Find an equation for the nth term of the arithmetic sequence.

30 POINTS!!!
Find an equation for the nth term of the arithmetic sequence.
a19 = -92, a20 = 6

A an = -1856 + 98(n - 1)
B an = -1856 - 98(n - 1)
C an = -1856 - 98(n + 1)
D an = -1856 + 98(n + 1)

This doesn’t include the Einstein problem cause I didn’t have that one.

Answer:

1)0.125

2)127.825

Step-by-step explanation:

Answer:

t=-19/7

Step-by-step explanation:

you need to isolate for t which means you need to get t all alone on one side of the equation. Do do that you can divide both sides by 7. This gives you -19/7=7t/7

we know that anything divided by itself is 1 so we get -19/7=t

This is the simplest for because 19 and 7 are both prime numbers, so you can't simplify them.

Answer:

C. 1796.08 [tex]in^2[/tex]

Step-by-step explanation:

Area of circle is [tex]\pi r^2[/tex], r is the radius

remember radius is from the center to the edge, so it is half the diameter

now we need to find the area of the large circle (table) minus the small circle (hole)

the radius of the large circle is 48/2 which is 24

the area is [tex]\pi 24^2[/tex] replacing r in the formula with 24, the radius. Using 3.14 as pi, the answer is 1808.64

the radius of the small circle is 4/2 which is 2

the area is [tex]\pi 2^2[/tex] so the calculated value would be 12.56

now subtract the area of the hole (small circle) from the area of the table (large circle)

1808.64 - 12.56 = 1796.08

and there's your answer

hope that helps, lmk if it doesn't :)

Answer:

Step-by-step explanation:

r₁ = radius of tabletop = 24 in

r₂ = radius of hole = 2 in

area of hole = πr₂² = 4π in²

area of tabletop = πr₁² - πr₂² = 576π - 4π = 572π ≈ 1796.08 in²

Answer:

25 ft

Step-by-step explanation:

This is a right triangle, so we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

15^2 + 20 ^2 = x^2

225+400= x^2

625 = x^2

Take the square root of each side

sqrt(625) = sqrt(x^2)

25 = x

Answer:

There are no statements

Step-by-step explanation:

If you put up the statements, I'll edit my answer

Answer:

200

Step-by-step explanation:

delta math

its 200.456 before rounding

Answer:

Division to get 28

Step-by-step explanation:

Answer:

11.17 ft

Step-by-step explanation:

Since the swing hangs from a beam 10 feet high with the seat hanging 2 feet above the ground, the swing moves in an arc of radius r = 10 ft - 2 ft = 8 ft.

Now, since the swing moves back and forth from -130° to -50° to the horizontal, the length of arc L it moves in is given by

L = Δθ/360 × 2πr where  Δθ = change in angle of the swing = θ₂ - θ₁ where θ₁ =  -50° and θ₂ = -130°. So, Δθ = θ₂ - θ₁ = -130° -(-50°) = -130° + 50° = -80°.

Substituting r and  Δθ into L, we have

L = -80°/360° × 2π(8 ft)

= -8/36 × 16π ft

=  -32π/9 ft

= -100.53/9 ft

= -11.17 ft

Ignoring the negative sign, the length of arc L = 11.17 ft. So, the swing moves back and forth 11.17 ft

Answer:

B

Step-by-step explanation:

The solution is

Option A - True

The volume of the rectangular cargo is 2187 feet³

Option B - True

The volume of the rectangular cargo is 2187 feet³

Option C - True

The volume of the rectangular cargo is 2187 feet³

Option D - True

The volume of the rectangular cargo is 2187 feet³

What is the Volume of a Rectangle?

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the cargo hold be a rectangular prism

Now , the dimensions of the rectangular prism is

18 feet x 13.5 feet x 9 feet

And , the Volume of Rectangle = Length x Width x Height

Substituting the values in the equation , we get

Volume of Rectangle = 18 x 13.5 x 9

Volume of Rectangle = 2187 feet³

a)

The number of boxes = 6

The dimensions of the cargo be = 9 feet x 4.5 feet x 9 feet

So , the volume of the cargo = number of boxes x 9 x 4.5 x 9

On simplifying the equation , we get

Volume of the cargo = 6 x 364.5

Volume of the cargo = 2187 feet³

b)

The number of boxes = 81

The dimensions of the cargo be = 3 feet x 3 feet x 3 feet

So , the volume of the cargo = number of boxes x 3 x 3 x 3

On simplifying the equation , we get

Volume of the cargo = 81 x 27

Volume of the cargo = 2187 feet³

c)

The number of boxes = 24

The dimensions of the cargo be = 4.5 feet x 4.5 feet x 4.5 feet

So , the volume of the cargo = number of boxes x 4.5 x 4.5 x 4.5

On simplifying the equation , we get

Volume of the cargo = 24 x 91.125

Volume of the cargo = 2187 feet³

d)

The number of boxes = 12

The dimensions of the cargo be = 9 feet x 4.5 feet x 4.5 feet

So , the volume of the cargo = number of boxes x 9 x 4.5 x 4.5

On simplifying the equation , we get

Volume of the cargo = 12 x 182.25

Volume of the cargo = 2187 feet³

Hence , the volume of the rectangular cargo is 2187 feet³

To learn more about volume of rectangle click :

https://brainly.com/question/25422723

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Answer:

m∠2=9

Step-by-step explanation:

Hello There!

