The winning snail moves 1/2 inch per second. How far will the snail travel in 5 seconds, 30 seconds,1 minute, 1 hour.

Answer:

5.5

Hope it helps!

Answer:

2x = -y

Step-by-step explanation:

The energy diagrams of a mass in a spherical bowl can be analyzed to understand the potential energy distribution and the equilibrium points of the system.

In a spherical bowl, the gravitational potential energy is the dominant factor. As the mass moves within the bowl, its position relative to the center of the bowl determines its potential energy. The height of the mass above the bottom of the bowl corresponds to the potential energy at that point.

When analyzing the energy diagrams, several key points can be observed:

Lowest Point: The lowest point in the bowl represents the stable equilibrium position. At this point, the potential energy is at its minimum, and any slight displacement will cause the mass to move back towards the equilibrium position.

Highest Point: The highest point in the bowl represents the unstable equilibrium position. At this point, the potential energy is at its maximum, and any displacement will cause the mass to move away from the equilibrium position.

Potential Energy Curve: The energy diagram will have a curved shape, where the potential energy increases as the mass moves away from the equilibrium position. The shape of the curve will depend on the specific shape of the bowl.

Equilibrium Points: Apart from the lowest point, there may be other equilibrium points in the bowl where the potential energy is locally minimum. These points represent positions where the mass can temporarily rest without rolling down further, but they are not as stable as the lowest point.

Overall, analyzing the energy diagrams of a mass in a spherical bowl allows us to understand the equilibrium positions, potential energy distribution, and stability of the system. It provides insights into the behavior of the mass and how it will respond to external forces or disturbances.

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The electric field at the point directly to the east of the negatively charged point is directed towards the charge, that is, west of the point.

The correct option is D.

A negative point charge has an electric field focused at it. Thus, the electric field at the point directly to the east of the negatively charged point is directed towards the charge, that is, west of the point.

The electric field is defined as that of the electric force per unit of charge. The direction of the field is assumed to represent the direction of the force it would impose on a positive test charge. The electric field radiates outward from the a positive charge and inward from a negative point charge.

The field lines never cross. The field lines lie parallel to the charge's surface. The quantity of charge and indeed the number of field lines are proportionate.

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I understand that the question you are looking for is:

What is the direction of the electric field directly to the east of an isolated negative point charge?

A. north

B. south

C. east

D. West

Answer:

(2, 3)

Step-by-step explanation:

The solution of two equations on a graph is where they intersect. In this case (2, 3) is the answer.

Answer:

(x,y) = (2,3) so C?

Step-by-step explanation:

=> y = x/2+2

=> y = x + 1

from that info, you can tell y = y, meaning x/2 + 2 = x+1

solving:

=> x/2 + 2 = x + 1

=> 1/2x +2 = x + 1

=> -x             -x

=> - 1/2x + 2 = 1

=> -2                -2

=> -1/2x = -1

=> * 2/-1   * 2/-1

=> x = 2

solve using substitution now:

(let's plug it in to the easiest y = statement)

=> y = x+1

=> y = 2 +1

=> y = 3

(2,3) is your answer

Answer:

If the sales 2 years ago were x, the sales last year were 1.12x and this year's sales were 1.12 * (1.12x). We can write 1.12 * (1.12x) = 81427 so that means x = $64913.

Answer:

3.57

Step-by-step explanation:

P=SP -CP

=290-280=10

P%=\(\frac{P*100}{CP}\)

=\(\frac{10*100}{280}\)

=\(\frac{1000}{280}\)

=3.57

Answer:

I think the error in Cynthia's answer is when she multiplied

Step-by-step explanation:

-2x(x^2 - 3) here

It should be = -2x^2 + 4x^2 - 2

\(\displaystyle \lim_{x\to \infty} 1+\cfrac{ln(x)}{x}\implies \lim_{x\to \infty} \cfrac{x+ln(x)}{x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{using L'Hopital once} }{\cfrac{\frac{d}{dx}[x+ln(x)]}{\frac{d}{dx}(x)}}\implies \cfrac{ ~~ 1+ \frac{ 1 }{ x } ~~ }{1}\implies 1+\cfrac{1}{x}\implies \cfrac{x+1}{x}\)

\(\stackrel{ \textit{using L'Hopital twice} }{\cfrac{\frac{d}{dx}[x+1]}{\frac{d}{dx}(x)}}\implies \cfrac{1}{1}\implies 1 \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to \infty} \cfrac{x+ln(x)}{x}\implies \lim_{x\to \infty} 1\implies \text{\LARGE 1}\)

Answer:

hope this could help u

Step-by-step explanation:

The functions in decreasing order of their periods are given below:

The branch of mathematics concerned with specific functions of angles and their application to calculations.

