Which statement describes ?
The series diverges because it has a sum of 4.
The series converges because it has a sum of 4.
The series diverges because it does not have a sum.
The series converges because it does not have a sum.
Answer: B
The series converges because it has a sum of 4.
Step-by-step explanation:
The convergence or divergence of a series depends on the sum of the series and its common ratio. The series converges because its sum is b
The series is given as:
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n[/tex]
A geometric series is given as:
[tex]T_n = ar^{n-1}[/tex]
So, we rewrite the series as follows:
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n[/tex]
Apply law of indices
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^{n-1} \times (\frac{2}{3})[/tex]
Rewrite
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} 2 \times (\frac{2}{3})(\frac{2}{3})^{n-1}[/tex]
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} \frac{4}{3}(\frac{2}{3})^{n-1}[/tex]
So, we have:
[tex]T_n = \frac{4}{3}(\frac{2}{3})^{n-1}[/tex]
Compare the above series to: [tex]T_n = ar^{n-1}[/tex]
[tex]a = \frac{4}{3}[/tex]
[tex]r = \frac{2}{3}[/tex]
The sum of the series to infinity is:
[tex]S_{\infty} = \frac{a}{1 - r}[/tex]
So:
[tex]S_{\infty} = \frac{4/3}{1 - 2/3}[/tex]
[tex]S_{\infty} = \frac{4/3}{1/3}[/tex]
[tex]S_{\infty} = 4[/tex]
i.e. [tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = 4[/tex]
Also:
The common ratio (r)
[tex]r = \frac{2}{3}[/tex]
[tex]r = \frac{2}{3}[/tex] [tex]< 1[/tex]
When common ratio is less than 1, then such series is convergent.
Hence, (b) is true because it has a sum of 4
Read more about series at:
https://brainly.com/question/10813422
2.
Find the value of x.
110°
(x + 30)
po
In how many ways can 5 different novels, 4 different mathematics books, and 1 biology book be arranged on a bookshelf if: (a) The books can be arranged in any order? Your answer is: 3628800 (b) The mathematics books must be together and the novels must be together? Your answer is : 6 (c) The mathematics books must be together but the other books can be arranged in any order? Your answer is: 5040
Answer:
(a) 3628800 ways
(b) 17280 ways
(c) 120960 ways
Step-by-step explanation:
Given
[tex]Novels = 5[/tex]
[tex]Maths = 4[/tex]
[tex]Biology = 1[/tex]
[tex]Total = 10[/tex]
Solving (a): Arrangement with no restriction.
We simply count each book with no restriction. i.e. 10 books
So, the number of arrangement is:
[tex]Arrangement =10![/tex]
[tex]Arrangement =10*9*8*7*6*5*4*3*2*1[/tex]
[tex]Arrangement =3628800[/tex]
Solving (b): Maths book together and Novels together
First, arrange the 4 maths books as:
[tex]Maths = 4![/tex]
Next, arrange the 5 novels as:
[tex]Novels = 5![/tex]
Lastly, take the 4 maths book as [1], the 5 novels as [1] and the remaining [1] biology book.
So, we have: 3 books
Arrange 3 books, we have:
[tex]Books = 3![/tex]
Total arrangement is:
[tex]Total = 4! * 5! * 3![/tex]
[tex]Total = 4*3*2*1 * 5*4*3*2*1 * 3*2*1[/tex]
[tex]Total = 17280[/tex]
Solving (c): Maths book together
First, arrange the 4 maths books as:
[tex]Maths = 4![/tex]
Next, take the 4 maths book as [1], then the remaining 6 books (i.e. 5 novels and 1 biology)
So, we have: 7 books
Arrange 7 books, we have:
[tex]Books = 7![/tex]
Total arrangement is:
[tex]Total = 4! * 7![/tex]
[tex]Total = 4*3*2*1 * 7*6*5*4*3*2*1[/tex]
[tex]Total = 120960[/tex]
Plz help this is due today i would have done it myself but i totally forgot about these so PLZ HELP AND NO LINKS AND NO GROSS PICTURES OR I REPORT
Answer: That is right
Step-by-step explanation:
Answer:
b) triangle, not regularStep-by-step explanation:
This appears to be a scalene triangle. Therefore, it is a triangle, not regular. This is because scalene triangles have measures that are different on all sides and angles. Therefore, it is irregular.
find the cost of fencing a rectangular field 250m long and 130m wide at rupees 30 per meter
Answer:
(250+250+130+130)*30=22,800
CAN SOMEONE PLS DO TBJS U HAVE TO SHOW WORK BUT ITS EASG AND DOESNT NEED TO BE PERFECTT
Answer:
area? is that what u need? or perimeter
Step-by-step explanation:
What 2+2? I forgot :( points hehe
Answer:
4
Step-by-step explanation:
2+2=4
Find the volume.
pls help!
