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Answer:

8.4*10^-3

Step-by-step explanation:

Move the decimal point 3 places in order to get a number in the one's place.

Answer:

40 is answer follow me I give you the answer

Answer:

40 i think

Step-by-step explanation:

The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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Answer: 1.5 hours

Step-by-step explanation:

14 times in 21 hours

1 time would be 21 ÷ 14

21 ÷ 14 = 1.5

It took 1.5 hours to orbit the earth 1 time

Hope I helped!

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

The rate of change of the radius of the cone when the radius is 3 inches is 0.\(\overline 3\) inch/minute

Step-by-step explanation:

The given parameters are;

The radius of the cone = 3 inches

dV/dt = 9·π in.³/min

The height, h = 3 × Radius, r

The formula for the volume of a cone, V is V = 1/3×π×r²×h = 1/3×π×r²×3×r = π·r³

Therefore, we have;

dV/dt = dV/dr × dr/dt

dV/dr =3·π·r²

∴ dr/dt = dV/dt/(dV/dr) = 9·π/(3·π·r²) = 3/r²

When r = 3 inches, we have;

dr/dt = 3/r² = 3/(3²) = 1/3 inch/minute

The rate of change of the radius of the cone when the radius is 3 inches = 0.\(\overline 3\) inch/minute

Answer:

Total cost= 99 + 2.97x

Step-by-step explanation:

Giving the following information:

Fixed cost= $99

Variable cost= 3% per person

First, we need to calculate the 3% of 99:

Unitary variable cost= 99*0.03= $2.97

Now, we establish the total cost structure:

Total cost= 99 + 2.97x

x= number of people in attendance

Finally, suppose 200 people attend the party:

Total cost= 99 + 2.97*200

Total cost= $693

Answer:

115.7 km/h

Step-by-step explanation:

velocity = distance/time

velocity = (0.9 km)/(28 s) = 0.032143 km/s

The velocity is 0.032143 k/s. The question is answered, but since km/s is not a common unit of speed, we can convert to a more common unit of speed such as km/h.

velocity = (0.9 km)/(28 s)[(3600 s)/(1 h)] = 115.7 km/h

Answer:

The plans will cost the same when the amount you have to pay for talking for "x" minutes on Plan A is the same has what you have to pay for talking for the same number of "x" minutes when using Plan B.

$$ Plan A = $$ Plan B

To find the charge on each plan we add the base rate to the per minute call rate for each.

Plan A = $27 + $0.11x

Plan B = $13 + $0.15x

Let's drop the $ sign for now and get rid of the decimal point by multiplying by 100.

2700 + 11x = 1300 + 15x

Subtracting 11x and 1300 from both sides:

4x = 1400

x = 350 min.

Using this result the plans both cost $65.50 for 350 min of talk time.

Step-by-step explanation:

boom   :)

We cannot solve the corresponding first-order linear ODE using this technique.

The method of integrating factors is a technique used to solve first-order linear ordinary differential equations (ODEs) of the form:

y'(x) + p(x) y(x) = q(x)

where p(x) and q(x) are continuous functions on some interval I. The idea of the method is to multiply both sides of the equation by an integrating factor, which is a function u(x) chosen to make the left-hand side of the equation the derivative of a product:

u(x) y'(x) + p(x) u(x) y(x) = u(x) q(x)

The goal is to choose u(x) so that the left-hand side of the equation is the derivative of u(x) y(x). If we can find such a function u(x), we can integrate both sides of the equation to obtain:

u(x) y(x) = ∫ u(x) q(x) dx + C

where C is a constant of integration.

Now, if we cannot find an explicit formula for u(x) or the integral ∫ u(x) q(x) dx, the method of integrating factors fails. In other words, we cannot use this technique to solve the ODE. This is because without an explicit formula for u(x), we cannot integrate both sides of the equation to obtain a solution for y(x).

