At a baseball game, 45% of the fans are wearing jackets. Also, 30% of the fans are wearing baseball caps. Whether a fan is wearing a jacket is independent of whether the fan is wearing a baseball cap. What is the probability that a randomly selected fan is not wearing a jacket and is wearing a baseball cap?
A13.5%
B16.5%
C75%
85%​

The values of the variables x = 5√5, z = 20 and y = 10√5.

A triangle is a geοmetric shape with three sides and three angles. It is a pοlygοn and οne οf the simplest and mοst cοmmοn shapes in geοmetry. The three sides οf a triangle can be οf different lengths οr the same length, and the three angles can alsο vary in size. The sum οf the angles in a triangle is always 180 degrees. Triangles are used in many applicatiοns in mathematics, science, engineering, and everyday life.

Here,

To solve this problem, we can use the Pythagoras theorem, which is:

c² = a² + b²

In the smallest triangle:

x² = 5² + 10²

x² = 125

x = √125

x = 5√5

Then for medium triangle:

y² = 10² + z²

Again for Largest triangle:

(5 + z)² = (5√5)² + y²

y² = (5 + z)² - (5√5)²

Both formula have like term y², So taking it common we have:

(5 + z)² - (5√5)²  = 10² + z²

Solve for Z :

(5 + z)² - 125  = 100 + z²

+ z² + 10z - 125  = 100 + z²

z² -  z² + 10z - 125 + 25 = 100

10z  = 100 + 125 - 25

10z  = 200

z  = 200/10

z = 20

When z = 20. Then y will be

y² = 10² + z²

y² = 10² + 20²

y² = 100 + 400

y² = 500

y = √500

y = √500

y = 10√5

Thus, We have the values of the variables x = 5√5, z = 20 and y = 10√5.

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The equation for the new function F(t) is F(t) = (27/5)t + 23. This function converts the temperature in Celsius as a function of time t to the temperature in Fahrenheit.

We are given the conversion formula F(t) = (9/5)C(t) + 32, where F(t) represents the temperature in Fahrenheit, and C(t) represents the temperature in Celsius as a function of time t. To find the equation for the new function F(t), follow these steps:

1. Identify the given equation for C(t). This should be provided in the problem statement.
2. Substitute the equation for C(t) into the conversion formula F(t) = (9/5)C(t) + 32.

For example, let's assume the equation for C(t) is C(t) = 3t - 5.

Step 1: We have the equation C(t) = 3t - 5.

Step 2: Substitute C(t) into the conversion formula:

F(t) = (9/5)(3t - 5) + 32

Now, simplify the equation:

F(t) = 9/5(3t) - 9/5(5) + 32
F(t) = (27/5)t - 9 + 32
F(t) = (27/5)t + 23

So, the equation for the new function F(t) is F(t) = (27/5)t + 23. This function converts the temperature in Celsius as a function of time t to the temperature in Fahrenheit.

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For diameter 12 inches the would take approximately 904.78 cubic inches of air to inflate the soccer ball.

Diameter is a straight line segment that passes thrοugh the center οf a circle οr sphere, cοnnecting twο pοints οn the circumference. It is the lοngest chοrd οf the circle οr sphere and its length is twice the radius.

Tο find οut hοw much air is needed tο inflate the sοccer ball, we need tο first calculate the vοlume οf the ball. The fοrmula fοr the vοlume οf a sphere is:

V = (4/3)π[tex]r^3[/tex]

where r is the radius of the sphere.

Since the diameter of the soccer ball is 12 inches, the radius is half of that, or 6 inches. We can substitute this value into the formula and simplify:

V = (4/3)π([tex]6^3[/tex]) = 904.78 cubic inches

This is the volume of the fully inflated soccer ball. If the ball is currently deflated, we need to add enough air to bring its volume up to 904.78 cubic inches.

The amount of air needed will depend on the pressure of the air being used to inflate the ball. If we assume that the pressure is constant, we can use the ideal gas law to calculate the volume of air needed:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

Since we are assuming that the pressure and temperature are constant, we can simplify the formula to:

V = (n/R)P

where n/R is a constant for a given amount of gas, and P is the pressure.

Without knowing the pressure of the air being used, we cannot calculate the exact amount of air needed. However, we can assume a standard pressure of 14.7 pounds per square inch (psi) and use this to calculate the volume of air needed.

Assuming a pressure of 14.7 psi, we can calculate the volume of air needed as follows:

V = (n/R)P = (1/14.7)(14.7) = 1 cubic inch

Therefore, it would take approximately 904.78 cubic inches of air to inflate the soccer ball. However, the exact amount of air needed will depend on the pressure of the air being used.

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The radius r that produces the minimum surface area is 1.06 cm and the height h is 1.41 cm.

Let r be the radius of the cylinder and h be the height. You can find the equation for the volume of a solid by adding the volumes of the two hemispheres and the cylinder.

Volume = [tex](2/3)πr^3 + πr^2h[/tex] = 10 cubic centimeters

Now let's find the values ​​of r and h that minimize the surface area of ​​the solid. This area consists of three parts:

Curved surfaces of two hemispheres and sides of a cylinder. This can be expressed as:

surface area = [tex]2πr^2 + 2πrh[/tex]

To find the values ​​of r and h that minimize this expression, we can use the Lagrangian multiplier method. Given that the volume of the solid is 10 cubic centimeters, we want to minimize the surface area. So it looks like this:

[tex]f(r, h) = 2πr^2 + 2πrh + λ[(2/3)πr^3 + πr^2h - 10][/tex]

Taking the partial derivatives for r, h, and λ and setting them to zero gives

[tex]4πr + 2πh = 2πr^2λ + (4/3)πr^3λ[/tex]

[tex]2πr = πr^2λ + πrhλ[/tex]

Solving these equations simultaneously gives:

h = 4r/3

λ = 2/(3r)

Substituting these values ​​into the volume equation gives:

[tex]r^2h = 5/3[/tex]

Substituting h = 4r/3 from above, we get:

[tex]r^3 = 15/8pi[/tex]

Taking the cube root of both sides gives:

r=1.06cm

Substituting this value for r into the formula for h yields:

h=1.41cm

Therefore, the radius r that produces the minimum surface area is about 1.06 cm and the height h is about 1.41 cm.

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Answer: Let's use "A" to represent Adam's current age, and "T" to represent Teri's current age.

From the first sentence of the problem, we know that:

A = T - 15

This is because Adam is 15 years younger than Teri.

Now let's use the second sentence of the problem. It says that 10 years ago, Tori was 4 times as old as Adam was then. So, if we subtract 10 from each person's current age, we get:

(T-10)/4 = (A-10)

We can simplify this equation by substituting A = T - 15:

(T-10)/4 = ((T-15)-10)

Simplifying this equation further:

(T-10)/4 = (T-25)

Multiplying both sides by 4:

T-10 = 4(T-25)

Distributing the 4:

T-10 = 4T-100

Subtracting T from both sides:

-10 = 3T-100

Adding 100 to both sides:

90 = 3T

Dividing both sides by 3:

T = 30

So Teri is currently 30 years old. Using A = T - 15, we can find that Adam is:

A = T - 15 = 30 - 15 = 15

So Adam is currently 15 years old.

Step-by-step explanation:

the use of a cambered wing design is an important advancement in the history of airplane wing design, allowing for greater lift and improved performance.

The design of airplane wings has undergone significant changes over the years, with advancements in technology and understanding of aerodynamics leading to more efficient and effective designs. One such change is the use of a wing's upper surface to create the lower surface, a design feature known as the "cambered wing."

A cambered wing is characterized by a curved upper surface and a flatter lower surface. The curve of the upper surface causes air to flow faster over the top of the wing than underneath, creating a region of low air pressure above the wing and high air pressure below the wing. This difference in pressure generates lift, which is what keeps the airplane aloft.

The idea of using a cambered wing design to generate lift was first proposed by Sir George Cayley, a British scientist and engineer, in the early 19th century. However, it was not until the early 20th century that the design was fully understood and implemented in airplane wings.

The key change made to the upper portion of the wing to form the lower section is the addition of camber, or curvature, to the upper surface of the wing. This curve causes the air to flow faster over the top of the wing, creating a region of low pressure that generates lift. The lower surface of the wing is typically flatter to allow for a smooth flow of air underneath the wing and reduce drag.

In addition to the shape of the wing, other factors such as wing size, angle of attack, and airspeed can also impact lift and aerodynamic performance. These factors must be carefully considered in the design and construction of airplane wings to ensure safe and efficient flight.

Overall, the use of a cambered wing design is an important advancement in the history of airplane wing design, allowing for greater lift and improved performance.

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In a right triangle CDL, the horizontal distance between points D and L is |x2 - x1| blocks, and the vertical distance between points D and L is |y2 - y1| blocks.

We need to determine the horizontal and vertical distances between points D (x1, y1) and L (x2, y2) in a right triangle CDL.
Identify the coordinates of points D and L.
Let D = (x1, y1) and L = (x2, y2)
Calculate the horizontal distance between points D and L.
Horizontal distance = |x2 - x1|
Calculate the vertical distance between points D and L.
Vertical distance = |y2 - y1|

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Answer:

A. The first step is to perform the multiplication operation, which is 8*2.

B. The second step is to perform the addition and subtraction operations from left to right, which gives us the simplified expression of 6 + 20 + 16.

C. The value of the expression is 42.

Step-by-step explanation:

For the given question, the first step in evaluating the expression 6 + (24 - 4) + 8 x 2 is to perform any multiplication or division operations , since they take precedence over addition and subtraction. In this case, 8 x 2 equals 16, so we can simplify the expression to 6 + (24 - 4) + 16.

The second step is to perform any addition or subtraction operations, working from left to right. In this case, 24 - 4 equals 20, so we can further simplify the expression to 6 + 20 + 16.

Finally, we can add the remaining numbers to get the value of the expression: 6 + 20 + 16 = 42. Therefore, the value of the expression is 42.

Answer:

The answer is b. Marital problems.

Step-by-step explanation:

Marital problems have not been consistently found to impair immune functioning.

Nonprobability sampling carries more risk of selection bias than probability sampling because nonprobability sampling does not use randomization.What is nonprobability sampling?A nonprobability sampling is a method of selecting participants for a study that does not allow the researcher to use a random selection process.

Nonprobability sampling, also known as purposive sampling, is a technique that involves choosing participants based on subjective criteria, such as availability or willingness to participate. This method is frequently used in research that investigates hard-to-reach populations, such as homeless individuals or drug addicts.

A key feature of probability sampling is that it allows the researcher to obtain a representative sample of the population, minimizing the risk of selection bias. In contrast, nonprobability sampling does not provide the same level of assurance that the sample will be representative. Because participants are chosen based on subjective criteria rather than random selection, there is a greater risk of selection bias.

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The required rate of  increasing in volume of a sphere when diameter is 80 mm is equals to 25600π mm^3/s

let 'V' be the volume of the volume of a sphere

'r' be the radius of the sphere.

The formula for the volume of a sphere in terms of its radius,

V = (4/3) × π × r^3

Taking the derivative with respect to time, we get,

dV/dt = 4× π × r^2 × (dr/dt)

where dV/dt is the rate of change of the volume,

dr/dt is the rate of change of the radius,

And π is a constant.

The rate of change of the radius dr/dt is 4 mm/s.

Calculate the rate of change of the volume when the diameter is 80 mm.

Diameter = 2 (radius)

This means the radius is 40 mm.

Substituting the values in the formula above, we get,

⇒dV/dt = 4 × π × (40 mm)^2 ×(4 mm/s)

Simplifying this expression, we get,

⇒ dV/dt = 25600π mm^3/s

Therefore, the volume of the sphere is increasing at a rate of 25600π mm^3/s when the diameter is 80 mm.

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Answer:

The polynomial 2y^2 -15y-8 is not prime. It can be factored as (2y+1)(y-8).

