Let f(x)=2x and g(x)=2x. Graph the functions on the same coordinate plane. What are the solutions to the equation f(x)=g(x) ? Enter your answers in the boxes. X = or x =.

Answer:

N = 7.5 pounds

Step-by-step explanation:

Formula for the radioactive decay is given by,

\(N=N_0e^{-\lambda t}\)

Here, N = Final amount

N₀ = Initial amount

λ = Decay constant

t = Duration of decay

Now we can substitute the values from the given question,

N = \(15e^{-(0.0231\times 30)}\)

N = \(15e^{-0.693}\)

N = 15(0.5)

N = 7.5 pounds

In conclusion, based on the provided information, the pairs of triangles that appear to be congruent are Triangle ABC and Triangle DEF, Triangle BCD and Triangle EFG, and Triangle CDE and Triangle FGH.

To determine which pairs of triangles appear to be congruent, we need to examine their corresponding sides and angles. Congruent triangles have the same shape and size, which means their corresponding sides are equal in length and their corresponding angles are equal in measure.

Let's analyze the given information about the triangles:

Triangle ABC:

Side AB is parallel to side DE and has the same length as side DE.

Side BC is parallel to side EF and has the same length as side EF.

Angle ABC is congruent to angle DEF.

Triangle BCD:

Side BC is parallel to side EF and has the same length as side EF.

Side CD is parallel to side FG and has the same length as side FG.

Angle BCD is congruent to angle EFG.

Triangle CDE:

Side CD is parallel to side FG and has the same length as side FG.

Side DE is parallel to side GH and has the same length as side GH.

Angle CDE is congruent to angle FGH.

From the given information, we can observe that the pairs of triangles that appear to be congruent are:

1. Triangle ABC and Triangle DEF: These triangles have corresponding sides AB and DE, BC and EF, and angle ABC and angle DEF that are congruent.

2. Triangle BCD and Triangle EFG: These triangles have corresponding sides BC and EF, CD and FG, and angle BCD and angle EFG that are congruent.

3. Triangle CDE and Triangle FGH: These triangles have corresponding sides CD and FG, DE and GH, and angle CDE and angle FGH that are congruent.

It is important to note that our observation of apparent congruence is based on the given information. To establish formal congruence, we would need additional information, such as the congruence of a third pair of corresponding sides or angles, to apply congruence postulates or theorems.

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The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

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Answer:

x = 2, x = 8

Step-by-step explanation:

Calculate the distance using the distance formula and equate to 5

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = A (x, - 1) and (x₂, y₂ ) = B(5, 3)

d = \(\sqrt{(5-x)^2+(3+1)^2}\)

   = \(\sqrt{(5-x)^2+4^2}\)

   = \(\sqrt{(5-x)^2+16}\) , thus

\(\sqrt{(5-x)^2+16}\) = 5 ( square both sides )

(5 - x)² + 16 = 25 ( subtract 16 from both sides )

(5 - x)² = 9 ( take the square root of both sides )

5 - x = ± \(\sqrt{9}\) = ± 3 ( subtract 5 from both sides )

- x = - 5 ± 3 , thus

- x = - 5 + 3 = - 2 ( multiply both sides by - 1 )

x = 2

or

x = - 5 - 3 = - 8 ( multiply both sides by - 1 )

x = 8

Answer:

Step-by-step explanation:

The formula to find the distance between 2 points in the coordinate plane is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We have our distance, and we also have all the coordinates but the first x.  Fillling in with what we have gives us this:

\(5=\sqrt{(5-x_1)^2+(3-(-1))^2}\)

which simplifies to

\(5=\sqrt{(5-x_1)^2+(4)^2}\) . Expanding that binomial gives us:

\(5=\sqrt{25-10x+x^2+16}\) .  Combining like terms gives us:

\(5=\sqrt{x^2-10x+41}\) which is the same thing as above, only in standard form for polynomials. Now we need to get that x out from under that square root sign. We do that by squaring both sides to get:

\(25=x^2-10x+41\) . Now we have to factor to solve for x. We'll put everything on one side of the equals sign, set the polynomial equal to 0, then factor.

