What’s life about and why are we here on this earth

The sequence is geometric, so

[tex]a_n = r a_{n-1}[/tex]

for some constant r. From this rule, it follows that

[tex]a_3 = r a_2 \implies 20 = 2r \implies r = 10[/tex]

and we can determine the first term to be

[tex]a_2 = r a_1 \implies 2 = 10 a_1 \implies a_1 = \dfrac15[/tex]

Now, by substitution we have

[tex]a_n = r a_{n-1} = r^2 a_{n-2} = r^3 a_{n-3} = \cdots[/tex]

and so on down to (D)

[tex]a_n = r^{n-1} a_1 = 10^{n-1} \cdot \dfrac15[/tex]

(notice how the exponent on r and the subscript on a add up to n)

Answer:

13n+20 is the correct answer to ypur question

Step-by-step explanation:

Answer:

D. 6(9 + 5)

Step-by-step explanation:

Answer:

58π mi.

Step-by-step explanation:

The diameter of the circle = the hypotenuse of the right triangle ( by the angle subtended by a diameter theorem).

By Pythagoras:

diameter^2 = 40^2 + 42^2

=  3364

Diameter = 58 mi.

Now the circumference

= diameter * π

= 58π mi.

Answer: X is 11,

Step-by-step explanation:

Hope it helps you

Answer:

  [tex]X=\left[\begin{array}{cc}-5&2\\0&8\\8&1\end{array}\right][/tex]

Step-by-step explanation:

Solving the given matrix equation, we find ...

  X = (1/4)(C - B)

These operations, subtraction and multiplication by a scalar, are done on a term-by-term basis. A calculator or spreadsheet can do these for you.

For example, the middle right term (row 2, col 2) is ...

  (38 -6)/4 = 32/4 = 8

Answer:

[tex]X =\begin {bmatrix} -5 & 2\\0 &8\\8 & 1\end{bmatrix}[/tex]

Step-by-step explanation:

[tex] Given \:\: B=\begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix} \: and\: C=\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}[/tex]

To Solve: 4X + B = C

[tex]\implies 4X + \begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix}=\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}[/tex]

[tex]\implies 4X =\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}- \begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix}[/tex]

[tex]\implies 4X =\begin {bmatrix} -12-8 & 6-(-2)\\-1 -(-1)& 38-6\\24-(-8) & -6-(-10)\end{bmatrix}[/tex]

[tex]\implies 4X =\begin {bmatrix} -12-8 & 6+2\\-1 +1 & 38-6\\24+8 & -6+10\end{bmatrix}[/tex]

[tex]\implies 4X =\begin {bmatrix} -20 & 8\\0& 32\\32 & 4\end{bmatrix}[/tex]

[tex]\implies X =\frac{1}{4}\begin {bmatrix} -20 & 8\\0& 32\\32 & 4\end{bmatrix}[/tex]

[tex]\implies X =\begin {bmatrix} \frac{-20}{4} & \frac{8}{4}\\\\\frac{0}{4}& \frac{32}{4}\\\\ \frac{32}{4} & \frac{4}{4}\end{bmatrix}[/tex]

[tex]\implies X =\begin {bmatrix} -5 & 2\\0 &8\\8 & 1\end{bmatrix}[/tex]

Answer:

i think it b i dont know for sure

Step-by-step explanation:

Answer:

A: Service Fee = $55
   Hourly Rate = $ 73
B: $288

Step-by-step explanation:

A: the service rate increases by $5 per year, so year 8 would be $20 more than year 4 (5*4)
  The hourly rate increases by $3 per year, so year 8 would be $12 more than year 4 (3*4)

B. Service fee for year 9 would be $60 ($5 more than year 8) and the hourly rate would be $76 per hour ($3 more than year 8). This gives you Service Fee + (Hourly rate * 3) = $60 + ($73*3) = $60 + $228 = $288

Answer:

B.

