If f(x) = 3x and g(x)= 1/x, what is the domain of (g*f) (f)?

x≥0
all real numbers except x = 0
x∠0
all real numbers

Quotient: 0.0009775. The decimal point is moved 4 places to the left in both the divisor and the dividend.

Quotient: 0.0023835. The decimal point is moved 2 places to the left in both the divisor and the dividend.

By moving the decimal point in the divisor and the dividend, we can perform long division to find the quotients. To check the dividend, we can multiply the quotients by the divisor and see if the result matches the dividend.

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Answer: the final answer is 1 4/5 or 9/5

Step-by-step explanation:

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

3 3/4 turns into 15/4 and 2 1/12 turns into 25/12

Second: then flip the 2nd fraction so it becomes 12/25

now multiply straight across: 15/4 x 12/25

15 x 12=180

4 x 25=100

180/100= 9/5= 1 1/4

Simplest form of quotient of given fractions is 9/5.

The given fractions are \(3\frac{3}{4}\) and \(2\frac{1}{12}\).

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

\(3\frac{3}{4}\) can be written as \(\frac{15}{4}\) and \(2\frac{1}{12}\) can be written as \(\frac{25}{12}\).

Keep 15/4 and change division sign to multiplication sign and reverse the fraction 25/12 as 12/25.

That is , \(\frac{15}{4} \div \frac{25}{12} = \frac{15}{4} \times \frac{12}{25}\)

\(=\frac{3}{1} \times \frac{3}{5} =\frac{9}{5}\)

So, quotient = 9/5

Therefore, simplest form of quotient of given fractions is 9/5.

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solution

For this case we can do the following:

Then the final answer for this case would be 0

Answer:

a) x + y = 30

   2x + 4y = 80

b) chickens - 20

    pigs - 10

Step-by-step explanation:

a) x + y = 30

   2x + 4y = 80

b) x + y = 30 (1) times by 2

   2x + 4y = 80 (2) times by 1

   2x +2y = 60 (1)

   2x + 4y = 80 (2)

Take 1 away from 2.

2y = 20

y=10

Substitute it back into the original equations.

x+y=30

x + 10 = 30

x = 20

the radius of the distance between the middle point of the circle and the outside, we have the diameter which is 6 so the radius will be 3

slant height is

\(\sqrt{r^2+h^2}\)

h is 4.7 and r is 3

\(\sqrt{3^2+4.71^2} \\5.58427\)

slant height is 5.58427

lateral surface area

\(\pi r\sqrt{h^2+r^2}\)

\(\pi (3)\sqrt{4.71^2+3^2} \\52.63053\)

lateral surface area is 52.63053

total surface area

\(\pi r(r+\sqrt{h^2+r^2})\)

\(\pi 3(3+\sqrt{4.71^2+3^2})\)

\(80.90486\)

total surface area is 80.90486

The slant height of the cone is 5.6km, the total surface area is 50.4πkm, the lateral surface area is 16.8π km.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreases to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

In the given question radius of the cone is (6/2) km = 3 km.

The slant height of the cone is 5.6 km.

The total surface area of the cone is = π×3(3 + 5.6) km.

= 3π(16.8) km.

= 50.4π km.

lateral surface area is = π×3×5.6 km.

= 16.8π km.

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Each solid plastic cylinder with a radius of 2.51 cm and length of 5.64 cm has a charge of approximately 282.46 Coulombs.

To find the charge of each cylinder, we need to use the formula for the charge of a uniformly charged solid cylinder, which is given by Q = λ * V, where Q is the charge, λ is the charge density, and V is the volume of the cylinder.

First, we need to calculate the volume of each cylinder. The formula for the volume of a cylinder is V = π * r^2 * h, where r is the radius and h is the height or length of the cylinder.

Using the given values, we have r = 2.51 cm and h = 5.64 cm. Converting these values to meters, we get r = 0.0251 m and h = 0.0564 m.

Calculating the volume of each cylinder:

V = π * (0.0251 m)^2 * (0.0564 m) = 7.0925e-5 m^3

Now, we need to find the charge density λ. The charge density for each cylinder is given by λ = Q / V, where Q is the charge and V is the volume.

Since the radius and length are the same for all four cylinders, the charge density will also be the same. Therefore, we can calculate the charge density using one of the cylinders.

