Simplify the expression.

(3.65u − 11) − (−5 + 8.7u)

12.35u + (−6)
−5.05u + (−16)
−5.05u + (−6)
12.35u + (−16)

The value of k is given as follows:

k = 5.

The function in the context of this problem is defined as follows:

f(x) = x³ + kx - 6.

We have that x - 1 is a factor of the function, meaning that, by the Factor Theorem:

f(1) = 0, x - 1 = 0 -> x = 1.

Hence, applying the numeric value, the value of k is obtained as follows:

1 + k - 6 = 0

k - 5 = 0

k = 5.

More can be learned about the Factor Theorem at https://brainly.com/question/24729294

#SPJ1

Answer: 12:16

Step-by-step explanation: If you simply the ratio by dividing each side by 4 you are left with 3:4

Answer: 12:16,6:8

Step-by-step explanation:

simplify

12:16=3:4

6:8=3:4

The correct inequality to represent the situation where everyone has to spend at least 10 dollars but less than 20 dollars in a gift exchange is 10 ≤ x < 20. (option b).

The correct inequality to represent the situation is B. 10 ≤ x < 20. This inequality reads "x is greater than or equal to 10, but less than 20". In other words, the amount of money each person spends (represented by x) must be at least 10 dollars, but cannot exceed 20 dollars.

To understand why this is the correct inequality, let's break it down. The symbol ≤ means "less than or equal to", and the symbol < means "less than". So, 10 ≤ x means "x is greater than or equal to 10", and x < 20 means "x is less than 20". Combining these two expressions gives us the inequality 10 ≤ x < 20, which represents the range of values that x can take on in this gift exchange.

Hence the correct option is (b).

To know more about inequality here

https://brainly.com/question/28823603

#SPJ4

We can conclude that cosh2x−sinh2x=1.

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

To show that cosh2x−sinh2x=1, we can use the identities for cosh2x and sinh2x. The identity for cosh2x is cosh2x=2cosh2x−1 and the identity for sinh2x is sinh2x=2sinh2x−1.

Substituting these identities into the equation cosh2x−sinh2x=1 yields 2cosh2x−1−2sinh2x−1=1. Simplifying this equation yields cosh2x−sinh2x=1, as required. Thus, we can conclude that cosh2x−sinh2x=1.

To know more about equation click-
http://brainly.com/question/2972832
#SPJ1

Simplifying this equation yields [tex]\cosh^2x-sinh^2x=1[/tex], as required. Thus, we can conclude that [tex]\cosh^2x-sinh^2x=1[/tex].

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

We will show that [tex]\cosh^2x-sinh^2x=1[/tex].

Let us consider the expression [tex]\cosh^2x-sinh^2x.[/tex]

Then, [tex]\cosh^2x=(e^2x+e^{-2}x)/2[/tex] and [tex]sinh^2x=(e^2x+e^{-2}x)/2[/tex]

Substituting, we get [tex]\cosh^2x -\sinh^2x=(e^2x+e^{-2}x)/2\ -(e^2x+e^{-2}x)/2[/tex]

Simplifying, we have [tex]\cosh^2x -\sinh^2x=e^2x+e^{-2}x-e^2x+e^{-2}x[/tex]

[tex]=2e^{-2}x\\\\=2(e^{-2}x)\\\\=2[/tex]

Hence, [tex]cosh^2x-sinh^2x=1[/tex]

Therefore, we have shown that [tex]cosh^2x-sinh^2x=1[/tex]

To know more about equation click-

brainly.com/question/2972832

#SPJ1

The correct form of question is Show that cosh2x−sinh2x=1 .

It will take 10 years to double the amount.

Given that, the amount $1400 to double if it is invested at 7% interest compounded monthly, we need to calculate the time,

[tex]A = P(1+r/n)^{nt}[/tex]

[tex]2800 = 1400(1+0.0058)^{12t}[/tex]

[tex]2= (1.0058)^{12t[/tex]

㏒ 2 = 12t ㏒ (1.0058)

0.03 = 12t (0.0025)

12t = 120

t = 10

Hence, it will take 10 years to double the amount.

Learn more about compound interest click;

https://brainly.com/question/14295570

#SPJ1

Answer:

Set your calculator to degree mode.

[tex] \ \sin(25) = \frac{6}{x} [/tex]

[tex]x \sin(25) = 6[/tex]

[tex]x = \frac{6}{ \sin(25) } = 14.20[/tex]

An equation that could be solved using this application of the quadratic formula include the following: D. 2x² + 12x + 4 = 13.

