Answers
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Related Questions
Given that (-8,-6) is on the graph of f(x), find
the corresponding point for the function
f(x) - 3
Answers
Answer:-8,-9
Step-by-step explanation:
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Answers
Answer:
;)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
Step-by-step explanation:
yes yes do the ;))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
This table gives a few (x, y) pairs of a line in the coordinate plane. What is the x-intercept of the line?
Answers
Answer:
x=-14
Step-by-step explanation:
The x-intercept of a line is the value of x that makes y=0.
A line can be expressed in its slope-intercept form:
y=mx+b
Once determined the equation of the line, the x-intercept can be calculated by setting y=0 and solving for x.
Let's find the slope of the line.
Suppose we know the line passes through two points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's pick the first two points of the table (-94,24) (-74,18). The slope is:
[tex]\displaystyle m=\frac{18-24}{-74+94}=\frac{-6}{20}=-\frac{3}{10}[/tex]
The equation of the line is:
[tex]\displaystyle y=-\frac{3}{10}x+b[/tex]
Now use one of the points to find b, for example (-94,24):
[tex]\displaystyle 24=-\frac{3}{10}\cdot (-94)+b[/tex]
Operating:
[tex]\displaystyle 24=\frac{141}{5}+b[/tex]
Solving:
[tex]b=24-\frac{141}{5}=-\frac{21}{5}[/tex]
The complete equation of the line is:
[tex]\displaystyle y=-\frac{3}{10}x-\frac{21}{5}[/tex]
To find the x-incercept, set y=0 and solve:
[tex]\displaystyle 0=-\frac{3}{10}x-\frac{21}{5}[/tex]
[tex]\displaystyle x=\frac{\frac{21}{5}}{-\frac{3}{10}}=-\frac{21}{5}\cdot \frac{10}{3}[/tex]
x=-14
what percenr of 60 is 15
Answers
Answer:
9%
Step-by-step explanation:15% of 60 is 9%
Answer:
25%
Step-by-step explanation:
4. What is the slope of the line that contains the points (-6,1) and (4,-4)? A. 2 B. -2 C. 1 2 a 1 D. 2
Answers
Answer:
It would be -[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Use the slope formula to find the slope m.
Part D
If Tristan attaches a 4-kilogram weight to the spring, how far will it stretch?
Answers
Answer:
x = 4 into the equation y = 3x, or locate the answer on the graph: y = 3x = 3(4) = 12.
The spring stretches 12 inches with a 4-kilogram weight attached to it.
Step-by-step explanation: so its 12
Substitute x = 4 into the equation y = 3x, or locate the answer on the graph: y = 3x = 3(4) = 12.
The spring stretches 12 inches with a 4-kilogram weight attached to it.
What is the solution set for - 4x + 10 = 5(x + 11)? HELPPPPPPP
Answers
Answer:
-5
Step-by-step explanation:
-4x +10 =5(x +11)
-4x +10 =5x +55
-4x - 5x =55 - 10
-9x =45
x=-45 :9
x=-5
. Steve drove for 812 hours at 72 miles per hour. How much distance did he travel?
Answers
Answer:
58464
Step-by-step explanation:
Multiply the two numbers
Answer:
If Steve drives for 812 hours at 72 miles per hour, he drives 58,464 miles in total.(Side Note: if you mean 8 1/2 hours then it's 612 miles
Step-by-step explanation:
To find distance dealing with time and speed, we can use the formula d=rt.
D= Distance
R= Speed
T= Time
Now we plug in our values! D=72 × 812 and we get D= 58,464 miles or if you meant 8 1/2 hours, then it's 612 miles
Hope this helps! :)
How many times larger is the value of 370,000 than 370
Answers
Answer:
1000 is the answer that you are looking for
hope this helps\
How can you describe two numbers that add to zero?
Answers
Answer:
I think it its 0 its called the additive identity because when you add it to a number, the result you get is the same number.
Step-by-step explanation:
For example, 5 + 0 = 5 Any two numbers whose sum is zero, such as 3 and -4, because 3 + (-3) = 0.
Round the numbers to estimate the quotient.
29 1/5 divided by 4 6/7
Which numbers should be used?
____divided by____
The estimated quotient is:
Answers
Answer:
29.2 divided by 4.9 = 6.0
Step-by-step explanation:
29.2 divided by 4.9 = 5.95918367
5.95918367 → 6.0
Key:
→ = rounded to the nearest tenth
Answer:
29 ÷ 5 the estimated quotient is 5 4/5
Step-by-step explanation:
I took the test (;
Determine whether each equation represents a proportional relationship.
y = 3 + x
Proportional Relationship
Not a Proportional Relationship
y = 1.6%
y = 3/(4x)
y = x
y = 12x
y = 2x + 1
Answers
Answer:
Proportional Relationship: I Not a Proportional Relationship:
y=1.6x I y=3/(4x)
y=x I y=2x+1
y=12x . I y=3+x
Explanation:
I took the test and that's how i got these answers.
last question below, or select another question
For a Saturday matinee, adult tickets cost $8.50 and kids under 12 pay only $7.00. If 80 tickets are sold for a total
of $605, how many of the tickets were adult tickets and how many were sold to kids under 12?
