Hi! Please explain how you got your answer thanks! :)) ​

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Volume

= 4 / 3 πr ^ 3

= 4 / 3 × π × 93

= 972π

= 3053.6280592893 feet3

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Branilest?

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There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

[tex]\displaystyle\sum_{n=1}^N a(n) = 2332[/tex]

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

[tex]\displaystyle\sum_{n=1}^N (21n-20) = 2332[/tex]

Expand the sum on the left as

[tex]\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332[/tex]

and recall the formulas,

[tex]\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n[/tex]

[tex]\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2[/tex]

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

Answer:

y = 4 root 3, x = 8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Hi! Because the equation is y=5x-4, it tells is that it intersects with the y axis at -4, and that it's slope goes up 5, right 1. Since B is the only graph that shows that, the answer is b.

Answer:

$840

Step-by-step explanation:

4 weeks = 28 days

28 x 30 = 840

Answer:

Find the following measure for this figure. Area of circle = 36 I square units. Image: Find the following measure for this figure.

Step-by-step explanation:

Answer:

16.3

Step-by-step explanation:

The height of the building to the nearest tenth is 16. 3 ft

The situation forms a right triangle.

The length of the ladder is the hypotenuse of the triangle formed.

The distance from the foot of the ladder to the bottom of the building is the adjacent sides.

Therefore,

c² = a² + b²

where

c = hypotenuse

a and b are the other two legs.

b² = 29² - 24²

b² = 841 - 576

b = √265

b = 16.2788205961

b = 16.3 ft

learn more on right angle here: https://brainly.com/question/23919428?referrer=searchResults

Answer:  No two students ran same distance

Step-by-step explanation:

Given

Stacy ran [tex]\frac{9}{12}[/tex] of a km i.e.

[tex]\Rightarrow 1\times \dfrac{9}{12}=\dfrac{3}{4}=0.75\ km[/tex]

Jules ran [tex]\frac{4}{5}[/tex] of a km i.e.

[tex]\Rightarrow 1\times \dfrac{4}{5}=0.8\ km[/tex]

Raul ran [tex]\frac{3}{4}[/tex] of mile i.e.

[tex]\Rightarrow 1\times \dfrac{3}{4}=0.75\ miles\\\\\text{1 mile=1.6 km}\\\\\Rightarrow 0.75\ miles=1.2\ km[/tex]

So, no two students ran the same distance.

Answer:

30.1 ft²

Step-by-step explanation:

The area of a triangle with an included angle and two sides cam be found using the formula, A = ½*ab*sin(C)

a = 7 ft

b = 9 ft

C = 73°

Plug in the values

Area = ½*7*9*sin(73)

Area = 30.1235998 ≈ 30.1 ft² (nearest tenth)

Answer:

The proportion that can be used to estimate the height of the tree is option;

A. [tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex]

Step-by-step explanation:

The given parameters in the question are;

The medium through which the person looks at the top of the tree = A mirror

The angle formed by the person and the tree with the ground = Right angles = 90°

The distance of the person from the mirror, d₁ = 5 ft.

The height of the person, h₁ = 6 ft.

The distance of the tree from the mirror, d₂ = 12 ft.

The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂

Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;

TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar

The corresponding legs are;

The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively

The distances of the person and the tree from the mirror, which are BM = 5 ft. and MR = 12 ft. respectively

∴ The angle formed by the incident light from the tree on the mirror, θ₁ = ∠TMR

The angle of the reflected light from the mirror to the person, θ₂ = ∠AMB

Given that θ₁ = θ₂, we have;

tan(θ₁) = tan(θ₂)

∴ tan(∠TMR) = tan(∠AMB)

[tex]tan\angle X = \dfrac{Opposite \ leg \ length \ to \ reference \ angle}{Adjacent \ leg \ length \ to \ reference \ angle}[/tex]

[tex]tan(\angle TMR) = \dfrac{TR}{MR} = \dfrac{h}{12}[/tex]

[tex]tan(\angle AMB) = \dfrac{AB}{BM} = \dfrac{6}{5}[/tex]

From tan(∠TMR) = tan(∠AMB), we have;

[tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex]

[tex]\therefore h = \dfrac{6 \, ft.}{5 \, ft.} \times 12 \, ft. = 14.4 \, ft.[/tex]

The height of the tree, h = 14.4 ft.

Therefore, from the proportion [tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex] the height of the tree can be estimated.

Answer:

Mrs.Royal's ticket costs $800.

Step-by-step explanation:

Child's Ticket= x

Adult's Ticket= 4x

4x-x=600

3x=600

x=200

200*4=800

Answer:

3.4

Step-by-step explanation:

just divide 8.16 by 2.4

:)

Answer:

angle 13 and 16 is your answer ☺️☺️☺️

Answer:

∠13 and ∠16.

Step-by-step explanation:

The definition of adjacent angles is "two angles that have a common vertex and a common side but do not overlap" (Varsity Tutors). In accordance with the standards, only angles 13 and 16 are adjacent.