\(0=x^2-10x+16\) is our polynomial now. a = 1, b = -10, c = 16. The product ac is 1 * 16 which is 16. Some combination of the factors of 16 will result in a -10. So we need the factors of 16.

16: {1, 16}, {2, 8}, {4, 4}

The only combination of those factors that will result in a -10 is the second pair, {2, 8}. If we add 2 and 8 we get 10, but in order for our 10 to be negative, both 2 and 8 have to be negative. So we rewrite the polynomial in terms of -2 and -8:

\(0=x^2-8x-2x+16\)

Now we can factor by grouping. Group the first 2 terms together and the second 2 terms together without moving any of their positions:

\(0=(x^2-8x)-(2x+16)\)

From each set of parenthesis we will now factor out what's common.  x is common in the first set of ( ), and 2 is common in the second set of ( ):

\(0=x(x-8)-2(x-8)\)

What's common now is the binomial (x - 8). So we'll factor that out now:

\(0=(x-8)(x-2)\)

By the Zero Product Property, either

x - 8 = 0 or x - 2 = 0.

If x - 8 = 0, then x = 8. If x - 2 = 0, then x = 2.

It looks like we have 2 solutions. Let's try them both and see if, when we stick an 8 and then a 2 into our distance formula, the distance is 5:

\(d=\sqrt{(5-8)^2+(4^2)}\) is

\(d=\sqrt{(-3)^2+(4)^2}\) is

\(d=\sqrt{9+16}\) is

\(d=\sqrt{25}\) which does in fact equal 5. Now let's try the 2:

\(d=\sqrt{(5-2)^2+(4)^2}\) which is

\(d=\sqrt{(3)^2+(4)^2}\) is

\(d=\sqrt{9+16}\) is

\(d=\sqrt{25}\) which also comes out to equal 5.

So the 2 values of x which will work here are 2 and 8.

Answer:

Step-by-step explanation:

k= 15

k+12 ≥ 20

15+12 ≥20

27 ≥ 20 True

The riddle mentioned in the question is about a farmer who is traveling along with a sack of rye, a goose, and a mischievous dog.

He comes to a river that he must cross from east to west, and there is a boat available to do so.  Therefore, the farmer takes the goose back to the east side and leaves it there. He then takes the sack of rye across the river, drops it off with the dog, and goes back to the east side to pick up the goose. In this manner, all of the farmer's possessions can be safely transported across the river without any of them being lost to the dog or the goose.This riddle is a classic example of a type of logical puzzle known as a "transport problem."

The goal of a transport problem is to determine how to transport one or more objects from one location to another while satisfying certain constraints, such as the size of the transport vehicle or the safety of the objects being transported.

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The correct option is \(\(b.\)  \(f(x) = -\frac{{(x - 4)^2}}{5}\).\) The function that has a range of \(\(\{y | y \leq 5\}\)\) is option \(\(b.\)  \(f(x) = -\frac{{(x - 4)^2}}{5}\).\)

To determine this, let's analyze the options:

\(\(a.\)  \(f(x) = \frac{{(x - 4)^2}}{5}\)\): This function will have a range of  \(\(y\)\)-values greater

than or equal to 0, so it does not have a range of \(\(\{y | y \leq 5\}\).\)

\(\(b.\)  \(f(x) = -\frac{{(x - 4)^2}}{5}\)\) : This function is a downward-opening parabola, and when we substitute various values of \(\(x\)\) , we get \(\(y\)\)-values less than or equal to 5. Therefore, this function has a range of \(\(\{y | y \leq 5\}\).\)

\(\(c.\)   \(f(x) = \frac{{(x - 5)^2}}{4}\)\): This function is an upward-opening parabola, and its

range will be  \(\(y\)\)-values greater than or equal to 0, so it does not have a

range of \(\(\{y | y \leq 5\}\).\)

\(\(d.\)   \(f(x) = -\frac{{(x - 5)^2}}{4}\)\): This function is a downward-opening parabola, and its range will be \(\(y\)\)-values less than or equal to 0, so it

does not have a range of \(\(\{y | y \leq 5\}\).\)

Therefore, the correct option is \(\(b. f(x) = -\frac{{(x - 4)^2}}{5}\).\)

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You have a total of 288 different combinations of shirts, suits, and ties in your closet.

