-cosx = 8sinx for values of x between 0 and 360, solve for x

50 different greek armies, the upper class and the lower class soldiers battalions can be sent.

The Greek army can form different battalions by choosing 4 upper class soldiers and 8 lower class soldiers from a total of 5 upper class soldiers and 10 lower class soldiers. This problem can be solved using a combination formula known as a binomial coefficient.

The number of different battalions that can be sent is:

(5 choose 4) * (10 choose 8) = 5*10 = 50

Different battalions can be formed by choosing 4 upper class soldiers and 8 lower class soldiers from a total of 5 upper class soldiers and 10 lower class soldiers. Therefore, 50 different battalions can be sent.

So, 50 different battalions can be sent.

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Juan's claim is incorrect. We have to disprove Juan's claim. He says that the solution to the given system of equations is unique only to the equations y = 5x-2 and y = 1/2x +7.

What we can do is that, we can introduce a third equation. This third equation should have the same solution as the first two.

Example of such an equation is,

y = -3x + 1

We can solve the system of three equations,

y = 5x - 2

y = 1/2x + 7

y = -3x + 1

We can use the first two equations first and find values of x and y,

5x - 2 = 1/2x + 7

Multiplying both sides by 2,

10x - 4 = x + 14

Subtracting x from both sides,

9x - 4 = 14

Adding 4 to both sides,

9x = 18

Dividing both sides by 9,

x = 2

Now we know x = 2.

We can use either of the first two equations to find y,

y = 5x - 2 = 5(2) - 2 = 8

This satisfies all three equations.

So finally we can say Juan's claim is not correct. There are other equations there having the same solution as the first two.

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Answer:

$0.24 per m

Step-by-step explanation:

Answer: 16482

Step-by-step explanation:

Let's divide the number into three parts:

sixteen thousand | four hundred |eighty-two

A thousand is 1000, so sixteen thousand should be 16000.

A hundred is 100, so four hundred should be 400.

Eighty-two is just 82.

Let's add all of these:

\(16000+400+82=16482\)

The cost of tickets for senior citizen and students are $11 and $13 respectively.

To solve this problem, we have to write out system of equations and solve the value of the unknown.

Let;

We can express the problem mathematically as;

\(6x + 4y = 118..eq(i)\\14x + 8y = 258 ...eq(ii)\)

Solving for x and y;

\(6x + 4y = 118..eq(i)\\14x + 8y = 258 ...eq(ii)\\x = 11, y = 13\)

From the calculations above, the value of x and y are 11 and 13 respectively.

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When an indicator variable x has a probability of 1/4 and a probability of 3/4, the value of E[(1 x)(1-x)] is 3/8.

The probability of an event occurring is defined by probability. There are numerous real-life scenarios in which we must forecast the outcome of an occurrence.

To calculate E[(1-X)X], we first need to determine the probability distribution of X.

From the problem statement, we know that P(X=0) = 1/4 and P(X=1) = 3/4.

Now we can calculate the expected value of (1-X)X as follows:

E[(1-X)X] = (1)(P(X=0)(1-P(X=0))) + (1)(P(X=1)(1-P(X=1)))

           = P(X=0)(1-P(X=0)) + P(X=1)(1-P(X=1))

           = (1/4)(3/4) + (3/4)(1/4)

           = 3/16 + 3/16

           = 6/16

           = 3/8

Therefore, E[(1-X)X] = 3/8.

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Answer:

B. (2, -6)

Sorry if you don't need this anymore...

The required rate for water being poured into the cup when the water level is 9 cm = 40.5π cm³/sec

For given question,

We have been given the height of a conical paper cup i.e., h = 10 cm

and the radius of a conical paper cup r = 10 cm

The cup is being filled with water so that the water level rises at a rate of 2 cm/sec

We need to find the rate at which water being poured into the cup when the water level is 9 cm

We know that the volume of the cone is \(V=\frac{\pi r^2 h}{3}\)

We can relate h and r as we know that the slope = h/r

                                                                                  = 10/5

                                                                                  = 2

Now, we make the volume a formula in a single variable

\(\Rightarrow V=\frac{\pi (\frac{h}{2} )^2 h}{3}\\\\\Rightarrow V=\frac{\pi h^3}{12}\)