Answer:
(8*6*8)÷2=192ft^3
Step-by-step explanation:
find the volume like you would a rectangular cube and then devide it in half. so L*H*W/2
Which one of the figures is the Pre-Image? Please help me no links!
Answer:
the one in black
Step-by-step explanation:
on an air Indian flight there are 9 boys 5 indian children, 9 men, 7 foreign boys 14 indians, 6 indian male and 7 foreign female. What is the number of people on board the plane.
Answer:
Is it 57?
Step-by-step explanation:
helpppppppppppppppppp
what statement is not true about the absolute value of 6
Answer:
I can't answer this sorry dude and next time show us the picture so that we can understand
Solve for x
Can someone please help??I've been stuck on this for far to long
Answer:
x = 7
Step-by-step explanation:
We need to find the value of x in the given figure. It can be calculated using ratio.
We know that,
4+3 = 7
Taking ratios,
[tex]\dfrac{7}{3}=\dfrac{14}{x-1}[/tex]
or
[tex]\dfrac{1}{3}=\dfrac{2}{x-1}\\\\x-1=6\\\\x=6+1\\\\x=7[/tex]
So, the value of x is equal to 7.
The length of the rectangle is six times it’s width. If the perimeter is 84yd find the length and width
Answer:
W = 6
L = 36
Step-by-step explanation:
2L + 2W = 84
L = 6W
Substitute for L in the first equation
2 (6W) + 2W = 84
12W + 2W = 84
14W = 84
W = 6
Substitute W in the first equation
2L + 2(6) = 84
2L + 12 = 84
2L = 72
L = 36
Plug both values in both equations to be sure
2(36) + 2(6) = 84
36 = 6 * 6
Hope that helps!
Help please asap will mark brainliest !
Answer:
b = 29
Step-by-step explanation:
C x D = A x B
15(11x - 91) = 7(2x + 10)
165x - 1365 = 14x + 70
add 1365 to both sides of the equation:
165x = 14x + 1435
subtract 14x from both sides:
151x = 1435
divide both sides by 151:
x = 9.5
b = 2(9.5) + 10 = 29
34 in. 14 in. What is the area of the triangle?
3) A Diplodocus was a 90 ft. long plant-eating dinosaur. The Triceratops was 28 ft. long plant- eating dinsoaur. How many INCHES longer was the Diplodocus than the Triceratops?
Answer:
The Diplodocus was 744 in longer than the Triceratops.
Step-by-step explanation:
90 ft = 90 * 12 = 1080 in
28 ft = 28 * 12 = 336
1080 in - 336 in = 744 in
The area between z = 1.74 and z = 1.25
Round your answer to three decimal places.
Answer:
The area between z = 1.74 and z = 1.25 is of 0.065.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The area between two values of Z is given by the subtraction of the pvalue of the larger value by the smaller.
The area between z = 1.74 and z = 1.25.
This is the pvalue of z = 1.74 subtracted by the pvalue of z = 1.25.
z = 1.74 has a pvalue of 0.959
z = 1.25 has a pvalue of 0.894
0.959 - 0.894 = 0.065
The area between z = 1.74 and z = 1.25 is of 0.065.
The coordinates of a rectangle, LMNO, are L(- 1,3), M(2,3), N(2, - 5), and 0(- 1,- 5).
a. What is the length and width of this rectangle?
b. What is the perimeter of the rectangle?
c. What is the area of the rectangle?
Answer:
length = 8; width = 3
perimeter = 22
area = 24
Step-by-step explanation:
L(- 1,3), M(2,3)
LM = |-1 - 2| = 3
M(2,3), N(2, - 5)
MN = |-5 - 3| = 8
length = 8; width = 3
perimeter = 2(L + W) = 2(8 + 3) = 22
area = LW = 8 × 3 = 24
A national study, that revealed a normal distribution, revealed that the average time a student spends studying statistics on a weekend is 60 minutes. A random sample of 11 students in BU 203 were asked to record their statistic study time over a weekend. The sample revealed an average study time of 44.27 minutes with a standard deviation of 20.4. With an alpha of 5% State the null hypothesis (H0) and the alternate hypothesis (H1). Draw the distribution.
Answer:
Null hypothesis = H0 : μ = 60
Alternative hypothesis = H1 : μ < 60
Step-by-step explanation:
From the question given :
μ = 60 minutes
xbar = 44.27 minutes
s = 20.4 minutes
The alternative hypothesis is the claim ; which is to hypothesize that the average studying time is 44.27 (which is less than the population average studying time)
The null hypothesis is the initial truth and it is the opposite of the alternative hypothesis.
The hypothesis are :
H0 : μ = 60
H1 : μ < 60
#11-14 Answers are on the side
Please help, I will give brainliest. No links please.
A projectile is shot into the air. The altitude of the projectile after t seconds is modled by the function graphed. Time t is measured in secinds and altitude h(t) is measured in feet.
Which of these statements are true?
A) The projectile reaches a maximum altitude of 12 feet.