In your closet, you have 4 blue shirts, 3 plaid shirts, and 2 striped shirts. You have 1 blue suit, 2 black suits, and 1 brown suit. You also have 2 blue ties, 3 red ties, and 3 pink ties. To find the total number of different combinations, you need to multiply the number of choices for each category.

Number of shirt combinations = 4 (blue shirts) + 3 (plaid shirts) + 2 (striped shirts) = 9
Number of suit combinations = 1 (blue suit) + 2 (black suits) + 1 (brown suit) = 4
Number of tie combinations = 2 (blue ties) + 3 (red ties) + 3 (pink ties) = 8

Total combinations = Number of shirt combinations x Number of suit combinations x Number of tie combinations = 9 x 4 x 8 = 288

Therefore, you have a total of 288 different combinations of shirts, suits, and ties in your closet.

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complete question:

You are starting your new job and have to wear a dress shirt, suit, and tie every day. In your closet, you have 4 blue shirts, 3 plaid shirts, and 2 striped shirts. You have 1 blue suit, 2 black suits, and 1 brown suit.

You also have 2 blue ties, 3 red ties, and 3 pink ties. How many different combinations of shirts, suits, and ties do you have in your closet?

You have 288 different combinations of shirts, suits, and ties in your closet.

To find the number of different combinations of shirts, suits, and ties in your closet, we can multiply the number of options for each item.

First, let's consider the shirts. You have 4 blue shirts, 3 plaid shirts, and 2 striped shirts. To calculate the number of combinations of shirts, we add up the number of options for each type:

4 blue shirts + 3 plaid shirts + 2 striped shirts = 9 total options for shirts.

Next, let's look at the suits. You have 1 blue suit, 2 black suits, and 1 brown suit. Again, we add up the number of options for each type:

1 blue suit + 2 black suits + 1 brown suit = 4 total options for suits.

Lastly, we'll consider the ties. You have 2 blue ties, 3 red ties, and 3 pink ties.

Adding up the options for each type gives us:

2 blue ties + 3 red ties + 3 pink ties = 8 total options for ties.

To find the total number of combinations, we multiply the number of options for each item:

9 options for shirts x 4 options for suits x 8 options for ties = 288 different combinations.

Therefore, you have 288 different combinations of shirts, suits, and ties in your closet.

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Assuming that the iron plate is lifted to a height against the gravitational force, we can use the formula for potential energy:

Potential Energy = mass x gravity x height

where mass is in kg, gravity is 9.81 m/s^2, and height is in meters.

Rearranging the formula to solve for height, we have:

height = Potential Energy / (mass x gravity)

Plugging in the given values, we have:

height = 2000 J / (10 kg x 9.81 m/s^2)

height = 20.34 meters (rounded to two decimal places)

Therefore, the height of the iron plate is approximately 20.34 meters.

The actual area in square feet of the base of the building given the scale model will be; 418 square feet.

Since scale drawing is a reduced form in the dimensions of an original image / building / object.

Therefore, Scale of the drawing = original dimensions / dimensions of the scale drawing

Length of the base = 2 x 47 = 94 ft

Width of the base = 1 x 47 = 47

Area = 47 x 94 = 4418 square feet

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To know the average value of Given functions are:

1.\(`f(x) = e^(1/z) / z^2` in [2,5]\)

2. \(`f(x) = 4 / (1+t^2)` in [0,5]\)

3. \(`f(x) = x^2 / (x^3+8)^2` in [-1,1]\)

4.\(`f(x) = ln(u) / u` in [1,5]\)

We have to find the average value of each function on the given interval.

