What is the common difference for this arithmetic sequence?
-6, -2, 2, 6, 10, ...

Answer:

Step-by-step explanation:

H0 : μ ≥ 6

H1 : μ < 6

Test statistic :

n = 20

Sample Mean, x = 3

σ = 1.5

Test statistic = (x - μ) ÷ σ/sqrt(n)

Test statistic = (3 - 6) ÷ 1.5/sqrt(20)

Test statistic = - 3 / 0.3354101

Test statistic = −8.944271

Since, sample size is < 30 ;

Obtaining the Critical value using the from T;

Tcritical at 0.05, df = 19 = - 1.729

Tstatistic < Tcritical

−8.944271 < - 1.729

Hence, we reject the Null:

We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.

Answer:

Step-by-step explanation:

Circumference of circle = 2π18 = 36π inches.

40° is 1/9 of a circle. Arc length = 1/9 of circumference = 4π inches.

Answer:

Perimeter=18; Area= 18

Step-by-step explanation:

For perimeter, the vertical sides are 3 and the Horizontal sides are 6. So 6+6+3+3= 18

For area, the vertical side is 3 and the Horizontal side is 6, this 6*3=18

Answer:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

Lim n → ∞ (a_n+1 / a_n)

Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

Lim n→ ∞ (-1/2)^(n-n+1)

Lim n→ ∞ (-1/2)^1 = -1/2

Since the limit is less than 0, then, the series converge...

Sum to infinity

Using geometric progression formula

S∞ = a / 1 - r

Where

a is first term

r is common ratio

So, first term is

a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1

a_1 = -4

Common ratio r = a_2 / a_1

a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2

a_2 = 2

Then,

r = a_2 / a_1 = 2 / -4 = -½

S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

It looks like the series is

[tex]\displaystyle \sum_{n=1}^\infty \frac{n^{2n}}{(1+n)^{3n}} = \sum_{n=1}^\infty \left(\frac{n^2}{(1+n)^3}\right)^n[/tex]

Checking for convergence is most easily done with the (Cauchy) root test for convergence: the infinite series

[tex]\displaystyle \sum_{n=1}^\infty a_n[/tex]

converges absolutely if the limit

[tex]\displaystyle \lim_{n\to\infty} \sqrt[n]{|a_n|} < 1[/tex]

Here we have

[tex]\displaystyle \lim_{n\to\infty} \sqrt[n]{\left|\left(\frac{n^2}{(1+n)^3}\right)^n\right|} = \lim_{n\to\infty} \frac{n^2}{(1+n)^3} = 0 < 1[/tex]

so the given series converges.

Answer:

The first three terms of the geometry sequence would be [tex]1[/tex], [tex]5[/tex], and [tex]25[/tex].

The sum of the first seven terms of the geometric sequence would be [tex]127[/tex].

Step-by-step explanation:

Let [tex]d[/tex] denote the common difference of the arithmetic sequence.

Let [tex]a_1[/tex] denote the first term of the arithmetic sequence. The expression for the [tex]n[/tex]th term of this sequence (where [tex]n\![/tex] is a positive whole number) would be [tex](a_1 + (n - 1)\, d)[/tex].

The question states that the first term of this arithmetic sequence is [tex]a_1 = 1[/tex]. Hence:

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let [tex]r[/tex] denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

[tex]\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d[/tex].

Ratio between the third term and the second term of the geometric sequence:

[tex]\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}[/tex].

Both [tex](1 + 2\, d)[/tex] and [tex]\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)[/tex] are expressions for [tex]r[/tex], the common ratio of this geometric sequence. Hence, equate these two expressions and solve for [tex]d[/tex], the common difference of this arithmetic sequence.

[tex]\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}[/tex].

[tex](1 + 2\, d)^{2} = 1 + 12\, d[/tex].

[tex]d = 2[/tex].

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be [tex]1[/tex], [tex](1 + (3 - 1) \times 2) = 5[/tex], and [tex](1 + (13 - 1) \times 2) = 25[/tex], respectively.

These three terms ([tex]1[/tex], [tex]5[/tex], and [tex]25[/tex], respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be [tex]r = 25 /5 = 5[/tex].

