The correct option is (D) i.e. It took 15 gallons of water to fill the swimming pool.
What is Measurement?
Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, volume, and many others. It is used to quantify and describe the properties of objects and phenomena in the natural world, as well as in many fields of science, engineering, commerce, and everyday life.
Measurements are typically made using standard units, such as meters for length, kilograms for mass, seconds for time, and so on.
We are given that, there are 3.8 liters in 1 gallon.
So, we can say that,
1 gallon = 3.8 liters
Now, It took 57 liters of water to fill a small swimming pool
we can convert it into gallons as follows:
1 gallon = 3.8 liters
1 / 3.8 gallon = 1 liter
57 / 3.8 gallon = 57 liters
So, 57 liters = 15 gallons of water.
Hence, (d) is the correct option.
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Straight Line Graphs Question. I tried to solve the section (a) part of the question correctly I followed the gradient method plugging in the values and got [tex]y = \frac{1}{6} x + 1.6 (recurring). However the answer is y = \frac{1}{2} x + 3.[/tex]. Where am I going wrong? Can someone explain step by step how to solve this please.
The equation of the straight line joining A to B is y = (1/2)x + 3, the equation of the straight line joining B to C is y = (1/2)x + 3, and A, B, and C are collinear.
What are collinear points?
Collinear points are three or more points that lie on the same straight line. In other words, if three points A, B, and C are collinear, then there exists a straight line that passes through all three points. To determine if three or more points are collinear, we can find the slope of the line that passes through any two of the points. If the slope is the same for all possible pairs of points, then the points are collinear. Otherwise, they are not collinear.
a) To find the equation of the straight line joining A to B, we can use the slope-intercept form of the equation of a line:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
The slope of the line passing through A and B is:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (-8, -1) and (x₂, y₂) = (-4, 1).
m = (1 - (-1)) / (-4 - (-8)) = 2/4 = 1/2
To find the y-intercept, we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
where (x₁, y₁) = (-8, -1) and m = 1/2.
y - (-1) = (1/2)(x - (-8))
y + 1 = (1/2)(x + 8)
y = (1/2)x + 3
Therefore, the equation of the straight line joining A to B is y = (1/2)x + 3.
b) To find the equation of the straight line joining B to C, we can use the same method:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (-4, 1) and (x₂, y₂) = (12, 9).
m = (9 - 1) / (12 - (-4)) = 8/16 = 1/2
Using point-slope form with the point (x₁, y₁) = (-4, 1) and slope m = 1/2:
y - 1 = (1/2)(x - (-4))
y - 1 = (1/2)x + 2
y = (1/2)x + 3
Therefore, the equation of the straight line joining B to C is y = (1/2)x + 3.
c) From the equations of the lines joining A to B and B to C, we can see that both lines have the same slope of 1/2. This implies that the three points A, B, and C are collinear, i.e., they lie on the same straight line.
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Find the interest on $4000 at 3.5% annual interest for 1 year 6 months
the interest for 1 year:
[tex]3.5\% \cdot 4000 = 140[/tex]
the interest for 6 months:
[tex]\dfrac{140}{2} = 70[/tex]
the interest for 1 year 6 months:
[tex]140+70 = \bf \$ 210[/tex]
Use the diagram to find the measure of the given angle m
After calculating the straight angle we know that ∠BAC is (A) 150°.
What is the straight angle?
A straight angle in geometry is one that is 180 degrees in length.
It looks like a straight line, which is why it is known as a straight angle.
In other words, it is an angle whose sides are in the same straight line but opposite to the vertex.
A straight angle in geometry is an angle with a vertex point that is at 180 degrees.
In other words, an angle becomes a straight angle when its arms point in the opposite direction.
So, we know that s straight angle is always 180°.
∠BAD is a straight angle.
We can also observe that:
∠BAD = ∠BAC + ∠CAD
Now, solve as follows:
∠BAD = ∠BAC + ∠CAD
180 = ∠BAC + 50
180 - 50 = ∠BAC
130° = ∠BAC
Therefore, after calculating the straight angle we know that ∠BAC is (A) 150°.
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A car uses data to help determine the color of cars to order for this year. The data displays how many cars were sold the previous year Each dot represents 10 cars. Use the dot plot to answer the question
Number of Cars Per Color to Stock
O 100
O 190
019
025
Therefore , the solution of the given problem of dot plot comes out to be on the dot plot, 19 vehicles were sold that were not white.
