Answer:
c
Step-by-step explanation:
i just took a test on it
The sequence converges to 0.
What is geometric sequence?"It is a type of sequence where the ratio of every two consecutive terms is a constant."
Formula to find the nth term of geometric sequence:"[tex]a_n=a_1\times r^{n-1}[/tex]
where [tex]a_1[/tex] is the first term, and r is the common ratio."
What is the convergent sequence?"If [tex]\lim_{n \to \infty} a_n[/tex] exists and is finite we say that the sequence is convergent.
where [tex]a_n[/tex] is the n-th term of the sequence."
What is the divergent sequence?" If [tex]\lim_{n \to \infty} a_n[/tex]doesn't exist or is infinite we say the sequence diverges.
where [tex]a_n[/tex] is the n-th term of the sequence."
For given question,
We have been given a sequence.
36, - 6, 1, - , . . .
The first term of the sequence is [tex]a_1=36[/tex]
[tex]\frac{-6}{36}=-\frac{1}{6}\\\\ \frac{1}{-6}=-\frac{1}{6}[/tex]
The ratio of every two consecutive terms is a constant.
⇒ [tex]r=-\frac{1}{6}[/tex]
So, the n-th term of given geometric sequence would be,
[tex]a_n=36\times (-\frac{1}{6})^{n-1}[/tex]
Now we determine whether the sequence is convergent or divergent.
[tex]\lim_{n \to \infty} a_n \\\\= \lim_{n \to \infty}36\times (-\frac{1}{6} )^{n-1}\\\\=36\times \lim_{n \to \infty} (-\frac{1}{6} )^{n-1}\\\\=36\times 0\\\\=0[/tex]
Since [tex]\lim_{n \to \infty} a_n[/tex] exists and is finite we say that the sequence is convergent.
Therefore, the sequence converges to 0.
Learn more about the convergent sequence here:
https://brainly.com/question/21961097
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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 2.13 and 2.99
Answer:
Approximately 68% of the students have grade point averages that are between 2.13 and 2.99.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this question, we have that:
Mean = 2.56
Standard deviation = 0.43
What percentage of the students have grade point averages that are between 2.13 and 2.99?
2.56 - 0.43 = 2.13
2.56 + 0.43 = 2.99
Within one standard deviation of the mean, so, by the Empirical Rule:
Approximately 68% of the students have grade point averages that are between 2.13 and 2.99.
Please help and will give brainliest
9514 1404 393
Answer:
12 m³
Step-by-step explanation:
The bottom platform has dimensions 2m × 4m × 3m, so a volume of ...
V = LWH
V = (2 m)(4 m)(3 m) = 24 m³
The top platform has dimensions 2m × 3m × 2m, so a volume of ...
V = (2 m)(3 m)(2 m) = 12 m³
The bottom platform has a larger volume by ...
24 m³ -12 m³ = 12 m³
The bottom prism has a 12 m³ larger volume.
Answer:
the answer is 12m squared
Select two ways you could display bivariate data.
1.Table
2.Map
3.Notation
4.Graph
help me FAST :> math problem 15 points come on please
Answer:
D
Step-by-step explanation:
z+nm is equiveland to mn+z since its the same equation but wrote in different positions.
Answer: the answer is D
Z + nm
The table shows the number of sodas left in the vending machine after each hour.
Time in Hours
0
1
2
3
Number of Sodas 310 290 270 250
If the pattern stays the same, which expression gives the number of sodas left after t hours?
A. 250 - 200
B. 290 - 200
C. 310 - 20t
D. 330 - 200
Answer: A
Step-by-step explanation: -20
2x - 3
L
M
x + 4
X =
?
Answer: 7
Step-by-step explanation:
2x - 3 = x + 4
2x - x - 3 = 4 Mius x from the both side
x - 3 = 4
x = 7 Add the 3 from both side
4x+3y=16
y=x+3
X=
Y=
__________________________
4x + 3y = 16
x = -3 / 4 y + 4
y = -4 / 3 x + 16 / 3
___________________________
y = x + 3
x = y - 3
y = x + 3
___________________________
Which triangle has 2 equal sides?
A) equilateral triangle
B) isosceles triangle
C) scalene triangle
Answer:
isosceles triangle is the correct answer
hope it helps
it has two equal sides
Answer:
B
Step-by-step explanation:
Isoceles triangle is defined by two equal sides
The coordinate point E(8,-10) after a dilation with scale factor of 2.5, centered at the origin, becomes the point
O (20,-25)
O (16, -20)
O (10.5, -7.5)
O (5.5, -12,5
Answer:
20,-25
Step-by-step explanation:
The sum of two numers is 58. The smaller number is 14 less than the larger number. What are the two numbers?
Three friends were comparing how much money they each have saved. Sami has $41.79. Charlotte has $38.91. Celeste has $41.68. Which list shows the names in order from least amount saved to greatest?