Step-by-step explanation:

the range is the y values of the line.

so it would be [3, 6]

Answer:

the correct answers are A, C, and D

Step-by-step explanation:

Those are the only ones that make sense enough!

What is the average height of 6th grade students?

And

What was the low temperature...?

Those responses will be given as numerical values

E.G. 162cm or 2 degrees Celsius (2*C)

(Edit: the first & third options are the correct ones)

Hope this helps!

Answer:

384.29 in²

Step-by-step explanation:

The radius of these circles is 5 in.

- As the radii are equal, and 4 of them are used to make up the side of the square. [20 ÷ 4 = 5]

To find the area of circle, you use the formula [tex]\pi r^{2}[/tex]

[tex]\pi[/tex] · (5)² = 25[tex]\pi[/tex]

The area of the square equals the length x width

20 · 20 = 400

To find the area of the shaded region, subtract these values.

400 - 25[tex]\pi[/tex] ≈ 389.29 in²

○ 2,350 square feet

○ 2,450 square feet

○ 2,500 square feet

● 2,400 square feet answer

Step-by-step explanation:

wellcome

rip

Answer:

Step-by-step explanation:

no, because positive 4 is 8 more than negative 4.

Answer:

one positive n one negative equals a positive

Step-by-step explanation:

no?

B

&

D

Step-by-step explanation:

Answer:

The Answers are A and D

Step-by-step explanation:

I took the test and got em right!

Answer:

.1, 1.2, 0, 1.5, 0, 1.4 // 19.2, .8, 70.2, .7, 4791.7, .7

Step-by-step explanation:

The first set is if you meant the first number divided BY the second and the second set of numbers is if you meant it vice versa. If it was worded better I could understand better.

Answer:

ITS B because sqrt 11 is 3.something

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form:

[tex]y=mx+b[/tex]

To find linear equations in slope-intercept form:

We're given:

First, determine the slope of the line.

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points that fall on the line

⇒ Plug in the given points (2,6) and (4,16):

[tex]m=\dfrac{16-6}{4-2}\\\\m=\dfrac{10}{2}\\\\m=5[/tex]

⇒ Therefore, the slope of the line is 5. Plug this back into the general form:

[tex]y=5x+b[/tex]

Now, determine the y-intercept.

[tex]y=5x+b[/tex]

⇒ Plug in one of the given points:

[tex]6=5(2)+b\\6=10+b\\b=-4[/tex]

⇒ Therefore, the y-intercept is -4. Plug this back into our original equation:

[tex]y=5x-4[/tex]

[tex]y=5x-4[/tex]

Answer:

[tex]\displaystyle k = \frac{1}{32}\ln\frac{1}{2} \approx -0.02166[/tex]

Step-by-step explanation:

The decay formula is given by:
[tex]\displaystyle P(t) = P_0e^{kt}[/tex]

Where k is some constant, P₀ is the initial population, and t is the number of years.

Because the substance has a half-life of 32 years, P(t) = 1/2P₀ when t = 32. Substitute:
[tex]\displaystyle \frac{1}{2}P_0 = P_0 e^{k(32)}[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} \frac{1}{2} & = e^{32k} \\ \\ \ln\left(e^{32k}\right) & = \ln\left(\frac{1}{2}\right) \\ \\ 32k & = \ln\frac{1}{2} \\ \\ k & = \frac{1}{32}\ln\frac{1}{2} \\ \\ &\approx -0.02166\end{aligned}[/tex]

In conclusion, the value of k is about -0.02166.

The value of k in the exponential decay formula is k = 0.022

To find the constant k in the decay formula for the radioactive substance, we can use the formula for exponential decay, which is given by:

N(t) = N₀*exp(-kt)

where:

The half-life of the substance is the time it takes for half of the substance to decay, which is 32 years in this case. So, after one half-life, N(t) = N₀ / 2.