The problem states that the angles are complementary angles

Complementary angles are angles that have measures that add up to equal 90

So given one of the angles we can find the missing angle by subtracting the known angle from 90

90 - 81 = 9

so we can conclude that the measure of angle 2 is 9

Answer: [tex]-3\hat{i}-6\hat{j}+2\hat{k}[/tex]

Step-by-step explanation:

Given

[tex]\vec{a}=2\hat{i}+4\hat{j}-5\hat{k}\\\vec{b}=\hat{i}+\hat{j}+\hat{k}[/tex]

[tex]\vec{c}=\hat{j}+2\hat{k}[/tex]

The addition of the three is [tex]\vec{a}+\vec{b}+\vec{c}[/tex]

[tex]\vec{a}+\vec{b}+\vec{c}=(2\hat{i}+4\hat{j}-5\hat{k})+(\hat{i}+\hat{j}+\hat{k})+(\hat{j}+2\hat{k})[/tex]

[tex]\vec{a}+\vec{b}+\vec{c}=3\hat{i}+6\hat{j}-2\hat{k}[/tex]

vector opposite to the vector  [tex]\vec{a}+\vec{b}+\vec{c}\ \ \text{is}\ -(\vec{a}+\vec{b}+\vec{c})[/tex]

[tex]\therefore -(\vec{a}+\vec{b}+\vec{c})=-3\hat{i}-6\hat{j}+2\hat{k}[/tex]

Answer:

35

Step-by-step explanation:

6 pies = 21 cups of apples

1 pie =  3.5 cups of apples

10 pies = 35 cups of apples

Answer:

40 Square Units

Step-by-step explanation:

Easy way to find area: Diagonal 1 * Diagonal 2 divide by 2 = your answer

Diagonal 1 (AC) = 5 + 5 = 10

Diagonal 2 (BD) = 4 + 4 = 8

10 + 8 = 80, 80/2 = 40

Answer: 40 square units

Step-by-step explanation:

(125/5)×3=75

75 participate jogging

25×2=50

50 participate in cycling

Answer:

C

Step-by-step explanation:

first we want to find the missing angle at the top

to do that we subtract the given angles by 180

the square indicates that the angle is a right angle or that it equals 90

180-90-40=50

we know that the angle equal to 50 and x are supplementary angles so they will add up to equal 180 so to find x we subtract 50 from 180

180-50-130 so the answer is c

have a great day :D

Answer:

a₁ = 37

Step-by-step explanation:

In an arithmetic progression the common difference d is

d = a₂ - a₁ = a₃ - a₂ , that is

2x - 18 - (x + 1) = 2x - 1 - (2x - 18) ← distribute and simplify both sides

2x - 18 - x - 1 = 2x - 1 - 2x + 18

x - 19 = 17 ( add 19 to both sides )

x = 36

Thus

a₁ = x + 1 = 36 + 1 = 37

Complete question :

A newspaper report claims that 30% of all tea-drinkers prefer green tea to black tea. Dr. Huber is the office manager at a company with thousands of employees. He wonders if the newspaper's claim holds true at his company. To find out, Dr. Huber asks a simple random sample of 125 tea-drinking employees which the prefer: green tea of black tea. Here's Dr. Huber's null hypothesis: H_0 : The proportion of all tea-drinkers at the company that prefer green tea to black tea is...

What is an appropriate way for Dr. Huber to finish his null hypothesis?

A. ...equal to 30%

B. ...less than 30%

C. ...greater than 30%

D. ...not equal to 30%

Answer:

A. ...equal to 30%

Step-by-step explanation:

Given the incomplete hypothesis statement for the Null ;

The null hypothesis: H_0 is declared as : The proportion of all tea-drinkers at the company that prefer green tea to black tea equal 30

The alternative hypothesis on the other side is the opposite statement or hypothesis.

Answer:

22

Step-by-step explanation:

180 - 90 - 68

Answer:

22

Step-by-step explanation:

4x+2=150 150-2=148 148/4= 37

Answer:

37

Step-by-step explanation:

first option, 37..................................................................................................................................................................................................................................................................................................

Answer:

6 and 2

Step-by-step explanation:

6 times 2 is 12 and 6 plus 2 is 8

Answer:

Sample Response: To use the distributive property, distribute multiplication by 2 to both terms inside the parentheses. The products are 2(11) and 2(y). The equivalent expression is 22 + 2y

Step-by-step explanation:

you're welcome

Answer:

9)m≤54

11)x>30

13)y≤40

Step-by-step explanation:

9)m−18≤36

Add 18 to both sides.

m≤36+18

Add 36 and 18 to get 54.

m≤54

11)9x>270

Divide both sides by 9. Since 9 is positive, the inequality direction remains the same.

x=270/9

Divide 270 by 9 to get 30.

x>30

13)y/5≤8

Multiply both sides by 5. Since 5 is positive, the inequality direction remains the same.

y≤8×5

Multiply 8 and 5 to get 40.

y≤40

Answer: 1/7

Step-by-step explanation:

Answer:

(4,2) (11,3)

Step-by-step explanation: