A manufacturer finds that the revenue generated by selling x units Of a certain commodity is given by the function R (x) = 60x - 0.4x(squared) where the revenue R (x) Is measured in dollars.
What is the maximum revenue, and how many units should be manufactured to obtain this maximum

Step-by-step explanation:

4/3 + 11/12

3 = 12 = 12

12 ÷ 3 = 4

12 ÷ 12 = 1

4 × 4 = 16

1 × 11 = 11

16 + 11 = 27/12

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Explanation:

This equation represents a line, so there are many points that are solutions to the equation. To fill in this boxes we just have to pick a x-value that's in the domain, replace it into the equation and solve for y. The domain of this function is all real numbers, so any number will work.

Using x = 1:

Answers:

A solution is (-24) = 8( 1 ) - 32

The magnitude of the final velocity of the cue ball is (B) 0.56m/s.

How to calculate the magnitude of the final velocity?

The magnitude of the final velocity can be calculated by following the steps:

Assuming all pool balls have the same mass: 0.4kg

Let the final velocity of the cue ball be x.

Now, To find the final velocity:

Therefore, the magnitude of the final velocity of the cue ball is (B) 0.56m/s.

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The correct question is given below:

In a game of pool, a 0.4 kg cue ball is traveling at +0.80 m/s when it hits a slower striped ball moving at +0.38 m/s. After the collision, the striped ball moves off at +0.62 m/s. What is the magnitude of the final velocity of the cue ball? Assume all pool balls have the same mass.

A. 0.20 m/s

B. 0.56 m/s

C. 1.0 m/s

D. 1.8 m/s

Answer: 0.56m/s

Step-by-step explanation:

a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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Answer:

A=130

Step-by-step explanation:

Answer:

16 blocks. 12.8=(.8)x

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

because it both so it come out to be 16

For a 3×3 matrix A, with the real eigenvalue is 2 and two complex conjugate eigenvalues, the complex conjugate eigenvalues of matrix A are equal to 1 ± i.

Eigenvalues are defined as a special set of scalar points that is associated with set of linear equations and matrix equations. We have a matrix A of order 3×3. It has real and complex eigenvalues. As we know number of eigenvalues for 3×3 matrix are 3. The real eigenvalue, λ

= 2

Number of complex eigenvalues= 2

Also, the determinant of matrix A, det(A) = 50

Trace of matrix A, tr(A) = 8

We have to determine the complex eigenvalues.

The characteristic polynomial for 3×3 is written as below, f( λ )= det(A − λI3 )= −λ³ + 4λ² - 6 λ + 4.

For eigenvalues, −λ³ + 4λ² - 6 λ + 4 = 0

Now, one of eigenvalue of matrix is 2, λ = 2. Using the synthesis division, for calculating the remaining, follow the steps present in above figure. In the last step of division we get a quadratic equation, -λ² + 2λ - 2 = 0, solve it by quadratic formula, \(λ = \frac{-2 ± \sqrt{ 2² - 4 (-2)(-1)}}{2(-1)}\)

\(= \frac{-2 ± \sqrt{4 - 8 }}{-2}\)

=> λ = 1 ± i

Hence, required values are 1 ± i.

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Answer:

4 tickets = £111.52

Step-by-step explanation:

1 ticket = £ 27.88

Multiplying both sides by 4

=> 4 tickets = £111.52

Answer:

0.175438596491

Step-by-step explanation:

I did 14/79.8, btw I counted with my fingers

<3 <3 <3 <3 <3

Three segments a, b, and c using net sales as the basis for allocation is = $475,000.

Based on the given conditions,

Three segments are a , b , c

The segment a of trump enterprises have net sales = $300,000

The segment b of trump enterprises have net sales = $150,000

The segment c of trump enterprises have net sales = $50,000

a net sales + b net sales + c net sales = $300,000 + $150,000 + $50,000

= $500,000

If the unit is eliminated, then the a net sales and b net sales will be gone, but the c net sales will be allocated to other business units.

So instead of losing $500,000,

A decision is made to allocate the pool = $25,000

The company's net sales as the basis for allocation by $500,000 - $25,000 = $475,000

Therefore,

Three segments a, b, and c using net sales as the basis for allocation is =

$475,000.