Now, let's set up the equation for one half-life:

N(t) = N₀ * exp(-k * 32)

Since N(t) = N₀ / 2 after one half-life, we can write:

N₀ / 2 = N₀ * e^(-k * 32)

Now, divide both sides by N₀:

1/2 = exp(-k * 32)

To solve for k, take the natural logarithm (ln) of both sides:

ln(1/2) = -k * 32

k = ln(1/2) / -32

k = 0.022

Learn more about half-life at:

https://brainly.com/question/1160651

#SPJ3

Answer:  

g(x) has the smallest possible y-value of -3

Step-by-step explanation:

f(x) = 3ˣ - 3   This is an exponential graph shifted down three units. So, it has an asymptote at y = -3, which means it approaches -3 but does not touch it.Range: y > 3   (-3, ∞)   g(x) = 7x² - 3  ⇒ g(x) = 7(x - 0)² - 3   This is a parabola with vertex at (0, -3) Range: y ≥ 3   [-3, ∞)

Answer:

1/89

Step-by-step explanation:

Two digit numbers include all numbers from 10 to 99. 99-10 = 89. Therefore the probability that Simon guesses the number correctly on the first try is 1 out of 89 which can be written as 1/89.

Answer: 18,840*pi

Step-by-step explanation:

The volume of a globe would be 4/3*pi*radius^3 so that would be 4/3*14,130= 18840*pi or approximately 59,187.6055

The two parabolas intersect for

[tex]8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2[/tex]

and so the base of each solid is the set

[tex]B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}[/tex]

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, [tex]|x^2-(8-x^2)| = 2|x^2-4|[/tex]. But since -2 ≤ x ≤ 2, this reduces to [tex]2(x^2-4)[/tex].

a. Square cross sections will contribute a volume of

[tex]\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x[/tex]

where ∆x is the thickness of the section. Then the volume would be

[tex]\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}[/tex]

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

[tex]\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x[/tex]

We end up with the same integral as before except for the leading constant:

[tex]\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx[/tex]

Using the result of part (a), the volume is

[tex]\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}[/tex]

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

[tex]\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x[/tex]

and using the result of part (a) again, the volume is

[tex]\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}[/tex]

Answer:

11 feet

Explanation:

Here given:

====================

Solving steps:

⇒ 1/2 * (15 + b) * 7.6 = 98.8

⇒ (15 + b) * 7.6 = 197.6

⇒ (15 + b) = 26

⇒ b = 11 ft

Let unknown be x

Answer: 4

Step-by-step explanation: how i know by guessing

Answer: 147.2

Step-by-step explanation:

(8+15) = 23

23 x 6.4= 147.2

Answer: 147.2

Step-by-step explanation: 8+15= 23 so 23*6.4 is 147.2

Let that be y

Now solve

Each youth ticket costs 7$

Answer So you can add a number with the letter t and then add and then you can 35 dollers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Scalar factor Multiplication in Matrix.

So from the above matrix, -3A , is just simply multiplying the -3 to every element of the matrix, so we get as,

===> -3A = | -9 -18 |

| -24 -21 |

| -6 6 |

hence the correct option is B.

Answer:

192 liters

Step-by-step explanation:

Tank A

w = 100 + 80.5m

where:

Therefore, when m = 4:

⇒ w = 100 + 80.5(4) = 422 liters

Tank B

Given ordered pairs:  (0, 154)  (2, 384)  (6, 844)

[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{384-154}{2-0}=115[/tex]

Point-slope form of linear equation: [tex]\sf y-y_1=m(x-x_1)[/tex]

(where m is the slope and (x₁, y₁) is a point on the line)

[tex]\sf \implies y-154=115(x-0)[/tex]

[tex]\sf \implies y=115x+154[/tex]

Therefore, the equation for Tank B is:

w = 115m + 154

Therefore, when m = 4:

⇒ w = 115(4) + 154 = 614 liters

Difference

614 - 422 = 192 liters

Find equation for tank B

Slope:-

Equation in point slope form

For tank B

Put 4on both

Tank A:-

TankB

Difference:-