I) Average value of\(`f(x) = e^{(1/z)} / z^2`\) in [2,5] The average value of\(`f(x) = e^{(1/z)} / z^2   on [2,5]\) is given by:

\(`1/(5-2) ∫(2)^{(5)} e^{(1/z)} / z^2 dz`\)

Now,  let `\(u = 1/z`\\\), then `\(du/dz = -1/z^2\)` and `\(dz = -du/u^2`\).

Substitute `u` and `dz` in the above integral, then it becomes \(`1/(5-2) ∫(1/5)^{(1/2)} e^u du = 1/3 (e^{(1/5)} - e^{(1/2)})\)`.

Therefore, the average value of `f(x) = e^(1/z) / z^2` on [2,5] is `1/3 (e^(1/5) - e^(1/2))`.

II) Average value of `f(x) = 4 / (1+t^2)` in [0,5] The average value of `f(x) = 4 / (1+t^2)` on [0,5] is given by:

`1/(5-0) ∫(0)^(5) 4 / (1+t^2) dt`

Now, let `t = tan(x)`, then `\(dt = sec^2(x) dx`.\)

Substitute `t` and `dt` in the above integral, then it becomes

`\(1/5 ∫(0)^{(arctan(5)}) 4 / (1+tan^2(x)) sec^2(x) dx = 1/5 ∫(0)^{(arctan(5)}) 4 dx = 4/5 arctan(5)`\).

Therefore, the average value of \(`f(x) = 4 / (1+t^2)` on [0,5]\) is `4/5 arctan(5)`.

III) Average value of `\(f(x) = x^2 / (x^3+8)^2` in [-1,1]\)

The average value of `\(f(x) = x^2 / (x^3+8)^2` on [-1,1]\)is given by: \(`1/(1-(-1)) ∫(-1)^{(1)} x^2 / (x^3+8)^2 dx`\)

Now, let \(`u = x^3+8`\), then \(`du/dx = 3x^2`\) and \(`dx = du/3x^2`\).

Substitute `u` and `dx` in the above integral, then it becomes

\(`1/2 ∫(1)^{(9)} 1 / u^2 du = 1/2 (-1/u) |_{(1)^{(9)}} = (1-1/9)/2 = 4/9`\).

Therefore, the average value of `\(f(x) = x^2 / (x^3+8)^2` on [-1,1]\) is `4/9`.

IV) Average value of `f(x) = ln(u) / u` in [1,5] The average value of \(`f(x) = ln(u) / u`\) on [1,5] is given by:

\(`1/(5-1) ∫(1)^{(5)} ln(u) / u du`\)

Now, let `v = ln(u)`, then `dv/du = 1/u` and `\(du = e^v dv`.\)

Substitute `v` and `du` in the above integral, then it becomes

\(`1/4 ∫(0)^{(ln(5)}) v e^v dv = 1/4 (v e^v |_{(0)^(ln(5)}) - ∫(0)^{(ln(5)}) e^v dv) = 1/4 ((ln(5) - 1) e^{ln}(5) + 1) = (ln(5) + 1)/4`\).

Therefore, the average value of `f(x) = ln(u) / u` on [1,5] is `(ln(5) + 1)/4`.

Hence, the average values of the given functions are:

1. \(`f(x) = e^{(1/z)} / z^2` on [2,5] is `1/3 (e^{(1/5)} - e^{(1/2)})`\).

2. \(`f(x) = 4 / (1+t^2)` on [0,5] is `4/5 arctan(5)`\).

3.\(`f(x) = x^2 / (x^3+8)^2` on [-1,1] is `4/9`\).

4. \(`f(x) = ln(u) / u` on [1,5] is `(ln(5) + 1)/4`\).

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The average values of the function f on the given interval for the given functions are as follows:

1. f(x) = e1/z / z2 [2, 5]

The average value of the function is given by:

av(f) = (1/(5-2)) * ∫\(2^5e^{(1/x)\)/ \(x^2\) dx = (1/3) * ∫\(2^5e^{(1/x)\) / \(x^2\) dx

The above integral is not an elementary function, so we leave it as it is.

