determine whether the series converges, and if so find its sum. ∑k=1[infinity]1(k 1)(k 2)= (enter dne if the sum does not exist.)

To answer this question, we need to apply the rules of "PEMDAS".

Thus:

- we first deal with the numbers in the "Parentheses" or brackets

- then we perform the "Multiplication" operation

- and then we perform the "Subtraction" operation

This is done as follows:

- by dealing with the numbers in the parentheses, we get:

- now, by dealing with the multiplication, we have:

- finally, we deal with the subtraction, as follows:

The 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

What is Confidence interval?

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

As given,

n = 150 = drivers

x = 100 = wear seat belts.

We have to find 95% confidence interval for proportion P that do not wear seat belt.

From 150 we have 100 wear seat belts

Not wear seat belt = 150 - 100

Not wear seat belt = 50

P = 50/150

P = 0.33

95% confidence interval for P is

CI = (P - zα/2√(P(1 - P)/n), P + zα/2√(P(1 - P)/n))

For 95% CI, zα/2 = 1.96

Substitute values,

CI = (0.33 - 1.96√(0.33(1 - 0.33)/150), 0.33 + 1.96√(0.33(1 - 0.33)/150))

CI = (0.33 - 0.075, 0.33 + 0.075)

CI = (0.255, 0.405)

Therefore 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

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The value of a + b for the function y = (9/2)x^3 is 7.5. The coefficient a is 9/2 and the exponent b is 3.

The given function y = (9/2)x^3 can be written in the form y = ax^b, where a and b are real numbers. To determine the values of a and b, we compare the given function with the general form.

In the given function, the coefficient of x^3 is (9/2), which represents the value of a. Therefore, a = 9/2.

The exponent of x is 3, which represents the value of b. Therefore, b = 3.

To find the value of a + b, we simply add the values obtained: 9/2 + 3 = 15/2 = 7.5.

Therefore, the value of a + b for the given function is 7.5.

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Answer:

x=1/3

y=-7

Step-by-step explanation:

using the elimination method, you can add both equations vertically, to eliminate the x

-3x+y=-8

3x+2y=-13

3y=-21

y=-7

we then fix the value of y into the first equation

-3x+y=-8

-3x-7=-8

-3x=-8+7

-3x=-1

x=1/3

Answer:

$372

Step-by-step explanation:

108.50 / 7 = 15.50

he earns $15.50 each hour

24 x 15.50 = 372

he would earn $372 in 24 hours

Answer:

$372

Explaination :

7 hour $108.50

1 hour - (180.50 ÷ 7) = $15.5

24 hours - (15.5x24) = $372

a. The bank can initially lend out $15.00.

b. The money in the economy changes by $20.00.

c. The money multiplier is 4.

d. Eventually, $80.00 will be created by the banking system from Jon's $20.00.

Let us analyze each section separately:

a. To calculate the amount of money the bank can initially lend out, we need to determine the bank's reserves.

Given that the bank keeps 25% of its money in reserves, we can find the reserves by multiplying the deposit amount by 0.25.

In this case, the deposit amount is $20.00, so the reserves would be $20.00 * 0.25 = $5.00. The remaining amount, $20.00 - $5.00 = $15.00, is the money that the bank can initially lend out.

b. When Jon deposits the $20.00 bill into the bank, the money in the economy remains unchanged because the physical currency is converted into a bank deposit. Therefore, there is no change in the total money supply in the economy.

c. The money multiplier determines the overall increase in the money supply as a result of fractional reserve banking. In this case, the reserve requirement is 25%, which means that the bank can lend out 75% of the deposited amount.

The formula to calculate the money multiplier is 1 / reserve requirement. Substituting the value, we get 1 / 0.25 = 4.

Therefore, the money multiplier is 4.

d. To calculate the amount of money created by the banking system, we multiply the initial deposit by the money multiplier. In this case, Jon's initial deposit is $20.00, and the money multiplier is 4.

So, $20.00 * 4 = $80.00 will be created by the banking system from Jon's $20.00 deposit.

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Of the given values, a. range = 3.8, b. variance (s²) = 1.79 and c. standard deviation = 1.34.

To calculate the range, we subtract the smallest number from the largest number in the set. In this case, the largest number is 9.9 and the smallest number is 6.4, so the range is 9.9 - 6.4 = 3.8.

To calculate the variance, we need to find the mean of the set of numbers first. The mean is the sum of all the numbers divided by the total count. In this case, the sum of the numbers is 84.4 and there are 11 numbers in total. So the mean is 84.4 / 11 = 7.67.

Next, we calculate the squared difference for each number by subtracting the mean from each number and squaring the result. We sum up these squared differences and divide by the total count.

The variance is the average of the squared differences. After performing these calculations, we find the variance to be 1.79.

The standard deviation is the square root of the variance. Taking the square root of 1.79 gives us a standard deviation of approximately 1.34.

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Answer:

Step-by-step explanation:

-4.32193257293

Answer:

Surface Area = 12 in^2

Step-by-step explanation:

Since all the triangles are the same, find the area of one triangle and multiply it by 4.

A = b * h

        2

A = 3 * 2  =    A = 3 in^2                    3 * 4 = 12 in^2

        2

The value of h used to solve the equation by completing the square is 2.25.

To solve the equation x^2 + 3x - 9 = 0 using the method of completing the square, we add a constant term (h) to both sides of the equation to create a perfect square trinomial on the left side. The value of h that is used in this step depends on the coefficient of the x term (3).

To determine the value of h, we take half of the coefficient of the x term, square it, and add it to both sides of the equation. In this case, the coefficient of the x term is 3, so:

Step 1: x^2 + 3x + h = 9 + h

To find the value of h, we take half of 3, which is 3/2 or 1.5. We square 1.5 to get 2.25. So, the value of h used to solve the equation by completing the square is 2.25.

Please note that this is the value used in the specific step mentioned, and further steps may be required to complete the solution of the equation.

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2/3 is equal to 2 divided by 1/3, which is equal to 2 multiplied by 3. Therefore, the equivalent expression is 2 divided by 1/3 fraction.

The expression 2/3 is equivalent to 2 divided by 1/3. This is because 2/3 can be written as 2 multiplied by 3, which is equal to 6. This can be represented in fraction form as 2 divided by 1/3. To calculate this expression, we need to divide 2 by 1/3, which is equal to 2 multiplied by 3. Therefore, the equivalent expression is 2 divided by 1/3, which is equal to 6. 2/3 is equal to 2 divided by 1/3, which is equal to 2 multiplied by 3. Therefore, the equivalent expression is 2 divided by 1/3.

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Answer:

x = 65 y =65 z = 65

Step-by-step explanation:

∠x = ∠y because they are subtended by the same arc

only options that have x and y = each other is 1 and 3

it's definitely not 1 because 50, 50 and 50 make 150 and triangles = 180

so it's 3

50 + 65 + 65 = 180

The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

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1. For Joshua's triangle; the distance of the green side of the triangle d₃ is 5.

2. For Murney's triangle, the perimeter of the triangle is 12.

3. For Grace, Abby and Chris's triangle, the perimeter of the triangle is 5 + √17 +  4√2.

4. For Chloe's triangle, the perimeter of the triangle is 11 + √65.

The distance of the triangles is calculated as follows;

For Joshua's triangle;

The length of d₁, d₂, and d₃ is calculated as follows;

d₁ = √ [(3 - 2)² + (2 - 0)²] = √5

d₂ = √ [(-1 - 3)² + (4 - 2)²] = 2√5

d₃ = √ [(-1 - 2)² + (4 - 0)²] = 5

The distance of the green side of the triangle d₃ = 5

For Murney's triangle, the perimeter of the triangle is calculated as;

BC = √ [(4 - 4)² + (6 - 2)²] = 4

AC = √ [(1 - 4)² + (2 - 2)²] = 3

AB = √ [(4 - 1)² + (6 - 2)²] = 5

Perimeter = 4 + 3 + 5 = 12

For Grace, Abby and Chris's triangle, the perimeter of the triangle is calculated as;

AC = √ [(-3 - 2)² + (2-2)²] = 5

BC = √ [(1 - 2)² + (2 + 2)²] = √17

AB = √ [(1 + 3)² + (2 + 2)²] = 4√2

Perimeter = 5 + √17 +  4√2

For Chloe's triangle, the perimeter of the triangle is calculated as;

AC =  √ [(-3 - 4)² + (2-2)²] = 7

BC =  √ [(4 - 4)² + (6-2)²] = 4

AB =  √ [(4 + 3)² + (6-2)²] = √65

Perimeter = 7 + 4 + √65 = 11 + √65

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Answer: 4,5

Step-by-step explanation

Writing linear equations given two points can be a useful skill when graphing linear equations.

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The measure of one of the sides of the new square, to the nearest whole number, is 15 meters.

The total area of the 26 pieces of cardboard is:

26 x (3²) = 234 square meters

If we rearrange the pieces to form a square, then the area of the square will be 234 square meters.

Let's find the length of one side of the square:

Area of the square = (length of one side)²

234 = (length of one side)²

Taking the square root of both sides, we get:

length of one side = √(234)

Using a calculator, we get:

length of one side ≈ 15.297

Rounding to the nearest whole number, we get:

length of one side ≈ 15

Therefore, the measure of one of the sides of the new square, to the nearest whole number, is 15 meters.

