domain of f(x)=(1/4)^x

What is the domain of f(x)

O A. x>0

OB. All real numbers

O C. y>0

O D. x<0

? Need help asap

Since [tex]a,b,c[/tex] are in geometric progression, if [tex]r[/tex] is the common ratio between consecutive terms, then

[tex]a=a[/tex]

[tex]b = ar[/tex]

[tex]c=ar^2[/tex]

Since [tex]a,b,c[/tex] are also in arithmetic progression, if [tex]d[/tex] is the common difference between consecutive terms, then

[tex]a = a[/tex]

[tex]b = a + d \implies d = b-a[/tex]

[tex]c = b + d = a + 2d \implies c = a + 2(b-a) = 2b-a[/tex]

Given that [tex]abc=27[/tex], we have

[tex]abc = a\cdot ar\cdot ar^2 = (ar)^3 = 27 \implies ar = 3 \implies a = \dfrac3r[/tex]

[tex]b = \dfrac3r \cdot r = 3[/tex]

[tex]c = \dfrac3r \cdot r^2 = 3r[/tex]

It follows that

[tex]c = 2b-a \iff 3r = 6 - \dfrac3r[/tex]

Solve for [tex]r[/tex].

[tex]3r - 6 + \dfrac3r = 0[/tex]

[tex]3r^2 - 6r + 3 = 0[/tex]

[tex]r^2 - 2r + 1 = 0[/tex]

[tex](r-1)^2 = 0[/tex]

[tex]\implies r=1 \implies a=b=c=3[/tex]

so the only possible sequence is {3, 3, 3, …}.

The variable overhead rate variance is: c. $6,052 U.

First step is to calculate variable component of the predetermined overhead rate using this formula

Variable component of the predetermined overhead rate= Budgeted variable manufacturing overhead/Budgeted hours

Let plug in the formula

Variable component of the predetermined overhead rate=$ 28,200/12,000 labor-hours

Variable component of the predetermined overhead rate=$2.35 per labor-hour

Second step is to calculate  variable overhead rate variance using this formula

Variable overhead rate variance=(AH×AR)-(AH×SR)

Let plug in the formula

Variable overhead rate variance= $ 26,967- ( 8,900 labor-hours×$2.35 per labor-hour)

Variable overhead rate variance= $ 26,967- $20,915

Variable overhead rate variance= $6,052 U (Unfavorable)

Therefore the variable overhead rate variance is: c. $6,052 U.

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Based on the given summation notation, the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n

The expression is given as:

43Σn=1(3+9n)

As a general rule, if a summation notation is represented using the following expression

Σ(a + bn)

The equivalent expression of the above summation notation is

Σa + bn

Where the variable a is a constant in the expression

This means that:

Σ(a + bn) = Σa + bn

Using the above equation as a guide, we have the following equivalent equation

43 Σ n=1 (3+9n) = 43 Σ n=1 3 + 43 Σ n=1 9n

Hence, based on the given summation notation; the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n

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Answer:

D on 3dg I took the best

Step-by-step explanation:

Answer:

Area = 33 inches squared

Step-by-step explanation:

The formula for the area of a kite is:

Area = ½ × (d)1 × (d)2

To find the first diagonal (d1):

d1 = 7 in + 4 in = 11 in

To find the second diagonal (d2):

The triangles on the right of the kite must be 3 4 5 triangle since it is a right triangle with a hypotenuse of 5 and a side of 4, we know half of a diagonal would be 3 inches.

d2 = 3 in + 3 in = 6 in

Now we can plug the diagonals into the area formula.

Area = ½ × 11 × 6 = 33 inches squared

Answer: A = 33 in²

Step-by-step explanation:

Given information:

Longer side = 7 in

Shorter side = 4 in

Shorter Hypotenuse = 5 in

Given formula:

A = (1/2) × (d₁) × (d₂)

Please refer to the attachment below for a graphical understanding

Determine the length of the shorter side (vertical) through the Pythagorean theorem

a² + b² = c² (Pythagorean theorem)

(4)² + b² = (5)² (Substitute values into the equation)

16 + b² = 25

b² = 25 - 16

b² = 9

b = 3  or b = -3 (rej)

Substitute values into the given formula

A = (1/2) × d₁ × d₂

A = (1/2) × (7 + 4) × (3 + 3)