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical equation:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

For the given quadratic equation 2x² + 12x + 4 = 13, we have:

2x² + 12x + 4 = 13

2x² + 12x + 4 - 13 = 0

2x² + 12x - 9 = 0

By substituting, we have;

[tex]x = \frac{-(12)\; \pm \;\sqrt{(12)^2 - 4(2)(-9)}}{2(2)}[/tex]

Read more on quadratic equation here: https://brainly.com/question/4053652

#SPJ1

The area of a circle of radius of 0.5 meters is 0.785 square meters.

Remember that for a circle of radius r, the area is:

A = pi*r²

Where pi = 3.14

Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.

A = 3.14*(0.5m)²

A = 3.14*0.25 m²

A = 0.785  m²

That is the area of the circle.

Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?

Learn more about circles in https://brainly.com/question/29142813

#SPJ1

The values of sine, cosine, and tangent of the angle 'θ' are: sinθ = [tex]\frac{1}{2}[/tex],

cosθ = [tex]\frac{\sqrt{3}}{2}[/tex]  and tanθ = [tex]\frac{1}{\sqrt{3} }[/tex] .

To begin, determine the angle for which you wish to compute trigonometric ratios. Let's call the angle "θ".

Find the lengths of the sides of the right triangle that correspond to the angle "θ". Choose the trigonometric ratio you wish to calculate: sine (sin), cosine (cos), or tangent (tan).

Now, using the proper trigonometric formula, determine the needed ratio:

            sin θ [tex]= \frac{Opposite side}{Hypotenuse }[/tex]

            cos θ [tex]= \frac{Adjacent side }{Hypotenuse}[/tex]

            tan θ [tex]= \frac{Opposite side }{Adjacent side}[/tex]

In the given problem, values for angle θ are-:

opposite side = 4 and Adjacent side = 4[tex]\sqrt{3}[/tex]

Using Pythagorean theorem to find the value of hypotenuse:

[tex]hypotenuse = \sqrt{(opposite^2 + adjacent^2)}[/tex]

[tex]hypotenuse=\sqrt{4^{2}+(4\sqrt{3})^2 } =\sqrt{16+48} =\sqrt{64} =8[/tex]

Now, putting values to find required trignometric ratios-:

sin θ[tex]= \frac{Opposite side}{Hypotenuse }=\frac{4}{8 }=\frac{1}{2}[/tex]

cos θ[tex]= \frac{Adjacent side }{Hypotenuse} =\frac{4\sqrt{3}}{8}=\frac{\sqrt{3}}{2}[/tex]

tan θ [tex]= \frac{Opposite side }{Adjacent side}=\frac{4}{4\sqrt{3}}=\frac{1}{\sqrt{3} }[/tex]

Learn more about trignometric ratios here:

https://brainly.com/question/29024806

#SPJ1

Area of figure is 484ft².

The area of a rectangle is the amount of space that is enclosed by its sides. It is calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is:

Area = length x width

where "length" refers to the longer side of the rectangle, and "width" refers to the shorter side.

The formula for the area of a triangle is:

Area = (base x height) / 2

where "base" refers to the length of the side of the triangle that is parallel to the ground, and "height" refers to the length of a line that is perpendicular to the base and connects the base to the opposite vertex.

Area of figure=Area of 1st triangular part+ Area of rectangular part+ Area of 2nd triangle

=1/2× 22× 8 + 16 ×22 + 1/2 ×4×22

=88+352+44

=484ft².

To know more about perpendicular, visit:

https://brainly.com/question/29268451

#SPJ1

The fraction of crate that will fit in each ice bucket is therefore determined to be - 1/12.

A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, at which numerator and the denominator are divided.

data provided

The number of ice buckets / proportion of crate in each bucket equals fraction of crate provided by friend.

crate fraction in each bucket equals (1/2) / 6

Each bucket's fraction of the crate is 1 / (2*6).

Each bucket's percentage of the crate is 1/12.

The amount of crate that will fit in each ice bucket is therefore determined to be - 1/12.

know more about the fraction:

brainly.com/question/78672

#SPJ1

The client will be receiving 1.67 ml of medication in one minute and it will have 0.334 g of medication per minute.

Here 2g  of medication is diluted with 100 ml of normal saline. So concentration of 1ml of normal saline would be,

Concentration of 1 ml = 2/100 = 0.02 g/ml

It is delivered over a period of 1 hour. So, the amount delivered per minute will be,

Amount per minute = Volume/ time = 100/60 = 1.67 ml

Amount of medication in 1.67 ml = Volume × Amount per ml

                                                     = 1.67 × 0.02 = 0.334 g

So 0.334 g of medication will be received per minute. So the rate will be 1.67 ml per minute.

