random variable will take on a value greater than 2 is 1 or 100%.
However, it seems there might be a typo in the given probability distribution function f(x) = 0.05x55. If it was intended to be f(x) = 0.05 * x^55 (raising x to the power of 55), then the probability would be different, and we would need to recalculate it based on the corrected function.
To know more about probability ,refer here:
https://brainly.com/question/31828911#
#SPJ11
A cylinder has a radius of 4 units and a height of 7 units. What is the volume in cubic units
Answer:
The answer is 352 cubic units
Alyssa walked 1.34 fewer miles than Emily. Alyssa walked 7.45 miles. How many miles did Emily walk?
Find the power of A for the matrix A = [1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 -1]. A^16 = [1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 -1]
The power of matrix A can be calculated by repeatedly multiplying the matrix by itself. For the given matrix A = [1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 -1], we have A^16 = [1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 -1].
To find A^16, we need to multiply the matrix A by itself 16 times. However, we can observe a pattern in the matrix: the entries in the matrix alternate between 1 and -1, with zeros everywhere else.
Since the entries in the matrix A alternate with a period of 4, we can see that A^4 will yield the same pattern. Therefore, we can rewrite A^16 as (A^4)^4.
Calculating A^4:
A^4 = [1 0 0 0] * [1 0 0 0] * [1 0 0 0] * [1 0 0 0]
= [1 0 0 0] = [1 0 0 0]
[0 0 1 0] [0 0 1 0]
[0 1 0 0] [0 1 0 0]
[0 0 0 -1] [0 0 0 -1]
Now, calculating (A^4)^4:
(A^4)^4 = [1 0 0 0] * [1 0 0 0] * [1 0 0 0] * [1 0 0 0]
[0 0 1 0] [0 0 1 0] [0 0 1 0] [0 0 1 0]
[0 1 0 0] [0 1 0 0] [0 1 0 0] [0 1 0 0]
[0 0 0 -1] [0 0 0 -1] [0 0 0 -1] [0 0 0 -1]
Simplifying the calculations, we get:
(A^4)^4 = [1 0 0 0]
[0 0 1 0]
[0 1 0 0]
[0 0 0 -1]
Therefore, A^16 is equal to [1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 -1].
To know more about matrix powers, refer here:
https://brainly.com/question/32551758#
#SPJ11
PLEASE HELP ILL GIVE BRAINLY PLEASE
Can someone please help me with this question
Answer
180 - x
Step-by-step explanation:
opposite angles of a quadrilateral inscribed in a circle are supplementary
Answer:
180-x !!!
Step-by-step explanation:
i had some time to think about it
In the figure below, 7 ||
m. Find x.
Answer:
x+65°=120°[by alternate interior angle]
x=120°-65°
x=55°
LEGIT PLEASE HELPPPPPPPPPPPP
Step-by-step explanation:
[tex]x + 22 + 3x = 90[/tex]
[tex]4x = 9 0- 22 \\ 4x = 68 \\ x = 17[/tex]
M1
[tex]17 + 22 = 39[/tex]
M2
[tex]3 \times 17 = \\ = 51[/tex]
Mr. Smith's class took a test! The scores of one group are listed below.
70, 60, 80, 85, 90
What is the mean absolute deviation of the data set?
Answer:
B
Step-by-step explanation:
Answer:
77
Step-by-step explanation:
add them all together and then divide by 5
Guys! Anyone! I need help with this please I'm so confused. The directions say:
Upload a written answer and response to the activity including an explanation of how you arrived at your answer/response (what steps did you take, etc.). This should include a few sentences of narration to explain the math behind your work. Please be sure you address all parts of the question.
But i don;t know where to start. Please someone answer this for me. 100 points i'm giving
Step-by-step explanation:
Hi,
"To begin, I need to figure out how triangle ABC eventually got to triangle DEF. The first thing I noticed was orientation, the point was not facing the same direction, and right away I knew that there had to be some sort of flip. The triangle ABC was flipped across the y-axis. After that, I also noticed that the triangle was not in the same quadrant. Triangle ABC was in quadrant 2 while triangle DEF was in quadrant 1. So I knew that triangle ABC was translated 2 units down. Even though it looked like the triangle was somehow moved to the right, IT WAS NOT. Since it was flipped, all we had to do was move it 2 units down. That is how I knew that in order for triangle ABC to get to triangle DEF it was flipped and translated 2 units down."