Assuming the charge density is λ, we can rearrange the formula to solve for λ:

λ = Q / V

Given that λ = 2.0 μC/m^3 (microCoulombs per cubic meter), we have:

2.0e-6 C/m^3 = Q / (7.0925e-5 m^3)

Solving for Q:

Q = (2.0e-6 C/m^3) * (7.0925e-5 m^3)

Q = 1.4185e-10 C

Therefore, the charge of each cylinder is 1.4185e-10 C, which is approximately equal to 282.46 Coulombs.

Each solid plastic cylinder with a radius of 2.51 cm and length of 5.64 cm has a charge of approximately 282.46 Coulombs. This calculation is based on the given charge density of 2.0 μC/m^3 and the formula for the charge of a uniformly charged solid cylinder.

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Answer:

-24

Step-by-step explanation:

absolute value of -24 would make it +24

-1 times 24 is -24

Answer: -24

Step-by-step explanation:

The absolute value of a number is how far away the said number is from zero, so -24's would be 24.

24 x -1 = -24

Answer:

You need to give the options so i can tell you which expression it is.

Step-by-step explanation:

Answer: 1. The additive inverse of a number is what you can add to that number for the sum to be zero. For real numbers, such as rational numbers, that means the additive inverse can be found by just flipping the sign of the number. The additive inverse property says if you add a number and its additive inverse, then the sum is zero.

For example, let's use the number 3. The additive inverse of 3 is -3, since 3 + (-3) = 0. This is also true the other way around. The additive inverse of -3 is 3.

When subtracting rational numbers, remember that subtracting is the same as adding a negative! That means 3 - 3 is the same as 3 + (-3) or -3 - (-3) is the same as -3 + 3. Both of these sums involve a number and its additive inverse and they add up to zero.

Answer:

The equation of the line is:

y

=

5

6

x

−

15

6

Explanation:

The equation of the line will be in the form:

y

=

m

x

+

c

where  

m

is the slope (gradient) and  

c

is the y-intercept.

To find the slope, we use:

m

=

y

2

−

y

1

x

2

−

x

1

It doesn't matter which point we decide is  

(

x

1

,

y

1

)

and which we choose as  

(

x

2

,

y

2

, since the formula will work either way.

m

=

0

−

(

−

5

)

3

−

(

−

3

)

=

5

6

Now we can use the slope and the coordinates of one point - either will do - to find the y-intercept:

y

=

m

x

+

c

0

=

5

6

(

3

)

+

c

=

15

6

+

c

Rearranging:

c

=

0

−

15

6

=

−

15

6

Over all, then, the equation of the line is:

y

=

5

6

x

−

15

6

The equation of the line is:

y

=

5

6

x

−

15

6

Explanation:

The equation of the line will be in the form:

y

=

m

x

+

c

where  

m

is the slope (gradient) and  

c

is the y-intercept.

To find the slope, we use:

m

=

y

2

−

y

1

x

2

−

x

1

It doesn't matter which point we decide is  

(

x

1

,

y

1

)

and which we choose as  

(

x

2

,

y

2

, since the formula will work either way.

m

=

0

−

(

−

5

)

3

−

(

−

3

)

=

5

6

Now we can use the slope and the coordinates of one point - either will do - to find the y-intercept:

y

=

m

x

+

c

0

=

5

6

(

3

)

+

c

=

15

6

+

c

Rearranging:

c

=

0

−

15

6

=

−

15

6

Over all, then, the equation of the line is:

y

=

5

6

x

−

15

6

Step-by-step explanation:

We want to find the equation of the line that passes through the points (0, 3) and (5, -3). The linear equation is y = (-6/5)*x + 3

A general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope can be written as:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

In this case, we know that the line passes through (0, 3) and (5, -3) then the slope is:

\(a = \frac{-3 - 3}{5 - 0} = \frac{-6}{5}\)

Then the line is:

y = (-6/5)*x + b

To get the value of b, we use the fact that the line passes through (0, 3), so we have:

3 = (-6/5)*0 + b

3 = b

Then the linear equation is just:

y = (-6/5)*x + 3

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The lower bound of the speed of the bus is 75.65 km/h.