Let [tex]a_1[/tex] and [tex]r[/tex] denote the first term and the common ratio of a geometric sequence. The sum of the first [tex]n[/tex] terms would be:

[tex]\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}[/tex].

For the geometric sequence in this question, [tex]a_1 = 1[/tex] and [tex]r = 25 / 5 = 5[/tex].

Hence, the sum of the first [tex]n = 7[/tex] terms of this geometric sequence would be:

[tex]\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}[/tex].

Answer:

sin θ/2 = ± √2/13

Step-by-step explanation:

tan θ = - 12/5       (in quadrant 4)      sin θ = - 12/13   and   cos θ = 5/13

sin θ/2 = ± (√1 - cos θ) / 2 = ± (√1 - 5/13) / 2 = ± √8/13 / 2 = ± √2/13

tan θ/2 = (1 - cos θ) / sin θ = sin θ / (1 + cos θ)

Let you to calculate the tan θ/2 part by yourself

The fraction of each piece of a cake is 1/6.

Given that, Joe has four birthday cakes to share with his 24 guests joe doesn't eat cake.

We need to find what fraction is each piece of cake.

A fraction represents a part of a whole or, more generally, any number of equal parts. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Now, 4 cakes are shared among 24 guests.

So, 24/4=6

Thus, each cake needs to divide into 6 slices.

Therefore, the fraction of each piece of a cake is 1/6.

To learn more about the fractions visit:

https://brainly.com/question/1301963.

#SPJ2

Answer:dont lnow sorry. Only if u give me robux

Step-by-step explanation:

Answer: the answer for x is ( x = 2 (y+8)    a the

answer for y = x-16\2

Answer:

B & D

Step-by-step explanation:

B & D

Answer:

8

Step-by-step explanation:

8*8 = 64

b*h = a

Answer:

2 pies because you need 2 lb for each pie

Step-by-step explanation:

Answer:

yes it is valid influence because he asked all 25 student in her math class

Answer:

2.75632 rounded to 5 decimal places

Step-by-step explanation:

a(r^n-1)/r-1 is the formula for sum of geometric series

where a= first term (1.4)

n= number of terms(6)

r= common ratio(0.5)

Answer:

D

Step-by-step explanation:

The answer is D, because when you divide x by a negative the sign changes

Answer:

40,000

Step-by-step explanation:

Answer:

r = 0.732 d = 1.46 C = 4.6

Step-by-step explanation:

Answer:

16.62

Step-by-step explanation:

formula for area of a circle is [tex]\pi r^{2}[/tex] 4.6 is the diameter and radius is 1/2 of diameter so [tex]\pi 2.3^{2}[/tex] is the equation

Answer:

25

Step-by-step explanation:

20 : 100 = 5 : x

x = (5 x 100) / 20 = 25

Answer:

13

Step-by-step explanation:

it is on 100th place so 100th term is 13

Answer:

401

Step-by-step explanation:

arithmetic sequence formula: an=a1+d(n-1)

n= term # you're looking for

d= common difference

a1= 1st term in sequence

a100=5+4(100-1)

5+4(99)

5+396

a100=401

Answer:

Perimeter

P = P1+P2

P1 = 4a           P2=2(a+b)

P1=4*5           P2=2(3+5)

P1=20            P2=2*8

                     P2=16

P = 20+16

P=36

Area

A=A1+A2

A1=[tex]a^{2}[/tex]                 A2=a*b

A1=[tex]5^{2}[/tex]                 A2=3*5

A1=25                A2=15

A=25+15

A=40

Answer:

Hi yes ik I'm not that good at math but wouldn't it be

a n=1∗1 n =1

Answer:

Given data:

Put the data in the ascending order:

Mean, the average:

Median, average of middle two numbers:

Mode, the most repeated number:

Mean is normally the best measure of central tendency, same applies to this data.

Answer:

a=55

Step-by-step explanation:

20%/100=0.2

a=11/0.2

a=55

Answer:

y=4

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation

x=2 is where you could fold the quadratic function and have the sides overlap perfectly