The velocity of a particle moving along a straight line is given by v(t)=1.3tln(0.2t+0.4) for time t≥0. What is the acceleration of the particle at time t=1.2 ?

Answer:

E=Mc squared

Step-by-step explanation:

The last to appear in the ones position of a number in the Fibonacci sequence is 6.

The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21 , … starts with two 1s, and each term afterward is the sum of its two predecessors.

The next terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946.

Here, it can be seen that  is the last to appear in the ones position of a number in the Fibonacci sequence.

Thus, The last to appear in the ones position of a number in the Fibonacci sequence is 6.

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The horses' average speeds are approximately:

(a) mi/s: 0.0102 mi/s

(b) mi/h: 58.06 mi/h

To calculate the horses' average speeds, we need to calculate the speed as distance divided by time.

We have:

Distance: 1.50 miles

Time: 147 seconds

(a) To calculate the average speed in mi/s, we divide the distance by the time:

Average speed = Distance / Time

Speed of Fiddle Isle = 1.50 miles / 147 seconds ≈ 0.0102 mi/s

Speed of John Henry = 1.50 miles / 147 seconds ≈ 0.0102 mi/s

(b) To calculate the average speed in mi/h, we need to convert the time from seconds to hours:

Average speed = Distance / Time

Since 1 hour has 3600 seconds, we can convert the time to hours:

Time in hours = 147 seconds / 3600 seconds/hour

Speed of Fiddle Isle = 1.50 miles / (147 seconds / 3600 seconds/hour) ≈ 58.06 mi/h

Speed of John Henry = 1.50 miles / (147 seconds / 3600 seconds/hour) ≈ 58.06 mi/h

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The assumption that the population variances are not equal and that the two populations are normally distributed is −35.713332; 0.313332.

To assume that the population variances are not equal and that the two populations are normally distributed:

Given:

So, df = n1 + n2 - 2; 11 + 18 - 2 = 27.

T critical = T0.01, 27 = 2.473

Let,

Then,

Now,

Therefore, the assumption that the population variances are not equal and that the two populations are normally distributed is −35.713332; 0.313332.

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The equation given, 5x + 10y, does not represent the total amount of fiber in a package containing x apples and y oranges.

To calculate the total amount of fiber in a package containing x apples and y oranges, you would need to know the amount of fiber in each apple and orange and the number of apples and oranges in the package.

For example, if each apple contains 3 grams of fiber and each orange contains 2 grams of fiber, and there are x apples and y oranges in the package, the total amount of fiber in the package would be:

Total fiber = (3 grams of fiber per apple)(x apples) + (2 grams of fiber per orange)(y oranges)

Total fiber = 3x + 2y grams

what is number?

A number is a mathematical concept used to represent quantity or magnitude. Numbers can be used to count objects, measure distances or sizes, perform calculations, and describe various other mathematical concepts. The most basic types of numbers are the natural numbers, which include all positive integers (1, 2, 3, ...), and sometimes zero (0) as well. Other types of numbers include fractions, decimals, negative numbers, complex numbers, irrational numbers, and more. Numbers are a fundamental concept in mathematics and are used extensively in many fields, including science, engineering, economics, and finance.

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The correct answer is (4x^3 - 8x^2 )

Solve by using Foil's Method

Multiply (x - 3)(4x^2)

Begin, by multiplying together, the first terms of binomial

= x * 4x^2 = 4x^3

Now, multiply the last term of binomial.

= -3 * 4x^2 = -12x^2

Sum up the partial products starting from the first to last product from the first to last product and collect it:

=(4x^3 - 8x^2 )

Now, Let us know

What is Foil's Method ?

FOIL a mathematical series of steps used to multiply two binomials.

By definition we have the meaning of FOIL is given by:

F: First

O: Outer

I: Inner

L: Last

Binomial is simply an expression that consist of two variables or terms separated by either the addition sign (+) or subtraction (-).

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The dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: h = (36 - x^2) / 8x = (√3)/2 feet

Let the length and width of the base be x, and let the height be h.

The surface area of the top is x^2, and the surface area of the remaining four sides is \(2(xh + xh) = 4xh\).

The cost of the top is \(x^2\), and the cost of the remaining four sides is \(2(4xh) = 8xh\). Therefore, the total cost is:

\(C(x,h) = x^2 + 8xh\)

We know that the total cost is $36, so we have:

\(x^2 + 8xh = 36\)

Solving for h, we get:

\(h = (36 - x^2) / 8x\)

The volume of the box is given by:

\(V(x,h) = x^2h\)

Substituting h in terms of x, we get:

\(V(x) = x^2 ((36 - x^2) / 8x)\)

Simplifying, we get:

\(V(x) = (1/8) x (36x - x^3)\)

To find the dimensions of the box that will have the greatest volume, we need to find the value of x that maximizes V(x). We can do this by taking the derivative of V(x) with respect to x, setting it equal to 0, and solving for x:

\(V'(x) = (1/8) (36 - 3x^2) = 0\)

Solving for x, we get:

x = 2√3

Therefore, the dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: \(h = (36 - x^2) / 8x\) = (√3)/2 feet

The volume of the box is:

\(V = x^2h\)= (2√3)^2 ((√3)/2) = 9√3 cubic feet

Note: To confirm that this value represents the maximum volume, we can check that V''(x) < 0, which indicates a maximum point. We have:

\(V''(x) = (1/8) (-6x) = -3x/4\)

At x = 2√3, V''(x) = -3(2√3)/4 = -3√3/2 < 0, so this is indeed a maximum point.