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Answer:

a. v

Step-by-step explanation:

Given

\(3v - 8\)

Required

Identify the variable

Literary, variable means things that change in values;

Going by this definition, we have that:

3 -> This is not a variable because its value will always be 3

v -> This is a variable because its value can change once its value changes, the result of the expression will also change

- -> This is not a variable; it is an arithmetic operator to subtract

8 -> This is not a variable because its value will always be 8

Take for instance

\(v = 2\)

\(3v - 8 = 3 * 2 - 8 = 6 - 8 = -2\)

When \(v =5\)

\(3v - 8 = 3 * 5 - 8 = 15 - 8 = 7\)

Notice that there's a difference in both results;

This is as a result of v being a variable

Based on the given simple statements, "The scroll is open" and "The writings are visible," we can determine which compound statements would also be true.

The scroll is not open or the writings are visible.

This compound statement would be true. Since the first simple statement states that the scroll is open, the negation of this statement would be that the scroll is not open. The second simple statement states that the writings are visible, which aligns with this compound statement. Therefore, this compound statement is true.

The scroll is open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, the second part of this compound statement contradicts the given information.

The scroll is open or the writings are visible.

This compound statement would be true. It directly matches the given simple statements, where both the scroll being open and the writings being visible are mentioned. Therefore, this compound statement is true.

The scroll is not open or the writings are not visible.

This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, neither part of this compound statement aligns with the given information.

The compound statements that would be true are:

The scroll is not open or the writings are visible.

The scroll is open or the writings are visible.

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Answer:

A. 15: 1, 3, 5, 15

20x: 1, 2, 4, 5, 10, 20, x

Step-by-step explanation:

The general solution of the differential equation is: y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t), where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.

The given differential equation is a second-order homogeneous linear differential equation with constant coefficients. Its characteristic equation is obtained by assuming a solution of the form y = e^(rt), where r is a constant. Substituting this into the differential equation, we get:

r^2 e^(rt) - 6r e^(rt) + 10 e^(rt) = 0

Dividing both sides by e^(rt) (which is non-zero), we get:

r^2 - 6r + 10 = 0

Solving for r using the quadratic formula, we get:

r = (6 ± sqrt(6^2 - 4(1)(10))) / 2

r = 3 ± i

Therefore, the general solution of the differential equation is:

y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t)

where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.

This solution consists of a linear combination of two functions: the exponential function e^(3t) and the periodic function cos(t) or sin(t), which oscillates between -1 and 1. The exponential function represents the growth or decay of the system, while the periodic function represents the oscillations or vibrations of the system. The constants c1 and c2 determine the amplitude and phase of the oscillations, respectively. The behavior of the system depends on the signs and magnitudes of the real and imaginary parts of the roots, which determine whether the solutions are overdamped, critically damped, or underdamped.

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Answer:14/15 + 42/11

Step-by-step explanation:

After 40 minutes both the clocks will chime together

In the above question, it is given that

There are two clocks which chimes at different times  

One clock is chiming in every = 5 minutes

Another clock is chiming in every = 8 minutes

We need to find how many minutes will it be before both clocks chime together

To find the time when both the clock bells chime together, we need to find the lowest common multiple of 5 and 8

5 = 1 x 5

8 = 2 x 2 x 2

LCM of (5 , 8) = 1 x 5 x 2 x 2 x 2  = 40

Therefore, after 40 minutes both the clocks will chime together

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Answer:

73.5 feet

Step-by-step explanation:

The length of a tree =42 feet

Mr. Ash estimates that this tree is 75% as tall now as it will be when fully grown.

We need to find the length of the tree when it is fully grown. It means we need to find the 75% of 42 and adding 42 to it as follows :

\(T=75\%\times 42+42\\\\=\dfrac{75}{100}\times 42+42\\\\=73.5\ ft\)

So, the tree will be 73.5 feet tall when it is fully grown.

The equation for split times is 4x= 198.608  and the value of x is 49.652

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Let x be the split time

all 4 of the split times were the same.

4x= 198.608

=> x= 198.608/4 = 49.652

The equation for split times is 4x= 198.608  and the value of x is 49.652

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The box is totally submersed in paint, how many square cm of painted surface will there be = 2216 cm^2

Having four right angles makes a rectangle a quadrilateral. It can alternatively be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is a rectangle with four equally long sides.

The external dimensions of the

base are 16 cm by 24 cm,

the external height is 10 cm

So , finding the area of A1 , A2 , A3

A1 = 2* 16* 10 + 2* 24 * 10 + 1 * 16 * 24

   = 1184

A2 = 2 * 14 * 9 + 2 * 22 * 9 + 1 * 14 * 22

    =  956

A3 = 16 *24 - 14 * 22

     = 76

Total area will be :

A = 1184 + 956 + 76

   = 2216 cm^2

The box is totally submersed in paint, how many square cm of painted surface will there be = 2216 cm^2

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Answer:

210

Step-by-step explanation:

Answer:

Hope the picture will help you

Answer:

  4) Stored chemical energy is converted to mechanical energy.

Step-by-step explanation:

The battery represents energy stored in the form of chemical compounds. The motion represents mechanical energy. The transfer occurs between these forms of energy.

  4) Stored chemical energy is converted to mechanical energy.