For example, consider the following first-order linear ODE:

y'(x) + x^2 y(x) = x

We can see that p(x) = x^2 and q(x) = x. To apply the method of integrating factors, we need to find a function u(x) such that:

u(x) y'(x) + x^2 u(x) y(x) = x u(x)

We can see that u(x) = e^(x^3/3) is a suitable integrating factor, as it makes the left-hand side of the equation the derivative of e^(x^3/3) y(x). Multiplying both sides of the equation by e^(x^3/3), we obtain:

e^(x^3/3) y'(x) + x^2 e^(x^3/3) y(x) = x e^(x^3/3)

which is equivalent to:

(d/dx)(e^(x^3/3) y(x)) = x e^(x^3/3)

Integrating both sides with respect to x, we obtain:

e^(x^3/3) y(x) = ∫ x e^(x^3/3) dx + C

We can see that the integral on the right-hand side of the equation does not have an explicit formula, so we cannot find an explicit solution for y(x) using the method of integrating factors. In other words, the method fails in this case.

In conclusion, if we cannot compute an explicit formula for one or both of the integrals that appear in the method of integrating factors, we cannot solve the corresponding first-order linear ODE using this technique.

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Answer:

B. h(x) = -3x + 4.

Step-by-step explanation:

I am assuming that the vertical shift is upwards,

A refection in the x axis gives -3x

Vertical shift upwards of 4 gives -3x + 4.

Answer:

Step-by-step explanation:

a) sum of angle on the straight line TRW is 180.

Given <TRS = 2x+10

<SRW = x-10

<TRS+<SRW = 180

2x+10+x-10 = 180

3x = 180

x = 180/3

x = 60°

<TRV = 180°-(2x+10)

Substitute x = 60° into the expression

<TRV = 180-(2(60)+10)

<TRV = 180-(120+10)

<TRV = 180-130

<TRV = 50°

2) From the diagram attached <MHJ= <LHK (oppositely directed angle)

Given

<MHJ= x+15

<LHK = 2x-20

Substitute the given data into the formula to get x

x+15= 2x-20

x-2x = -15-20

-x = -35

x = 35°

Next is to get the measure of <MHJ

<MHJ = x+15

<MHJ = 35+15

<MHJ = 50°

Parabola equation , characteristic points

Vertex is the point of minimum-max value

A Directrix is a line outside parabola

Vertex is at (x,y) = (4,-5)

Parabola equation in general is

(x-h)^2 = 4•c•(y-k)

here c = -9

and (h,k) = (4,-5)

Then

(x-4)^2 = 4•(-9) •(y+5) = (-36)•(y+5)

(x-4)^2 = (-36)•(y+5)

Now divide by (-36)

-0.06((x-4)^2 = y + 5

-0.06(x-4)^2 - 5 = y

Looking at options, right answer comes to be D) , last option

Answer:

15%

Step-by-step explanation:

3÷20=0.15

0.15×100=15

Answer:

A: (x-5.5)^2 + (y-4)^2=12.25

Step-by-step explanation:

(b) There are two Nash equilibria in this game:(S, S): Both A and B choose to Stop. Neither player has an incentive to deviate as they both receive a payoff of 0, and any deviation would result in a lower payoff.

(C, C): Both A and B choose to Continue. Similarly, neither player has an incentive to deviate since they both receive a payoff of -1, and any deviation would result in a lower payoff. (c) There is no dominant strategy in this game. A dominant strategy is a strategy that yields a higher payoff regardless of the actions taken by the other player. In this case, both players' payoffs depend on the actions of both players, so there is no dominant strategy. (d) The Subgame Perfect Nash equilibria (SPNE) can be found by considering the game as a sequential game and analyzing each subgame individually.

In this game, there is only one subgame, which is the entire game itself. Both players move simultaneously, so there are no further subgames to consider. Therefore, the Nash equilibria identified in part (b) [(S, S) and (C, C)] are also the Subgame Perfect Nash equilibria of this game.

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Sοfia needs tο reduce each side οf the phοtο by 7/2 inches.

A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn οf the fοrm ax² + bx + c = 0, where x represents an unknοwn variable, and a, b, and c are cοnstants. It can have at mοst twο sοlutiοns.