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Answer:

Step-by-step explanation: Let x represent the number in the algebraic expression, then 6 less means the following:

x-6

The maximum percentage of the channel bandwidth peak for pure ALOHA occurs at (E) one attempt every 2 slots.

What is ALOHA?

ALOHA is a computer networking term that refers to a random access protocol for wireless networks. It was created in the 1970s at the University of Hawaii. It is a protocol for transmitting packets on a shared communication channel that does not have collision detection. Each packet is transmitted with the hope of successfully reaching the destination without being obstructed by another packet or station in the network.

What is Pure ALOHA?

Pure ALOHA is a type of ALOHA protocol that is unslotted. A station may send frames at any time, and collisions are resolved by detecting them. Pure ALOHA has a maximum throughput of 18%.

When it comes to the question, the maximum percentage of the channel bandwidth peak for pure ALOHA occurs at (E) one attempt every 2 slots.

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The line  (a) is perpendicular and the other lines are neither parallel nor perpendicular.

The given equations of lines are:

To find whether the given lines are parallel, perpendicular or neither, we need to find the slopes of each of the lines. The slope of the line can be determined by the equation of the line in the form of y = mx + b where m is the slope of the line. Let's find the slope of each line now.

a) y = 1- x => y = -x + 1 The slope of the line is -1.

b) x - 2y = 4 y = x + 4 => x - y = -4 The slope of the line is 1.

c) 3y = 9x + 1 => y = 3x + 1/3 The slope of the line is 3.

d) 4y = 8x + 1 => y = 2x + 1/4 The slope of the line is 2.

x + 3y = 4 => 3y = -x + 4 => y = -1/3 x + 4/3 The slope of the line is -1/3.

2y = 3 - 4x => y = (-4/2)x + 3/2 => y = -2x + 3 The slope of the line is -2.

Now, let's determine whether the given lines are parallel, perpendicular, or neither.

a) The slope of line a is -1 and the slope of line b is 1. As the slopes are negative reciprocals of each other, the given lines are perpendicular to each other.

b) The slope of line c is 3 and the slope of line d is 2. As the slopes are not the negative reciprocals of each other, the given lines are neither parallel nor perpendicular to each other.

c) The slope of line b is 1 and the slope of line e is -1/3. As the slopes are not the negative reciprocals of each other, the given lines are neither parallel nor perpendicular to each other.

d) The slope of line e is -1/3 and the slope of line f is -2. As the slopes are not the negative reciprocals of each other, the given lines are neither parallel nor perpendicular to each other.

Hence, the given lines are perpendicular to each other for a). The given lines are neither parallel nor perpendicular for b), c), d) and e).

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Answer:

7.

lateral surface area of traingular prism=perimeter of traingle ×length=[5+3+4]×6=72cm²

curved surface area=2[area oftraingle]=2×1/2×4×3

=12cm²

now

total surface area=72cm²+12cm²=84cm²

8.

volume of traingular prism=area of traingle ×length

=1/2×12×3.4×4=81.6cm³

Step-by-step explanation:

• first triangle •

the third angle = 180-56-37 = 87°

the 4 cm's side is located between angle 56° and 87°

• second triangle •

the third angle = 180-56-37= 87°

the 4 cm' side is located between angle 37° and 87°

so, both of triangles are not congruent, because the 4 cm's side is not located between the same angles

Answer:

root of 256 is 16.....so the value of X is 16

Answer:

the answer is D 128

Step-by-step explanation:

To use the integral test, we need to evaluate the following integral: ∫[infinity]1 6/5x dx Using integration by substitution with u = 6/5x, we get: ∫[infinity]1 6/5x dx = (5/6)∫[infinity]6/5 1 du.

Evaluating this integral gives us: (5/6)∫[infinity]6/5 1 du = (5/6)(1/u)|[infinity]6/5 = (5/6)(0 - 5/6) = -25/36 Since the integral evaluates to a finite value, and the series has the same general term as the function being integrated, we can conclude that the series is convergent by the integral test.

The new limits for the integral will be 5 (lower) and infinity (upper). ∫(5 to infinity) 6/u * (1/5) du. Thus, the integral is divergent. Since the integral is divergent, the original series Σ (n = 1 to infinity) 6/(5n) is also divergent.