Dot plot: What is it?The most typical way to display data in a graph is to demonstrate how two additional factors relate to one another. Digital and hand-drawn sketches are both acceptable. From the beginning position, move two or more pieces to the correct and three pieces up. The reference system must display the numerals for positions 2, 3, and 4. In your points, be very clear.
Here,
The following numbers are shown as follows based on the dot plot:
Number of scarlet vehicles: 5
=> 8 black vehicles total.
=> 6 white vehicles total.
=> One silver vehicle is equal to four grey cars.
=> Blue vehicle count equals one.
The following vehicles are not white vehicles based on the aforementioned criteria.
Thus, we have the depiction shown below.
=> Number of scarlet vehicles: 5
=> 8 black vehicles total.
=> number of silver vehicles Equals 1
=> 4 grey vehicles totaled
=> Blue vehicle count equals one.
These wavelengths combine to give us the following
=> Total = 5 + 8 + 1 + 4 + 1
Analyze the amount
=> Overall = 19
Therefore, there are 19 vehicles.
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Answer: Its 190. The problem states each dot represents 10 cars. 19 out of 25 dots weren't white. 19*10 is 190.
Step-by-step explanation:
In the figure below, find the exact value of . (Do not approximate your answer.)
The value for x is 4√3. The solution has been obtained by using the Pythagoras theorem.
What is Pythagoras theorem?
Pythagoras' Theorem states that the square of a right - angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides.
We are given the length of the hypotenuse to be 8.
Let the base be 'y'.
So, using Pythagoras theorem,
[tex]x^{2} + y^{2} = 8^{2}[/tex]
From this, we get
[tex]y^{2} = 8^{2} - x^{2}[/tex] ...(1)
Also,
[tex]2^{2} + Perpendicular^{2} = y^{2}[/tex] ...(2)
From the figure, we also know that
[tex]6^{2} + Perpendicular^{2} = x^{2}[/tex]
So,
[tex]Perpendicular^{2} = x^{2} - 6^{2}[/tex]
On substituting this in (2), we get
[tex]2^{2} + x^{2} - 6^{2} = y^{2}[/tex] ...(3)
On equating (2) and (3), we get
⇒[tex]2^{2} + x^{2} - 6^{2} = 8^{2}-x^{2}[/tex]
⇒ 4 + [tex]x^{2}[/tex] - 36 = 64 - [tex]x^{2}[/tex]
⇒ [tex]2x^{2}[/tex] - 32 = 64
⇒ [tex]2x^{2}[/tex] = 96
⇒ [tex]x^{2}[/tex] = 48
⇒ x = 4√3
Hence, the value for x is 4√3.
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Consider one triangle whose sides measure units, units, and 2 units. Consider another triangle whose sides measure 2 units, units, and units. Are these triangles congruent, similar, or both? Explain your answer.
The triangles are cοngruent.
How to find if two triangles are congruent?Tο determine whether the twο triangles are cοngruent, similar, οr bοth, we need tο cοmpare their cοrrespοnding sides and angles.
Let's first cοmpare their cοrrespοnding sides:
Triangle 1: sides measure x, x, and 2 units
Triangle 2: sides measure 2 units, x, and x
The sides x and x are the same in bοth triangles, and the side 2 units in triangle 1 cοrrespοnd tο the side 2 units in triangle 2. Hοwever, the οrder οf the sides is different in the twο triangles. We can reοrder the sides in triangle 2 sο that they match the οrder οf the sides in triangle 1:
Triangle 2: sides measure x, x, and 2 units
Nοw we can see that the twο triangles have the same side lengths and are therefοre cοngruent.
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Use set-builder notation to indicate set numbers as described.
Answer
{x||
The set of all real numbers between 5 and 9, including 5
The set of all real numbers between 5 and 9, including 5, can be represented by the set-builder notation {x ∈ ℝ | 5 ≤ x ≤ 9}.
What is set-builder notation, and how is it used in mathematics?A compact, mathematical notation is used to represent a set of components using set-builder notation. In set-builder notation, we express the attributes or features that the components of the set must have in order to be included in the set. The standard format for set-builder notation is x | P(x), where x is a variable that denotes the set's elements and P(x) is a predicate or condition that lists the characteristics each member must possess in order to be included in the set.
We can represent the set of all real numbers as:
{x ∈ ℝ | 5 ≤ x ≤ 9}
This notation reads "the set of all x in the real numbers such that x is between 5 and 9, including 5."
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what is another name for line qr?
Answer: Another name would be Line RQ
Not sure if this is what you're looking for but hope it helps!
Make a scatter plot of the data pairs (year, attendance). Draw a trend line and write its equation. Estimate the attendance at U.S. theme parks in 2005.