The first one will be:

1. y= -10 sin (x/5-2π)

then,

2. y= 5 csc (3x)+6

then,

3. y=-3cos(x+2π)

then,

4. y= 2/3 cot [(x/4) +6]

then,

5. y= -1/2 tan (5x/6 + π)

Hence, all above are arranged in order of their decreasing periodic function.

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Answer:

A and D

Step-by-step explanation:

4×3=12

4×d=4d

12+4d

Then;(4×d)+(3×4)=4d +12

Same expression

The second rectangular park with dimensions of 71 yards by 72 yards has the same perimeter as the first park but a larger area.

The perimeter of the first rectangular park is 2(55 + 88) = 286 yards. To find the dimensions of the second rectangular park with the same perimeter but a larger area, we need to use the formula for the perimeter of a rectangle: P = 2l + 2w.

Let's call the width of the second park "w" and the length "l". We know that the perimeter of the second park is also 286 yards, so:

2l + 2w = 286

Simplifying this equation, we get:

l + w = 143

Now, we need to find the dimensions that will give us the largest possible area. We know that the area of a rectangle is A = lw. We want to maximize A, so we need to find the values of l and w that will give us the largest possible product.

One way to do this is to use the fact that the sum of two numbers is constant. In other words, if we fix the value of l + w, the product lw will be largest when l and w are as close as possible to each other.

Since l + w = 143, we can choose l = 71 and w = 72 (or vice versa) to get the largest possible area.

To check that this works, we can calculate the area of the two parks:

- The area of the first park is A1 = 55 x 88 = 4840 square yards
- The area of the second park is A2 = 71 x 72 = 5112 square yards

So the second rectangular park with dimensions of 71 yards by 72 yards has the same perimeter as the first park but a larger area.

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Answer:

Equation of the line (slope-intercept form):  y = 2/3x + 4

Step-by-step explanation:

We can find the equation in slope-intercept form, whose general form is

y = mx + b, where

y-intercept, b:  We see on the graph that the line intersects the y-axis at the point (0, 4).  Thus, the y-intercept (b in the slope-intercept equation) is 4.

Slope, m:  We can find the slope using the slope formula, which is

m = (y2 - y1) / (x2 - x1), where

We see from the line intersects the x-axis at (-6, 0).  Thus, we can allow (-6, 0) to be our (x1, y1) point and (0, 4) to be our (x2, y2) point:

m = (4 - 0) / (0 - (-6))

m = (4) / (0 + 6)

m = 4 / 6

m = 2/3

Since the slope of the line is 2/3 and the y-intercept is 4, the equation of the line is y = 2/3x + 4

The collection of sample averages, known as the sampling distribution, would have an average that is equal to the average height of the entire population.

When measuring the height of each team and calculating their average, we are essentially taking samples from the population of all teams. The sampling distribution is created by repeating this process multiple times and calculating the average for each sample. According to the central limit theorem, as the sample size increases, the sampling distribution approaches a normal distribution regardless of the shape of the population distribution.

Therefore, the average of the sampling distribution, which represents the average height of all teams, would be equal to the average height of the entire population. The sampling distribution allows us to make inferences about the population based on the collected samples and provides a measure of the variability of the sample averages.

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Answer:

(

i

4

)

11

(

i

2

⋅

i

)

(i4)11(i2⋅i)

thats the answer

Answer:

The answer is 346.185 if its diameter is 22.

Answer:

Step-by-step explanation:

The product of a negative two and a positive three is equal to negative six (-6).

Question: Are the following sets subspaces of R^3 under usual addition and scalar multiplication defined on R 3 ? Explain clearly. 1. W1 = {(a1,a2,a3) E R^3 a1= 2a3, and a2 = -7a3}2. W2 = {(a1,a2,a3) E R^3 2a1= 4a2 + 5a3 = 3}3. W3 = {(a1,a2,a3) E R^3 2a1= 4a2 + 5a3 = 0}

Answer: Yes, the sets W1, W2, and W3 are subspaces of R^3 under usual addition and scalar multiplication defined on R 3. In order to be a subspace, the set must satisfy the following conditions: (1) closure under addition, (2) closure under scalar multiplication, and (3) the existence of a zero element.