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Answer:

27^4

2.74*10^2

4.27*10^2

Step-by-step explanation:

in exponential notation the number is expressed like this.

The function f(x) is defined as f(x) = sin(5x + π/4), where π/4 is equivalent to 45 degrees in radians. This function represents a sinusoidal wave with a frequency of 5 cycles per unit of x and a phase shift of π/4 to the left (or in the negative x direction).

The amplitude of the wave is 1, since the sine function oscillates between -1 and 1.

To graph this function, you can start by choosing some x-values to plug into the equation. For example, if you choose x = 0, you get f(0) = sin(π/4) = √2/2. If you choose x = π/10, you get f(π/10) = sin(π/2) = 1.

Once you have a few points, you can plot them on a graph and connect them to form the wave. Because the function has a period of 2π/5, you only need to graph one cycle from 0 to 2π/5, and then repeat it for every subsequent interval of 2π/5.

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Answer:

B.

Step-by-step explanation:

When you use your debit card, you are purchasing something and using money. Therefore, you are withdrawing money from your account to pay for an item.

Answer:

100 mins or 1⅔ hrs

Step-by-step explanation:

¾ hr = ¾ × 60 mins

¾ hr = 45 mins

55 + 45 = 100

100 mins = 100 × hr/60

100 mins = 1⅔ hrs

Answer:

100 mins or 1⅔ hrs

Step-by-step explanation:

¾ hr = ¾ × 60 mins

¾ hr = 45 mins

55 + 45 = 100

100 mins = 100 × hr/60

100 mins = 1⅔ hrs

So it took them  1 2/3 hrs to get to school

Answer:

\(x=-20\)

Step-by-step explanation:

\(\frac{x}{5}+7=3\\ \\\frac{x}{5}+7-7=3-7\\ \\\frac{x}{5}=-4\\ \\\frac{x}{5}*5=-4*5\\ \\x=-20\)

Answer:

-20

Step-by-step explanation:

The width can be written as the polynomial:

W = (2/3)*a + (1/3)*b

For a rectangle of length L and width W, the area is:

A = L*W

Here we know that:

L = 3a + 15b

And we know that the area expression is A = 2a^2 + 11ab + 5b^2

We can assume that the width is something like:

W = xa + yb

We want to find the values of x and y.

Using the area formula we can write the product of polynomials.

2a^2 + 11ab + 5b^2 = (3a + 15b)*( xa + yb)

Expanding the right side we get:

2a^2 + 11ab + 5b^2 = 3xa^2 + (3a)*(yb) + (15b)*(xa) + 15yb^2

2a^2 + 11ab + 5b^2 = (3x)a^2 + (3y + 15x)ab + (15y)b^2

comparing like terms, we will get the equations:

3x = 2

3y + 15x = 11

15y = 5

With equations 1 and 3 we get:

x = 2/3

y = 5/15 = 1/3

And with the second equation we can corroborate that:

3*(1/3) + 15*(2/3) = 1 + 30/3 = 11

So the width is:

W = (2/3)*a + (1/3)*b

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Answer:

Your answer is correct

Step-by-step explanation:

(2^5/4)² = 4^5/2 = √4^5

The correct answer is option B which is \(\sqrt{2^5}\).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression will be solved as follows:-

\(E = ([ 2^{\frac{1}{2}} \times 2^{\frac{3}{4}}])^2\\E = (2^{({\frac{1}{2}+\frac{3}{3}})})^2\\E = (( 2 )^ {\frac{5}{4})}^2 \\E = ( 2 ) ^{\frac{5}{2}}\\E = \sqrt{2^5}\)

Therefore the correct answer is option B which is \(\sqrt{2^5}\).

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Answer:

first one (2*2*2*3*3)

Step-by-step explanation:

2*2*2*3*3=72

~ Use the distance formula to measure the lengths of the sides.

~ Use the slope to check whether sides are perpendicular and form right angles.

~ Use the slope to check whether the diagonals are perpendicular to each.

I hope this helps ^-^

The value of the third angle that can be found in the information given about the congruent triangles will be 45°.

From the complete information, the angles that are given in the triangle are 76° and 59°.

It should be noted that the value of the total angles that are in a triangle is 180°. Therefore, the value of the last angle will be:

= 180° - (76° + 59°)

= 180° - 135°

= 45°

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The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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