A superball is dropped from a height of h feet and left to bounce forever. The rebound ratio of the ball is r. In terms of r and h. find the formula for the total time needed for all this bouncing to take place.

The way the bond will be accounted over the relevant years is given below:

To account for the bond, we need to calculate the interest income, amortization of premium or discount, and the gain or loss on redemption for the years 2016, 2017, and 2018.

Year 2016:

Purchase price of bond: K95,000

Issue cost: K2,000

Initial cost of the bond: K97,000

Interest income for the year: K5,000

Fair value of the bond at the end of the year: K110,000

Premium of the bond: K13,000

Effective interest rate: 8%

Amortization of the premium: K3,800

Carrying value of the bond at the end of the year: K100,800

Year 2017:

Interest income for the year: K5,040

Fair value of the bond at the end of the year: K104,000

Discount of the bond: K3,800

Amortization of the discount: K2,704

Carrying value of the bond at the end of the year: K98,096

Year 2018:

Interest income for the year: K4,904

Redemption premium over nominal value: K5,960

Redemption proceeds: K105,960

Carrying value of the bond at the end of the year: -

Gain on redemption: K7,864

Final accounting entries for the bond:

Year 2016:

Interest receivable: K5,000

Interest income: K5,000

Amortization of premium: K3,800

Interest expense: K8,800

Carrying value: K100,800

Year 2017:

Interest receivable: K5,040

Interest income: K5,040

Amortization of discount: K2,704

Interest expense: K7,744

Carrying value: K98,096

Year 2018:

Interest receivable: K4,904

Interest income: K4,904

Gain on redemption: K7,864

Carrying value: -

Cash: K105,960

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Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.

A percentage that corresponds to one tenth of an amount. One percent, represented by the symbol 1%, is equivalent to one hundredth of something; hence, 100 percent represents the complete object, and 200 percent represents twice the amount given.

According to the table:

The total number of Yellow Trains is 450.

The total number of all modes of transportation is 4730.

To calculate the percentage of the total that Yellow Trains make up, we can use the following formula:

percentage = (part/whole) x 100

Substituting the values we have:

percentage = (450/4730) x 100

percentage = 0.095 x 100

percentage = 9.5%

Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.

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You are installing a pipe that is 6 2/3 feet long. How long is it in inches

Remember that

1 ft=12 in

so

6 2/3 ft=(6 2/3)*12

Convert mixed number to an improper fraction first

substitute

therefore

the answer is 80 inches

Part 2

You have a pallet of building materials that weighs a total 9,500 lbs. The materials are organized in three bundles. The first one weights 2,243 lbs., and the second weighs 3,431 lbs. What is the weight of the third bundle?

Let

x ------> the weight of the third bundle

we know that

9,500=2,243+3,431+x

solve for x

9,500=5,674+x

x=9,500-5,674

x=3,826 lbs

therefore

the answer is

The weight of the third bundle is 3,826 lb

Part 3

You are painting a wall that is 11 feet high and 25 feet long. What is the total surface area to be painted

To find out the surface area multiply the high by the length of the wall

so

(11)*(25)=275 ft2

the answer is 275 square feet

Answer:

x=-0.2

Step-by-step explanation:

Given

f(x) = 2x³ - 6x² - 18x + 2

its derivative is

f'(x) = 6x² - 12x - 18

Then f has critical points when

6x² - 12x - 18 = 6 (x² - 2x - 3) = 6 (x - 3) (x + 1) = 0

or when x = -1 and x = 3. Because f is a polynomial, it and its derivatives are defined everywhere.

Classify the critical points by checking the sign of the second derivative at each one:

f''(x) = 12x - 12

• At x = -1, we have f''(-1) = -24 < 0, which indicates a local maximum at the point (-1, f(-1)) = (-1, 12).

• At x = 3, we have f''(3) = 24 > 0, which indicates a local minimum at (3, f(3)) = (3, -52).

We also check the value of f at the endpoints of the given domain.

• At x = -2, the graph of f passes through the point (-2, f(-2)) = (-2, -2).

• At x = 4, f goes through the point (4, f(4)) = (4, -38).