2. f(x) = 4 / 1+t2 [0, 5]

The average value of the function is given by:

av(f) = (1/(5-0)) * ∫\(0^{54\) / (1+\(t^2\)) dt

= (1/5) * [arctan(t)]\(0^5\)

= (1/5) * [arctan(5) - arctan(0)]

≈ 0.65 (approximately)

3. f(x) = x2 / (x3+8)2 [-1, 1]

The average value of the function is given by:

av(f) = (1/(1-(-1))) * ∫\(-1^1x^2\) / \((x^3+8)^2\) dx

On making the substitution x³+8 = u, we get:

av(f) = (1/2) * ∫\(0^{80.5\) /\(u^2\)du

On integrating, we get:

av(f) = [-0.25/u]\(0^8\)

= -0.03125

4. f(x) = ln(u) / u [1, 5]

The average value of the function is given by:

av(f) = (1/(5-1)) * ∫\(1^5\)ln(u) / u du

On integrating, we get:

av(f) = [ln(u) - 1]\(1^5\)

≈ 0.225 (approximately)

Therefore, the average values of the function f on the given interval for the given functions are:

1. f(x) = e1/z / z2 [2, 5] ≈ ∫\(2^5e^{(1/x)} / x^2\)dx / 3

2. f(x) = 4 / 1+t2 [0, 5] ≈ 0.65 (approximately)

3. f(x) = x2 / (x3+8)2 [-1, 1] = -0.03125

4. f(x) = ln(u) / u [1, 5] ≈ 0.225 (approximately)

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Answer:

Evaluating Exponents. An exponent is a number that tells how many times the base number is used as a factor. For example, 34 indicates that the base number 3 is used as a factor 4 times. To determine the value of 34, multiply 3*3*3*3 which would give the result 81

Answer:

I think it's the last one; The ball pushing the dog's paw.

Step-by-step explanation:

It makes the most sense. :|

Answer:

12.5%

Step-by-step explanation:

900 - 800 = 100

Gotta pay $100 more

100 / 800 = 0.125

Answer:

80% of the fish in the school pond are goldfish.

Step-by-step explanation:

To find the percentage of goldfish in the pond, we need to divide the number of goldfish by the total number of fish and multiply by 100.

percent of goldfish = (number of goldfish / total number of fish) x 100%

So, in this case:

percent of goldfish = (296 / 370) x 100%

percent of goldfish = 0.8 x 100%

percent of goldfish = 80%

Answer:

The short pieces are 10  cm each and the long pieces are 15 cm each.

Step-by-step explanation:

We cut a 60cm rope into 5 pieces. There are 3 short pieces that measure the same and the other 2 pieces are 5cm longer than the short ones. How long are the pieces?

let the length of the short pieces is p.

Length of longer pieces = p + 5

So,

60 = 3 p + 2 (p+ 5)

60 = 3 p + 2p + 10

5 p =  50

p = 10 cm

So, the short pieces are 10  cm each and the long pieces are 15 cm each.

Answer:

Step-by-step explanation:

\(\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}\)

(-6, 7)    ⇒   x₁ = -6,  y₁ = 7

(-6, -3)    ⇒   x₂ = -6,  y₂ = -3

x₁ = x₂ = -6  means there in no slope;

the line is parralel to Y-axis, and its equation is x = -6

Answer:

Hi how are you doing today Jasmine

Part (b)

The scale 1 cm = 2 m means we'll multiply whatever the cm distance is by 2 to get the meter distance in real life.

The shed is 3 cm by 3 cm on paper. It corresponds to 6 meters by 6 meters in real life.

----------

The cement pad is 6 meters by 10 meters in real life because it's originally 3 cm across and 5 cm vertical. We double each dimension as done before, and replace "cm" with "m".