Differentiating above equation with respect to time,

\(\Rightarrow V'=\frac{3\pi h^2 h'}{12} \\\\\Rightarrow V'=\frac{\pi h^2 h'}{4}\)

Substituting values,

\(\Rightarrow V'=\frac{\pi \times 9^2\times 2}{4}\\\\\Rightarrow V'=40.5\pi~~cm^3/sec\)

Therefore, the required rate for water being poured into the cup when the water level is 9 cm = 40.5π cm³/sec

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Answer:

The first option

Step-by-step explanation:

Unit Price

Option one is $0.17 per ounce

Option two is $0.18 per ounce

Hope its right, so sorry if it isn't...

The area of the region R bounded by the graph of f(x) = x^2(x-6) and the x-axis on the interval [-1, 7] is approximately 371.00 square units.

To find the area of the region R bounded by the graph of f(x) = x^2(x-6) and the x-axis on the interval [-1, 7], we need to integrate the function f(x) over that interval. The area can be calculated using the definite integral:

Area = ∫[a,b] f(x) dx

In this case, a = -1 and b = 7. Let's calculate the area using integration:

Area = ∫[-1,7] x^2(x-6) dx

To solve this integral, we expand the polynomial and simplify:

Area = ∫[-1,7] (x^3 - 6x^2) dx

Next, we integrate term by term:

Area = (1/4)x^4 - (2/3)x^3 | [-1,7]

Now, we substitute the upper and lower limits of integration:

Area = [(1/4)(7^4) - (2/3)(7^3)] - [(1/4)(-1^4) - (2/3)(-1^3)]

Simplifying further:

Area = (1/4)(2401) - (2/3)(343) - (1/4)(1) + (2/3)(-1)

Area = 600.25 - 228.33 - 0.25 - 0.67

Area ≈ 371.00 (rounded to the nearest hundredth)

Therefore, the area of the region R bounded by the graph of f(x) = x^2(x-6) and the x-axis on the interval [-1, 7] is approximately 371.00 square units.

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The circumference of the circle is approximately 31.42 cm and the area of the circle is approximately 157.08 cm².

A circle circumscribed about a square with sides of 10cm has a circumference of approximately 31.42 cm and an area of approximately 157.08 cm².

If a circle is circumscribed about a square, the diameter of the circle is equal to the diagonal of the square. In this case, the diagonal of the square is:

d = √(10² + 10²) = √(200) = 10√(2) cm

The radius of the circle is half the diameter, so:

r = 5√(2) cm

The circumference of the circle is:

C = 2πr = 10π√(2) cm

The area of the circle is:

A = πr² = 50π cm²

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To prove that the set of irrational numbers is uncountable, we can use a proof by contradiction. The idea is to assume that the set of irrational numbers is countable, and then show that this assumption leads to a contradiction.

Assumption: Let's assume that the set of irrational numbers is countable.

Recall that a set is countable if its elements can be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...).

Now, consider the set S of all real numbers between 0 and 1 (exclusive) that can be expressed as decimals without repeating or terminating. In other words, S consists of all the irrational numbers between 0 and 1.

We can represent the numbers in S as a list:

S = {x1, x2, x3, x4, ...}

Now, let's construct a new number y by choosing the digits of y such that the ith digit is different from the ith digit of xi (i.e., y is different from xi at the ith decimal place). In other words, y differs from each number xi in the list at least at one decimal place.

Let y = 0.y1y2y3y4...

Now, by construction, y is a decimal number between 0 and 1 without repeating or terminating decimals. Therefore, y is an irrational number.

However, notice that y differs from each xi in the list at least at one decimal place. This means that y is not equal to any xi in the list, leading to a contradiction with our assumption that the set of irrational numbers is countable.

Thus, we have reached a contradiction, and our assumption that the set of irrational numbers is countable must be false.

Therefore, the set of irrational numbers is uncountable.

This proof demonstrates that there are more irrational numbers than natural numbers, showing the uncountability of the set of irrational numbers.