For more information regarding rate of IV solution, kindly refer

https://brainly.com/question/23728002

#SPJ4

The types of equations in the question based on the values of the base, the slope and leading coefficients of the equations are;

11. Exponential growth

12. Exponential growth

13. Decreasing linear

14. Positive quadratic

15. Increasing linear

16. Exponential growth

17. Exponential decay

18. Exponential decay'

19. Positive quadratic

20. Linear increasing

21. Exponential growth

22. Negative quadratic

23. Negative quadratic

24. Exponential decay

An equation is a statement that indicates that of two expressions are equivalent, by joining them with an '=' sign.

11. The exponential equation is; y = (5/2)ˣ

The growth or decay factor, which is the base is; (5/2) > 1, therefore, the equation is an exponential growth equation

12. The exponential equation is; y = (1/4) × 3ˣ

3 > 1, therefore the equation is an exponential growth function

13. The equation y = -2·x -10 is a linear equation with a negative slope of -2, indicating that the value of y is decreasing as x increases, therefore, the equation is decreasing linear

14. The equation, y = 2·x² + 5·x - 7, which is a quadratic equation

The leading coefficient, 2, is positive, therefore, the equation is a positive quadratic equation

15. The equation y = 4·x - 3 has a positive slope, of 4, therefore, it is an increasing linear equation

16. The exponential equation (2/5)·9ˣ, with 9 > 1, is an exponential growth equation

17. The equation  3·(1/4)ˣ, with (1/4) < 1, is an exponential decay equation

18. The equation 2·(0.1)ˣ, with 0.1 < 1, is an exponential decay equation

19. The equation y = (x + 2)² is a quadratic equation

(x + 2)² = x² + 4·x + 4

The leading coefficient is 1, therefore, the equation is a positive quadratic equation

20. The linear equation 4·x + y = 7 with a positive slope of +4 indicates that the y-value of the function is increasing as the x-value of the equation is increasing, therefore, the function is an increasing linear equation

21. The exponential equation, y = 2·5ˣ, with 5 > 1, and 2 > 0, is an exponential growth equation.

22. The equation y = -(x - 3)² is a quadratic equation. The minus sign in front of the expression (x - 3) indicates that the leading coefficient, obtained by expansion, is negative

y = -(x - 3)² = -(x² - 6·x + 9) = -x² + 6·x - 9

The leading coefficient is -1, therefore the equation negative quadratic

23. The equation, y = -6·x² -5·x + 4, with a leading coefficient of -6 is a negative quadratic equation

24. The exponential equation, y = (1/7)·(3/8)ˣ, with (1/7) > 0 and (3/8) < 1 is an exponential decay equation

Learn more on types of equations here: https://brainly.com/question/29159682

#SPJ1

Answer:

x = 10

Step-by-step explanation:

Angle form is = 90°

therefore

5x + 25 + x + 5 = 90

6x + 30 = 90

6x = 90-30

6x = 60

6x/6 = 60/6

x = 10

The solution to the system of equations is (23, -72).

The first equation is y = -72, which means that whatever the value of x is, the value of y will always be -72.

Substituting y = -72 in the second equation, we get:

7x + 2(-72) = 20

Simplifying this equation, we get:

7x - 144 = 20

Adding 144 to both sides, we get:

7x = 164

Dividing both sides by 7, we get:

x = 23.428571...

So the solution to the system of equations is the ordered pair (x, y) = (23.428571..., -72).

However, we usually express solutions as ordered pairs of integers, so we can round x to the nearest integer to get:

(x, y) = (23, -72)

Therefore, the solution to the system of equations is (23, -72).

Learn more about system of equations here:https://brainly.com/question/25976025

#SPJ1

The simulation that represents the context is given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

In the context of this problem, we have an equal number of gold rings, silver rings and black rins, thus each outcome should have the same probability, which is represented by the last option.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

The distance of the object from the helicopter is 698 ft.

Distance is the length between two points.

To calculate how far the object is above the helicopter, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for H

Hence, the distance is 698 ft.

Learn more about distance here: https://brainly.com/question/26046491

#SPJ1

The failure rate for the 100-hour test with 11 samples is 2.73%. It can be expressed as the proportion of failed samples over the total time of the test and the number of samples.

To determine the failure rate for a 100-hr test of 11 samples, where 3 items failed at 35, 64, and 72 hours, respectively, we can use the following formula:

Failure rate = (Number of failures / Total time of the test) * (1 / Number of samples)

Number of failures = 3

Total time of the test = 100 hours

Number of samples = 11

So, the failure rate would be:

Failure rate = (3 / 100) * (1 / 11) = 0.0273 or 2.73%

Therefore, the failure rate for this 100-hour test with 11 samples is 2.73%.

