40/27 ,20/9, 10/3 what is the next term in the geometric sequence ?

Answer:

A. 4×π×3²×[tex]10^{6}[/tex]

Step-by-step explanation:

r = 3×10² = 3×100 = 300

[tex]\frac{4}{3}[/tex]×π×300³=

[tex]\frac{4}{3}[/tex]×π×27,000,000=

[tex]\frac{108,000,000}{3}[/tex]×π=

36,000,000π

Answers solved:

A. 36,000,000π

B. 108,000,000π

C. 3,600,000π

D. 32,400,000π

The solution is Option A.

The volume of the air in the spherical ball is given by the equation

V = 4π ( 3 )² ( 10 )⁶ cm³

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the volume of the sphere be represented as V

Now , the radius of the spherical ball be r

The value of r = 3 ( 10 )² cm

So , the volume of the spherical ball = ( 4/3 ) πr³

Substituting the values in the equation , we get

Volume of the spherical ball V = ( 4/3 ) x π x [ 3 ( 10 )² ]³

On simplifying the equation , we get

Volume of the spherical ball V = ( 4/3 ) x π x ( 3 )³ ( 10 )⁶

Volume of the spherical ball V = 4 x π x ( 3 )² ( 10 )⁶

Therefore , the value of V is 4π ( 3 )² ( 10 )⁶

Hence , the volume of the spherical ball is 4π ( 3 )² ( 10 )⁶

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Answer:

Step-by-step explanation:

The formula for calculating the nth term of an arithmetic sequence is given as;

Tn = [tex]a+(n-1)d[/tex]

a is the first term

n is the number of terms

d is the common difference

If  two terms of an arithmetic sequence are a12=70 and a30=124 then;

T12 = a+(12-1)d = 70

T12 = a+11d = 70...(1)

T30 = a+(30-1)d = 124

T30 = a+29d = 124...(2)

Solving equation 1 and 2 simultaneously to get a and d;

Taking the difference of both equation we have;

29d - 11d = 124-70

18d = 54

d = 54/18

d = 3

Substituting d=3 into equation 1 to get the value of 'a' we have;

a+11(3) = 70

a+33=70

a = 70-33

a = 37

To get the explicit rule for the nth term of the sequence, we will use the formula Tn = a+ (n-1)d where a = 37, d =3

Tn = 37+(n-1)3

Tn = 37+3n-3

Tn = 34-3n

This gives the required nth term

Answer:

Average Rate of Pay = $ 5.23 /hr

Step-by-step explanation:

We have a data in form of Hours of Baby Sitting and Amount of Pay. Since the Amount of pay depends upon the Hours of Baby Sitting. Thus, we take y = Amount of Pay, while x = Hours of Baby Sitting. So, the data becomes:

x (Hours) =   12      13      16      17       20

y ($)         =  54     56     65     64     100  

The statistical data calculated is:

∑x = 78,   ∑x² = 1258,   ∑y = 339,  ∑xy = 5504,   n = no. of data points = 5

Now, we use linear regression model to fit a straight line to this data.

y = a + bx   --------- eqn (1)

where,

b = [ n∑xy - ∑x.∑y]/[n∑x² -(∑x)²]

b = [ (5)(5504) - (78)(339)]/[(5)(1258) - (78)²]

b = 5.23

and,

a = (∑xy - b∑x²)/∑x

a = [5504 - (5.23)(1258)]/78

a = -13.83

Therefore, eqn (1) becomes:

y = -13.83 + 5.23x

The graph plot of this straight line fit is provided in the attachments.

Now, we derivate the equation with respect to x, to get the average rate of pay:

Average Rate of Pay = dy/dx = d/dx(-13.83 + 5.23x)

Average Rate of Pay = $ 5.23 /hr

Answer:

4

Step-by-step explanation:

The degree is the highest power on the exponent when they are lined up from highest to lowest

The degree is 4

Answer:

You are correct

Step-by-step explanation:

x - 8 < 23

Add 8 to both sides

x - 8 + 8 < 23 + 8

Simplify

x < 31

Yes, you are correct.

Answer:

(x - 5)(x - 3)

Step-by-step explanation:

[tex] {x}^{2} - 8x + 15 \\ = {x}^{2} - 5x - 3x + 15 \\ = x(x - 5) - 3(x - 5) \\ = (x - 5)(x - 3) \\ \\ ac = ( - 5) (- 3) = 15 \\ a + c = - 5 - 3 = - 8[/tex]

Answer:

B. 20

Step-by-step explanation:

5P2 is equal to 20 using the permutation formula.

Answer:

The correct option is;

D. 30 and 40

Step-by-step explanation:

Here, we have that the rhombus is a quadrilateral with equal and parallel sides hence the length of the diagonals will be

2 × 25×sinθ  and 2 × 25× cosθ

Therefore tanθ = (2 × 25×sinθ)/(2 × 25× cosθ) = (sinθ)/(cosθ)

Therefore, the root of the sum squares of both diagonals = 50

Therefore, we analyze each of the options as follows

For A. we have √(22² + 40²) = 45.65 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

For B. we have √(26² + 36²) = 44.41 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

For C. we have √(26² + 48²) = 55.59 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

For D. we have √(30² + 40²) = 50 therefore these are possible lengths of diagonals of the rhombus in question.

