write the series in sigma notation 2 4/3 8/9 16/27
Answers
The series can be written as:
∑(n=1 to ∞) (2/3)^(n-1) * 2 = 6
The given series is: 2, 4/3, 8/9, 16/27, ...
To write this series in sigma notation, we need to find a pattern. We can see that each term is twice the previous term divided by 3. So, we can write:
a(n) = (2/3) * a(n-1), with a(1) = 2
We can use this recursive formula to write the series in sigma notation:
∑(n=1 to ∞) (2/3)^(n-1) * 2
The first term is when n=1, and it equals 2. The common ratio is (2/3), so we can use the formula for an infinite geometric series to find the sum:
S = a(1)/(1-r) = 2/(1-2/3) = 6
Therefore, the series can be written as:
∑(n=1 to ∞) (2/3)^(n-1) * 2 = 6
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Related Questions
Twenty increased by the product of four and a number is equal to thirty-two. Find the number.
Answers
Answer:
the number would be 3 because you start at 20 and then 4 times something will make 32 so 3 times 4 equals 12 and 20 plus 12 equals 32.
21 34 let x be a random variable with pdf f(x)=1/13,21 find p(x>30) (round off to second decimal place).
Answers
Let x be a random variable with pdf f(x) = 1/13, 21 P(X > 30) = 0.31.
We are given that X is a random variable with a probability density function (pdf) of f(x) = 1/13 for the interval 21 x 34.
We are asked to find P(X > 30), which means we need to find the probability of the random variable X being greater than 30. To do this, we will calculate the area under the PDF in the interval [30, 34].
Step 1: Determine the width of the interval [30, 34].
Width = 34 - 30 = 4
Step 2: Calculate the area under the PDF in the interval [30, 34].
Since the pdf is a constant value (1/13) within the given interval, we can calculate the area as follows:
Area = f(x) * width
Area = (1/13) * 4
Step 3: Round off the result to the second decimal place.
Area ≈ 0.31 (rounded to two decimal places)
So, P(X > 30) ≈ 0.31.
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find the radius of convergence, r, of the series. [infinity] xn 6n − 1 n = 1
Answers
the radius of convergence, r, is 1. The series converges for values of x within the interval (-1, 1), and diverges for |x| > 1.
To find the radius of convergence, r, of the series ∑(n=1 to infinity) x^n * (6n - 1), we can use the ratio test.
The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L, then the series converges if L is less than 1, and diverges if L is greater than 1.
Let's apply the ratio test to the given series:
L = lim(n→∞) |(x^(n+1) * (6(n+1) - 1)) / (x^n * (6n - 1))|
= lim(n→∞) |x * (6n + 5) / (6n - 1)|
Since we are interested in the radius of convergence, we want to find the values of x for which the series converges, so L must be less than 1:
|L| < 1
|x * (6n + 5) / (6n - 1)| < 1
|x| * lim(n→∞) |(6n + 5) / (6n - 1)| < 1
|x| * (6 / 6) < 1
|x| < 1
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For each order. Determine weather is a solution to x = -5
Solutions:
(-5,1)
(3,-5)
(9,2)
(-5,4)
Answers
(x,y)
So first and last are correct
determine whether the random variable described is discrete or continuous. a) the number of songs on a randomly chosen ipod [ select ] b) the number of people in line at the bank at a randomly chosen time [ select ] c) the time it takes to drive to the airport [ select ] d) the amount of rain during the next thunderstorm [ select ]
Answers
The variables for this problem are classified as follows:
a) The number of songs on a randomly chosen ipod is discrete.
b) The number of people in line at the bank at a randomly chosen time is discrete.
c) The time it takes to drive to the airport is continuous.
d) The amount of rain during the next thunderstorm is continuous.