Let's start by calculating the area οf the οriginal phοtο:

10 inches x 12 inches = 120 square inches

If Sοfia wants tο reduce the phοtο by the same amοunt οn each side, she will need tο subtract the same value frοm bοth the length and width οf the phοtο. Let's call this value x.

Sο, the new dimensiοns οf the phοtο will be:

(10 - 2x) inches x (12 - 2x) inches

And the area οf the new phοtο will be:

(10 - 2x) inches x (12 - 2x) inches = 120/8 = 15 square inches

Expanding the abοve equatiοn, we get:

120 - 44x + 4x² = 15

Rearranging and simplifying, we get a quadratic equatiοn:

4x² - 44x + 105 = 0

We can sοlve fοr x using the quadratic fοrmula:

x = [44 ± √(44² - 4(4)(105))] / (2(4))

x = [44 ± √(1936 - 1680)] / 8

x = [44 ± √(256)] / 8

x = (44 ± 16) / 8

Taking the pοsitive rοοt, we get:

x = 7/2

Sο, Sοfia needs tο reduce each side οf the phοtο by 7/2 inches.

The new dimensiοns οf the phοtο will be:

(10 - 2(7/2)) inches x (12 - 2(7/2)) inches = 3 inches x 5 inches

And the area οf the new phοtο will be:

3 inches x 5 inches = 15 square inches

Therefοre, the new phοtο will be 1/8 οf the οriginal phοtο.

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Answer: √5-√3

Step-by-step explanation:

\(\displaystyle\\\frac{1}{\sqrt{5}+\sqrt{3} } +\frac{1}{2} (\sqrt{5} -\sqrt{3})\\\)

Let us reduce this expression to a common denominator:

\(\displaystyle\\\frac{1+\frac{1}{2}(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3}) }{\sqrt{5} +\sqrt{3} } =\\\\\frac{1+\frac{1}{2}((\sqrt5)^2 -(\sqrt{3} )^2) }{\sqrt{5}+\sqrt{3} } =\\\\\frac{1+\frac{1}{2}(5-3) }{\sqrt{5} +\sqrt{3} } =\\\\\frac{1+\frac{1*2}{2} }{\sqrt{5} +\sqrt{3}} =\\\\\frac{1+1}{\sqrt{5} +\sqrt{3} } =\\\\\frac{2}{\sqrt{5}+\sqrt{3} }\)

Let's get rid of the irrationality in the denominator:

\(\displaystyle\\\frac{2(\sqrt{5}-\sqrt{3} ) }{(\sqrt{5} +\sqrt{3})(\sqrt{5} -\sqrt{3}) } =\\\\\frac{2(\sqrt{5}- \sqrt{3} )}{(\sqrt{5})^2-(\sqrt{3})^2 }=\\\\\frac{2(\sqrt{5} -\sqrt{3}) }{5-3} =\\\\\frac{2(\sqrt{5}-\sqrt{3}) }{2} =\\\\\sqrt{5}-\sqrt{3}\)

Answer:

if the question is an objective question

Answer:

32 trucks.

Step-by-step explanation:

3:1

Every time 3 SUV's are sold, one truck is sold. This would also mean that \(\frac{3}{4}\) of both trucks and SUV's sold are SUV's. If we divide 128 into fourths, then you get 32. One fourth of 128 is 32. So, they should have 32 trucks (and 96 SUV's)

The kernel of the homomorphism G → Sym(G\H) is the intersection of all conjugates of H in G.


Let H be a subgroup of G and consider the action of G on the set G\H, where G acts on G\H by left multiplication.

The homomorphism G → Sym(G\H) assigns to each element g in G the permutation of G\H induced by the action of g on G\H.

The kernel of this homomorphism is the set of elements in G that fix every element of G\H under the action. In other words, it is the intersection of all conjugates of H in G, denoted as ⋂(gHg^(-1)).

Now, suppose G is infinite but has a subgroup H of finite index k. This means that there are k distinct left cosets of H in G.

