Find the perimeter of this semi-circle with radius, r = 19cm. Give your answer rounded to 1 DP.

The maximum value of z, subject to the given constraints, is 239943.

To solve the given problem using the two-stage method, we'll break it down into two stages: Stage 1 and Stage 2.

Stage 1:

The first stage involves solving the following optimization problem:

Maximize: z = Maximize x₁ + x₂

Subject to:

x₁ ≤ 20

x₂ ≤ 20

Stage 2:

In the second stage, we'll introduce the additional constraints and objective function from the given equation:

Maximize: z = 2 × 3x₄ - 4x₂ + 4xy₁₂ + 598 × x₁ × x₂ + x₂ + 263

Subject to:

x₁ ≤ 20

x₂ ≤ 20

x₃ = x₁ × x₂

x₄ = x₂ × 263

x₅ = x₁ ×x₂ + x₂

Now, let's solve these stages one by one.

Stage 1:

Since there are no additional constraints in Stage 1, the maximum value of x₁ and x₂ will be 20 each.

Stage 2:

We can substitute the maximum values of x₁ and x₂ (both equal to 20) in the equations:

z = 2 × 3x₄ - 4x₂ + 4xy₁₂ + 598 × x₁ × x₂ + x₂ + 263

Replacing x₁ with 20 and x₂ with 20:

z = 2 × 3x₄ - 4 × 20 + 4 × 20 × y₁₂ + 598 × 20 × 20 + 20 + 263

Simplifying the equation:

z = 2 × 3x₄ - 80 + 80× y₁₂ + 598 × 400 + 20 + 263

z = 2 × 3x₄ + 80 × y₁₂ + 239743

Since we don't have any constraints related to x₄ and y₁₂, their values can be chosen arbitrarily.

Therefore, the maximum value of z will be achieved when we choose the largest possible values for 3x₄ and y₁₂:

z = 2 × 3 × (20) + 80 × 1 + 239743

z = 120 + 80 + 239743

z = 239943

Hence, the maximum value of z, subject to the given constraints, is 239943.

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is she clear?  we dunno, but we know she scored 50 of 120.

if we take 120(origin amount) to be the 100%, what's 50 off of it in percentage?

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 120 & 100\\ 50& x \end{array} \implies \cfrac{120}{50}~~=~~\cfrac{100}{x} \implies \cfrac{ 12 }{ 5 } ~~=~~ \cfrac{ 100 }{ x } \implies 12x=500 \\\\\\ x=\cfrac{500}{12}\implies x=\cfrac{125}{3}\implies x=41\frac{2}{3}\qquad \textit{yeap, Mary is clear \checkmark}\)

Answer:

Step-by-step explanation:

If point D is located on the segment CE, then point C, D and E lies on the same line i.e they are collinear. Mathematically, CD+DE = CE

Given CD = 24 and DE = x and CE = 5x, on substituting this values in the equation we have;

\(24+x = 5x\\5x-x = 24\\4x = 24\\x = 24/4\\x = 6\)

Since CE = 5x, CE = 5(6) = 30

The measure of segment CE is 30

Premise 1: Hard water can damage home appliances. Premise 2: A water softening system can prevent hard water. Conclusion: Therefore, a water softening system can prevent damage to home appliances.

The argument consists of two premises and a conclusion. Premise 1 states that hard water can cause damage to home appliances. Premise 2 states that a water softening system can prevent hard water. The conclusion drawn from these premises is that a water-softening system can prevent damage to home appliances.

In standard form, the argument is presented by listing the premises first, followed by the conclusion. This format helps to clearly identify the statements being made and their logical relationship. By representing the argument in this way, it becomes easier to analyze the structure and validity of the reasoning presented.

Therefore, the standard form representation of the argument is:

Premise 1: Hard water can damage home appliances.

Premise 2: A water softening system can prevent hard water.

Conclusion: Therefore, a water softening system can prevent damage to home appliances.

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Answer:

4.

Step-by-step explanation:

8*1 / 1*2

= 8/2

= 4.

\(8\times \dfrac 12 = 4\)

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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Answer:

saclene obtuse

Step-by-step explanation:

sides all different and one angles is obtuse

The triangle DEF's section EF measures 24 units in length.

As per the data given in the above question are as bellow,

The provided details are as follow,

Procedure: Calculating the length that results from distorting a triangle by a scale factor

The triangle mentioned in the previous sentence is summarised in the diagram below. Using a trigonometric relationship, we discover that the following formula best describes the length of the section EF:

\($\sin a^{\circ}=\frac{E F}{D E}$\)

If we know that DE=30 and \($\sin a^{\circ}=\frac{4}{5}$\), then the length of the segment EF is:

\(E F=D E \cdot \sin a^{\circ} \\& E F=30 \cdot\left(\frac{4}{5}\right) \\\)

EF=24

Sine (sin), cosine (cos), and tangent (tan), which are defined in terms of the ratios of the sides of a right triangle, are the fundamental trigonometric functions.

