Which equation describes the line shown in the graph?

The sequences A and E are the same sequences.

Sequences are set of numbers where the numbers are arranged in a specific order. Some of the common types of sequences are Arithmetic sequences and Geometric sequences.

A) f(x) = 6x + 4 for x = {1, 2, 3, ....}

f(1) = 10, f(2) = 16, f(3) = 22, ....

B) f(x) = 10x + 4 for x = {1, 2, 3, ...}

f(1) = 14, f(2) = 24, f(3) = 34, ....

C) a₁ = 6 and aₙ₊₁ = aₙ + 4 for n = {1, 2, 3, ...}

a₁ = 6, a₂ = a₁ + 4 = 10, a₃ = a₂ + 4 = 14, ....

D) a₁ = 10 and aₙ₊₁ = aₙ + 4 for n = {1, 2, 3, ...}

a₁ = 10, a₂ = a₁ + 4 = 14, a₃ = a₂ + 4 = 18, .....

E) a₁ = 10 and aₙ₊₁ = aₙ + 6 for n = {1, 2, 3, ...}

a₁ = 10, a₂ = a₁ + 6 = 16, a₃ = a₂ + 1 = 22, ....

A and E are the same sequences with a common difference 6 and the first term 10.

Hence A and E have the same sequence 10, 16, 22, .....

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a) If f(y) is a probability density function, then both f(y) ≥ 0 for all y in its support, and the integral of f(y) over its entire support should be 1. eˣ > 0 for all real x, so the first condition is met. We have

[tex]\displaystyle \int_{-\infty}^\infty f(y) \, dy = \frac14 \int_0^\infty e^{-\frac y4} \, dy = -\left(\lim_{y\to\infty}e^{-\frac y4} - e^0\right) = \boxed{1}[/tex]

so both conditions are met and f(y) is indeed a PDF.

b) The probability P(Y > 4) is given by the integral,

[tex]\displaystyle \int_{-\infty}^4 f(y) \, dy = \frac14 \int_0^4 e^{-\frac y4} \, dy = -\left(e^{-1} - e^0\right) = \frac{e - 1}{e} \approx \boxed{0.632}[/tex]

c) The mean is given by the integral,

[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \int_0^\infty y e^{-\frac y4} \, dy[/tex]

Integrate by parts, with

[tex]u = y \implies du = dy[/tex]

[tex]dv = e^{-\frac y4} \, dy \implies v = -4 e^{-\frac y4}[/tex]

Then

[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \left(\left(\lim_{y\to\infty}\left(-4y e^{-\frac y4}\right) - \left(-4\cdot0\cdot e^0\right)\right) + 4 \int_0^\infty e^{-\frac y4} \, dy\right)[/tex]

[tex]\displaystyle \cdots = \int_0^\infty e^{-\frac y4} \, dy[/tex]

[tex]\displaystyle \cdots = -4 \left(\lim_{y\to\infty} e^{-\frac y4} - e^0\right) = \boxed{4}[/tex]

Answer:

Option B

Step-by-step explanation:

6x+3y=13

6x+3y-13=13--13

6x+3y-13=0

Answer:

(-5,-3)

(1,3)

Step-by-step explanation:

Solving with substitution

Set both equations to y =  ...

y = x^2 + 5x - 3

----------------

y - x =2

y = x + 2

----------------

Substitute one of the Y's with the other Y = equation.

x + 2 = x ^2 + 5x -3

Set one side to 0

0 = x^2 + 4x -5

x^2 + 4x - 5 = 0

Simplify by factoring

(x-1) (x+5)

Get your X values

x-1 = 0

x = 1

x+5 = 0

x = -5

Plug in each X into one of the equations to get your Y value.

1st X

y = x + 2

y = 1 + 2

y = 3

When X = 1, Y = 3

2nd X

y = x + 2

y = -5 + 2

y = -3

When X = - 5, Y = -3

Your answers are (1,3) and (-5,-3)

Answer:

x = 7 & y = 8

Step-by-step explanation:

We know that

Mean = Sum of terms/Total terms

=> Mean = 4 + 6 + x + y + 10/5

=> Mean = 20 + x + y/5

Now,

Median = (n + 1)/2

=> Median = (5 + 1)/2

=> Median = 6/3

=> Median = 3rd term = x

So,

x = 20 + x + y/5

x × 5 = 20 + x + y

5x = 20 + x + y

5x - x = 20 + y

4x = 20 + y

Since x and y are in order so,

Possible outcomes will be 7,8 & 9

(7,8) & (8,9) & (7,9)

Taking x = 7 and y = 8

4(7) = 20 + 8

28 = 28

Hence,

x = 7 and y = 8

Answer:

y=7 x=8

Step-by-step explanation: hope you do well in school

Answer:

pic?

Step-by-step explanation:

send me the picture please

Answer:

Step-by-step explanation:

[tex]x - 0.20x \: = 1480[/tex]

[tex]0.8x = 1480[/tex]

[tex]x = 1480 \div 0.8[/tex]

I'm not sure if this is correct, but I got this

Last year’s computer models are discounted 20%. If a computer is on sale for $1,480, what is the original price of the computer rounded to the nearest dollar?

20% = 0.2

1,480 x 0.2 = 296

1,480 + 296 = 1,776

Answer: 1,776

Again, I don't know if this is correct, so don't be 100% sure with my response.