Answer:false

Step-by-step explanation:

The resulting polynomial expression is 3x⁴ + 11x³ - 31x² - 99x + 36, and the correct answer is (A) -4x² - 2x + 4, which matches this expression after combining like terms.

To find the sum of the given polynomials, we need to multiply them using the distributive property and then combine like terms. This involves multiplying each term of the first polynomial by each term of the second polynomial, then simplifying the resulting expression by combining any like terms. After performing the multiplication and simplification steps, we end up with the polynomial expression 3x⁴ + 11x³ - 31x² - 99x + 36. Therefore, the correct answer is (A) -4x² - 2x + 4, which matches this expression after combining like terms.

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Answer:

A

Step-by-step explanation:

These are cross angles

The standard deviation of the sampling distribution is 0.00702.

In this case, we know that 8% of all adults in Ohio support the increase. We can use this information, along with the sample size of 1500, to calculate the standard deviation of the sampling distribution. The formula for the standard deviation of the sampling distribution is:

standard deviation = √ [(population proportion x (1 - population proportion)) / sample size]

Plugging in the numbers, we get:

standard deviation = √ [(0.08 x 0.92) / 1500]

standard deviation = √0.00004928

standard deviation = 0.00702

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As per the information provided, the answer to all the parts in the question will be as follows:

a. To solve the LP problem by ignoring the integer constraints in Excel using Solver, we can follow the steps below:

Enter the objective function and the constraints in a new Excel worksheet: Objective function: Maximize 15x1 + 2x2 Constraints: 7x1 + x2 <= 23 3x1 - x2 <= 5

Open the Solver add-in by clicking on Data -> Solver in the Excel menu.

Set the objective function to maximize and set the variable cells to x1 and x2. Set the constraints by clicking on Add in the Solver Parameters dialog box.

Set the Solver options to "Assume Linear Model" and "Make Unconstrained Variables Non-Negative". Click Solve. The solution to the LP problem is x1=3, x2=2.714, with an optimal objective function value of 51.714.

b. If we round up fractions greater than or equal to 1/2, the solution becomes x1=3, x2=3, with an objective function value of 51. This is not the optimal integer solution, as we will see in part d.

c. If we round down all fractions, the solution becomes x1=2, x2=2, with an objective function value of 34. This is not the optimal integer solution either, as we will see in part d.

d. To solve the ILP problem in Excel using Solver, we can follow the steps below:

Open the Solver add-in by clicking on Data -> Solver in the Excel menu. Set the objective function to maximize and set the variable cells to x1 and x2. Set the constraints by clicking on Add in the Solver Parameters dialog box. Set the Solver options to "Assume Linear Model" and "Make Unconstrained Variables Non-Negative". Add integer constraints by clicking on Add in the Solver Parameters dialog box, and setting the integer constraints for x1 and x2. Click Solve.

The solution to the LP problem is x1=2, x2=3, with an optimal objective function value of 48.

As we can see, the optimal objective function value for the LP problem (48) is lower than that for the LP problem (51.714), regardless of rounding up or down.

e. The optimal objective function value for the ILP problem is always less than or equal to the corresponding LP's optimal objective function value because the LP problem allows fractional solutions, while the ILP problem only allows integer solutions. Introducing additional constraints that restrict the variables to integers can only reduce the feasible solution space, and thus lead to a lower optimal objective function value. The LP and ILP problems would be equal if the optimal solution for the LP problem happens to be an integer solution.

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Note that the full question is:

Given the following all-integer linear program: (COMPLETE YOUR SOLUTION IN EXCEL USING SOLVER AND UPLOAD YOUR FILE. BE SURE THAT EACH WORKSHEET IN THE EXCEL FILE CORRESPONDS TO EACH QUESTION BELOW ) Max 15x1 + 2x2 s. t. 7x1 + x2 < 23 3x1 - x2 < 5 x1, x2 > 0 and integer a. Solve the problem (using SOLVER) as an LP, ignoring the integer constraints.

b. What solution is obtained by rounding up fractions greater than or equal to 1/2? Is this the optimal integer solution? c. What solution is obtained by rounding down all fractions? Is this the optimal integer solution? Explain. d. Show that the optimal objective function value for the ILP is lower than that for the optimal LP (Eg. Resolve original problem using SOLVER with the Integer requirement). e. Why is the optimal objective function value for the ILP problem always less than or equal to the corresponding LP's optimal objective function value? When would they be equal?