----------

The hot tub is a circle so we don't get an exact measurement here. But we can determine a good estimate. It appears it's 2 cm across and 2 cm vertical. So that corresponds to 4 meters by 4 meters

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

Part (c)

On paper, the distance is 4.5 cm since we count out 4 full squares plus half a square when going a horizontal distance from the cement pad to the pool.

Therefore, the distance in real life is 9 meters

1 cm = 2 m

4.5*(1 cm) = 4.5*(2 m)

4.5 cm = 9 m

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

Part (d)

The flowerbed on paper has sides of 4 cm and 6 cm. Use the pythagorean theorem to find the hypotenuse is approximately 7.21 cm.

Double each dimension, and replace the 'cm' with 'm'

The side lengths of the actual flowerbed is 8 meters, 12 meters, 14.42 meters. That last value being approximate.

Add up the values to get the perimeter: 8+12+14.42 = 34.42

Answer: perimeter = 34.42 meters (approximate)

Answer:

Actual answer would be 77.75 but you would answer as 78 I believe.

Step-by-step explanation:

Since they're over the same denominator this means that 4n= 311.

311/4=n

n=77.75

Or for you it would be 78 rounded up.

Or for a fraction it would be 77 1/4.

(Thanks for reminding me)

Answer:

i think the answer is b

Step-by-step explanation:

that is 2x^2(x-3)

by expanding it gives 2x^3-6x^2

After walking for 2 hours in a direction 25 degrees west of north at a speed of 4 miles per hour, the coordinates of Janna's location is approximately (3.191 miles, 7.032 miles)

To determine the coordinates of Janna's location after walking for 2 hours in a direction 25 degrees west of north at a speed of 4 miles per hour, we can use trigonometry to calculate the displacement.

Given:

Direction: 25 degrees west of north

Speed: 4 miles per hour

Time: 2 hours

First, we need to determine the distance Janna has traveled. Using the formula:

Distance = Speed × Time

Distance = 4 miles/hour × 2 hours

Distance = 8 miles

Next, we can calculate the displacement in the vertical (north) and horizontal (east) directions using trigonometry.

Vertical displacement = Distance × sin(angle)

Horizontal displacement = Distance × cos(angle)

Angle = 25 degrees west of north

Angle = 90 degrees - 25 degrees

Angle = 65 degrees

Vertical displacement = 8 miles × sin(65 degrees)

Vertical displacement ≈ 7.032 miles

Horizontal displacement = 8 miles × cos(65 degrees)

Horizontal displacement ≈ 3.191 miles

Finally, we can determine the coordinates of Janna's location by adding the displacements to the initial position (0, 0).

Coordinates = (Horizontal displacement, Vertical displacement)

Coordinates ≈ (3.191 miles, 7.032 miles)

Therefore, after walking for 2 hours in a direction 25 degrees west of north at a speed of 4 miles per hour, Janna's location is approximately (3.191 miles, 7.032 miles).

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Answer:

TU ≈ 12.96

Step-by-step explanation:

Using the Altitude on Hypotenuse theorem

(leg of outer triangle)² = (part of hypotenuse below it) × (whole hypotenuse)

TU² = UV × SU = 6 × 28 = 168 ( take square root of both sides )

TU = \(\sqrt{168}\) ≈ 12.96 ( to the nearest hundredth )

(i) Marked price is $ 30,000

(ii) Cost price Inclusive tax = $29,160

(iii) VAT paid by the wholesaler is $

(i) Marked Price:

The displayed price is the price reported to the clearing house as increased or decreased. The total return associated with risk-free main trades must be included in the main broker's fees.

Cost Price for wholesaler = $25,000

  Marked price = $25,000+ 20/ 100 ×$25,000

                          = $30,000

(ii) Cost Price inclusive Tax:

In a retail system, cost is a specific cost that is the price per unit. This value is used as a key factor in determining profitability, and in some stock market theories, it is used to determine the cost of owning a stock.