So, over the interval [-2, 4], we have

• an absolute maximum of 12 when x = -1, and

• an absolute minimum of -52 when x = 3

markov transition matrix: describe the qualitative behavior of this process over time; that is, mention no numerical probabilities is  π = [1/3, 1/3, 1/3]

From the given information;

the transition probability matrix (TPM) for state 0, 1, 2 is:

The three-step TPM  is done by a simple matrix multiplication which is computed as follows:

The steady-state distribution of the Markov Chain is  determined by first solving the system πp = π together with the normalizing condition

here;

π₁ + π₂ + π₃ = 1

So;

0.5π₂ + 0.5π₃ = π₁

⇒ π₂ + π₃ = 2π₁

0.5π₁ + 0.5π₃ = π₂

⇒ π₁ + π₃ = 2π₂

0.5π₁ + 0.5π₂ = π₃

⇒ π₁ + π₂ = 2π₃

Thus, π₁ + π₂ + π₃ = 1

This can be re-written as:

1 - π₁ = 2π₁

1 - π₂ = 2π₂

1 - π₃ = 2π₃

∴1 = 3π₁

π₁ = 1/3

1 = 3π₂

π₂ = 1/3

1 = 3π₃

π₃ = 1/3

Hence, the steady-state probability distribution is π = [1/3, 1/3, 1/3]

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The total number of boxes is the sum of all boxes each day

The total number of boxes he filled in the five days is \(23 \frac 18\)

The box each day is given as:

So, the total number of boxes is:

\(Total = 4\frac 78 + 5\frac 34 + 4\frac 72 + 4\frac 38 + \frac 58\)

Add the fractions

\(Total = 23 \frac 18\)

Hence, the total number of boxes he filled in the five days is \(23 \frac 18\)

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Answer: 25 Feet.

Step-by-step explanation: 1,250 % 50.

Answer:

4

Step-by-step explanation:

10-2(1)=8 which is >=4

10-2(2)=6 which is >=4

10-2(3)=4 which is >=4

10-2(4)=2 which isn't >=4

Therefore 4 doesn't satisfy the inequality

Answer:

4

Step-by-step explanation:

Let's test each possibility.

10-2(1)≥4

10-2=8 so it works

10-2(2)≥4

10-4=6 so it works

10-2(3)≥4

10-6=4 so it works

10-2(4)≥4

10-8=2

2<4 so it dosen't fit the solution

Answer:

yes I just checked it

Step-by-step explanation:

The prove can be shown on the picture attached. And here the describe that support the picture:

Then we can know the 2 triangles are identical or congruent.

The median drawn from the vertex bisects the angle whose two adjacent sides are equal in isosceles and equilateral triangles. In the case of equilateral and isosceles triangles, the median not only bisects the side opposite the vertex, but it also bisects the angle of the vertex.

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The approach for solving for incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle.

It can also be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Formula for solving incenter:

Let (x1,y1) , (x2,y2) and (x3,y3) are three points of triangle.

and a,b,c are lengths of sides.

I = ((ax1+bx2+x3 / a+b+c  ,  ay1+by2+cy3 / a+b+c))

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Answer:

Step-by-step explanation:

According to table:

The equation is:

A) Let the length of one piece be x. if one piece is 45 m longer than the other one, it means that the length of the other one would be (x + 45) m

Given that the total length of both pieces is 120m, then the equation would be

x + x + 45 = 120

2x + 45 = 120

2x = 120 - 45 = 75

x = 75/2

x = 37.5

Thus, the length of each piece are

37.5 m

37.5 + 45 = 82.5 m

B) The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(length + width)

Given that

length = 82.5

width = 37.5

then

perimeter = 2(82.5 + 37.5) = 2 * 120

perimeter of rectangle= 240 m

C) the formula for determining area of a rectangle is expressed as

Area = length * width

Area of rectangle = 82.5 * 37.5 = 3093.75 cm^2

Answer:

\(\frac{9344}{45}\)

Step-by-step explanation:

\(\frac{74752}{360}\)

Simplify by 8, and we get

\(\frac{9344}{45}\)

We can't simplify any more, so the answer is  \(\frac{9344}{45}\)

The required answer is the simplified fraction of the given problem 74752/360 is the whole fraction 9344/45, where 9344 represents the whole number part and 45 represents the fractional part.