A construction of the scatter plot of the data pairs (year, attendance) is shown below.
An equation of the line of best fit (trend line) is y = 0.19x + 308.93.
The estimated attendance for the year 2005 is approximately equal to 336 people.
How to determine an equation of the line of best fit for the data set?In order to determine an equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the number of years would be plotted on the x-axis of the scatter plot while the number of attendance would be plotted on the y-axis of the scatter plot.
Based on the scatter plot (see attachment) which models the relationship between the number of years and attendance, an equation for the line of best fit is given by:
y = 5.43x + 254.42
Lastly, we would determine the predicted attendance for the year 2005:
Years, t = 2005 - 1990 = 15 years.
y = 5.43(15) + 254.42
y = 81.45 + 254.42
y = 335.87 ≈ 336 people.
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Use set-builder notation to indicate set numbers as described.
Answer
As
{x|
The set of all real numbers between 5 and 7, including 5
Consider the following figure.
(Note that the figure is not drawn to scale.)
46°
72°
53°
L
57°
K
Order the side lengths IJ, JL, IK, JK, and LK from least to greatest.
O
The order of the side lengths of the triangles from the least to the greatest is Lk < JL < IJ < JK < IK.
How does angle opposite to a side of triangle affect its size?
If the angle facing a side of a triangle increases, then the length of the opposite side may also increase. This is because the larger the angle, the more vertical the opposite side becomes, and therefore the longer it may become.
Conversely, if the angle facing a side of a triangle decreases, then the length of the opposite side may also decrease. This is because the smaller the angle, the less vertical the opposite side becomes, and therefore the shorter it may become.
From the given diagram, the largest side of the triangle will be the side directly opposite the largest angle.
Also, the smallest side of the triangle will be the side directly opposite the smallest angle.
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Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 4(m∠Y) − 135°. Find m∠Y.
Answer:The value of angle y is 40°.
Complementary angles are the angles that have their sum equal to 90°.
Therefore, based on the information given, the value of angle y will be calculated thus:
x + y = 90°.
4y - 110° + y = 90°
Collect like terms
4y + y = 90° + 110°
5y = 200°
y = 200/5
y = 40°
The value of angle y is 40°.
Step-by-step explanation:
Pre-Algebra Grade 8 (Connections) (Portfolio) Unit 2, Lesson 11 SufaceAra and Volume in the real world. I need some help to get a better understanding of the assignment.
Calculating the surface area οr vοlume οf a fοrm is impοrtant in a variety οf real-wοrld situatiοns, such as when determining hοw much water is required tο fill a pοοl (rectangular prism) οr hοw much wrapping paper is required tο wrap a candle (cylinder) οr basketball (square) (sphere).
Where wοuld yοu emplοy vοlume and surface area in daily life?The tοtal area that all οf a 3D οbject's faces enclοse is referred tο as surface area. Fοr instance, the surface area οf a cube is its surface area if we need tο determine hοw much paint is needed tο paint it.
The idea οf surface areas has practical implicatiοns in wrapping, painting, and ultimately creating things tο create the best pοssible design.
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The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes 9 hours for a car moving at 35 mph.
How long does the trip take for a car moving at 21 mph ?
At the start of the month, the counter on the copy machine reads 6,583. At the end of the moth, it reads 82,110. The copies cost 1 1/3 cents a piece. What was the approximate total cost of the copies for this month?
Answer:
$1007.03
Step-by-step explanation:
You want the cost of copies for the month at 1 1/3 cents each if the copy counter ran from 6583 to 82110 during the month.
Number of copiesThe number of copies made is the difference in counter readings:
82110 -6583 = 75,527 . . . . . copies made
CostEach costs 1 1/3 = 4/3 cents, so the cost of these copies is ...
(75,527 copies) × (4/3 cents/copy) = 100702 2/3 cents ≈ 100703 cents
There are 100 cents in a dollar (or other currency unit), so the cost is about ...
(100703¢)/(100¢/$) = $1007.03
The total cost of copies for the month is about $1007.03.
__
Additional comment
The currency unit is not specified in this problem. There are a number of world currencies in which the smallest denomination is 1 cent. The US dollar, the Euro, and the Aruban Guilder are some of them.
what is 3 plus 3???
as a joke :)
Answer:6
Step-by-step explanation:biyhfdvsauybi
unit 10 hw 4 can yall pls help me
Answer:33
Step-by-step explanation:
33
the factor of 70
the common factor of 70
[tex]the factor of 70[/tex]
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
What is a factor?
A factor is a number that completely divides another number. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product because the product is divisible by them.