Answer:

Step-by-step explanation:

its doc sus

Step-by-step explanation:

See image:

Answer:

Unlikely

likely

neither likely or unlikely

Step-by-step explanation:

In order to lose one pound for weight per week, Maddie must consume 1800 calories per day.

Firstly we need to know the number of calories Maddie wants to loose. As per the fact, 1 pound equals 3500 calories. Thus, she must eat 3500 calories less than regular in a week.

Now, one week has seven days. So, number of calories to be reduced each day = 3500/7

Number of calories = 500 calories.

The required calorie intake = current calorie intake - calories to not be consumed

Required calorie intake = 2300 - 500

Required calorie intake = 1800 calories.

Thus, Maddie must consume 1800 calories per day.

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Answer:

g(x) is the square root of 4x^2 + 4x + 1.

Step-by-step explanation:

We are given that f(x) = x^2 + 1 and f(g(x)) = 4x^2 + 4x + 2.

To find g(x), we need to substitute g(x) into the expression for f and simplify:

f(g(x)) = (g(x))^2 + 1 = 4x^2 + 4x + 2

Subtracting 1 from both sides, we get:

(g(x))^2 = 4x^2 + 4x + 1

Taking the square root of both sides (remembering to include both the positive and negative roots), we get:

g(x) = ±√(4x^2 + 4x + 1)

However, we need to choose the sign of g(x) such that f(g(x)) matches the given expression of f(g(x)) = 4x^2 + 4x + 2.

Let's try using the positive root first:

g(x) = √(4x^2 + 4x + 1)

Then we can find f(g(x)):

f(g(x)) = (g(x))^2 + 1 = 4x^2 + 4x + 2

This matches the given expression, so we can conclude that:

g(x) = √(4x^2 + 4x + 1)

Therefore, g(x) is the square root of 4x^2 + 4x + 1.

The margin of error using a 99% confidence interval is 6.21. This means that we can be 99% confident that the true mean score of all Biology students (not just the sample) falls within a range of 92 ± 6.21.

What is percentage?

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

To calculate the margin of error using a 99% confidence interval, we need to use the formula:

Margin of error = z* (standard deviation / √n)

Where:

z* = the z-score associated with the confidence level, which is 2.576 for a 99% confidence level (using a standard normal distribution table).

standard deviation = 9.38

n = 20

Plugging in the values, we get:

Margin of error = 2.576 * (9.38 / √20)

= 6.21 (rounded to two decimal places)

Therefore, the margin of error using a 99% confidence interval is 6.21. This means that we can be 99% confident that the true mean score of all Biology students (not just the sample) falls within a range of 92 ± 6.21.

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In an trial, there's a 1/6 chance that the coming gravestone chosen from the bag will be green.

Experimental probability, occasionally appertained to as empirical probability, is grounded on valid trials and sufficient attestation of the circumstance of events. A number of real tests are carried out to ascertain whether any event will do. Random trials are tests that have an changeable outgrowth. similar trials' results are noway certain. To establish their possibility, arbitrary trials are conducted constantly. Each repeating of an trial which is done a destined number of times is appertained to as a trial. The experimental probability formula is defined as follows in mathematics

Probability of an Event P( E) = Number of times an event occurs /Total number of trials.

According to question,

The experimental liability that a green marble will be the coming one drawn from the bag is equal to the total number of green marbles divided by the total number of marbles.

2/( 2 + 10)

= 2/12

= 1/6

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Answer:

The slope of the best-fit line shows that as time increases, the total number of calories that a teenager consumes throughout the day also increases.

Plotting the graph of the inequality we get a line passing through the point x = 5.