By the first isomorphism theorem, G/ker(φ) is isomorphic to a subgroup of Sym(G\H), where φ is the homomorphism G → Sym(G\H).

Since G/ker(φ) is a subgroup of Sym(G\H), and Sym(G\H) is finite, G/ker(φ) must also be finite. Therefore, ker(φ) is a normal subgroup of G and has finite index in G.

Thus, if G is infinite but has a subgroup of finite index, it also has a normal subgroup of finite index.

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Answer:

5/33

Step-by-step explanation:

five apples and seven peaches = 12 total

P( apple) = number of apples / total

               = 5/12

No replacement since you ate it

four apples and seven peaches = 11 total

P( peach) = number of peach / total

               = 4/11

P(apple, no replacement, peach) = 5/12 * 4/11 = 5/33

Answer: The correct answer is that each construction worker built 3/7 of (each) shed. Or 0.429 of (each) shed.

Step-by-step explanation: This is correct because you would do 3 / 7 = 3/7. You would do the amount of sheds they built, divided by the number of workers that build it. They built a shed about every 3 days. Or 3 1/3 days to be exact.

(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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The probability that the nurse will find the two patients is P =  0.49.

We know that the probability that the nurse finds the client on a particular day is 0.7

So, each time that the nurse goes that a home, that probability is the same and is independent of what happened before.

So if the nurse goes to two houses, the probability that she will find the client on the first home is 0.7

And the probability that she will find the client on the second home is 0.7

Then the joint probability (the product of the two individual ones) is:

P = 0.7*0.7 = 0.49

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Thus,  there are 720 different Loco Mocos that can be ordered if we consider all six protein options, but this number can vary depending on individual preferences and availability.

A Loco Moco is a popular Hawaiian dish that usually consists of a base of white rice topped with a hamburger patty, a fried egg, and brown gravy.

However, it can be customized by adding different types of proteins such as Portuguese sausage, bacon, turkey, hot dog, salmon, or mahi. So, how many different Loco Mocos can be ordered?

If we consider all six proteins listed in the question, we have six options for the first protein, and then five options left for the second protein (since one has already been used), four options for the third protein, three for the fourth, two for the fifth, and one for the sixth.

Using the multiplication principle, we can calculate the total number of different Loco Mocos as follows:

6 x 5 x 4 x 3 x 2 x 1 = 720

Therefore, there are 720 different Loco Mocos that can be ordered if we consider all six proteins. However, this number can vary depending on the number of protein options available at a particular restaurant or if a customer chooses to only add one or two proteins to their Loco Moco.

In conclusion,  there are 720 different Loco Mocos that can be ordered if we consider all six protein options, but this number can vary depending on individual preferences and availability.

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(i) Variable: Width of the last upper molar

(ii) Type of variable: The width of the last upper molar is a continuous and quantitative variable, as it can take on any numerical value within a range (in this case, measured in millimeters).

(iii) Observational unit: The observational unit is the specimens of the extinct mammal Acropithecus rigidus. Each specimen represents a unique unit of observation in the study.

(iv) Sample size: The sample size is 36. This means that the paleontologist measured the width of the last upper molar in 36 individual specimens of Acropithecus rigidus.

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it A

Step-by-step explanation:

Answer:

-11.48

Step-by-step explanation:

-7.2 + (-4.28)

-7.2 - 4.28

-11.48

The point (2, 3) is in the exterior of the circle with the equation (x - 5)^2 + (y + 3)^2 = 25.

The given circle has the equation (x - 5)^2 + (y + 3)^2 = 25, and you want to determine whether the point (2, 3) is interior, exterior, or on the circle.

First, substitute the coordinates of the point into the equation: (2 - 5)^2 + (3 + 3)^2. This simplifies to (-3)^2 + (6)^2, which equals 9 + 36 = 45. Now, compare the resulting value to the constant term (25) in the circle equation.

Since 45 > 25, the point (2, 3) is in the exterior of the circle. The reason is that the equation would be equal if the point were on the circle, and the left side of the equation would be less than 25 if the point were in the interior.

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