Multiplication and division are the two techniques for determining factors. Rules of divisibility can also be applied.
The given number is 70.
70 is completely divisible is 1.
70 is completely divisible is 2.
70 is completely divisible is 5.
70 is completely divisible is 7.
70 is completely divisible is 10.
70 is completely divisible is 14.
70 is completely divisible is 35.
70 is completely divisible is 70.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
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create a hanger to represent 7 = 4x + 2
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The values of x in the equation are x = 1 and x = 13
How to determine the value of xEquations are mathematical statements that express the equality of two expressions using mathematical symbols such as variables, numbers, and operations.
From the question, we have the following parameters that can be used in our computation:
(x - 7)^2 = 36
Take the square root of both sides of the equation
So, we have the following representation
x - 7 = ±6
Add 7 to both sides
x = 7 ± 6
Evaluate the expression
x = 1 and x = 13
Hence, the solutions are 1 and 13
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Esfandairi Enterprises is considering a new three-year expansion project that requires an initial fixed asset investment of $2.18 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life. The project is estimated to generate $1,730,000 in annual sales, with costs of $640,000. The project requires an initial investment in net working capital of $290,000, and the fixed asset will have a market value of $240,000 at the end of the project.
a. If the tax rate is 24 percent, what is the project’s Year 0 net cash flow? Year 1? Year 2? Year 3? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers in dollars, not millions of dollars, e.g., 1,234,567.)
b.
If the required return is 12 percent, what is the project's NPV? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Answer:
a
Step-by-step explanation:
bece u sr gģ v vyvy bleh gm have g GMV Espanola unmet yucky nvm i gifted go by Grau Cinco
The net present value of the project is $0.15 million.
What is the net present value?Net present value is the present value of after-tax cash flows from an investment less the amount invested.
hee, we have,
The first step is to determine the cash flow of the project.
Cash flow = (sales - cost - depreciation) × (1 - tax) + depreciation
Depreciation = (cost of the asset ) / useful life
Depreciation = $2.18 million / 3
Depreciation = 0.727 million
Cash flow = (1.645 - 0.61 - 0.727) x (1 - 0.21) + 0.727 = $0.97 million
Net present value = -2.18 million + 0.97 / 1.12 + 0.97 / 1.12² + 0.97 / 1.12³
= $0.15 million
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easy question for people, btw the question is not for me lol
Maya spent 2 hours on her phone, then she was left with 38% battery left.
then after another hour passed by and now it is 9%.
How many hours and minutes did she spend on her phone
Perform the operation. ( 8 � 2 + 3 � − 4 ) + ( − 2 � 2 + 8 � ) (8x 2 +3x−4)+(−2x 2 +8x)
Therefore, the simplified expression is 6x² + 11x - 4.
What is expression?In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, −, ×, ÷, ^) that represents a quantity or a mathematical relationship between quantities. Expressions can include variables, which are letters that represent unknown or varying values. Expressions can be simple or complex, and they can be used to represent mathematical formulas, equations, inequalities, and functions. Expressions can be evaluated by replacing the variables with specific values and performing the arithmetic operations according to the rules of algebra. Expressions can also be simplified by combining like terms, distributing multiplication, and factoring. Simplifying expressions can help us to better understand their structure and relationships, and it can make them easier to work with in calculations and problem-solving.
Here,
To perform the operation (8x² + 3x - 4) + (-2x² + 8x), we need to combine like terms, i.e., terms that have the same variable and exponent.
First, let's combine the x² terms:
8x² - 2x² = 6x²
Next, let's combine the x terms:
3x + 8x = 11x
Finally, let's combine the constants:
-4 + 0 = -4
Putting it all together, we have:
(8x² + 3x - 4) + (-2x² + 8x) = 6x² + 11x - 4
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Find [ f.g](-4) for f(x) = x - 8 and g(x)=-x^2 +2
Answer: Buckle up this answer is gonna be a rollercoaster and here we go.
To find f.g, we first need to evaluate g(-4) and then use the result as the input for f(x).
We have:
g(-4) = -(-4)^2 + 2 = -16 + 2 = -14
Now, we use this result as the input for f(x):
f(g(-4)) = f(-14) = -14 - 8 = -22
Therefore, f.g = -22.
What a short ride.
Find the zero(s) of the following function f(w)=w^2+13w+40
Answer:
To find the zeros of the function f(w) = w^2 + 13w + 40, we need to solve the equation f(w) = 0.
We can factor the quadratic expression as (w + 8)(w + 5) = 0.