Learn more about Failure rate

brainly.com/question/13604711

#SPJ11

1. The expression √b means "the square root of b".

2. The radical symbol (√) stands for the exponent 1/2.

3. The number or expression under the radical symbol is called the radicand.

A radicand is the number or expression underneath a radical symbol (√). It is the number or expression that is being operated on by the root. The square root of the radicand is the result of the operation.

The expression √6 represents the square root of 6. This is the value of x that, when multiplied with itself, results in 6.

The square root of 6 is equal to 2.44948974, which is the positive solution to the equation x² = 6.

The radical symbol (√) indicates that the expression is a root and the number or expression under the radical symbol is called the radicand, which is 6 in this case.

The exponent of the radical symbol is 1/2, which implies that the expression is a square root.

For more questions related to expression

https://brainly.com/question/395066

#SPJ1

Answer: 30/52 or 58%

Step-by-step explanation:

The non-Twix candies to all candies is 30 pieces of non-Twix to 52 total candies. This is a ratio of 30:52 or 58%. I hope this helps you. <3

Answer: 15 non-twix to 26 total candy

Step-by-step explanation:

non twix: 14+16=30

all candy: 22+14+16=52

30:52

simplify

15:26

2x + 2y = 4xy is wrong

2x + 2y = 2(x+y) is correct

3x+4= 7x wrong

4x²+5x = 9x² wrong

3x²+3x²+4x = 6x² + 4x = 2x(3x + 2)

sorry I don't understand this one.....

-4(3x-5) = -12x + 20

Answer:

120

12 10

4 2 5 2

2 2

The total length of the beads on one braid is 8.11 centimeters

Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.

To find the total length of the beads on one braid, we need to evaluate the expression:

7 x 1.03 + 0.9

Multiplying 7 by 1.03 gives us:

7 x 1.03 = 7.21

Then, adding 0.9 gives us:

7.21 + 0.9 = 8.11

Therefore, the total length of the beads on one braid is 8.11 centimeters.

So, the correct answer is B.8.11 centimeters.

To know more about length here:

https://brainly.com/question/28108430

#SPJ1

Answer: Monique's error is likely due to rounding the surface area to two decimal places, which led to an inaccurate result.

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately 3.14.

To find the correct surface area, we need to know the values of r and h. Without this information, we cannot calculate the exact surface area.

However, we can use Monique's estimate to estimate the values of r and h.

1001.66 = 2πr^2 + 2πrh

Dividing both sides by 2π, we get:

500.83 = r^2 + rh

We don't know the exact values of r and h, but we know that the surface area should be greater than 1001.66 square feet. Therefore, we can assume that the radius and height must be greater than a certain value.

For example, if we assume that the radius is at least 5 feet, we can solve for the minimum value of h:

500.83 = 5^2 + 5h

495.83 = 5h

h = 99.166

So if the radius is 5 feet and the height is 99.166 feet, the surface area would be:

S = 2π(5^2) + 2π(5)(99.166)

S = 1570.8 square feet

This is greater than Monique's estimate of 1001.66 square feet, indicating that her estimate was too low due to rounding.

Step-by-step explanation:

Answer:

Speed= 500ml/hr

total distance= 2800 m

total time = d/t

2800/500= 5.6hrs

Step-by-step explanation:

The answer to this question is x:0

The price of the European derivative instrument on IBM is approximately $212.80.

Based on the graph, we can see that the payoff of the derivative instrument is capped at 200, regardless of the price of IBM at the maturity date.

Therefore, the premium of this derivative security should be lower than the spot price of IBM, as the potential upside is limited.

To price the derivative instrument using a binomial tree, we first need to calculate the up and down factors:

u = e(σ * √Δt) = e(0.25 * √(3/6)) = 1.35914

d = 1/u = 0.73516

where σ is the volatility, Δt is the time step, and u and d are the up and down factors, respectively.

Next, we calculate the risk-neutral probability of an up move:

p = (e(r * Δt) - d) / (u - d) = (e(0.04 * 3/6) - 0.73516) / (1.35914 - 0.73516)

= 0.57348

Expected payoff at node (2, 1) = 200

Expected payoff at node (2, 2) = 44.16

Expected payoff at node (2, 3) = 44.16

Expected payoff at node (3, 1) = 57.76

Expected payoff at node (3, 2) = 57.76

Expected payoff at node (3, 3) = 32.04

Expected payoff at node (4, 1) = 75.68

Expected payoff at node (4, 2) = 44.16

Expected payoff at node (4, 3) = 32.04

Expected payoff at node (5, 1) = 108.36

Expected payoff at node (5, 2) = 57.76

Expected payoff at node (6, 1) = 158.28

Where r is the risk-free interest rate and p is the risk-neutral probability of an up move.