Simplify values in the parenthesis

A = (1/2) × 11 × 6

Simplify by multiplication

A = (11/2) × 6

[tex]\Large\boxed{A=33}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The area of the garden is 74 square feet

The complete question is added as an attachment

From the attached figure, we have the following shapes and dimensions:

The rectangular area is

A1 = 10 * 5

Evaluate

A1 = 50

The area of the trapezoid is

A2 = 0.5 * Sum of parallel bases * height

This gives

A2 = 0.5 * (10 + 6) * 3

Evaluate

A2 = 24

The total area is

Total = A1 + A2

This gives

Total = 50 + 24

Evaluate

Total = 74

Hence, the area of the garden is 74 square feet

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The true statement is (c) the function f(x) is an exponential function

From the table, we can see that:

This means that the table represents an exponential function

The rate is then calculated as:

f(n) = f(1) * r^n-1

Using f(3), we have

102 = 17 * r^3-1

This gives

r^2 = 6

Take the square roots

r = 2.45

Hence, the true statement is (c) the function f(x) is an exponential function

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Answer:

810 is the number that represents the same amount.

Hope this helps :)

Hello and Good Morning/Afternoon!

Let's take this problem step by step:

Let's consider some facts:

 ⇒ angles are opposite each other

    ⇒ by the Vertical Angle Theorem

        ⇒ angles opposite each other are equal in measure

So:

 [tex]\hookrightarrow 4x + 12 = 64[/tex]

Let's solve

  [tex]4x + 12 = 64\\4x = 52\\x = 13[/tex]

x's value is 13

Answer: 13

Hope that helps!

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The first five terms of the recursive sequence are 5, 12, 19, 26 and 33.

In this question we have a linear recursive equation that requires the value of the immediately previous element to generate the next one. Then, we need to evaluate the expression for the first five elements:

i = 1

a₁ = 5

i = 2

a₁ = 5, a₂ = a₁ + 7

a₂ = 5 + 7

a₂ = 12

i = 3

a₂ = 12, a₃ = a₂ + 7

a₃ = 12 + 7

a₃ = 19

i = 4

a₃ = 19, a₄ = a₃ + 7

a₄ = 19 + 7

a₄ = 26

i = 5

a₄ = 26, a₅ = a₄ + 7

a₅ = 26 + 7

a₅ = 33

The first five terms of the recursive sequence are 5, 12, 19, 26 and 33.

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In the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0

Radical equations are expression that are under the square root. For instance √x is a radical expression.

Given the equation expressed as:

x − 5 = √3x −11

Square both sides to have;

(x-5)² = (√3x −11 )²

This can be further expressed as:

(x-5)² =3x −11

Expand

x² -10x + 25 = 3x - 11

Equate to zero

x² -10x + 25 - 3x +11 = 0
x² -10x - 3x +36 = 0
x² - 13x + 36 =0

Hence in the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0

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Based on the time taken by the jet when flying with the wind versus against it, the rate of the jet and jet streams are:

The speed of the jet flying against the wind is:

= 3,000 / 3

= 1,000 mph

The speed with the jet stream is:

= 5,360 / 4

= 1,340 mph

Assuming the speed of the jet is x and the rate of wind is y, the formulas are:

x - y = 1,000

x + y = 1,340

Solving gives:

2x = 2,340

x = 1,170 mph

The rate of jet stream is:

x - y = 1,000

1,170 - y = 1,000

y = 170 mph

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We want to find [tex]x[/tex] such that

[tex]\mathrm{Pr}(X \le x) = 0.81[/tex]

where [tex]X[/tex] is the random variable for test scores, and [tex]X\sim\mathrm{Normal}(63,9.3^2)[/tex].

Transform [tex]X[/tex] to [tex]Z\sim\mathrm{Normal}(0,1)[/tex] using the relation

[tex]X = \mu + \sigma Z \implies Z = \drac{X-63}{9.3}[/tex]

so that

[tex]\mathrm{Pr}(X \le x) = \mathrm{Pr}\left(\dfrac{X-63}{9.3} \le \dfrac{x-63}{9.3}\right) = \mathrm{Pr}\left(Z \le \dfrac{x-63}{9.3}\right) = 0.81[/tex]

Applying the inverse CDF of [tex]Z[/tex] (denoted by [tex]\Phi^{-1}[/tex]), we have

[tex]\dfrac{x-63}{9.3} = \Phi^{-1}(0.81) \approx 0.8779[/tex]

Solve for [tex]x[/tex].