The lower bound of the speed of the bus is 6 hours, when the time of motion is corrected to the nearest half hour is calculated as follows;

The speed of the bus is calculated as follows;

v = distance / time

the lowest bound distance travelled by the bus = 435 km

the lowest bound of time of motion = 5 ³/₄ hour = 5.75 hr

The lowest bound speed = 435 km / 5.75 hr

                                          = 75.65 km/h

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The Sample standard deviation of 12 is 62

To determine the sample size needed to construct a 95% confidence interval for the population mean, μ, with a margin of error E=3 and a sample standard deviation s=12, follow these steps:

1. Find the critical value (z-score) for a 95% confidence interval. The critical value for a 95% confidence interval is 1.96.

2. Use the formula for determining sample size: n = (z * s / E)²
  Here, z = 1.96, s = 12, and E = 3.

3. Plug in the values and calculate the sample size:
  n = (1.96 * 12 / 3)²
  n = (7.84)²
  n ≈ 61.47

4. Round up to the nearest whole number to get the minimum sample size required: 62.

So, the sample size needed to construct a 95% confidence interval for the population mean with a margin of error of 3 and a sample standard deviation of 12 is 62.

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Answer:

4739 CDs

Step-by-step explanation:

Given the function that models the rate at which the disc is sold expressed as;

R(t)=20,000e^−0.12t

t is the number of weeks since the CD was first released

We are to look for the number of CDs that are expected to be sold during the first 12 weeks after the release. To do this, you will simply substitute t = 12 into the modeled function and get R(12) as shown;

R(t)=20,000e^−0.12t

R(12)=20,000e^−0.12(12)

R(12)=20,000e^−1.44

R(12)=20,000(0.2369)

R(12) = 4738.56

Hence the total number of CDs expected to be sold to nearest thousand is 4739 CDs

Answer:

127,000

Step-by-step explanation:

you take the integral from 0 to 12 of R(t)

Answer:20

π

cm or about

62.8

cm.

Step-by-step explanation:

The formula for a circumference of a circle is

2

π

r

, where

r

is the radius. We can plug our known value of the radius (

10

cm) into the formula and solve.

Answer:

78.5

Step-by-step explanation:

To rewrite the given parametric equations as Cartesian equations, we need to eliminate the parameter t. For the first equation, we get the Cartesian equation y = (3/2)x - (5/4). For the second equation, we get the Cartesian equation y = ln(x^2).

For the first equation x(t) = 3t - 2, y(t) = 5t^2, we need to eliminate t to get the Cartesian equation. Solving for t in terms of x, we get t = (x + 2)/3. Substituting this value in the equation for y, we get y = 5((x+2)/3)^2. Simplifying this, we get y = (3/2)x - (5/4).

For the second equation x(t) = e^(2t), y(t) = e^(4t), we need to eliminate t to get the Cartesian equation. Taking the natural logarithm of both sides of the equation for y, we get ln(y) = 4t.

Solving for t, we get t = ln(y)/4. Substituting this value in the equation for x, we get x = e^(2(ln(y)/4)), which simplifies to x = y^(1/2). Therefore, the Cartesian equation for this parametric equation is y = ln(x^2).

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On a purchase of $140, if $25 off coupon is applied followed by 35% off coupon, a) the cost will be $74.75, b) the functional representation will be

g°f = 0.65x - 16.25 : x = $140 . If 35% off coupon is applied followed by $25 off coupon, c) the cost will be $66 and   d) functional representation will be  f°g = 0.65x - 25 : x = 140

Here we are given two functions f and g.

f reduces the cost by $25 and g is the function that reduces it by 35%. This means that it will make the amount equivalent to 65% of the original.

Now f will be

f(x) = x - 25

g(x) = 0.65x

a)

The cost before applying the coupons is $140.

Now after applying finction f and reducing 25$ we get

$140 - $25

= $115

Now after applying 35% off coupon, the cost will be 65% of the previous one.

Hence the final cost will be

65/100 X 115

= $74.75

b)

Here we need to use function notation to represent the cost after the two coupons are applied.