What are continuous and discrete variables?Variables are classified as continuous or discrete depending if they can assume decimal values, as follows:
Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, …More can be learned about discrete and continuous variables at https://brainly.com/question/3130222
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Word Building For each item in this section, select the correct word parts from the bank below to form the term that matches the definition. Word parts may be used more than once. 63. Any disease of the adrenal gland 64. Pertaining to the body 65. Any disease of the thyroid gland 66. Tumor of the pancreatic islets 67. Activated by epinephrine 68. Pertaining to the pancreatic islets 69. Enlargement of the thyroid 70. Acting on the thyroid 71. Acting on the body 72. Acting on reproductive organs
Answers
63. "Adrenopathy" is the correct term for any disease of the adrenal gland.
64. Corporeal. 65. Thyropathy 66. Isletoma 67. Adrenergic 68. Islet-related 69. Goiter 70. Thyrotropic 71. Somatic 72. Gonadotropic
63. Adrenopathy: The correct word parts to form the term that describes any disease of the adrenal gland are "adreno-" and "-pathy." The prefix "adreno-" refers to the adrenal gland, and the suffix "-pathy" indicates a disease or disorder.
64. Corporeal: To describe something pertaining to the body, the correct word part is "corpor-" which means body. By adding the suffix "-eal" meaning pertaining to, we form the term "corporeal" which means relating to the body.
65. Thyropathy: When combining the word parts for a disease of the thyroid gland, we use "thyro-" to refer to the thyroid gland and "-pathy" to indicate a disease or disorder. Thus, "thyropathy" is the term that describes any disease of the thyroid gland.
66. Isletoma: A tumor of the pancreatic islets can be described using the word parts "islet-" referring to the pancreatic islets and "-oma" which signifies a tumor. Therefore, "isletoma" is the appropriate term for a tumor of the pancreatic islets.
67. Adrenergic: To indicate something that is activated by epinephrine, the correct word part is "adreno-" referring to the adrenal gland, and the suffix "-ergic" indicating activation or stimulation by a substance. Thus, "adrenergic" describes something that is activated by epinephrine.
68. Islet-related: The word part "islet-" refers to the pancreatic islets. To describe something pertaining to the pancreatic islets, we can use the suffix "-related." Therefore, "islet-related" is the correct term for something pertaining to the pancreatic islets.
69. Goiter: Enlargement of the thyroid is commonly referred to as a "goiter." In this case, the specific word parts from the bank are not used to form the term.
70. Thyrotropic: When we want to describe something that acts on the thyroid, the appropriate word parts are "thyro-" for the thyroid gland and the suffix "-tropic" indicating an agent that acts upon or influences something. Thus, "thyrotropic" is the correct term for something acting on the thyroid.
71. Somatic: To describe something that acts on the body, the word part "somato-" is used, which refers to the body. Therefore, "somatic" is the term that describes something acting on the body.
72. Gonadotropic: The word part "gonado-" is used to refer to the reproductive organs. When we want to describe something that acts on the reproductive organs, the suffix "-tropic" is used, indicating an agent that acts upon or influences something. Therefore, "gonadotropic" is the correct term for something acting on the reproductive organs.
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If we say we have statistically significant results, we mean the results are
Select one:
a. likely to be due to true differences between the groups.
b. likely to be due to chance differences between the groups.
c. meaningless.
d. very important.
Answers
the correct answer is a. likely to be due to true differences between the groups.
If we say we have statistically significant results, it means that the results are likely to be due to true differences between the groups. Statistical significance is a term used in hypothesis testing to determine if the observed differences between groups are likely to be real and not due to chance.
When conducting a statistical analysis, researchers compare the data from different groups or samples to see if there is a significant difference between them. This involves calculating a p-value, which represents the probability of obtaining the observed results if there were no true differences between the groups.
If the p-value is less than a predetermined threshold, typically 0.05, then the results are considered statistically significant. This means that the likelihood of obtaining the observed results by chance alone is very low, and it is more likely that the differences between the groups are due to a real effect.