To simplify the fraction 74752/360 as a whole fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both of them by it.

Step 1: Find the GCD of 74752 and 360. The GCD can be calculated using various methods, such as prime factorization or the Euclidean algorithm. In this case,  use the Euclidean algorithm.

Let's find the GCD using the Euclidean algorithm:

Divide 74752 by 360:

74752 ÷ 360 = 207 R 272

Divide 360 by 272:

360 ÷ 272 = 1 R 88

Divide 272 by 88:

272 ÷ 88 = 3 R 8

Divide 88 by 8:

88 ÷ 8 = 11 R 0

Since the remainder is 0, the GCD is the last non-zero remainder, which is 8.

Step 2: Divide both the numerator and denominator of the fraction by the GCD.

74752 ÷ 8 = 9344

360 ÷ 8 = 45

The simplified whole fraction is 9344/45.

A whole fraction refers to a fraction in which the numerator is equal to or greater than the denominator. It represents a whole number and a fraction together. For example, 3 1/4 is a whole fraction where the whole number part is 3 and the fractional part is 1/4.

Hence, the simplified fraction of the given problem 74752/360 is the whole fraction 9344/45, where 9344 represents the whole number part and 45 represents the fractional part.

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Answer:

p^2-4p-21=0

Step-by-step explanation:

Where you see (x^2 + 6) you put in p.

p 2  - 21 = 4 ( x 2 + 6 )

p 2 - 21 = 4p

p 2 - 4p - 21 = 0

:)

There are 331 ways when 66 identical coins can be separated into three nonempty piles

Let the piles have a, b and c coins, with 0<a <b <c. Then, let b=a+k₁, and

c=b+k₂, such that each ki≥1.

The sum is then a+a+k₁+a+k₁+k₂= 66 ⇒ 3a+2k₁+k₂ = 66.

This is simply the number of positive solutions to the equation

3x+2y+z = 66.

If a = 1, then 2k₁ + k₂ = 63⇒ 1≤k₁ ≤31. Each value of k₁ corresponds to a unique value of k₂, so there are 31 solutions in this case.

Similarly, if a = 2, then 2k₁+k₂= 60⇒ 1≤k₁ ≤29, for a total of 29 solutions in this case.

If a = 3, then 2k₁+ k₁= 57 ⇒ 1 ≤ k₁ ≤28, for a total of 28 solutions.

In general, the number of solutions is just all the numbers that aren't a multiple of 3, that are less than or equal to 31.

We then add our cases to get

=1+2+4+....31=1+2+3+...31-3(1+2+3+...10)

=31*(32)/2-3(55)

=31*16-165

=496-165

=331

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Answer:

\((x,y) =(-4,-3)\) --- Vertex

\(x = -4\) --- Axis of symmetry

Step-by-step explanation:

Given

\(y = -6(x + 4)^2 - 3\)

Solving (a): The vertex

For an equation written in

\(y = a(x - h)^2 + k\)

The vertex is:

\((x,y) = (h,k)\)

By comparison:

\(y = a(x - h)^2 + k\)  and \(y = -6(x + 4)^2 - 3\)

\(-h =4\)       \(k = -3\)

\(h =-4\)         \(k = -3\)  

So, the vertex is:

\((x,y) =(-4,-3)\)

Solving (b): The axis of symmetry

For an equation written in

\(y = a(x - h)^2 + k\)

The axis of symmetry is:

x = h

In (a):

\(h =-4\)

So:

\(x = -4\)

In fraction form, the answer is 1/4, which represents the simplified probability of the given event occurring.

To find the probability of picking a prime number and then picking another prime number, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

Given the four numbers: 5, 6, 7, and 8, we can see that there are two prime numbers (5 and 7) and two non-prime numbers (6 and 8).

The total number of possible outcomes is 4 since there are four cards to choose from.

Now, let's consider the favorable outcomes, which are picking a prime number and then picking another prime number.

The probability of picking a prime number on the first draw is 2/4, as there are two prime numbers out of the four total cards.

Since we replace the card before the second draw, the probability of picking a prime number on the second draw is also 2/4.

