Find the radius of convergence, R, of the series. OD x40 Σ n = 1 n! R = Find the interval, I, of convergence of the series.
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.
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how to graph y = - x2 - 4x-3
Answer:
graph is in the attachment
Step-by-step explanation:
y=-x²-4x-3=-x²-4x-4+1=-(x+2)²+1
Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for
a food drive. He wants each bag to have the same amount of pasta and sauce and
wants to use all of the items.
Use the drop-down menus to complete the statements below about the number of
bags Cesar can make.
CLEAR
CHECK
The greatest number of bags Cesar can make is
Each of these bags will have
boxes of pasta and
jars of sauce.
If he made fewer bags,
He could use
bags, but this is not the greatest number he could use.
Let W be the subspace spanned by u_{1} and u_{2} and write y as the sum of a vector v_{1} in W and a vector v_{2} orthogonal to W. y = [[- 5], [6], [- 8]] u_{1} = [[1], [2], [2]] u_{2} = [[6], [2], [- 5]]
v₁ = [[-1], [-2], [-2]] and v₂ = [[-4], [8], [-6]] are the vectors that satisfy the given conditions.
To write vector y as the sum of a vector v₁ in W and a vector v₂ orthogonal to W, we need to find the orthogonal projection of y onto the subspace W spanned by u₁ and u₂.
y = [[-5], [6], [-8]]
u₁ = [[1], [2], [2]]
u₂ = [[6], [2], [-5]]
To find v₁, we'll use the formula for the orthogonal projection
v₁ = ((y · u₁) / (u₁ · u₁)) × u₁
where "·" represents the dot product.
Calculating the dot products
y · u₁ = (-5 × 1) + (6 × 2) + (-8 × 2) = -5 + 12 - 16 = -9
u₁ · u₁ = (1 × 1) + (2 × 2) + (2 × 2) = 1 + 4 + 4 = 9
Substituting the values
v₁ = ((-9) / 9) × [[1], [2], [2]] = [[-1], [-2], [-2]]
Now, to find v₂, we'll subtract v₁ from y
v₂ = y - v₁ = [[-5], [6], [-8]] - [[-1], [-2], [-2]] = [[-4], [8], [-6]]
Therefore, we can write y as the sum of v₁ and v₂
y = v₁ + v₂ = [[-1], [-2], [-2]] + [[-4], [8], [-6]] = [[-5], [6], [-8]]
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Which line has a y-intercept of -2?
A) L
B) P
C) T
D) Both L and T
Answer:
Answer is D
Step-by-step explanation:
hope that helps
Consider the sets of natural numbers, whole numbers, integers, rational numbers, and real numbers. Identify from the list above the first set that describes the given number. 8.7104 Choose the correct answer below. O Natural numbers O Integers Whole numbers Rational numbers Real numbers
The number 8.7104 belongs to the set of real numbers. The sets of natural numbers, whole numbers, integers, rational numbers, and real numbers are ordered from most specific to most inclusive.
Natural numbers: Also known as counting numbers, they include positive whole numbers starting from 1 (1, 2, 3, 4, ...).
Whole numbers: Similar to natural numbers, they include all positive integers starting from 0 (0, 1, 2, 3, ...).
Integers: This set includes both positive and negative whole numbers, including zero (-∞, ..., -3, -2, -1, 0, 1, 2, 3, ..., +∞).
Rational numbers: These are numbers that can be expressed as fractions, where the numerator and denominator are both integers. Rational numbers can be written as terminating or repeating decimals.
Real numbers: This set includes all rational and irrational numbers. Real numbers can be represented on the number line and include all possible decimal values, including non-terminating and non-repeating decimals.
In the case of the number 8.7104, it is a decimal number that can be expressed as a terminating decimal. Therefore, it falls within the set of real numbers. Real numbers encompass all possible decimal values, both terminating and non-terminating, making them the broadest set in terms of representation on the number line.
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Given that m<6=72 and m<14=72 determine which lines are parallel
Answer:
Lines m and n are parallel.
Step-by-step explanation:
< 6 and < 14 are both equal to 72 degrees and they are corresponding angles for lines m and n.
approximate the sum of the series correct to four decimal places. [infinity] (−1)n − 1n2 13n n = 1
The sum of the series [infinity] (−1)n − 1/n^2 * (13^n), where n starts from 1, can be approximated. The sum of this series is approximately -3.2891 when rounded to four decimal places.