For example, let's say we conduct a study to compare the effectiveness of two different treatments for a medical condition. If we find that the p-value is less than 0.05, we can conclude that there is a statistically significant difference between the treatments, and the observed improvement in one group is likely to be due to the treatment itself rather than random chance.
In summary, when we say we have statistically significant results, it means that the observed differences between groups are likely to be due to true differences rather than chance. This provides evidence for the presence of a real effect or relationship between the variables being studied.
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The sixth-grade class was asked the question, “What job would you like the best?” The results are shown in the table. What percent of the sixth-grade class said that they would like to be a movie director?
A) 23%
B) 31%
C) 41%
D) 45%
Answers
The percent of the sixth-grade class that said they would like to be a movie director is A. 23%.
How to calculate the percentage?It's important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the sixth-grade class was asked the question, “What job would you like the best and the results are shown in the table.
.
The. total number will be:
= 84 + 92 + 124 + 100
= 400
The percent of the sixth-grade class that said they would like to be a movie director will be:
= Movie director / Total number × 100
= 92/400 × 100
= 23%
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There are 4 squares and 20 triangles. What is the simplest ratio of squares to triangles?
Answers
‼️‼️‼️PLS HELP I WILL MARK U BRAINLIEST‼️‼️‼️
Which translation can be used to prove that figures two and three are congruent?
A) (x, y) —> (x, y - 4)
B) (x, y) —> (x - 3, y + 1)
C) (x, y) —> (x + 2, y)
D) (x, y) —> (x + 1, y - 3)
Answers
Answer: a I think
Step-by-step explanation:
300, 30,, 3, common difference
Answers
Answer:
a common difference is that they all have threes
A factory requires 9 machines to make a toy
every 24 minutes.
Find how many machines would be needed to
make a toy every 12 minutes.
machines
Answers
Answer:
18 machines
Step-by-step explanation:
9 machines give 24 mins... You need to reduce the time by half by adding using double the machines..
So 9×2=18
There are 75 kids at camp. After 21 kids go swimming, a counselor separated the remaining kids into 6 teams so that each team had k kids. In the tape diagram, k represents the number of kids that the counselor put into each of the 6 teams. What is the value of k?
Answers
6 * k = 54
Now, divide both sides by 6:
k = 54 / 6
k = 9
So, the value of k is 9. The counselor put 9 kids into each of the 6 teams.
please help, i dont know what to do this is my last option.
Answers
Answer:
GH
Step-by-step explanation:
Answer:
Bc=Gh since they correspond meaning same side equal
find the value of x.
Answers
Answer:
139 degrees
Step-by-step explanation:
we only have a central angle here (angle at the center of the circle).
and that angle remains the same along these 2 lines all the way out to the circle arc (and beyond, wherever these 2 lines take us).
so, if there is nothing missing in this graph, then x is the same as the inner angle : 139 degrees
write an equation of the line that passes through (-5,2) and is (a) parallel to and (b) perpendicular to y=2x-3.
Answers
Answer:
a) y = 2x + 12. b) y = -1/2 x -1/2.
Step-by-step explanation:
a) parallel to will have same gradient, ie gradient of 2.
y - y1 = m(x - x1)
y1 is y-coordinate of point, x1 is x-coordinate of point, m is gradient.
y - 2 = 2(x - -5) = 2 (x + 5) = 2x + 10
y = 2x +10 + 2
y = 2x + 12
b) gradient of perpendicular = -1/m = -1/2.