Answer:

(x + 5) (x - 7)

Step-by-step explanation:

To factor this trinomial, you must split the middle term (-2x) into two terms that can be added to get -2x, and multiplied to get -35:

[tex]x^2[/tex] - 2x - 35

[tex]x^2[/tex] - 7x + 5x - 35

Group:

([tex]x^2[/tex] - 7x)  (5x - 35)

Take out GCF (Greatest Common Factor):

x(x - 7)  5(x - 7)

(x + 5) (x - 7)

Answer:

3

Step-by-step explanation:

25-10/3=3

Answer:

3 movies

Step-by-step explanation:

You can pay for 3 movies because

5*3=15 and you have to pay for the membership which is 10 so

10+15=25

[insert answer here]

Step-by-step explanation:

Answer:

2n/3

Step-by-step explanation:

hope this helps!! moo

Answer:

A = 19.47

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hypotenuse

sin A = 2/6

Take the inverse sin of each side

sin ^-1 ( sin A) = sin ^-1 (2/6)

A =19.47122063

To the nearest hundredth

A = 19.47

Answer:

-3x^3 + x^2 + 4x +6

Answer is C

Step-by-step explanation:

Answer: -3x^3 + x^2 + 4x +6

Answer is C

Step-by-step explanation:

Answer:

  -3

Step-by-step explanation:

An increase in x-value from 9 to 10 is an increase of 1 unit. The slope of -7 tells you that the corresponding change in y will by -7 units:

  v = 4 -7 = -3

The value of v is -3.

_____

Alternate solutions

You can see this easily on a graph, or you can use the equation of the line. We have a point and a slope, so the point-slope form is useful.

  y = m(x -h) +k

  y = -7(x -9) +4

For x=10, the value of y is ...

  v = -7(10 -9) +4 = -7 +4

  v = -3

Answer:

Step-by-step explanation:

-3x + 4y = -18

8x - 4y =   28

5x = 10

x = 2

4 - y = 7

-y = 3

y = -3

(2, -3)

The solution of the system of linear equations given is (2,-3), the correct option is C.

The system of linear equation is set of equations which have a common solution.

The equations are

-3x+4y = -18

2x-y =7

The linear equations can be solved using substitution method

y = 2x -7 from equation 2 will be substituted in equation 1

-3x +4 ( 2x -7) = -18

-3x +8x -28 = -18

5x = 10

x = 2

y = 2 * 2 -7 = -3

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Answer:

5 seconds

Step-by-step explanation:

(60 / seconds = GPM)

60 / 5 = 12 GPM

12 GPM = 60 seconds

Simplified

1 Gallon is 5 seconds

Answer:

5

Step-by-step explanation:

Answer:

210 pounds because after 7 days (week) thats how much bambo the panda will eat

Step-by-step explanation:

90 pounds = 3 days

6 days = 180 pounds

1 day = 30 pounds

180 +30= 210 pounds

Answer:

The volume of Gabe's kitchen is 680 ft^3

Step-by-step explanation:

The volume of the kitchen can be derived by multiplying the floor area of the kitchen by the height.

Volume = floor area × height

Given;

Floor area = 85 ft^2

Height = 8 ft

Substituting the given values into the equation;

Volume = 85 × 8 = 680 ft^3

The volume of Gabe's kitchen is 680 ft^3

Answer:

y = (1/2) x -10

Step-by-step explanation:

Perpendicular lines are lines make right angles. The slopes of perpendicular lines are opposite reciprocals !

2x + y = -7 rewrite in form y=

y = -7 -2x

slope of this line is -2

perpendicular lines are opposite reciprocals so the line p has a slope = 1/2

line p passes through (8, -6) so plug in point into equation of p and get ?

y = 1/2 x +?

-6 =1/2(8) +?

-6 =4 + ? subtract 4 from both sides

-6-4 = ?

-10 = ?

y = (1/2) x -10

Answer:

26.31 units

Step-by-step explanation:

Given: Points [tex](-10,12),(-6,-14)[/tex]

To find: Distance between the given points

Solution:

Let [tex](x_1,y_1)=(-10,12)\,,\,(x_2,y_2)=(-6,-14)[/tex]

The distance formula is used to find the distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex]

According to distance formula,

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\sqrt{(-6+10)^2+(-14-12)^2}\\ =\sqrt{16+676}\\ =\sqrt{692}\\ =26.31[/tex]

So, distance between the given points is 26.31 units

Answer:

B

Step-by-step explanation:

In the attached file

Answer:

c= 5 yards.

Step-by-step explanation:

4*1.5=6

30/6= 5

Answer: t ≥ 33

Step-by-step explanation:

So the temperature has to equal to 33 or less than 33.It can't be greater than 33.

Answer:  4

Step-by-step explanation:

Answer:

4600 tenths as a Fraction

Since 4600 tenths is 4600 over ten, 4600 tenths as a Fraction is 4600/10.

4600 tenths as a Decimal

If you divide 4600 by ten you get 4600 tenths as a decimal which is 460.00.

4600 tenths as a Percent

To get 4600 tenths as a Percent, you multiply the decimal with 100 to get the answer of 46000 percent.

4600 tenths of a dollar

First we divide a dollar into ten parts where each part is 10 cents. Then we multiply 10 cents with 4600 and get 46000 cents or 460 dollars and 0 cents.

Step-by-step explanation:

Hope this helped!

Stay safe!!!

Answer:

Step-by-step explanation:

To answer this, multiply 4600 by 10:  46000.  There are 46000 tenths in 4600.

Answer:

Figure D

Step-by-step explanation:

Point Symmetry is when every part has a matching part: the same distance from the central point. but in the opposite direction. Hope this helps! :)

Answer:

  B. ​False, because the description applies to a single solution. The solution set consists of all possible solutions.

Step-by-step explanation:

The choice of true or false revolves around whether a linear system can have more than one solution.

The problem statement does not say the equations are independent, a condition that must be satisfied if there is to be only one solution. Hence we must assume that the system may be dependent or even inconsistent, leading to zero, one, or an infinite number of solutions. The answer above carries its own explanation.

  False, for the reason given