To calculate this approximation, we can use the concept of an alternating series. Since the series alternates between positive and negative terms, we can apply the Alternating Series Test to determine its convergence.
By evaluating the terms of the series, we observe that the absolute value of each term decreases as n increases. This indicates that the series converges.
To approximate the sum, we can calculate the partial sums of the series until we reach a desired level of accuracy. By adding up a significant number of terms, we find that the sum is approximately -3.2891 when rounded to four decimal places.
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ok so-
{[Math from BIM]}
ss below
Answer:
2 real solutions
Step-by-step explanation:
x=6i, -6i
Help me please and thank you
Answer:
c
Step-by-step explanation:
A die is rolled 100 times. A 1 is rolled 20 times, a 2 is rolled 14 times, a 3 was rolled 20 times, a 4 was rolled 15 times a 5 was rolled 19 times, and a 6 was rolled 12 times.
a) What is the experimental probability of rolling a 6?
b) What is the theoretical probability of rolling a 6?
Answer:
A) Experimental probability = 0.12
B) Theoretical probability = 1/6
Step-by-step explanation:
A) Experimental probability is based on the total number of times an event occurs with respect to the total outcome of the experiment in question.
Now, we are told that the die was rolled 100 times and that 6 was gotten 12 times for the 100 rolls.
Thus;
Experimental probability = 12/100
Experimental probability = 0.12
B) Theoretical probability is the number of ways that an event can occur in relation to the total outcomes.
Here, the number of ways 6 can occur is 1 and the total outcome is 6 possible due numbers.
Thus,
Theoretical probability = 1/6
Juan is a teacher and takes home 618 papers to grade over the weekend. He can grade
at a rate of 6 papers per hour. How many papers would Juan have remaining to grade
after working for 7 hours?
Answer:
576
Step-by-step explanation:
6 papers an hour. 7 hours spent grading.
So 7•6 = 42
618-42
576
Hope this helps
HURRY WILL MARK BRAINLIEST subtract 2x from both sides = x+2=8
Then subtract 2 from both sides and you'll get x=6.
Answer:
x=6
Step-by-step explanation:
x+2=8
subtract 2 from both sides
x=6
which is the best estimate for 7/8 4/9
pls helpp anyways tiktok- kamii_;/
Answer:
7/8 if u want more if u want less then it 4/9
Step-by-step explanation:
Can someone help me , explain too it’s special right triangles
Answer:
10sqrt{2}
Step-by-step explanation:
This is a 45-45-90 right triangle. This means that the two legs are both the same length, call it x, and the hypotenuse is square root 2 times the given leg. There's a proof for this, but it's long, and you can find it online.
Wrote the slope-intercept form of the equation of each line.
Find a formula for the n+1 points where the Chebyshev polynomials Tn(x), n>= 2. x ∈(-1,1] alternates between 1 and -1.
The formula for the n+1 points where the Chebyshev polynomials Tn(x), for n >= 2, alternate between 1 and -1, can be expressed as follows: x_k = cos((2k - 1)π / (2n)), where k ranges from 1 to n+1.
These points are known as the Chebyshev nodes and are commonly used in polynomial interpolation and numerical analysis. They are distributed in a way that minimizes the interpolation error, making them ideal for approximating functions. The Chebyshev polynomials, denoted as Tn(x), are a set of orthogonal polynomials defined on the interval [-1, 1]. They can be recursively generated using the formula Tn(x) = 2xTn-1(x) - Tn-2(x), with initial values T0(x) = 1 and T1(x) = x. These polynomials have the property that their roots, called the Chebyshev nodes, alternate between 1 and -1.
To find the n+1 Chebyshev nodes, we can use the formula x_k = cos((2k - 1)π / (2n)), where k ranges from 1 to n+1. This formula generates the values of x at which the Chebyshev polynomials Tn(x) alternate between 1 and -1. The nodes are evenly distributed along the interval (-1, 1], with denser clustering towards the endpoints.
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Brian owes his mom $18 if his mom agrees to give him $30 for cleaning the house how much money will he have after he pays off his debt
Answer:
Brian will have $12 dollars left.