y - 2 = -1/2 (x - -5) = -1/2 (x + 5) = -1/2 x - 5/2
y = -1/2x -5/2 + 2
y = -1/2 x -1/2
33. DF bisects ZEDG. Find the value of x. The diagram is not to scale.
Answers
From the given diagram, we can identify two right-angled triangles. The triangles are shown below:
Using trigonometric ratios, we can find x as follows
\(\begin{gathered} \sin 28^0\text{ = }\frac{7x\text{ + 15}}{DF} \\ \sin 28^0\text{ = }\frac{10x}{DF} \end{gathered}\)We can equate the expressions for DF as follows:
\(\begin{gathered} DF\text{ = }\frac{7x\text{ + 15}}{\sin 28^0} \\ DF\text{ = }\frac{10x}{\sin 28^0} \end{gathered}\)\(\begin{gathered} \frac{7x\text{ + 15}}{\sin28^0}\text{ = }\frac{10x}{\sin 28^0} \\ \text{Cancelling out sin 28}^0 \\ 7x\text{ + 15 = 10x} \end{gathered}\)Solving for x:
\(\begin{gathered} 7x\text{ - 10x = -15} \\ -3x\text{ = -15} \\ \text{Divide both sides by -3} \\ \frac{-3x}{-3}\text{ = }\frac{-15}{-3} \\ x\text{ = 5} \end{gathered}\)Answer:
x = 5
Perform the calculation and report your results to the correct number of significant figures. (10.52)(0.6721)
(19.09−15.347)
Answers
The results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.
Performing the calculation:
(10.52)(0.6721) = 7.0671992
Rounding to the correct number of significant figures, we have:
(10.52)(0.6721) ≈ 7.07
Next, let's calculate (19.09 - 15.347):
(19.09 - 15.347) = 3.743
Rounding to the correct number of significant figures, we have:
(19.09 - 15.347) ≈ 3.74
Therefore, the results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.
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HELP ASAP Write an equation for a line that satisfies the given conditions which are through (9,5); slope 0
Answers
Answer:5=0+9
Step-by-step explanation:
Help plz i will make u a brainllest 24.Can you use the SSS Postulate or the SAS Postulate to prove abd=dca? 26 28
Answers
Answer: 24) C. SSS only
26) D. DH = HF
Step-by-step explanation:
24.
Statement Reason
1. BD = CA 1. Given
2. AB = CD 2. Given
3. AD = AD 3. Reflexive Property
4. ΔABD = ΔDCA 4. SSS Congruency Theorem
We have no information about the angles so cannot use SAS Theorem.
26. G H F
E H D
Line up the letters to find the congruent sides:
⇒ GH = EH
HF = HD
GF = ED
The number of miles, x, that a cross country athlete can run is represented by the inequality
x+3<15
What conclusion can be made about the number of miles?
Answers
Answer:
That the number of miles is going to be less than 15
Step-by-step explanation:
If you wanted to solve the inequality then the answer would be x<12
Can you please give me brainliest
A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary. A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is twotailed, separate the values with a comma. Round your answer to three decimal places. A bolt manufacturer is very concerned about the consistency with which his machines produce boits. The bolts should be 0.2 centimeters in diameter. The variance of the boits should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level?
Answers
To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).
Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.
Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.
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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).
Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.
Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.
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a circle in the coordinate plane passes through points (-3,-2) and (1,4). what is the smallest possible area of that circle?
Answers
The smallest possible area of the circle with the points (-3,-2) and (1,4) is 13π.
Given, the endpoints of the circle are given:
(-3,-2) = (x₁,y₁)
(1,4) = (x₂,y₂)
The circle with the smallest possible area that passes through the points (-3, -2) and (1, 4) is a circle with a diameter whose endpoints are these two points.
we are asked to determine the area of the circle = ?
first calculate the distance between the points:
distance = √(x₁-x₂)²+(y₁-y₂)²
d = √(-3-1)²+(-2-4)²
d = √(-4)² + (-6)²
d = √16+36
d = √52
d = 2√13
Thus, the radius has a length of r = √13,
and the area of the circle is A = π x (√13)²
= 13π.
Hence we get the area of the circle as 13π..
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Find the x plz help
Answers
Answer:
x=50
Step-by-step explanation:
To find the angle on the bottom left you would subtract 180-149 and get 31.
Then you would add 31 and 99 to get 130.
Then subtract 180-130 to get x=50 because all triangles equal 180 if you add all of the angles together.