Here it will clearly be g°f

Hence it will be

g°f = 0.65(x - 25) : x = $140

or, g°f = 0.65x - 16.25 : x = $140

c)

Here we will first apply the 35% off coupon to get

0.65 X 140

= $91

Now applying the $25 off coupon will give us

$66

d)

Now, here we will see that we will get the function

f°g = 0.65x - 25 : x = 140

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Answer:

$27,444.80

Step-by-step explanation:

12% of 22,540 is 2,704.8

add the amount she made

add the weekly salary (550 × 4)

Answer:

144*

Step-by-step explanation:

decagon has 10 sides every side is 144* angles

Answer:

144

Step-by-step explanation:

Answer:

D.) y < -1/5x + 1

Step-by-step explanation:

I sense that you're in a rush, so I'll spare you the lecture, haha.. Just trust.

The equation for the nth term of the given geometric sequence is Tₙ = \(8 * 9^{(n-1)\)

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. Let's denote the first term as "a" and the common ratio as "r."

Given the geometric sequence 8, 72, 648..., we can observe that each term is obtained by multiplying the previous term by 9. Therefore, the common ratio (r) is 9.

To find the nth term (Tₙ) of a geometric sequence, we can use the following formula:

Tₙ = \(a * r^{(n-1)\)

where "n" is the term number.

In this case, the first term (a) is 8, and the common ratio (r) is 9. Plugging these values into the formula, we get:

Tₙ = \(8 * 9^{(n-1)\)

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Answer:

y = 2x + 14

Step-by-step explanation:

y = mx + b to write the equation, we need 2 things: the slope and the y-intercept

y = ___x + ____

Slope:

Change in y over the change in x.  We find the change by subtracting.   The y values are 6 and -2.  The x values are -4 and -8

\(\frac{6- (-2)}{-4 -(-8)}\) = \(\frac{6+2}{-4+8}\) = \(\frac{8}4}\) = 2

The slope is 2.

y-intercept:

Use either of the points given and the slope 2 to find the y-intercept.  I am going to use the points(-4,6).  I will use -4 for x and 6 for y given from the point

y = mx + b

6 = 2(-4) + b

6 = -8 + b  Add 8 to both sides

14 = b

The y-intercept is 14.

y = 2x + 14

Helping in the name of Jesus.

To isolate cc in the equation (1/c - 1), we need to rearrange the equation to solve for cc. By applying algebraic manipulation, we can transform the equation into a form where cc is isolated on one side.

Let's start with the equation:

(1/c - 1)

To isolate cc, we can follow these steps:

Step 1: Combine the fractions by finding a common denominator. The common denominator is cc, so we rewrite 1 as cc/cc:

(cc/cc)/c - 1

Simplifying further, we have:

cc/ccc - 1

Step 2: Combine the terms:

(cc - ccc)/ccc

Step 3: Factor out cc:

cc(1 - cc)/ccc

Now we have cc isolated on one side of the equation.

In summary, by rewriting the equation (1/c - 1) as cc(1 - cc)/ccc, we have successfully isolated cc.

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This is not an example of horizontal integration.

Vertical integration in mathematics typically refers to the process of finding the antiderivative (integral) of a function with respect to the independent variable. It is a fundamental concept in calculus.

Horizontal integration is a business strategy where a company acquires or merges with other companies operating in the same industry or market to increase market share, reduce competition, and gain economies of scale.

The scenario described is an example of vertical integration. Vertical integration occurs when a company acquires or controls other companies that are involved in different stages of the same production process, such as acquiring suppliers or distributors.

In this case, the owner of the apple orchards is acquiring the machines to make apple juice from the apples, which is a different stage of the production process. Additionally, by buying trucks to transport the apple juice to retailers, the owner is controlling the distribution stage of the process as well.

This is not an example of horizontal integration, which would involve the owner acquiring or merging with other apple orchards to increase market share or reduce competition.

There is no indication in the scenario that the owner is engaging in collusion or violating antitrust practices, as these involve illegal or unethical actions to limit competition or manipulate markets.

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Answer:

m=13/7

Step-by-step explanation:

the equation for slope (m) is (y2-y1)/(x2-x1)

the given points are (0,5) and (-7,-8)

we can label them:

x1=0

y1=5

x2=-7

y2=-8

now substitute into the equation

m=(-8-5)/(-7-0)

m=-13/-7

m=13/7

the slope is 13/7

hope this helps!