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First you will get 4dz

Answer:

74 and 32

Step-by-step explanation:

Because the sides AC and BC are equal, their opposite angles will be equal. Therefore angle B will also be 74 degrees.

To find angle C, we subtract 74 and 74 from 180 because a triangle's angle measures should add up to 180 degrees.

180 - 74 - 74 = 32

-7ab + 12a

Explanation:

-ab+12a-6ab

Collect like terms:

-ab - 6ab + 12a

-ab is the same as -1ab. Add it to -6ab, you will get negative 7ab

-7ab + 12a

The simplified expression = -7ab + 12a

Explanation

We will have to find the population density of each of the regions

To get the population density, we will have to divide the population of each region and then divide by the area of the of each region

For part A

The population density of region A is

For region B

The area of region B is

The population density of region B is

For region C

The population density of region C

Thus, we can observe that Region C has a population density lower than 60 animals per square miles

Thus, option C is correct

Based on this scientist's model, the minimal amount of work the bird can expend to break open a whelk shell is 21.8.

The correct option is (b) 21.8

Based on the scientist's model, we need to find the minimal amount of work the bird can expend to break open a whelk shell using the function W(h) = (27.4h - 0.71 + 1)h. To do this, we will find the minimum value of the function.

Rewrite the function as a quadratic equation:
W(h) = 27.4h^2 - 0.71h + h
W(h) = 27.4h^2 + 0.29h

Find the vertex of the quadratic equation to find the minimum value. The formula for the x-coordinate of the vertex is h = -b / 2a, where a = 27.4 and b = 0.29.
h = -(0.29) / (2 * 27.4)
h ≈ 0.00531

Plug the value of h back into the original function to find the minimum amount of work.
W(0.00531) = 27.4(0.00531)^2 + 0.29(0.00531)
W(0.00531) ≈ 21.8

So, the minimal amount of work the bird can expend to break open a whelk shell, based on the scientist's model, is approximately 21.8. Your answer is (b) 21.8.

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Answer:

1,512

if not that then:

168

Answer:

379 cheeseburgers we’re sold on Friday

Step-by-step explanation:

504 x 3 / 4 =

1516 / 4 =

379 cheeseburgers sold

Answer:

i think it might be C

Step-by-step explanation:

very sorry if it's wrong

Answer:

26.88

Step-by-step explanation:

32% of 84

= \(\frac{32}{100}\) × 84

= 0.32 × 84

= 26.88

Answer:

Step-by-step explanation:

84 : 100 = 0.84

0.84 × 32 = 26.88

84 : 100 × 32 = 26.88

Step-by-step explanation:

The given equation `mx cx kx=f(t)` is a second-order linear differential equation with constant coefficients. The general solution to this type of equation is given by the sum of the complementary solution `x_c(t)` and the particular solution `x_p(t)`.

The complementary solution x_c(t) is the solution to the associated homogeneous equation mx cx kx=0. The characteristic equation for this homogeneous equation is mr^2 + cr + k = 0. Solving this quadratic equation gives two roots r_1 and r_2. The complementary solution can then be written as x_c(t) = C_1e^(r_1t) + C_2e^(r_2t).

The particular solution x_p(t) depends on the form of the function f(t). There are several methods for finding the particular solution, such as undetermined coefficients or variation of parameters.

Once the complementary and particular solutions are found, the general solution to the given differential equation is given by x(t) = x_c(t) + x_p(t). The constants C_1 and C_2 can then be determined using the initial conditions x(0)=0 and x'(0)=0.

Without more information about the function f(t), it is not possible to find a more specific solution to the given differential equation.

Answer:

m = 3

Step-by-step explanation:

Given

\(5^{4m}\) = \(5^{12}\)

Since the bases on both sides are equal ( both 5) the equate the exponents.