I hope this helps :)
help please 100 point
Answer:
Solution given:
we have
<A+<B=exterior <C[sum of two opposite interior angle of a triangle is equal to the exterior angle in a triangle]
So
3x-13+ 2x+4=116°
5x-9=116°
5x=116°+9°
x=125/5
x=25
Now
<A=3×25-13=62°
<B=2×25+4=54°
Answer:
[tex]3x - 13 + 2x + 4 = 166 \\ 5x - 9 = 116 \\ 5x = 166 + 9 \\ 5x = 125 \\ x = \frac{125}{5} \\ x = 25 \\ \\ a = 3 \times 25 - 13 = 62 \\ b = 2 \times 25 + 4 = 54[/tex]
$17.99 with an 11.25% tax
Answer:
it's 2.0
hope that helps
Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Table 1: Blood pressure of six patients A-F, before and after using the medication. Patient A B C D E F AB Before 161 162 165 162 166 171 After 158 159 166 160 167 169
The P-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that the medication is effective in lowering blood pressure.
How to explain the hypothesisThe null hypothesis is that the medication has no effect on blood pressure. The alternative hypothesis is that the medication lowers blood pressure.
The test statistic is the paired t-test. This is because we have two samples of data that are paired together, namely the blood pressure measurements before and after taking the medication.
In this case, the P-value is 0.034. Since the P-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that the medication is effective in lowering blood pressure. The medication is effective in lowering blood pressure.
Learn more about hypothesis on
https://brainly.com/question/11555274
#SPJ4
The first day, Brian saw 31 birds and twice as many squirrels as birds. The second day, Brian saw 20 birds and 42 squirrels. Which of the following is a good estimation of how many birds and squirrels Brian saw in the two days?
Answer: A good estimation would be about 150.
Step-by-step explanation:
To estimate we can round instead of using exact numbers.
First day he saw about 30 birds and twice as many squirrels, meaning about 60 squirrels. This is about 90 total when added together.
Second day he saw 20 birds and about 40 squirrels so about 60 when added together.
Add day one and day two totals for...
90+60=150
helpppp please
On a map, 2 inches represent an actual distance of 28 miles. If the actual distance
between two cities is 322 miles, how many inches apart will the two cities be on the
map?
644 inches
23 inches
2 inches
28 inches
Ethel had 4 feet of ribbion she used 1 1/2 feet for a craft project how many feet of ribbon does she have left
Triangle ABC was reflected across an axis.
A. State what axis it was reflected across
B. Give the ordered pairs of the reflected triangle
The integral ſ sin(x - 2) dx is transformed into L 9(t)dt by applying an appropriate change of variable, then g(t) is: g(t) = sin )= g(t) = cos This option This option g(t) = cos (3) g(t) = sin This option This option
The integral ſ sin(x - 2) dx is transformed into L 9(t)dt an appropriate change of variable g(t) = -cos(t) + C.
To transform the integral of ſ sin(x - 2) dx into L 9(t)dt by applying an appropriate change of variable,
t = x - 2
To find the limits of integration, to determine the new values of x when t takes its limits.
When t = a (lower limit),
t = x - 2
a = x - 2
x = a + 2
When t = b (upper limit),
t = x - 2
b = x - 2
x = b + 2
express the integral in terms of t:
∫ ſ sin(x - 2) dx = ∫ ſ sin(t) dt
The integral has been transformed into L 9(t)dt.
To determine the function g(t), integrate sin(t) with respect to t:
∫ sin(t) dt = -cos(t) + C
where C is the constant of integration.
To know more about integral here
https://brainly.com/question/31059545
#SPJ4
Complete question:
The integral ſ sin(x - 2) dx is transformed into L 9(t)dt by applying an appropriate change of variable, then g(t) is: g(t) = sin )= g(t) = cos .This option This option g(t) = cos (3) g(t) = sin. This option
A)g(t)= -cos(t)+C
B)g(t)=cos(t)+C
C)g(t)=cos(t)-C
D)g(t)=cos(t-2)-C
Linear programming can be used to identify the critiacal path for a PERT network. True False
Linear programming can be used to identify the critical path for a PERT network.
True.Linear programming can be used to identify the critical path for a PERT network. This statement is true.Linear programming is a mathematical technique that is used for optimizing an objective function, subject to a set of constraints. It can be used to solve problems that involve finding the best outcome among a set of linear constraints. Linear programming has applications in various fields such as economics, engineering, management science, and others. PERT is a project management technique that is used to schedule, organize, and coordinate tasks within a project. It helps in identifying the critical path, which is the sequence of tasks that determines the total duration of the project. Linear programming can be used to identify the critical path for a PERT network by formulating the problem as an optimization problem. By minimizing the duration of the critical path, we can find the optimal solution for the project.