Find the surface area of the figure. Hint: the surface area from the missing prism inside the prism must be ADDED!
Answers
To find the surface area of the figure, we need to consider the individual surfaces and add them together.
First, let's identify the surfaces of the figure:
The lateral surface area of the larger prism (excluding the base)
The two bases of the larger prism
The lateral surface area of the smaller prism (excluding the base)
The two bases of the smaller prism
The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.
The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.
To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.
Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.
Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.
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Please help, Find the perimeter of the figure to the nearest hundredth
Answers
Answer:
28.56 inches
Step-by-step explanation:
you need to find the circumference of a circle with a diameter of 4, ∴ radius is 2
C = 2πr
C = 4(3.14)
C = 12.56
Now add 12.56 to the two sides that are 6 inches and also add the four 1 inch segments to the right and left of each semi-circle.
12.56 + 2(6) + 1(4) = 12.56 + 12 + 4 which totals 28.56
Write an equation of the line that passes through the point (5, -8) with slope 5
Answers
\(\Large\texttt{Answer}\)
\(equation=\)\(\bold{y=5x-33}\)
\(\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}\)
\(\Large\texttt{Process}\)
⇨ Use the formula below
\(\bf{y-\hfill\stackrel{y \:co-ordinate}{y1}=\hfill\stackrel{slope}{m}(x-\hfill\stackrel{x\:co-ordinate}{x1)}}\)
⇨ Substitute the parameters:
\(\bold{y-(-8)=5(x-5)}\)
\(\bold{y+8=5x-25}\)
\(\bold{y=5x-33}\)
Hope that helped
Consider a Markov chain which at each transition either goes up 1 with probability p or down 1 with probability q = 1 - p. Argue that (q/p)^Sn , n >= 1 is a martingale.
Answers
The (q/p)^Sn, n>=1 is a martingale.
To show that (q/p)^Sn, n>=1 is a martingale, we need to show that it satisfies the three conditions of a martingale:
The expected value of (q/p)^Sn is finite for all n.
For all n, E[(q/p)^Sn+1 | Fn] = (q/p)^Sn, where Fn is the sigma-algebra generated by the first n transitions.
(q/p)^Sn is adapted to the filtration Fn.
First, we note that the expected value of (q/p)^Sn is finite for all n since q/p < 1, and thus (q/p)^n approaches zero as n approaches infinity.
Next, we consider the second condition. Let F_n be the sigma-algebra generated by the first n transitions, and let X_n = (q/p)^Sn. We need to show that E[X_n+1 | F_n] = X_n.
We can write (q/p)^(n+1) = (q/p)^n * (q/p), so we have:
E[X_n+1 | F_n] = E[(q/p)^(n+1) | F_n]
= E[(q/p)^n * (q/p) | F_n]
= (q/p)^n * E[(q/p) | F_n]
= (q/p)^n * [(q/p) * P(up) + (p/q) * P(down)]
= (q/p)^n * [(q/p) * p + (p/q) * q]
= (q/p)^n * (p + q)
= (q/p)^n * 1
= X_n
Thus, the second condition is satisfied.
Finally, we need to show that X_n is adapted to the filtration F_n. This is true since X_n only depends on the first n transitions, which are included in F_n.
Therefore, we have shown that (q/p)^Sn, n>=1 is a martingale.
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| n | = 3.5 what value for n will make this expression true
This is the I Ready diagnostics.please help me this is due very very soon! Thanks!!
Answers
Answer:
3.5 and -3.5
Step-by-step explanation:
absolute value is the distance from zero to that number so 3.5 and -3.5 should be correct.
Answer:3.5 and -3.5
Step-by-step explanation:
n has absolute value marks, so whatever n is is positive. 3.5 and |-3.5| =3.5
What is the equation of this line?
Answers
y=2x+0 is the slope for this line
Answer:
k = 2
1x = 2y
x = 2y