Hope this helps!

Answer: 10 m/s

Step-by-step explanation:

Given

Momentum of boy [tex]P=200\ kg.m/s[/tex]

Mass of boy is [tex]m=20\ kg[/tex]

Momentum is the product of mass and velocity

[tex]P=mv[/tex]

Substitute value

[tex]\Rightarrow 200=20\times v\\\Rightarrow v=10\ m/s[/tex]

Thus, the boy is moving with a velocity of 10 m/s

Answer: meters: 3 6 9 12

            Millimeters: 6,000 7,000 9,000

Step-by-step explanation:

Your adding by 3 in meters and then after 7,000 you have 9,000 then 10,000

I hope this helped!

Answer: 1: 6, 2: 7, 3: 9000, 4: 10

im sure thats it

Step-by-step explanation:

MARK ME AS BRAINLIEST OK FRIEND

Family is a group of people who want as well as choose to be together embraced by a bond so powerful and strong that not even the slightest test of trials and troubles can breach.Family means nobody gets left behind or forgotten.

Answer:

Hello There!!

Step-by-step explanation:

Family consists of parents and their children.

hope this helps,have a great day!!

~Pinky~

the answer is 640.

if you take 640 and multiply it by .23 (because of 23%), you get 147.2 which is exactly what you are looking for.

Hope this helps! :)

Answer:F(x)=4x-20

Step-by-step explanation:

The X on both sides is 12.

Answer:

The graph of f (x)=[x+2] after it is translated 4 units to the right

Answer:Noah spent  $46.80 on video game.

Step-by-step explanation:

Amount spent on game by Nathan =$62.40

Amount spent on game by Noah =3/4 as much as Nathan.

Therefore Noah spent 3/4 x $62.40= $46.80 on video game.

Answer:

Step-by-step explanation:

Answer:

A = 28.27

Step-by-step explanation:

Answer:

9pi meters^2

Step-by-step explanation:

The area of a circle is pi * r^2. Basically, pi is simplified to 3.14 but for an exact answer, you'd leave it as a symbol. the "r" stands for the radius which is given(3). we square 3 to get 9. so the answer should be 9 pi or about 28.26.

Answer:

Yes

Step-by-step explanation:

Answer:

The evidence does not support the math chairperson's claim that the percentage is no longer 40%

Step-by-step explanation:

The known population percentage of research in mathematics published by US authors = 40%

The proportion, p = 0.40

Therefore, q = 1 - p = 1 - 0.4 = 0.6

The number of articles in the sample = 130

The number of articles by US authors in the sample = 62

Therefore, the proportion of US authors in the sample, [tex]\hat p[/tex] = (62/130) × 100 =

[tex]0.4\overline{769230}[/tex]

∴ The percentage of US authors in the sample ≈ 47.7%

The null hypothesis, H₀; p = 0.4

The alternative hypothesis, Hₐ; p ≠ 0.4

The z-test is given as follows;

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p\cdot q}{n}}}[/tex]

[tex]z=\dfrac{0.477-0.40}{\sqrt{\dfrac{0.4\times 0.6}{130}}} \approx 1.792[/tex]

The p-value P(Z > 1.79) = 2 × (1 - 0.96327) = 0.07346

Therefore, given that the p-value is larger than 0.05 there is significant evidence in favor of the null hypothesis and we reject the alternative hypothesis

Therefore, also, there is not enough statistical evidence to support the math chairperson's claim that the percentage is no longer 40%.

Answer:

D

Step-by-step explanation:

HAHAHA

Answer:

E) 22

Step-by-step explanation:

[tex] l || m\: \&\:line\: j\: is \: their \: transversal [/tex]..... (given)

[tex]\therefore(5x - 16)\degree = (2x)\degree + 50\degree [/tex]

(Corresponding angles)

[tex]\therefore(5x - 16)\degree = (2x+50)\degree [/tex]

[tex]\therefore 5x - 16 = 2x+50 [/tex]

[tex]\therefore 5x - 2x = 16+50 [/tex]

[tex]\therefore 3x = 66 [/tex]

[tex]\therefore x =\frac {66}{3} [/tex]

[tex]\therefore x =22 [/tex]

Answer:

%40 Off

Step-by-step explanation:

Answer:

x = √72 and yes, it forms a Pythagorean triple

Step-by-step explanation:

a^2 + b^2 = c^2,

3 is a, x is b, anf 9 is c

3^2 + x^2 = 9^2

9 + x^2 = 81

Subtract 9 from both sides

x^2 = 72

x = √72

a Pythagorean triple is a^2 + b^2 = c^2, and this has it

Answer:

X = 9.4

Step-by-step explanation:

Pythagorean Theorem:

Formula: a² + b² = c²

- A Pythagorean triple consists of any three positive integers.

Answer: 7,720

The answer is 7,720! got the question correct with it

Number of cupcakes 2

number od cookies 5