Therefore, the zeros of the function are w = -8 and w = -5.
Step-by-step explanation:
Use a calculator to find the measure of
Answer:
The answer is 78.5° .................
Answer:
78.5°
Step-by-step explanation:
For <A, AC is the adjacent leg.
AB is the hypotenuse.
The trig function that relates the adjacent leg to the hypotenuse is the cosine.
cos A = adj/hyp
cos A = 3/15
cos A = 1/5
A = cos^-1 0.2
A = 78.5°
Use the graph to answer the questions:
1) a) slοpe m= 1, y-intercept =0 and equatiοn is y=x.
2) a) slοpe m=-1 , y-intercept = 4 and equatiοn is y=-x+4.
What is equatiοn?The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.
Here we knοw that, we can sοlve using any twο pοints.
1) Let us take any twο pοints, then
[tex](x_1,y_1)=(3,3) and (x_2,y_2) =(-3,-3)[/tex]
Now using slope formula ,
=> Slope m =[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{-3-3}{-3-3}=\frac{-6}{-6}=1[/tex]
Now using equation formula [tex]y-y_1=m(x-x_1)[/tex]
=> y-3=1(x-3)
=> y-3=x-3
=>y=x-3+3
=> y=x
Hence slope m=1, y-intercept = 0 and equation is y=x.
2) Let us take two points then
[tex](x_1,y_1)=(0,4) and (x_2,y_2)=(4,0)[/tex]
Now using slope formula ,
=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{0-4}{4-0}=\frac{-4}{4}=-1[/tex]
Now using equation formula then , [tex]y-y_1=m(x-x_1)[/tex]
=> y-4=-1(x-0)
=>y-4=-x
=> y=-x+4
Hence slope = -1 , y-intercept = 4 and the equation is y=-x+4.
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Solve for dc pleaseee
Applying the Trigonometric ratios, the length of DC is approximately 30 units.
How to Apply the Trigonometric Ratios?To find the length of DC, we have to apply the Trigonometric ratios.
First of all, find BD.
Considering right triangle ADB, we have:
Reference angle (∅) = 54°
Length of Hypotenuse = 20
Length of opposite side = BD = ?
Apply the sine ratio:
sin 54 = opp/hyp
sin 54 = BD/20
BD = sin 54 × 20
BD ≈ 16
Use the tangent ratio to find DC:
Reference angle (∅) = 28°
Length of adjacent side = DC = ?
Length of opposite side = BD = 16
tan 28 = opp/adj
tan 28 = 16/DC
DC = 16/tan 28
DC ≈ 30
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a) -7 + 8 = 1
b) 13 + -9 = 4
c) 23 + -9 = 14
d) -17 + 18 = 1
e) 14 + -26 = -12
f) -8 - 7 = -15
g) 13 - (+9) = 4
h) 23 – (9) = 20
i) 18 - -7 = -25
j) 26 - -14 = -40
are these correct?
Answer:
a) 1
b) 4
c) 14
d) 1
e) 12
f) 15
h) 20
i) 25
j) 40
Step-by-step explanation:
Some mistakes have been made.
Correct answers so far:
a, b, c, d, e, f are correct
h, maybe
Corrections:
g)
13 - ( + 9) can be rewritten as 13 - 9, which is 4
h) I assume the 9 is supposed to be a [tex]\sqrt{ 9}[/tex] ? If so, then the answer is correct
i) 18 - -7 can be rewritten as 18 + 7 = 25. The two negatives turn into a positive.
j)26 - -14 = 40. The two negatives turn into a positive.
How to find a surface area with 2in 6in 10in 8in 2in
The surface area of the rectangular prism is 376 square inches.
What is surface area?Surface area is the total area that the surface of a 3-dimensional object covers, including all of its faces and sides. It is measured in square units.
To find the surface area of a 3-dimensional object with dimensions of 2in, 6in, 10in, 8in, and 2in, you will need to add up the areas of each of its faces.
Assuming that the object is a rectangular prism, here are the steps to find its surface area:
Identify the dimensions of the rectangular prism: length, width, and height.
Length: 10in
Width: 8in
Height: 6in
Calculate the area of each face:
Front and back faces: length x height = 10in x 6in = 60 sq.in x 2 = 120 sq.in
Top and bottom faces: width x length = 8in x 10in = 80 sq.in x 2 = 160 sq.in
Side faces: height x width = 6in x 8in = 48 sq.in x 2 = 96 sq.in
Add up the areas of each face to get the total surface area:
Total surface area = 120 sq.in + 160 sq.in + 96 sq.in = 376 sq.in
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