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Note: The correct question would be as bellow,

A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees

15.5 units

24 units

30 units

37.5 units

Step-by-step explanation:i went on half of 84 wich was 42 so i found another problem that can equal into 84 wich was 63 green marbles 21 red             

Answer:

25958400

Step-by-step explanation:

\( {8}^{2} \times 6(4 + {8}^{2} \times (10 - 6) {)}^{2} \)

\( = 64 \times 6(4 + {2}^{6} \times 4 {)}^{2} \)

\( = 64 \times 6(4 + {2}^{6} \times {2}^{2} {)}^{2} \)

\( = 64 \times 6(4 + {2}^{8} {)}^{2} \)

\( = 64 \times 6(16 + 2048 + 65536)\)

\( = 64 \times 6 \times 67600\)

\( = 25958400\)

Answer: X = 10.20240940...

Step-by-step explanation:

x(2x + 9) = 2x^2 + 9x

2x^2 + 9x = 300

- 300 ON BOTH SIDES

2x^2 + 9x - 300 = 0

SOLVE USING THE QUADRATIC FORMULA

x = -b +/- all root (b)^2 - 4(a)(c) All over 2(a)

When all the values are plugged in:

When using "+" in the equation you should get:

x = 10.20240940…

When using "-" in the equation you should get:

x = −14.70240940…

Now.. you CANNOT have a negative length, so you cross of the negative value leaving you one value for x which is 10.20240940...

YOUR ANSWER IS:    x   =  10.20240940...

Answer:

Step-by-step explanation:

X=11

Answer:

need help

Step-by-step explanation:

Carla is 1.3 miles away from the home.

Given that, Carla leaves home and walks 40° easy to the north for 1.5 miles, then turns and continues due west for 2 miles.

The formula for the cosine rule is c=√(a²+b²-2ab cosC)

Here, c=√(1.5²+2²-2×1.5×2 cos40°)

c=√(2.25+4-6×0.7660)

c=√1.654

c=1.28

c=1.3 miles

Therefore, Carla is 1.3 miles away from the home.

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Answer:

x= 2, y= 1

Step-by-step explanation:

3x -y= 5 -----(1)

-x +y= -1 -----(2)

(1) +(2):

3x -y -x +y= 5 -1

2x= 4

Divide both sides by 2:

x= 4 ÷2

x= 2

Substitute x= 2 into (2):

-2 +y= -1

y= -1 +2

y= 1

Answer:

352 OZ

Step-by-step explanation:

One pound = 16 OZ

take 22 and multiply it by 16

22 x 16 = 352

Answer:

15 ounces per hour

Step-by-step explanation:

This is dimensional analysis, so we need to find conversion factors for ounces per pound and hours per day.  Once we have those we write the equation such that the units we need are left and the others cancel:

22lb/1 day  x  16 ounces/1 lb x 1 day/24hrs = 14.66666666666 ounces per hour

Since the problem was written with no decimals, our answer probably shouldn't either and in most cases like this we want to round to the nearest whole number, which is 15.

Answer:

$405.

Step-by-step explanation:

That would be 15% of $2700

= 2700 * 0.15

= $405

#46: B

#47: J

#48: C

#49: G

Answer:

\(x=33^{\circ}\)

Step-by-step explanation:

First off, your drawing is kinda inaccurate, because the \(124^{\circ}\) looks like a right angle, but as you drew it yourself it doesn't matter too much.

We know that the sum of the angles of a triangle will always equal \(180^{\circ}\), so we have that \(23+124+x=180\).

Combining like terms on the left side gives \(147+x=180\).

Subtracting \(147\) from both sides gives \(x=33\).

So, \(\boxed{x=33^{\circ}}\) and we're done!

Answer:

33°

Step-by-step explanation:

1. All angles in any triangle add up to 180°, so 23° + 124° + x° = 180.

2. Now, let's solve that equation we just wrote!

Step 1: Combine like terms

Step 2: Subtract 147 from both sides.

Therefore, x = 33°!

You can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

To find the slope of the secant line PQ, we need two points on the line: P(x, 4) and Q(3 - x, 3).

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the coordinates of P are (x, 4) and the coordinates of Q are (3 - x, 3). Plugging these values into the slope formula, we have:

slope = (3 - 4) / (3 - x - x)

slope = -1 / (3 - 2x)

To find the slope of the secant line for different values of x, we substitute those values into the expression for the slope.

For example, if x = 1, the slope of the secant line PQ is:

slope = -1 / (3 - 2(1))

slope = -1 / (3 - 2)

slope = -1 / 1

slope = -1

Similarly, you can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

And so on, you can calculate the slope of the secant line for different values of x.