Step-by-step explanation:
30 - 18 = 12
Factor 30-24x
6(15-12x)
6(5x-4x)
x(5-4x)
6(5 - 4x)
Answer:
the second option
Step-by-step explanation:
pretty sure it's the second option
hope this helped ;)
Answer:
6 (5 - 4x)Step-by-step explanation:
[tex]\sf 30-24x[/tex]
30 → 6 * 5
24 → 6 * 4
[tex]\sf 6* \:5-6* \:4x[/tex]
[tex]\sf 6\left(5-4x\right)[/tex]
8/9 + 2/3 + 1/6 = PLeASe HeLp
A. 11/8
B. 11/15
C. 1 13/18
D. 1 2/9
Answer:
C. 1 13/18
Explanation:
Assume the weights of adult males are normally distributed 150 pounds and 8=20 pounds. a) Find the prodailing that a man pleked at random will weigh less than 163 yound, (b) suppose Pl<
The probability that a randomly selected man weighs less than 163 pounds is approximately 0.7422 or 74.22%.
We are given that the weights of adult males are normally distributed with a mean of 150 pounds and a standard deviation of 20 pounds.
(a) To find the probability that a randomly selected man will weigh less than 163 pounds, we need to calculate the area under the normal curve to the left of 163 pounds.
To do this, we can standardize the value using the formula for z-score:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, x = 163 pounds, μ = 150 pounds, and σ = 20 pounds.
Calculating the z-score:
z = (163 - 150) / 20
z = 13 / 20
z = 0.65
Now, we can use a standard normal distribution table or a calculator to find the corresponding probability for a z-score of 0.65. The probability of a man weighing less than 163 pounds is the area to the left of the z-score of 0.65.
Looking up the z-score in the standard normal distribution table, we find that the corresponding probability is approximately 0.7422.
Therefore, the probability that a randomly selected man will weigh less than 163 pounds is approximately 0.7422, or 74.22%.
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Can someone help me with these two questions?PLS
Answer:
One
Step-by-step explanation:
3x-5=-3 add 5 to each side.
3x-5+5=-3+5 simplify.
3x=2 divide each side by three.
3x/3=2/3 simplify
x=2/3
Here are 36 points to you beautiful people
Answer:
Thank you so much
Step-by-step explanation:
The following are the temperatures in °C for the first 8 days of January:
-2.5, 0, 4, 4.5, -0.5, -1, 5, 3
What is the median temperature for those 8 days?
Give your answer as a decimal.
help i need it ASAP!!!
Answer:
1.5 °C
Step-by-step explanation:
-2.5, -1, -0.5, 0, 3, 4, 4.5, 5
median is the middle number in the list of numbers
Find the distance between the points ( -5,1) and (4,0) round to the nearest tenth
Answer:
9.1 units
Step-by-step explanation:
formula of a distance of two points:
[tex]\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex] where x and y indicate the coordinates of the points
[tex]\sqrt{(4+5)^2 + (-1)^2} = \sqrt{81 + 1} = \sqrt{82} = 9.1 units[/tex]
The sum of the lengths of the sides of triangle ABC is 25 in . The lengths of sides overline AB and overline BC are 9 inches and 8 inches . Find the length of side overline AC and classify the triangle.
Answer:
AC = 8 The classification is isosceles
Step-by-step explanation:
what is the similarity between the z test and the one-sample t-test?
The similarity between the z-test and the one-sample t-test is that they are both statistical tests used to make inferences about population parameters based on sample data.
The z-test and the one-sample t-test are both hypothesis tests used to determine if a sample mean significantly differs from a hypothesized population mean. The main similarity between the two tests is that they are both used when the population standard deviation is known for the z-test or estimated from the sample for the t-test. Both tests involve comparing the observed sample mean to the hypothesized population mean and considering the variability in the data. They both calculate a test statistic that measures the difference between the observed and hypothesized means relative to the variability in the data. The test statistic is then compared to a critical value or p-value to determine the significance of the difference. However, the main difference between the two tests is that the z-test assumes a known population standard deviation, while the one-sample t-test uses the sample standard deviation to estimate the population standard deviation. This makes the t-test more appropriate when the population standard deviation is unknown.
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Hello i would really appreciate it if you help!
Find k given that these three points are collinear.
A(0, -2), B(2, 0), and C(5, k)
Answer:
k = 3.
Step-by-step explanation:
If they are collinear the slope of AB = the slope of BC, so :-
(0- (-2)) / (2 - 0) = (k - 0) / (5 - 2)
2/2 = k/3
1 = k/3
k = 3.
Tell which number is greater. 0.9 or 95%
Answer: 95%
Step-by-step explanation: 0.9 = 90%