[tex]\dfrac{x-63}{9.3} \approx 0.8779[/tex]

[tex]x-63 \approx 8.1644[/tex]

[tex]x \approx 76.1644[/tex]

Then the cutoff test score for the 81% percentile is [tex]P_{81} \approx \boxed{76}[/tex].

Answer:

Joey needs 9 boxes.

Step-by-step explanation:

You will use the fact that a dozen is 12 cookies. You're trying to find how many dozen are in 100.

Something like:

12b = 100

or if you're studying inequalities:

12b >= 100

Divide by 12 to solve. See image. Interpret the results. See image.

The standard form the weight of a pitaya seed is 1 x 10⁷ ounces.

Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form. If you look closely, you will see that 1.23 is a decimal between 1.0 and 10.0, and as a result, we have the standard form of 123,000,000 as 1.23 x 10⁸.

Given that a pitaya, or dragon fruit, is a tropical fruit with pink skin and pulp filled with tiny black seeds. The weight of a pitaya seed is 1 x 10⁷ ounces.

The standard form can be written as:-

Weight = 10000000 ounces

Weight = 1 x 10⁷   ounces.

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Answer:

110 [%].

Step-by-step explanation:

if the initial area is 24 m² and final area 50.4 m², then the required percentage can be calculated as:

[tex]\frac{50.4}{24}*100-100=110[/tex] ,  

where 50.4/24*100 - the final percentage.

P.S. It means, the final value of the paint is 3*2.1=6.3 [liters].

[tex]\stackrel{\textit{\LARGE Line A}}{(\stackrel{x_1}{-8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{4})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-8)}}} \implies \cfrac{4 -5}{-5 +8}\implies -\cfrac{1}{3} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE Line B}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{-1 -1}{4 +0}\implies -\cfrac{1}{2}[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, and that parallel lines have equal slopes, well, those two slopes above aren't either, so since they're neither, and they're different, that means that lines A and B intersect.

The service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

a. Service charge rate

Service charge rate=Budgeted cost/ Budgeted activity base quantity

Help desks:

Service charge rate=$160,000/3,200 calls

Service charge rate=$50 per call

Network center:

Service charge rate=$735,000/9,800 devices

Service charge rate=$75 per device monitored

Electronic mail:

Service charge rate=$100,000/10,000 accounts

Service charge rate=$10 per user or per e-mail account

Local voice support:

Service charge rate=$124,600/8,900 phone extensions

Service charge rate=$14 per phone extension

b.  Help desk charge

Help desk charge =(Number of employees times × Percentage of office employees× Percentage with a computer ×Number of calls)× Service charge rate

Help desk charge:

(5,200 employee×25%×96%×1.5)× $50 per call

=$93,600

Network center charge:

[(5,200 employee×25%×96%)+ 600]× $75 per device

=$138,600

Electronic mail:

(5,200 employee×25%×96%×100)×$10 per user or per e-mail account

=$12,480

Local voice support:

(5,200 employee×25%)× $14 per phone extension

=$18,200

Therefore the service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

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By the fundamental theorem of calculus,

[tex]\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}[/tex]

In general,

[tex]\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}[/tex]

Answer:

ight first you add 4 to 6 and that gets you 10 so you left with p+5=10 then you subtract 5 from 10 so p is gonna be  5

Step-by-step explanation:

Based on the AED 40,000 net loss that the SoftNet line brings to Hava Racquets company, the incremental effect if the Softnet line is eliminated is that the company would save AED 10,000.

If Hava Racquets Company decides to scrap the Softnet line, then it means that they will no longer be incurring the AED 40,000 net loss that the line had brought to them.

They would instead incur a fixed cost of AED 30,000 which they can apply to their other operations.

This means that in exchange for a AED 40,000 loss, they would instead get  a AED 30,000 loss.

The savings on these losses is:

= 40,000 - 30,000

= AED 10,000

This means that Hava Racquets Company will make a saving of AED 10,000 if they eliminate the line.

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The insinuation of calling the volume of a solid 3-dimentional shape 10in³ is that the product of all of its dimensions as measured in units is; 10 in.³.