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Answer:

\( \boxed{ \bold{ \boxed{ \sf{15 {x}^{4} + 13 {x}^{2} y + 2 {y}^{2} }}}}\)

Option A is the correct option.

Step-by-step explanation:

\( \sf{(3 {x}^{2} + 2y)(5 {x}^{2} + y)}\)

Use the distributive property to multiply each term of the first binomial by each term of the second binomial.

Thenafter, Simplify

\( \dashrightarrow{ \sf{3 {x}^{2} (5 {x}^{2} + y) + 2y(5 {x}^{2} + y)}}\)

\( \dashrightarrow{ \sf{15 {x}^{4} + 3 {x}^{2} y + 10 {x}^{2} y + 2 {y}^{2} }}\)

\( \dashrightarrow{ \sf{15 {x}^{4} + 13 {x}^{2} y + 2 {y}^{2} }}\)

Hope I helped!

Best regards! :D

It is possible for a two-player game to have a pure Nash equilibrium but for the best response dynamics to not converge to that equilibrium. This occurs when there is a cycle of best responses, in which each player switches between two strategies that are both best responses to the other player's strategy.

As an example, consider the game in which each player simultaneously chooses one of two actions, A or B, and their payoffs are determined as follows:

If both players choose A, then each player receives a payoff of 1.

If both players choose B, then each player receives a payoff of -1.

If one player chooses A and the other chooses B, then the player who chose A receives a payoff of 2, and the player who chose B receives a payoff of -2.

This game has a pure Nash equilibrium in which both players choose A. However, the best response dynamics does not converge to this equilibrium.

If both players start by choosing A, then each player can improve their payoff by switching to B, since choosing B guarantees a payoff of -1, which is higher than the payoff of 1 they receive from choosing A. If both players switch to B, then they can again improve their payoffs by switching back to A, and so on.

Therefore, it is possible for a two-player game to have a pure Nash equilibrium but for the best response dynamics to not converge to that equilibrium.

Game theory is the study of strategic decision-making and the interactions of rational individuals in competitive situations. One important concept in game theory is the Nash equilibrium (NE), which is a set of strategies, one for each player, such that no player can improve their outcome by unilaterally changing their strategy.

Another concept is the best response dynamics, which is a process in which players iteratively choose the best response to their opponents' actions.

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Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

The triangles are similar   so

x + 46 + 78 = 180

x = 56°

The required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978

Explain the divisibility test of 11.

For a number to be divisible by 11, the difference between the sum of its odd digits (1st, 3rd, 5th...) and the sum of its even digits (2nd, 4th...) must be divisible by 11.

Calculation for the positive five-digit integer of the form ab,cba to be divisible by 11

Required 5 digit number is of the form, ab,cba

Using the divisibility test of 11, we get

(b + b) - (a + c + a) to be divisible by 11

i.e. 2b - (2a + c) to be divisible by 11

Replacing ab,cba using the greatest numbers, such as 7, 8 and 9 and checking its divisibility with 11

78,987 = 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO

87,978 = 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES

79,897 = 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO

97,879 = 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO

89,798 = 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO

98,789 = 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO

Thus, a positive 5-digit number is 87,978

Hence, the required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978

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Step-by-step explanation:

\( = \sum \limits_{n = 1}^{7} ( - 2. {6}^{n - 1} )\)

\( = \sum \limits_ {n = 1}^{n_{ \text{max}}} (a_1. {r}^{n - 1} )\)

\( \: \)

\(a_1 = - 2\)

\(n = 7\)

\(r = 6 \to r >1\)

\( \: \)

• Find S7.

\(s_n = a_1.( \frac{ {r}^{n} - 1}{r - n} )\)

\(s_7 = - 2.( \frac{ {6}^{7} - 1 }{6 - 1} )\)

\(s_7 = - 2.( \frac{279.936 - 1}{5} )\)

\(s_7 = - 2.( \frac{279.935}{5} )\)

\(s_7 = - 2 \: . \: 55.987\)

\(s_7 = - 111.974\)

The answer is B.

Xenophon will engage in a LOW level of advertising in trade journals.
in trade journals, we need to compare the payoffs for each scenario.

From the payoff matrix, we can see that if Ulysses chooses a low level of advertising, the payoff is $12 million if Xenophon also chooses a low level, and $13 million if Xenophon chooses a high level. Therefore, Ulysses will engage in a LOW level of advertising in trade journals.

If Xenophon chooses a high level of advertising, the payoff is $11 million if Ulysses chooses a low level, and $12 million if Ulysses also chooses a high level.Comparing the payoffs, Xenophon would prefer a high level of advertising if Ulysses chooses a low level (to obtain $11 million instead of $12 million), and a low level of advertising if Ulysses chooses a high level (to obtain $12 million instead of $13 million).

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Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

10x - 15 + 5x = 180

Step-by-step explanation:

Solve for x