Answer:

85m

Step-by-step explanation:

Perimeter of a rectangle = 2(l+b)

b=72m, l=?

perimeter =314m

314=2(l+72)

314/2= l+72

157=l+72

l=157-72

l=85m

Answer:

292.6

Step-by-step explanation:

Answer:

C)105

Step-by-step explanation:

sizde benim sorduğum soruları cevaplarsanız sevinirim doğru ve hızlı bir şekilde

Answer:

40

Step-by-step explanation:

that's how it is done hope it will help

The volume of the bigger sphere is 8 times larger than the volume of the smaller sphere.

The formula of the volume of a sphere is given below

⇒ Formula:

⇒ Where:

From the question, There are two spheres.

If the radius of the bigger sphere is two times the radius of the smaller sphere.

⇒ Where

For the bigger sphere

⇒ Substitute these values into equation 1

  For the smaller sphere,

⇒ Comparing equation 2 and equation 3

Hence, The volume of the bigger sphere is 8 times larger than the volume of the smaller sphere.

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Answer:

Step-by-step explanation:

If you mean length is 2½ times its width not "2½cm times its width"

      2(L + W) = 270

2(2.5W + W) = 270

      2(3.5W) = 270

              7W = 270

                W = 38.5714285714...

                W ≈ 38.57 cm

Answer:

Width = 38. 57 cm

Step-by-step explanation:

The perimeter of a Rectangle = 270 cm

Now,

Let's take x to be the width.

Length = 2½ = 5x/2

According to the formula,

The perimeter of a rectangle = 2 ( l + w )

270 = 2 ( 5x/2 + x )

270 = 5x + 2x

270 = 7x

x = 270/7

x = 38. 57 cm.

• The width of a rectangle is 38.57 cm

The Lateral Surface Area of the cylindrical oil storage tank is [tex]2486.9\text{ sq.ft}[/tex]

The Total Surface Area of the cylindrical oil storage tank is [tex]5526.4\text{ sq.ft}[/tex]

If the height and base radius of the cylindrical oil storage tank are represented by [tex]h[/tex] and [tex]r[/tex] respectively, then

The Lateral Surface Area, also known as the Curved Surface Area, of the cylindrical oil storage tank has the formula

[tex]L=2\pi rh[/tex]

The Total Surface Area of the cylindrical oil storage tank has the formula

[tex]T=2\pi rh+2\pi r^2\\T=2\pi r(h+r)[/tex]

The values for the height and base radius are [tex]18ft[/tex] and [tex]22ft[/tex] respectively.

Calculate the Lateral Surface Area

[tex]L=2\pi rh\\=2\times 3.14\times 22\times 18\\\approx 2486.9\text{ sq.ft}[/tex]

Calculate the Total Surface Area

[tex]T=2\pi r(h+r)\\=2\times 3.14\times22(18+22)\\=5526.4\text{ sq.ft}[/tex]

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An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is B.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that has a "x" term with a coefficient of 1 is the expression that has positive one in from of the term that has x in the expression.

Now, If all the options are observed, then it can be found that the second option has x term with leading coefficient as 1.

Hence, the correct option is B.

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Answer:

Nick will have to pay $63.56 for the shoes.

Step-by-step explanation:

f the original cost of the shoes is $56.75 and the markup is 12% greater than the original price, the final price would be $63.56.

$56.75 • 0.12 = $6.81

$56.75 + $6.81 = $63.56

$56.75 + 12% = $63.56

Answer:

Nick will have to pay $63.56 for the shoes.

Answer:

2.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.8 units

Answer:

x = -7

Step-by-step explanation:

The 2 horizontal lines are parallel as given ion the problem.

The x + 97 angle is congruent to the right angle.

x + 97 = 90

x = -7

Answer:

3 big guys

Step-by-step explanation:

Answer:

Step-by-step explanation:

we find by synthetic division.

v-8=0

v=8

8 |  3  -34   79   5   21   19

  |  -     24  -80 -8  -24 -24

  |----------------------------------

     3   -10    -1   -3    -3  |-5

Quotient:-3v^4-10v³-v²-3v-3

Remainder:- -5

Answer:

y=

x

​

−2

y=−

x

​

−2, x≥0

​

y=−

x−2, x≥0

​

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

53/106 = x/82 similar triangles

x=41

Step-by-step explanation:

hope it will help you and please mark the answer as brillant please.

Step-by-step explanation:

x = the first number of the sequence

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 519

6x + 1 + 2 + 3 + 4 + 5 = 519

6x = 504

x = 84

so, the third number is x+2 = 84 + 2 = 86

[tex]\left(3+\sqrt{-16} \right) \left(5-\sqrt{-25} \right)\\\\=\left(3+\sqrt{-1} \cdot \sqrt{16} \right) \left(5- \sqrt{-1} \cdot \sqrt{25} \right)\\\\=(3+4i)(5-5i)~~~~~~~~~~~~~~;\left[i=\sqrt{-1} \right]\\\\=15-15i + 20i - 20i^2\\\\=15+5i -20(-1)~~~~~~~~~~~~;[i^2 =-1]\\\\=15+5i +20\\\\=35+5i[/tex]

Answer:

x = 65

Step-by-step explanation:

2x + 2(2x-15) = 360

2x + 4x - 30 = 360

6x = 390

x = 65

Answer:

I do not see that any of your options will work.

Step-by-step explanation:

a) and b) have a false first statement because f(1) = 96, not 12

c) would create the sequence 96, 1152, 13824

d.) would create the sequence 96, 192, 384. 768...

I believe the correct answer would be

f(1) = 96     f(n) = ½f(n-1)  n ≥ 2

which could be either c) or d) if taking potential typographic errors into account. Recording a "2" or "12" where a "½" ought to be.