4m = 12 ( divide both sides by 4 )

m = 3

Yes, the solution of the dual offer computational advantages over solving the primal directly

Let us consider the given primal problem:

Minimize z = 50x₁ + 60x₂ + 30x₃

subject to

5x₁ + 5x₂ + 3x₃ ≥ 50

x₂- x₃ ≥ 20

7x₁ + 6x₂ - 9x₃ ≥ 30

5x₁ + 5x₂ + 5x₃ ≥ 35

2x₁ + 4x₂ + 15x₃ ≥ 10

12x₁ +10x₂ ≥ 90

x₂ - 10x₃ ≥ 20

x₁, x₂, x₃ ≥ 0

We will now form the dual problem by introducing the dual variables y₁, y₂, y₃, y₄, y₅, y₆, y₇, and the objective function of the dual problem is to maximize the sum of the right-hand side coefficients of the primal constraints multiplied by the dual variables.

The constraints of the dual problem are formed by the coefficients of the primal objective function.

Maximize w = 50y₁ + 20y₂ + 30y₃ + 35y₄ + 10y₅ + 90y₆ + 20y₇

subject to

5y₁ + y₂ + 7y₃ + 5y₄ + 2y₅ + 12y₆ ≥ 50

5y₁ + 5y₂ + 6y₃ + 5y₄ + 4y₅ + 10y₆ - 10y₇ ≥ 60

3y₁ - y₂ - 9y₃ + 5y₄ + 15y₅ ≥ 30

Now, we can solve this dual problem using the simplex method or any other optimization technique.

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Complete Question:

Solve the dual of the following problem, and then find its optimal solution from the solution of the dual. Does the solution of the dual offer computational advantages over solving the primal directly?

Minimize z = 50x₁ + 60x₂ + 30x₃

subject to

5x₁ + 5x₂ + 3x₃ ≥ 50

x₂- x₃ ≥ 20

7x₁ + 6x₂ - 9x₃ ≥ 30

5x₁ + 5x₂ + 5x₃ ≥ 35

2x₁ + 4x₂ + 15x₃ ≥ 10

12x₁ +10x₂ ≥ 90

x₂ - 10x₃ ≥ 20

x₁, x₂, x₃  ≥ 0

Since the distance from a point to point C is 1 and the distance from that same point to point B is 4, the point must be: C. point D.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

From the number line shown above, we have:

Distance = 4 + (-1)

Distance = 4 - 1

Distance = 3 (point D).

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the coordinates of point c is (9/2, -3/2)

The original coordinate = C(6, -2)

scale factor r =3/4

New coordinate (c) = scale factor × the original coordinate

c = 3/4(6, -2)

c = (3/4×6, -2×3/4)

c = (18/4, -6/4)

c = (9/2, -3/2)

Hence, the coordinates of point c is (9/2, -3/2)

The value of the rate of growth in Japan is - 0.55.

From the question above, :Birth rate = 7.7 per thousand

Death rate = 9.8 per thousand

Net migration = 0.55 per thousand

The rate of growth can be calculated using the following formula:

r = (birth rate - death rate) + net migration

Where,r = rate of growth

birth rate = number of live births per thousand in a population in a given year

death rate = number of deaths per thousand in a population in a given year

net migration = the difference between the number of people moving into a country (immigrants) and the number of people leaving a country (emigrants) per thousand in a given year

Putting the values in the formula we get,r = (7.7 - 9.8) + 0.55r = - 1.1 + 0.55r = - 0.55.

Therefore, the rate of growth in Japan is - 0.55.

Your question is incomplete but most probably your full question was:

thenet migration is confusing me. i thought of using the formula:[ (births + immigration) - (deaths + emmigration)] / total

population • 100 but im not sure how to do it with net migration.

Japan's birth rate is 7.7 per thousand and its death rate is 9.8 per thousand with a net migration of 0.55 ner thousand. Calculate r for Japan

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Answer:

1 and -3

Step-by-step explanation:

The zeros of a quadratic function are the points on the graph where the curve intercepts the x-axis (where y = 0).

From inspection of the attached graph, we can see that the curve intercepts the x-axis at x = -3 and x = 1.

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

The Zeroes of a function are the x - coordinates of points when the curve touches/cuts the x - axis, so ~ for the given curve the roots are :

\(\qquad \sf  \dashrightarrow \:1 \: \: and \: \: - 3\)

Therefore, the correct choice is D