It follows from the task content that the shape in discuss is a solid shape and consequently, one of it's measures is its volume which describes the space it occupies.

On this note, the meaning of a solid having a volume of 10in³ as indicated is that it's volume is; 10 times as large as the volume occupied by an object with unit dimensions 1“ x 1“ x 1“ in which case, the volume is; 1 in³.

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Answer:

[tex]-8c+6[/tex]

Step-by-step explanation:

[tex]2(-6c+3)+4c=-12c+6+4c=\boxed{-8c+6}[/tex]

Answer:

-8c + 6 and 3(-4c+2) + 4c

Step-by-step explanation:

khan

Answer:

  2800

Step-by-step explanation:

The choice at any node (except the edges) is to go right or go down.

To get from A to B requires a total of 4 choices to go down, and 4 choices to go right. Those can occur in any order. Locating the "right" choices in the list of "all" choices is effectively choosing 4 of 8. The number of ways those choices can be made is ...

  C(8, 4) = 8!/(4!(8-4)!) = 8·7·6·5/(4·3·2) = 70

Similarly a total of 2 choices must be made, 1 of which is a "right" choice. The number of ways those can be ordered is ...

  C(2, 1) = 2 . . . . . . . that is: (right, down) or (down, right)

A total of 6 choices must be made, of which 3 are "right." The number of possible orderings is ...

  C(6, 3) = 6·5·4/(3·2·1) = 20

Each set of choices is independent of the others, so the total possible number is the product of the numbers of choices on the subpaths:

  total paths = (70)(2)(20) = 2800

There are 2800 possible paths from A to D.

Answer: Moderate negative association

Step-by-step explanation:

The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.

In this problem we have a family of functions in implicit form, that is, a function of the form f(x, y, c) = 0. The equation of a orthogonal trajectory is always perpendicular to a particular form of a equation. First, we determine the first derivative of the given expression:

5 · x² - 2 · y² = C

10 · x - 4 · y · y' = 0

4 · y · y' = 10 · x

y' = (10 · x) / (4 · y)

y' = (5 · x) / (2 · y)

If f(x, y) = (5 · x) / (2 · y), then the differential equation for the orthogonal trajectories related to the family of functions is:

y' = - 1 / f(x, y)

y' = - (2 · y) / (5 · x)

dy / (2 · y) = - dx / (5 · x)

By indefinite integration we get the following solution to the ordinary differential equation:

(1 / 2) · ㏑ y = - (1 / 5) · ㏑ x + C

(1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C

The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.

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Answer:

the answer is 2880

Step-by-step explanation:

because you would use the formula (n - 2) x 180 which equals the sum interior angles of any polygon .

The letter n stands for number of sides so in this case you would do (18 - 2) x 180 so 16 × 180 = 2880

hope this helped :) pls ask if you need any more explanation .

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The y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4

The y-intercept of a function is the point where the value of x is zero. Given the function below;

4x-9y=36

when the value of x is zero, hence;

4(0) - 9y = 36

Simplify to have:

0 - 9y = 36

-9y = 36

Divide both sides by -9 to have:

-9y/-9 = 36/-9

y = -4

Hence the y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4

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Answer:

x = 8 ± [tex]\sqrt{10}[/tex]

Step-by-step explanation:

x² - 16x + 54 = 0 ( subtract 54 from both sides )

x² - 16x = - 54

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 54 + 64

(x - 8)² = 10 ( take the square root of both sides )

x - 8 = ± [tex]\sqrt{10}[/tex] ( add 8 to both sides )

x = 8 ± [tex]\sqrt{10}[/tex]

then

x = 8 - [tex]\sqrt{10}[/tex] , x = 8 + [tex]\sqrt{10}[/tex]

He will be left no money after buying 25 copies because he has 1900 rupees less.

Given that Usman buys 8 books that cost Rs. 120/ each, he will be left Rs. 140.

The cost of 1 books is Rs 120.

The cost of 8 book is 120×8=960.

The cost of 25 books is 120×25=3000

To find the money usman will left with him is the difference between the total money and the cost of 25 books.

Total money=960+140=1100

money left=Total money -cost of 25 books

money left=1100-3000

Usman have less money to buy 25 books. He has 1900 rupees less to buy 25 books.

Hence, Usman does leave any money with even he has less money to buy 25 books

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Answer:

i belive its graph B