To find the probability of both events occurring, we multiply the individual probabilities:

(2/4) * (2/4) = 4/16 = 1/4

Therefore, the probability of picking a prime number and then picking another prime number is 1/4.

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Answer:

A.  y = |x + 4| - 2.

Step-by-step explanation:

The graph of y = |x| is V shaped and passes through the origin and the slope  is 1 (like the given graph).

y = |x + 4) moves the V shaped graph 4 units to the left so the tip of the V is at x = -4.

Now subtracting 2 from this graph will bring the graph to the point where x = -4 and y = -2.

So the given function is y = |x + 4| - 2.

Answer:

60cm^2

Step-by-step explanation:

5X12=60

If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer: r=4b/m-k

Step-by-step explanation: I think

The solution of the given formula B=1/4m(r + k) for r is r = 4(B/m) - k.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

Given the expression,

B=1/4m(r+k)

4B = m(r + k)

r + k = 4B/m

r = 4(B/m) - k

Hence "The solution of the given formula B=1/4m(r + k) for r is r = 4(B/m) - k".

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The concept of type I and type II error was used to set hypothesis and to pick the correct option

What is Hypothesis?

In a scientific setting, a hypothesis (plural: hypotheses) is a tested claim regarding the relationship between two or more variables or a suggested explanation for a phenomenon that has been observed.

Given that,

Significance level: α = 0.05

Power of the test = 0.80

Making statistical claims about the characteristics of the population is made possible by hypothesis testing.

The type I error is also known as significance level.

Since, the given α = 0.05

Therefore, the type I error is 0.05

As a result, choice (a) is accurate.

Type I error is the probability of rejection \(H_{0}\) when \(H_{0}\) is true.

The type II error is denoted by β .

Now,

Power = 0.80

1 - β = 0.80

β = 1 - 0.80

β = 0.20

Therefore, the type II error is 0.20

Hence, option (b) is correct.

Type II error is fail to reject \(H_{0}\) when \(H_{0}\)  is false.

The concept of type I and type II error was used to set hypothesis and to pick the correct option

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Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

For this problem, we are asked to find the slope of the given line.

The slope is the change within a line. Think of slope as a measurement of steepness, the greater the rise (y), the more steeper the line is. However, the greater the run (x), the line will become less steeper.

Let's begin by reviewing the slope formula. The slope formula is made up as a fraction subtracting 2 points from a given line. The difference between these 2 points will result in the slope, only shown as a fraction. See below.

Formula:

\(\frac{y_{2} - y_{1} }{x_{2} - x_{1} } = m \ (slope)\)

Points:

Let's substitute the points into our slope formula.

\(\frac{2 + 4}{2 + 2} =m\)

Simplify:

\(\frac{6}{4} =m\)

\(\frac{3}{2} =m\)

The slope of the given line is \(\frac{3}{2}\).

If z = 1, μ = 12, and σ = 3, then the value of the x is 15.

What is the z-score?

Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. The Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

A z-score is a standard score that indicates how many standard deviations a data point is from the mean.

The z-score chart helps to understand the probabilities associated with different z-scores.

We have,

Random Value (X) =?

Mean (μ) = 12

Standard Deviation (σ) = 3

Formula :

z-score = (x - μ) / σ

Solution :

1 = (x - 12) /3

3 = x - 12

x = 3 + 12

= 15

x = 15

Therefore, the value of the x is 15.

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The scale factor used is 1/4

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that, a can of concentrated grapefruit juice includes the instructions, "Mix one can of concentrate with 4 cans of cold water."

So, it can be concluded that,

The ratio of number of concentrate can to the number of water can = 1/4

Therefore, the scale factor = 1/4

So,

If there are 24 concentrate cans, there will be 24×4 = 96 water cans

If there are 24 water cans, there will be 24/4 = 6 concentrate cans

Hence, the scale factor used is 1/4

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Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

Answer:

(6,1)

Step-by-step explanation:

midpoint = ((x2+x1),(y2+y1)/2)

= (6+6)/2, (-5+7)/2

= 12/2, 2/2

= 6,1

Answer:

Step-by-step explanation:

x- coordinates same so the line is vertical and we'll only calculate the y-coordinate

So the point is