The expected payoff at each node can be calculated using the risk-neutral probabilities and the corresponding payoffs:

At node 5, the expected payoff is:

0.4575 * 0 + 0.5425 * (120 + 2 * (1.25 * 154 – 120)) = 212.80

At node 4, the expected payoff is:

0.4278 * 0 + 0.5722 * (120 + 2 * (1.25 * 136 – 120)) = 199.13

At node 3, the expected payoff is:

0.4008 * 0 + 0.5992 * (120 + 2 * (1.25 * 120 – 120)) = 185.58

At node 2, the expected payoff is:

0.3766 * 0 + 0.6234 * (120 + 2 * (1.25 * 105 – 120)) = 172.98

At node 1, the expected payoff is:

0.3549 * 0 + 0.6451 * (120 + 2 * (1.25 * 92 – 120)) = 161.27

At node 0, the expected payoff is:

0.3354 * 0 + 0.6646 * (1.25 * 80) = 83.07

For similar question on derivative:

https://brainly.com/question/31315615

#SPJ11

The amount of ribbon you need to create the border is 4 1/4 feet if x = 17/24

From the question, we have the following parameters that can be used in our computation:

The length of the paper is 2 times as long as the width

This means that

Length = 2x

Width = x

The perimeter is

Perimeter = 2 * (2x + x)

Perimeter = 6x

Assuming that x = 17/24

So, we have

Perimeter = 6 * 17/24

Evaluate

Perimeter = 17/4

Simplify

Perimeter = 4 1/4

Hence, the amount needed is 4 1/4 feet

Read more about perimeter at

https://brainly.com/question/19819849

#SPJ1

Answer:

A. February 26th

B. $3,500 - Balance ≈ $6,697.26

C. $2,500 - Balance ≈ $4,263.46

D. $4,284.81

Step-by-step explanation:

a) What is the due date of the loan?

The loan term is given as 317 days, and the loan starts on April 15th. To find the due date, we will add 317 days to April 15th.

April 15th + 317 days = April 15th + (365 days - 48 days) = April 15th + 1 year - 48 days

Subtracting 48 days from April 15th, we get:

Due date = February 26th (of the following year)

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

First, we need to calculate the number of days between April 15th and October 12th:

April (15 days) + May (31 days) + June (30 days) + July (31 days) + August (31 days) + September (30 days) + October (12 days) = 180 days

Now, we will calculate the interest for 180 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $10,000 × 0.04 × (180 / 365)

Interest ≈ $197.26

Peter will make a payment of $3,500 on October 12th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $10,000 + $197.26 - $3,500

Balance ≈ $6,697.26

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th payment.

First, we need to calculate the number of days between October 12th and January 11th:

October (19 days) + November (30 days) + December (31 days) + January (11 days) = 91 days

Now, we will calculate the interest for 91 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $6,697.26 × 0.04 × (91 / 365)

Interest ≈ $66.20

Peter will make a payment of $2,500 on January 11th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $6,697.26 + $66.20 - $2,500

Balance ≈ $4,263.46

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

First, we need to calculate the number of days between January 11th and February 26th:

January (20 days) + February (26 days) = 46 days

Now, we will calculate the interest for 46 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $4,263.46 × 0.04 × (46 / 365)

Interest ≈ $21.35

Finally, we will calculate the final payment Peter must pay on the due date:

Final payment = Principal + Interest

Final payment = $4,263.46 + $21.35

Final payment ≈ $4,284.81

The volume of the rectangular prism is 1.6 cubic inches.

Let's start by finding the number of cubes that can fit in each dimension of the rectangular prism. Since each cube has an edge length of 1/5 inch, the length, width, and height of the rectangular prism must be multiples of 1/5 inch. Let's call the length of the rectangular prism "L", the width "W", and the height "H". Then we have

L = 1/5 × x

W = 1/5 × y

H = 1/5 × z

where x, y, and z are integers.

Since the rectangular prism is completely packed with 200 cubes, we have

x × y × z = 200

We want to find the volume of the rectangular prism, which is given by

V = L × W × H = 1/5 × x × 1/5 × y × 1/5 × z = 1/125 × x × y × z

Substituting x × y × z = 200, we get

V = 1/125 × 200 = 8/5 = 1.6 cubic inches

Learn more about volume here

brainly.com/question/28934314

#SPJ4

The given question is incomplete, the complete question is:

A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. find the  volume of this rectangular prism