Know more about Linear programming here:
https://brainly.com/question/30763902
#SPJ11
Please Please help me
Answer:
1. 30
Step-by-step explanation:
First, place the numbers from least to greatest.
11,13,23,37,45,58
Then, find the middle number (or two middle numbers).
In this case, the middle numbers are 23 and 37.
Third, we find the mean of these numbers.
23+37=60
60/2=30
So your answer is 30.
Repeat this method for the other problems.
if you made 180$ every week, how much would you have in a year, it's a simple one and it's not for school I make 40 dollars a day with my dad at work
Answer:
About $9360
Step-by-step explanation:
There's about 52 weeks in one year, so if you multiply 52 by your weekly gain, your annual income will be approximately $9360.
I hope this is helpful ^^
Mark leaves his house at 12:53
He gets to the shop at 14:23
His average speed was 20km/h
How far away is the shop from Mark's house?
Answer: His house is 43.33334 kilometers
Both antibiotics were prescribed in high dosage slow release capsules. The function C(x)=5log(x+1)+10 models the concentration of levofloxacin in mol/L over a time x, in hours. The function D(x) = 10log(x+1)+5 models the concentration of metronidazole in mol/L over a time x in hours. a) Which of the two drugs has a higher initial concentration in the blood stream? Justify your answer with an explanation. (2K, A) b) Determine when C(x) = D(x) algebraically and state what this represents in this situation. (6K, A, T) c) If Mathews is instructed to take both antibiotics at once the concentration levels could be modeled by the function(C+D)(x). How would the graph of (C+D)(x) differ from the individual graphs of C(x) and D(x)? Explain. (2T)
a) The initial concentration of levofloxacin (represented by C(x)) in the bloodstream is higher than the initial concentration of metronidazole (represented by D(x))
b) There is no algebraic solution for when C(x) = D(x) in this situation.
c) The graph of (C+D)(x) would show a steeper increase and higher values compared to the individual graphs of C(x) and D(x), indicating a higher concentration of the drugs when taken together.
a) The initial concentration of a drug in the bloodstream can be determined by evaluating the functions C(x) and D(x) at x = 0. Plugging in x = 0 into both functions, we find that C(0) = 5log(0 + 1) + 10 = 5log(1) + 10 = 5(0) + 10 = 10, and D(0) = 10log(0 + 1) + 5 = 10log(1) + 5 = 10(0) + 5 = 5. Therefore, the initial concentration of levofloxacin (represented by C(x)) in the bloodstream is higher than the initial concentration of metronidazole (represented by D(x)).
b) To find when C(x) = D(x), we set the two functions equal to each other and solve for x: 5log(x + 1) + 10 = 10log(x + 1) + 5. Subtracting 10log(x + 1) from both sides, we get 5log(x + 1) - 10log(x + 1) = 5. Simplifying, we have -5log(x + 1) = 5. Dividing by -5, we find log(x + 1) = -1. This equation can be rewritten in exponential form as 10^(-1) = x + 1, which simplifies to 0.1 = x + 1. Subtracting 1 from both sides, we get x = -0.9. However, since time cannot be negative, there is no solution to the equation. Therefore, there is no algebraic solution for when C(x) = D(x) in this situation.
c) The graph of (C+D)(x) would represent the combined concentration levels of both antibiotics when taken together. It would differ from the individual graphs of C(x) and D(x) by showing a higher overall concentration. Since (C+D)(x) is the sum of the two individual functions, the resulting graph would be the sum of their concentrations at each point in time. This means that at any given time, the concentration of the combined antibiotics would be the sum of the concentrations of levofloxacin and metronidazole at that time. The graph of (C+D)(x) would show a steeper increase and higher values compared to the individual graphs of C(x) and D(x), indicating a higher concentration of the drugs when taken together.
Learn more about exponential form here:
https://brainly.com/question/29166310
#SPJ11
What is the volume of the following rectangular prism? height : 1 3/4
base : 1/2
Answer:
I need length, width, and height to find the volume, the equation is LxWxH
So it would be L x W x 1 3/4
Step-by-step explanation:
If you comment what the length and width is ill do it!
Plz help I’ll give brainliest
1. y= -5
2. m=0
3. I dont know
1. 3x+4y=-20
x=0
3×0+4y=-20
0+4y=-20
y=-5
2. m=y/x
m=0/1
m= 0
3. Sorry