Sami, Celeste, Charlotte
Charlotte, Celeste, Sami
Celeste, Sami, Charlotte
Charlotte, Sami, Celeste
Answer:
B
Step-by-step explanation:
i got it right
(3uv/2u²-2v²)+5uv/3u²+3v2
Answer:
19/6 u^3 v + v^2
Step-by-step explanation:
3uv2
u2−2v2+
5uv3
u2+3v2
=32
u3v+−2v2+53
u3v+3v2
Combine Like Terms:
=32
u3v+−2v2+53
u3v+3v2
= (3
u3v+
53
u3v)+(−2v2+3v2)
In the figure above, sin 52=17/c. Based on the figure, which of the following equations is also true
A. Sin 38= c/17
B. Cos 38=17/c
C. Cos 52=17/c
D. Tan 52=c/17
Answer:
c. Cos 52 = 17/c
Step-by-step explanation:
sin(x) = cos(90-x)
Kelly took a survey of two different sets of
100
students to see what their favorite pizza toppings are and displayed the results in the table below.
Answer:
follow me and followback kita
Step-by-step explanation:
legit hindi ko alam sagot
The area of a sector of an circle of a radius 5 cm, formed by an arc of length is 3.5cm. what is the answer
Answer:
8.75cm²
Step-by-step explanation:
First we need to find the angle subtended by the arc
L = theta/360 * 2pir
3.5 = theta/360 * 2*3.14(5)
3.5 = theta/360 * 31.4
theta/360 = 3.5/31.4
theta/360 = 0.11146
theta = 0.11146 * 360
theta = 40.13 degrees
Area of the sector = theta/360 * pir^2
Area of the sector = 40.13/360 * 3.14*25
Area of the sector = 40.13/360 * 78.5
Area of the sector = 8.75cm
Hence the area of the sector is 8.75cm²
If abc+1=0, prove that: (1/1−a−b^-1)+(1/1−b−c^-1)+(1/1−c−a^−1)=1
Answer:
Hope it will help. I did it.
Hope the image is clear.
Answer:
2
Step-by-step explanation:
A stockbroker has money in three accounts. The interest rates on the three accounts are 7%, 8%, 9%. If she has twice as much money invested at 8% as she does in 7% Three times as much at 9%
as she has at 7%, and the total interest for the year is $150 how much is invested at each rate?
The stockbroker invested $___at 7%,$___at 8%, and $___at 9%
Answer:
x=amount invested at 7%
2x=amount invested at 8%
3x=amount invested at 9%
interest=principal*rate*time (time=1 year)
$150=0.07x+0.08*2x+0.09*3x
$150=0.07x+0.16x+0.27x
$150=0.50x
$1500=5x
x=$300 invested at 7%
2x=$600 invested at 8%
3x=$900 invested at 9%
Step-by-step explanation:
Please help me with this question.
Step-by-step explanation:
Mean of the origibal set = 20
No. of terms = 10
Sum = Mean x No. of terms
= 20 x 10 = 200
The sum of additional numbers to make the new set of observstion is 4 + 8 + 12...... + 40 = 220
New Sum = 200 + 220 = 420
The no of terms stay the same
New Mean = New Sum/ N
= 420/10
= 42
The length of stay at a specific emergency department in Phoenix, Arizona, in 2009 had a mean of 4.6 hours with a standard deviation of 2.9. Assume that the length of stay is normally distributed.
a. What is the probability of a length of stay greater than 10 hours?
b. What length of stay is exceeded by 25% of the visits?
c. From the normally distributed model, what is the probability of a length of stay less than 0 hours? Comment on the normally distributed assumption in this example.
Answer:
a) the probability of a length of stay greater than 10 hours is 0.03144
b) the length of stay is exceeded by 25% of the visits is 6.5 hrs
c)
P( X < 0 ) = 0.0559
The probability of length of stay less than 0 hours is 0.0559, length of stay cannot be less than 0. When the normal model is used, we assume that the LOF is approximately normally distributed.
The LOF is better modeled by the normal distribution near the mean and worse in the tails.
The probabilities in the left tail for the vales of X < 0 can be neglected.
Step-by-step explanation:
Given that;
mean μ = 4.6
standard deviation σ = 2.9
let x represent length of stay;
a. What is the probability of a length of stay greater than 10 hours?
p( x > 10 ) = p( x-μ/σ > 10-4.6 / 2.9 )
= p( Z > 1.86)
= P( Z < - 1.86 )
FROM THE Z SCORE TABLE;( Z < - 1.86 ) = 0.03144
p( x > 10 ) = 0.03144
Therefore, the probability of a length of stay greater than 10 hours is 0.03144
b) What length of stay is exceeded by 25% of the visits?
p( X > x ) = 0.25
so
p( X < x ) = 0.75
p( x-μ/σ < x-4.6 / 2.9 ) = 75
p( Z < x-4.6 / 2.9 ) = 0.75 ----- 1
also, from the standard normal table; P( Z < 0.67 ) = 0.75 ------ 11
from equation 1 and 11
x-4.6 / 2.9 = 0.67
x-4.6 = 2.9 × 0.67
x - 4.6 = 1.943
x = 4.6 + 1.943
x = 6.543 ≈ 6.5
Therefore, the length of stay is exceeded by 25% of the visits is 6.5 hrs
c) From the normally distributed model, what is the probability of a length of stay less than 0 hours?