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1 USD = 113.83 Japanese Yen

100 USD = 100 x 113.83 Japanese Yen

100 USD = 11,383.00 Japanese Yen

The appropriate type of t-test for this study is a one-sample t-test.

A one-sample t-test is used to determine whether a sample mean is significantly different from a known or hypothesized population mean. In this case, the researcher wants to compare the obesity rate in a small community to the known obesity rate in the United States. As the population variance is unknown, the appropriate test is a one-sample t-test instead of a z-test.

The test involves calculating the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, divided by the standard error of the sample mean. The t-statistic is then compared to the critical t-value from the t-distribution to determine whether the difference is statistically significant.

Therefore, a one-sample t-test is appropriate for this study.

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5 is d and idk question 5 sorry

a) The best response function of player i given action choice by player j is any demand between 0 and 1/2

b) The best response function of player 1 in a graph where player2's action is on the horizontal axis and that of player 1 on the vertical axis is illustrated below graph.

c) By using the  Nash equilibria, the best response function of player 1 is a step function with a discontinuity at 1/2.

Let's start with player 1. Suppose player 2 demands z2, then player 1's best response would be to demand the remaining amount, which is (1-z2). If z2 > 1/2, then player 1's best response would be to demand 0. If z2 = 1/2, then any demand between 0 and 1/2 would be a best response for player 1. If z2 < 1/2, then any demand between 1/2 and 1 would be a best response for player 1. Therefore, the best response function of player 1 can be written as follows:

BR1(z2) = {

1-z2 if z2 ≤ 1/2

0 if z2 > 1/2

}

If z1 = 1/2, then any demand between 0 and 1/2 would be a best response for player 2. If z1 < 1/2, then any demand between 1/2 and 1 would be a best response for player 2. Therefore, the best response function of player 2 can be written as follows:

BR2(z1) = {

1-z1 if z1 ≤ 1/2

0 if z1 > 1/2

}

To plot the best response function of player 1, we can use a graph where player 2's action is on the horizontal axis, and that of player 1 is on the vertical axis. The best response function of player 1 is a step function with a discontinuity at z2 = 1/2. It starts at (0,1), then drops to (0.5,0.5), and finally reaches (1,0).

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The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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Answer:

2. 7 + 4

3. 21 - 27

4. 8 - 28

Step-by-step explanation:

2. 1 (7+4) = 1×7 + 1×4 = 7 + 4

3. 3 (7-9) = 3×7 - 3×9 = 21 - 27

4. 4 (2-7) = 4×2 - 4×7 = 8 - 28

hope this helps :)

Answer:

1. the answer is 7+4

2. the answer is 21-9.

3. the answer is 8-7.

Hope this helps, have a great day/night, and stay safe!

Answer:

Step-by-step explanation:

-125/4

-124/4=-31

-31 1/4

It will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

To find out how long it will take, we can use the formula for compound interest:

A = P(1 + r)^t

Where A is the final amount, P is the principal amount, r is the interest rate, and t is the number of years.

In this case, we want to find out how long it will take for $100 to reach $500 when it grows at 10 percent per year. So we can plug in the values and solve for t:

500 = 100(1 + 0.10)^t

5 = (1.10)^t

Taking the natural logarithm of both sides:

ln(5) = t ln(1.10)

t = ln(5) / ln(1.10)

t = 14.87 years

So it will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

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Given:

The function is:

\(f(x)=4x^5-8x^4+8x^2-4x\)

To find:

The roots of the given equation.

Solution:

We have,

\(f(x)=4x^5-8x^4+8x^2-4x\)

For roots, \(f(x)=0\).

\(4x^5-8x^4+8x^2-4x=0\)

\(4x(x^4-2x^3+2x-1)=0\)

\(4x((x^4-1)+(-2x^3+2x))=0\)

\(4x((x^2+1)(x^2-1)-2x(x^2-1))=0\)

On further simplification, we get

\(4x(x^2+1-2x)(x^2-1)=0\)

\(4x(x-1)^2(x+1)(x-1)=0\)

\(4x(x+1)(x-1)^3=0\)

Using zero product property, we get

\(4x=0\)

\(x=0\)

Similarly,

\(x+1=0\)

\(x=-1\)

And,

\((x-1)^3=0\)

\(x=1\)

Therefore, the zeroes of the given function are \(-1,0,1\) and the factor form of the given function is \(f(x)=4x(x+1)(x-1)^3\).

The obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis. None of the option is correct.

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

The given equation of the function is;

\(y = -(x+2)^{1/3}+5\)

Hence,the obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis.

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Answer:

The function f(x) = sqrt(x - 2) + 3 represents a square root function that is shifted 2 units to the right and 3 units up from the parent function f(x) = sqrt(x).

The endpoint of the function occurs when the radicand (x - 2) is equal to zero, which means x = 2. So, the function has an endpoint at (2, 3).

Since the function involves a square root, the value of y cannot be negative. Therefore, the function is increasing to the right.

The correct graph that represents the function f(x) = sqrt(x - 2) + 3 is the one that shows a curve with an endpoint at (2, 3) that increases to the right.

Therefore, the answer is: The graph shows a curve with an endpoint at 2 comma 3 that increases to the right. A.

Answer:

18 is the answer

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Answer: The 6th term would be 243.

Step-by-step explanation:

The pattern in this sequence is that it is multiplying by 3 each time.

1 x 3 = 3, 3 x 3 = 9, 9 x 3 = 27.

Now what you want to do is multiply 27 by 3 to get a product of 81, which would be the 5th term.

Lastly, you would multiply 81 by 3 to get an answer of 243.

Answer:

60

Step-by-step explanation:

1 pound of water to 60 pounds of dry mix

If 1 gallon of water = 8 pounds of water, then, we would have,

8 pounds of water to 60 pounds of dry mix

This implies that 8 pounds of water would stir 60 pounds of dry mix. Therefore, in the table showing both possible combinations, what we would have in cell A would be amount of dry mix that would be combined with 8 pounds of water = 60 pounds.

Cell A = 60 pounds

Answer:

the 2 one is better because you get more pens

Step-by-step explanation:

you get more pens

Answer:

minute 600

Step-by-step explanation:

$1 = 100 pennies

60 = x pennies

x =6000/10

x = 600 minutes

Answer:

Step-by-step explanation:

For number 1.

If x = -2.

                    y = 4x + 3 = 4(-2) + 3 = -8 + 3 = -5

If x = 3

                    y = 4x + 3 = 4(3) + 3 = 12 + 3 = 15

If x = -4

                   y = 4x + 3 = 4(-4) + 3 = -16 + 3 = -13

If x = -5

                  y = 4x + 3 = 4(-5) + 3 = -20 + 3 = -17

If x = 5

                  y = 4(x) + 3 = 4(5) + 3 = 20 + 3 = 23

For number 2.

If x = -2

                 \(y = x^{2} + 4 + 2x = (-2)^{2} + 4 + 2(-2) = 4 + 4 - 4 = 4\)

If x = 3

                \(y = x^{2} + 4 + 2x = (3)^{2} + 4 + 2(3) = 9 + 4 + 6 = 19\)

If x = -3

                \(y = x^{2} + 4 + 2x = (-3)^{2} + 4 + 2(-3) = 9 + 4 - 6 = 7\)

If x = 4

               \(y = x^{2} + 4 + 2x = (4)^{2} + 4 + 2(4) = 16 + 4 + 8 = 28\)

If x = -4

               \(y = x^{2} + 4 + 2x = (-4)^{2} + 4 + 2(-4) = 16 + 4 -8 = 12\)

Answer:

1. Reflection across y-axis and translated down 1 unit

2. 270 degree counterclockwise rotation and translated right three units.

Step-by-step explanation:

For number 1, when you reflect across the y-axis, the polygon is one unit above the intended location, so you would move it down one.

For number two, when you rotate it 270 degrees counterclockwise, it is to the left three units, so you would move it to the right three units.

The number of times the sum would occur as 9 when the cube is tossed 180 times is 20.

The number of positive outcomes to all possible outcomes of an event is the ratio, which is known as probability. The number of good outcomes can be represented by the symbol x for an experiment with 'n' number of outcomes. The following equation can be used to determine an event's probability.

Favorable Results/Total Results = x/n, where Probability(Event)

Let us suppose you toss two cubes 180 times.

The sum of nine occurs when the combinations are:

(6, 3), (5, 4), (4, 5) and (3, 6).

The probability of getting a sum of 9 is:

P (9) = 4 / 36 = 1/9

The number of times we would the sum would occur as 9 when the cube is tossed 180 times.

180 (1/9) = 20

Hence, the number of times the sum would occur as 9 when the cube is tossed 180 times is 20.

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Answer:

U SHOULD PUT YA DOG OUTSIDE SAVE YA CAT

Answer:

you just said your dog was eating ketchup so imma assume he's fine now

Step-by-step explanation:

The series can be rewritten using summation notation as: ∑(10n + 3) from n = 1 to 13

In the given series, each term is obtained by adding 10 to the previous term. So, we can write the nth term as 10n + 3, where n represents the position of the term in the series.

Using the summation notation, we can write the sum of the series as the sum of the nth terms from n = 1 to 13.
Therefore, the summation notation is:

∑(10n + 3) from n = 1 to 13

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