B) The projectile reaches its maximum altitude after 12 seconds of flight.
C) The projectile is launched from the ground.
D) The altitude of the projectile is increasing on the interval 5<t<20
Answer:
B is the true statement
Step-by-step explanation:
A
We can see from the graph that the highest point occurs when the height in feet is 19.4, so statement A is untrue.
B
We can see from the graph that the highest point occurs after 12 seconds of flight, so statement B is true.
C
If the projectile were launched from the ground, when t=0, h=0, but since when t=0, h=5, we can see it was launched 5ft from the ground, so statement C is untrue.
D
On the interval 5<t<12, the altitude is indeed increasing, but after t=12, the projectile begins to fall and the altitude decreases, so statement D is untrue.
Which of the four Venn diagrams represents this?
Answer:
I would day option B does
Answer:
A is the correct answer
Step-by-step explanation:
debe tomar 4 fotos de una carrera. Cada vez que un corredor pasa a su lado, hay un 50% de probabilidad de que tome una foto de ese corredor. Además, para dos corredores cualesquiera, la probabilidad de que tome una foto de uno es independiente del otro. Una vez que obtenga 4 fotos, abandonará las instalaciones de la carrera y no intentará tomar más fotos. Si eres el sexto corredor en pasar al fotógrafo, entonces la probabilidad de que te tome una foto puede expresarse en la forma M / NM / N, donde MM y NN son números enteros positivos relativamente primos (es decir, su máximo común divisor es 1 ). Calcule M + NM + N.
Answer:
Ehhh waht ??im 10 jears old!
Step-by-step explanation:
Hahah
THERE IS A BATTLE BETWEEN THE TWO REPLIES DOWN BELOW! WHO WILL GET THE MOST LIKES?
Answer: Ok Good luck other contestant.
2/5÷1 7/8
how do I divide it
Answer:
0.21333333333 or 2 21/40
Step-by-step explanation:
2/5+17/8
=2/5*8/8+17/8*5/5
=16/40+85/40
=16+85/40
=101/40= 2 21/40
you can also use this link for any other problems like this
https://www.calculator.net/fraction-calculator.html?t1=2&op=%2B&t2=17&b1=5&b2=8&ctype=1&x=100&y=24
Express 1 min as a repeating decimal part of an hour.
A high school administrator is interested in determining the relationship between high school students' final grades in geometry and chemistry. She randomly samples 400 students who took both classes and records their final scores (out of 100 points) and carries out a simple linear regression, using the geometry grade as the response variable and the chemistry grade as the explanatory variable, since the students take chemistry before geometry. The resulting data was used to produce the following output.
Simple linear regression results:
Dependent Variable: Geometry
Independent Variable: Chemistry
Geometry = 3.6276926 + 0.91857341*Chemistry
Sample size: 400
R2= 0.55808158
Estimate of error standard deviation: 9.417521
Which of the following is a reasonable interpretation of the slope of this simple linear regression?
a. The slope of this regression cannot be interpreted because 0 is not in the range of chemistry scores.
b. Getting high grades in chemistry lead students to achieve high grades in geometry.
c. On average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score.
d. On average, a 1 percentage point difference in geometry score is associated with a 0.919 percentage point difference in chemistry score.
Answer: c. On average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score
Step-by-step explanation:
Given that:
Slope value = 0.91857341
The dependent and independent variables are ;
Dependent Variable: Geometry
Independent Variable: Chemistry
Slope is the rate of change in the dependent variable per unit change in the independent variable.
Hence, from the information given, we can conclude that for every 1% change in chemistry score (independent variable), there is a corresponding approximately 0.919% change in geometry score (dependent variable).
From the given data it can be concluded that on average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score. Hence option c) is correct.
Given :
She randomly samples 400 students who took both classes and records their final scores (out of 100 points). She carries out a simple linear regression, using the geometry grade as the response variable and the chemistry grade as the explanatory variable since the students take chemistry before geometry.Given the simple linear regression results that are:
The Dependent variable is Geometry.
The Independent variable is Chemistry.
Geometry = 3.6276926+0.91857341[tex]\times[/tex]Chemistry
Comparing the above equation with the slope-intercept form which is given by:
y = mx + c
Therefore, slope, m = 0.91857341.
It is also given that:
Sample size is 400
R2= 0.55808158
Estimate of error standard deviation: 9.417521
From the given data it can be concluded that on average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score. Hence option c) is correct.
For more information, refer to the link given below:
https://brainly.com/question/12402189
5,8, 21, 17, 10, 11,5
What is the median of the set of numbers?
Answer:
10
Step-by-step explanation:
Rearrange in order, 5, 5, 8, 10, 11, 17, 21 and the median would be 10.
PLEASE HELP ME PLEASE MAX POINTS
https://brainly.com/question/23269912
answer my other question, please! ^^
Answer:
I did the first one
Step-by-step explanation:
Hope I did it right