Discount = 10% of 30,000 = $3,000

Cost price for retailer = Marked price − Discount

                                  = $30,000−$3,000

                                  = $27,000

Cost price inclusive tax = $27,000+ 8/100 × $27,000

                                       = $29,160

(iii) Value added tax:

Value Added Tax (VAT) is a tax on the consumption of goods and services at every stage of the supply chain where value is added from initial production to the point of sale. The amount of VAT you pay is based on the product cost minus the material cost of the product already taxed in the previous step.

Cost price for wholesaler = $25,000

     Sale price for wholesaler = $27,000

     Profit for wholesaler = $27,000 − $25,000

                                        = $2,000

     VAT = 8/ 100 × $2,000

             = $160.

Complete Question:

Roxanne owns a TV store. she buys a Tv  from the manufacturer for Rs. 25,000. He marks the price of the TV 20% above his cost price and sell it to a retailer at 10% discount on the marked price. If the rate of VAT is 8%, find the:

(i) marked price.

(ii) retailer's cost price inclusive of tax.

(iii) VAT paid by the wholesaler.

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The domain and range of the rational function in this problem are given as follows:

The domain of a function is the set that contains all the input values that can be assumed by the function.

The function in this problem is a fraction, meaning that the denominator must assume values different of zero, hence the value outside the domain is:

x - 1 = 0 -> x = 1.

The range of a function is the set that contains all the output values that can be assumed by the function.

The function in this problem can be simplified by x - 1, hence at x = 1 it would assume a value of y = 7. However, for the range, we suppose that the function cannot be simplified, hence it is given by all real values except y = 7.

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A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of 5 line pairs per millimeter (B).

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of B. 5 line pairs per millimeter.
Here's a step-by-step explanation:

1. The sampling frequency is given as 10 pixels per millimeter.
2. According to the Nyquist-Shannon sampling theorem, the maximum spatial frequency (in line pairs per millimeter) that can be accurately represented is half of the sampling frequency.
3. Divide the sampling frequency (10 pixels per millimeter) by 2: 10/2 = 5 line pairs per millimeter.

So, the answer is B. 5 line pairs per millimeter.

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Option C: Less than \(\sqrt58\\\) inches but greater than 7 inches

Ramon wants to make an acute triangle with three pieces of wood. So far,

he has cut wood lengths of 7 inches and 3 inches.

What length must the longest side be in order for the triangle to be acute?

According to the property of triangle,

If the square of larger side of triangle is equating to the sum of square of smaller side.

If \(a^{2} < b^{2}+c^{2}\) the triangle is acute triangle.

where, 'a' is the larger side and 'b' ,'c' are the smaller side

According to the question, Let a =a , b = 7, c = 3

\(a^{2} < 7^{2}+3^{2}\\ a^{2} < 49+9\\ a < \sqrt58\)

Means to be acute triangle third side must be less than \(\sqrt58\) inches but greater than 7 inches.

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Answer:

less than 58 inches but greater than 7

Step-by-step explanation:

i got it right on edge

The quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

The time taken by substance to reduce to its half of its initial concentration is called half life period.

We will use the half- life equation N(t)

N e^{(-0.693t) /t½}

Where,

N is the initial sample

t½ is the half life time period of the substance

t2 is the time in years.

N(t) is the reminder quantity after t years .

Given

N = 13g

t = 350 years

t½ = 1599 years

By substituting all the value, we get

N(t) = 13e^(0.693 × 50) / (1599)

= 13e^(- 0.368386)

= 13 × 0.691

= 8.98

Thus, we calculated that the quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

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Answer:

$1,489.88 (nearest cent)

Step-by-step explanation:

To calculate gross pay, multiply the number of hours worked by the pay per hour.

Warren worked 36.5 hours one week and 32 hours the week before.

Therefore, the total number of hours Warren worked was:

Multiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:

Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).

Answer:

$1489.875

Step-by-step explanation:

Warren's gross pay for 36.5 hours last week can be calculated as follows:

Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875

Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:

Gross pay for 32 hours = $21.75/hour * 32 hours = $696

Adding the gross pay for the two weeks, we get:

Gross pay for 2 weeks = $793.875 + $696 = $1489.875