P( X < 0 ) = p( x-μ/σ < 0-4.6 / 2.9 )
= P( Z - 1.59)
from table;( Z - 1.59) = 0.0559
P( X < 0 ) = 0.0559
The probability of length of stay less than 0 hours is 0.0559, length of stay cannot be less than 0. When the normal model is used, we assume that the LOF is approximately normally distributed.
The LOF is better modeled by the normal distribution near the mean and worse in the tails.
The probabilities in the left tail for the vales of X < 0 can be neglected.
Can someone help me plzzzz with this math question!!!!!! “Buy one, get one free” special at T-Mobile for an iPhone 12. The cost is $1150. Calculate what you are actually paying for each item since you are getting two for one price. What is the sale price of each phone?
Answer:
$575
Step-by-step explanation
1150/2 = 575
Answer:
$1150
Step-by-step explanation:
because it is a buy one (for sale price), get one free
If the triangles below are similar, determine which of the statements below are TRUE. (There may be more than one correct answer.)
Similar Triangles
Question 5 options:
A.) BC¯¯¯¯¯≅YZ¯¯¯¯¯
B.) BC¯¯¯¯¯≅XY¯¯¯¯¯¯
C.) Side XY = 26
D.) Side BC = 48
E.) ∠A≅∠X
Answer:
Step-by-step explanation:
If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
The answers are:
Side XY = 26
BC ≅ XY
Side BC = 48
Find the measure of each angle
Answer:
4x=80 and 5x=100
Step-by-step explanation:
4x+5x=180
9x=180
1/9 (9x)=1/9 (180)
x=20
4(20)=80
5(20)=100
Help me on this question lol
Answer:
i think the answer is 10.5
Step-by-step explanation:
1.25 for a gallon means that 1.25 x 8 = 10. 0.4 gallons mean 1.25 divided by 0.4 which gets you 0.5. I think that's the right answer
Hope this helps!
Mark brainliest please
Answer:
$10.50
Step-by-step explanation:
What is the ratio of water to drink mix? (2 points)
What is the ratio of drink mix to water? (2 points)
plssssssssssssssssssssssss help me asap
To make his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix
What is the ratio of drink mix to mixed energy drink? (2 points)
What is the ratio of water to mixed energy drink? (2 points)
Answer:
8:3, or 8 to 3, or 3/6
Step-by-step explanation:
Answer:
8:3
Step-by-step explanation:
Which values are solutions to × < 10? A. × = 1 and × = 9 B. × = 18 and x = - 11 C. × = 9 and × = 15 D. × = 15 and × = 18
Answer:
A
Step-by-step explanation:
you need find the smaller numbers of 10 which would be in answer A. all the other answers are bigger than 10
PLEASE HELP
Which expression is equivalent to 5(w+4) when w=9?
O5(9)
O9(5)
O5(9)+4
O5(9)+20
Answer:
05(9)+20
Step-by-step explanation:
becasue i know and this was the only way to allow me to give you the answer
8ty grade math, please help.
-Find the volume-
Answer:
47.12389 Rounded is 47.12
Step-by-step explanation:
V=πr2h=π·12·15≈47.12389
Suppose that a committee is studying whether there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours. Construct a 95% confidence interval for the population mean time wasted. Which distribution should you use for this problem
Answer:
The t-distribution is used, as we have the standard deviation of the sample.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Step-by-step explanation:
We have the standard deviation for the sample, which meas that the t-distribution should be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 81 - 1 = 80
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.99
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.99\frac{4}{\sqrt{81}} = 0.88[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 8 - 0.88 = 7.12 hours.
The upper end of the interval is the sample mean added to M. So it is 8 + 0.88 = 8.88 hours.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Use the following coordinate plane to write the ordered pair for each point.
Step-by-step explanation: When finding the coordinates
of a given point, be very careful with your signs.
On the x-axis, left means negative and right means positive and
on the y-axis, down means negative, and up means positive.
So to find the coordinates for point A, we start at the origin,
which is the point (0, 0), and we move 2 units to the left and 4 units up.
So that's the point (-2, 4).
Remember to go left or right first, then up or down.
So for point B, we go 0 units to the left or right and 3 units down.
So that's the point (0, -3).
For point C, we move 4 units to th
right and 4 units down so tha's (4, -4).
HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!
Answer:
Step-by-step explanation:
Part A: (3,2)
connect all the points on the paper
Part B: 5 units. We know this since the x point for A is -2 and the point for B is 3. -2 to 3(absolute value of -2 plus 3)= 5