A mathematical notion called inequality examines two numbers or expressions to see if they are equal or not. When there is an inequality, one value is either more than or less than the other. "" (less than), ">" (greater than), "" (less than or equal to), and "" are used to denote inequality (greater than or equal to). In algebra and calculus, inequalities are frequently used to explain how variables relate to one another and to solve equations and systems of equations. In the actual world, inequalities are frequently used to compare measurements, quantities, and other variables.

The given function is x² > 25.

Simplifying the given inequality we have:

x > √25

x > 5 or -5

But - 5 is < x

So we have,

-5 < x < 5

Plotting the graph of the inequality we get a line passing through the point -5 < x < 5.

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The answer using scientific notation is simplified expression is [tex]4.0*10^{-5}[/tex]

What is expression?

Expressiοns in math are mathematical statements that have a minimum οf twο terms cοntaining numbers οr variables, οr bοth, cοnnected by an οperatοr in between. The mathematical οperatοrs can be οf additiοn, subtractiοn, multiplicatiοn, οr divisiοn.

Fοr example, x + y is an expressiοn, where x and y are terms having an additiοn οperatοr in between. In math, there are twο types οf expressiοns, numerical expressiοns - that cοntain οnly numbers; and algebraic expressiοns- that cοntain bοth numbers and variables.

[tex](5 \times 10^2)^-2[/tex] can be simplified as:

[tex]=(5 \times 10^2)^{-2} \\\\= 1/(5 * 10^2)^2 \\\\= 1/(5^2 * 10^4) \\\\= 1/25000\\\\ = 4 * 10^{-5}[/tex]

Therefore, the simplified expression is [tex]4.0*10^{-5}[/tex]

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According to given information, the length of the rectangular storage unit is 12 feet.

What is rectangle?

A rectangle is a two-dimensional shape with four sides and four right angles. It is a quadrilateral with opposite sides that are parallel and equal in length.

We can use the Pythagorean theorem to find the length of the storage unit. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the 5-foot-wide floor and the length of the storage unit form the two sides of a right triangle, with the diagonal (the distance from one corner to the opposite corner) being the hypotenuse. We can set up the equation as:

[tex]hypotenuse^2 = side1^2 + side2^2[/tex]

where side1 = 5 feet and hypotenuse = 13 feet.

Simplifying this equation, we get:

[tex]hypotenuse^2[/tex][tex]= 5^2 + side2^2[/tex]

169 = 25 + [tex]side2^2[/tex]

[tex]side2^2[/tex] = 144

side2 = 12

Therefore, the length of the storage unit is 12 feet.

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Thus, the line of best fit for the given speed x (miles per hour)  and their corresponding Braking distance y (feet) is drawn.

A mathematical idea that correlates points spread throughout a graph is called the line of best fit. The optimum technique to define the association between the dots is determined using scatter data in this type of linear regression.

Given table is:

Speed, x (miles per hour) -     20    30     40    50     60

Braking distance, y (feet) -     20    45     80    125    180

Plot the (x,y) coordinates on the graph:

(20, 20) , (30, 45), (40, 80), (50, 125), (60, 180)

line of best fit defines the line, which is the average of the values covering the given data.

For the given data: line of best fit is drawn.

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The surface area of the given right triangular prism is 84 in².

How to find the surface area of a right triangular prism?

To calculate the surface area of a right triangular prism, we need to find the area of all the faces and add them up.

First, let's find the area of the triangular bases. The base of the triangle is 8 in, and the height is 3 in, so the area of each triangular base is [tex]\frac{1}{2} \times base \times height = \frac{1}{2} \times 8 \times 3 = 12 \: {in}^{2}[/tex]

There are two triangular bases, so the total area of both bases is (2 × 12) in²= 24 in²

Now, let's find the area of the rectangular faces. The length of the rectangle is 5 in, and the breadth is 4 in.

So, the area of each rectangular face is length × breadth = 5 in × 4 in = 20 in²

There are three rectangular faces, so the total area of all three faces is 3 × 20 in² = 60 in².

Finally, we add the areas of the bases and the rectangular faces to get the total surface area.

Total surface area = 24 in² + 60 in² = 84 in²

Therefore, the surface area of this right triangular prism is 84 square inches.

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