Answers
Answer:
30 adult tickets and 50 child tickets
Step-by-step explanation:
605 = 8.5a + 7c
80 = a + c
620 = (8.5*40) + (7*40)
605 = (8.5*30) + (7*50)
a = 30 c = 50
help? z=m/x solve for x
Answers
Answer:
x=m/z
Step-by-step explanation:
How many pounds of a 15% copper alloy must be mixed with 700lb of a 30% copper alloy to maybe a 25.5% copper alloy
Answers
Answer:
[tex]300\; \rm lb[/tex].
Step-by-step explanation:
Let [tex]x[/tex] represent the mass (in pounds) of that [tex]15\%[/tex] copper alloy required, such that the final mixture would contain [tex]25.5\%[/tex] copper by mass.
Consider: if [tex]x[/tex] pounds of that [tex]15\%[/tex] copper alloy is mixed with [tex]700[/tex] pounds that [tex]30\%[/tex] copper alloy, what would be the mass of copper in the mixture?
Mass of copper in [tex]x[/tex] pounds of that [tex]15\%[/tex] copper alloy: [tex](0.15\, x)\; \rm lb[/tex].Mass of copper in [tex]700[/tex] pounds of that [tex]30\%[/tex] copper alloy: [tex]700 \times 0.30 = 210\; \rm lb[/tex].Therefore, the mixture would contain [tex](210 + 0.15\, x) \; \rm lb[/tex] of copper.
The mass of that mixture would be [tex](700 + x)\; \rm lb[/tex]. The mass fraction of copper in that mixture would be:
[tex]\displaystyle \frac{(210 + 0.15\, x)\; \rm lb}{(700 + x)\; \rm lb} \times 100\%[/tex].
This ratio is supposed to be equal to [tex]25.5\%[/tex]. These two pieces of equations combine to give an equation about [tex]x[/tex]:
[tex]\displaystyle \frac{(210 + 0.15\, x)\; \rm lb}{(700 + x)\; \rm lb} \times 100\% = 25.5\%[/tex].
[tex]\displaystyle \frac{210 + 0.15\, x}{700 + x} = 0.255[/tex].
Simplify and solve for [tex]x[/tex]:
[tex]210 + 0.15\, x= 0.255\, (700 + x)[/tex].
[tex](0.255 - 0.15)\, x= 210 - 0.255 \times 700[/tex].
[tex]\displaystyle x = \frac{210 - 0.255 \times 700}{0.255 - 0.15} = 300[/tex].
Therefore, [tex]300\; \rm lb[/tex] of that [tex]15\%[/tex] alloy would be required.
Two numbers add up to 64. One of the numbers is 24. What is the other number?
Answers
Answer:
40
Step-by-step explanation:
If there are two numbers and you're trying to find the other one, you can subtract 64 and 24, you would get 40
Check; 40 + 24 = 64
find the perimeter of the figure below composed of a rectangle and a semi circle round to the nearest tenths place
Answers
Given parameters:
We have two shapes, the rectangle and semi circle;
The problem is to find the perimeter of the shape given
The perimeter of a body is the total length of the body.
Here, it is the sum of the perimeter of the rectangle and semi-circle.
Note, to remove repetition, we to deduct 6 which is a common point to both of them.
Perimeter of a semi-circle = Circumference of semi- circle
= πr² x [tex]\frac{1}{2}[/tex]
The diameter here is 6 and radius is 3;
Circumference of semi-circle = π x 3² x [tex]\frac{1}{2}[/tex] = 14.14
Perimeter of rectangle = 2(6+8) = 28
The perimeter of the figure = 14.14 + 28 - 6 = 36.1
The perimeter of the figure is 36.1
find standard deviation, o, for the binomial distribution which has the stated values of n and p. round your answer to the nearest hundredth. n =503: p=0.7
Answers
Answer:
Step-by-step explanation:
N=503
P=0.7
Sqrt(503×0.7(1-0.7))=10.28
The standard deviation, for the binomial distribution, is 10.28 which has the stated values of n and p; n =503: p=0.7.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much the data is spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
We have:
The value of n = 503
The value of p = 0.7
For the binomial distribution:
As we know,
The formula for the standard deviation:
σ = √[p(1 - p)n]
Plug the values of p, and n, we get:
σ = √[0.7(1 - 0.7)503]
σ = √[0.7(0.3)503]
σ = √[0.21x503]
σ = √[105.63]
σ = 10.277 ≈ 10.28
Thus, the standard deviation, for the binomial distribution is 10.28 which has the stated values of n and p; n =503: p=0.7.
Learn more about the standard deviation here:
brainly.com/question/12402189
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What value of x makes the following equation true?