W1: W1 = {(a1,a2,a3) E R^3 a1= 2a3, and a2 = -7a3}. Closure under addition is satisfied since the set is closed under addition of vectors. Closure under scalar multiplication is satisfied since any scalar times a vector in the set is still in the set. The zero element (0,0,0) is also in the set. Thus, W1 is a subspace of R^3.

W2: W2 = {(a1,a2,a3) E R^3 2a1= 4a2 + 5a3 = 3}. Closure under addition is satisfied since the set is closed under addition of vectors. Closure under scalar multiplication is satisfied since any scalar times a vector in the set is still in the set. The zero element (0,0,0) is also in the set. Thus, W2 is a subspace of R^3.

W3: W3 = {(a1,a2,a3) E R^3 2a1= 4a2 + 5a3 = 0}. Closure under addition is satisfied since the set is closed under addition of vectors. Closure under scalar multiplication is satisfied since any scalar times a vector in the set is still in the set. The zero element (0,0,0) is also in the set. Thus, W3 is a subspace of R^3.

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By following the cooking instructions and taking necessary precautions, Mary can be assured that the seafood dish will be safe and free from pathogens when served.

Based on the information provided, the part of the recipe that reassures Mary that no pathogens will be present when she serves the dish could be the specific instructions for cooking the seafood. These instructions may include details on cooking time and temperature, which are important factors in killing any potential pathogens that could be present in the seafood.

When cooking seafood, it's crucial to reach the appropriate internal temperature to ensure food safety. Different types of seafood may have different recommended cooking temperatures, but generally, seafood should be cooked until it reaches an internal temperature of 145°F (63°C).

By following the cooking instructions in the recipe and ensuring that the seafood is cooked to the recommended temperature, Mary can be confident that any potential pathogens present in the seafood will be effectively destroyed.

It's important to note that proper handling, storage, and hygiene practices are also critical in preventing the growth and spread of pathogens. Mary should also ensure that she properly handles and stores the seafood before cooking it, and practices good hygiene, such as washing her hands and cleaning utensils and surfaces thoroughly.

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Answer:

y – y1 = m(x – x1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know that:

2x + 6 = 9.

Using this we want to find the values of different expressions.

The solutions are:

a) 4x + 12

You can see that if we grab the initial equation:

2x + 6 = 9

And multiply both sides by 2 we get:

2(2x + 6) = 2*9

4x + 12 = 18

So we just found the value of the expression.

b) 2x+9

Again we start with the original equation:

2x + 6 = 9

Now we add 3 in both sides:

2x + 6 + 3 = 9 + 3

2x + 9 = 12

We just fond the value of the expression.

c) x + 3

We start with:

2x + 6 = 9

Now we divide both sides by 2:

(2x + 6)/2 = 9/2

x + 3 = 4.5

d) -6x - 18

We start with:

2x + 6 = 9

Here we need to multiply both sides by -3 to get:

(2x + 6)*-3 = 9*-3

-6x -18 = -27

e) 2x + 1

We start with:

2x + 6 = 9

Now we subtract 5 in both sides:

2x + 6 - 5 = 9 - 5

2x + 1 = 4

f) 10x + 32

We start with:

2x + 6 = 9

Now we multiply both sides by 5:

5*(2x + 6) = 5*9

10x + 30 = 45

Now we add 2 to both sides:

10x + 30 + 2 = 45 + 2

10x + 32 = 47.

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Answer:

3888 is the correct answer.

Step-by-step explanation:

12×12×3×3×3=3888

Hope this helps you. Have a nice day!

Answer:

I think B is the right one.

Step-by-step explanation:

Hope this helped

Answer:

c.) \(x^{3} -16x^{2} +75x-108\)

Step-by-step explanation:

Check the attachment.

Answer:

(-1/10)

Step-by-step explanation:

I'll assume 1/4xy is (1/4)xy and not 1/(4xy).

(1/4)xy

(1/4)(-2/3)(3/5)

Multiple the numerators and denominators separately:

Numerator + 1*(-2)*3 = -6

Deniominator 4*3*5 = 60

Put them back together:  (-6/60)  This reduces to (-1/10)

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

86 minutes

If you want a step by step explanation please let me know in the comments .

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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