4 + 3x = 106
Answers
Answer:
34
Step-by-step explanation:
Step 1:
4 + 3x = 106 Equation
Step 2:
3x = 102 Subtract 4 on both sides
Step 3:
x = 102 ÷ 3 Divide
Answer:
x = 34
Hope This Helps :)
Solve for b. 4b-3b+7= 10
Answers
b = 3
Step-by-step explanation:
[tex]4b - 3b + 7 = 10[/tex]
Add similar terms :
[tex]4b - 3b = b \\ b + 7 = 10[/tex]
Collect like terms and simplify
[tex]b = 10 - 7 \\ b = 3[/tex]
Answer:
b=3 if i did it correctly. i apologize if it's wrong.
1. Diego earns $10 per hour babysitting. Assume that he has no money saved
before he starts babysitting and plans to save all of his earnings. Graph how
much money, y, he has after x hours of babysitting
Step 1:
Step 2
Step 3:
Answers
The required expression for the Digo earning is y = 10x and the graph of the expression is shown.
Given that,
Diego earns $10 per hour babysitting. Assume that he has no money saved
before he starts babysitting and plans to save all of his earnings.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Let the hours of babysitting be x,
According to the question,
Hourly rate is $10 for x hour the total charge is,
y = 10x
Thus, the required expression for the Digo earning is y = 10x and the graph of the expression is shown.
learn more about function here:
brainly.com/question/21145944
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Solve.
(4b^2 + 4)12b^2 - 5)
Answers
Can you conclude with a high degree of confidence that the population means for Iowa and New Jersey students are different? A. Because of the extremely low p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are not different. B. Because of the extremely high p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are different. C. Because of the extremely low p-value, we can reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are different. D. Because of the extremely high p-value, we cannot reject the null hypothesis with a very high degree of confidence. Hence, the population means for Iowa and New Jersey students are not different.
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
Option A is correct
Step-by-step explanation:
From the question we are told that
The 95% confidence interval of the mean score of all New Jersey third graders is (58.957 , 63.043)
The sample size is n = 184
The sample average is [tex]\mu = 65 \ points[/tex]
The standard deviation is [tex]\sigma = 13 \ points[/tex]
The 90% confidence interval for the difference in mean score between lowa and New Jersey is (-6.33 , -1.67 )
The p-value is [tex]p-value = 0.0048[/tex]
Generally given that the p-values is very low compared to the level of significance (100 -90 = 10% = 0.10 ) we can reject the null hypothesis which is usually a claim that the means of the population are the same )
Hence the population means are different .
how many centiliters are in 3 quarts?
Answers
Answer:
283-284
The real answer is like 283.906
Tia types 66 words in 3 minutes. She wants to know how many words she can type in 5 and 10 minutes if she keeps the same rate. How many words does Tia type in 1 minute? Find the unit rate.
Answers
Answer:
Step-by-step explanation:
she can type 22 words in 1 minute and it takes her .045 seconds to type 1 word
she can type 110 words in 5 minutes and 220 words in 10 minutes.
in 5 minutes she would type 110 words
in 10 minutes she would type 220 words.
1x2x3x4x5 will make brainliest
Answers
Answer:
120
Step-by-step explanation:
I wrote down the equation on paper and solved it
The product of the given numbers is 120.
The given expression is 1×2×3×4×5.
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
Here, 1×2×3×4×5 = 120
Therefore, the product of the given numbers is 120.
Learn more about the multiplication here:
https://brainly.com/question/1562995.
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The school store sells pencils at 24 for $3.00. Compute both unit rates and explain what each means.
Answers
Answer:
For $1.00 you can get 8 pencils
Step-by-step explanation: 24/3= 8
Can you give me Brainliest?
3 divided by 3 =1
So for $1 you can buys 8 pencils
Write the slope intercept form of the equation of the line through the given point with the given slope.
1) through: (3,4), slope = 2
2) through: (5,-5), slope=-6/5
Answers
Answer:
1) y = 2x-2
2) y = -6/5+1
Step-by-step explanation:
Which ratio is equivalent to 3:7?
A 6:7
B 3:21
C 24:56
D 15:30
Answers
Answer:
c
Step-by-step explanation:
Answer:
C. 24:56
Step-by-step explanation:
3/7 * 8/8
3*8 = 24
7*8 = 56
24/56
Hello! Please help with this fill in the blank, thanks!
Answers
Triangle ABC is rotated 180 degrees around point E, therefore, A maps to D, B maps to C, and C maps to B.
===================================================
Explanation:
If you were to rotate triangle ABC 180 degrees around point E, then it would line up perfectly with triangle DCB
Point A lands on point DPoint B lands on point CPoint C lands on point BNote how in the sequence ABC we have A first, B second, then C third
Then for the sequence DCB we have D first, C second, then B third
This order matters so we can pair up the points properly
A goes to D (A is first of ABC; D is first of DCB)B goes to C (B is second in ABC; C is second in DCB)C goes to B (C is third in ABC; B is third in DCB)