The triangle AGHI can be labeled by using the given information.
Find the expression for cos(1)?The triangle is labeled AGHI.cos(l) = (GH^2 + HI^2 - GI^2) / (2 * GH * HI) = (4^2 + 7^2 - 8.1^2) / (2 * 4 * 7) = 0.848048096156426.The triangle AGHI is an isosceles triangle, with two sides of equal length (GH and HI). The angle formed between GH and HI is mZH, which is a right angle. The length of the side GI is 8.1.To find the cos(l) of the triangle, we use the law of cosines, which states that c2 = a2 + b2 - 2abcos(l). In this case, c is 8.1, a is 4, and b is 7. Substituting these values into the equation yields cos(l) = (42 + 72 - 81.2) / (2(4)(7)) = -0.67.Therefore, the cos(l) of the triangle AGHI is -0.67.Label the triangle AGHI:The right-angle of the triangle is at the vertex of Z, so angle ZHG is 90°. The side opposite to angle ZHG is GH, which is equal to 4. The side adjacent to angle ZHG is HI, which is equal to 7. The side opposite to angle HGI is GI, which is equal to 8.1.To find the expression for cos(l), we can use the Cosine Law. Cos(l) = (GH^2 + HI^2 - GI^2)/2(GH)(HI). Substituting the given values, we get Cos(l) = (4^2 + 7^2 - 8.1^2)/2(4)(7). Hence, the expression for cos(l) is equal to -0.10205.To learn more about The triangle is labeled AGHI refer to:
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a jet airplane reaches 769. km/h on a certain flight. how long does it take to cover 272 m?Set up the math. But don't do any of it. Just leave your answer as a math expression. Also be sure your answers includes all the correct unit symbols.
The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.
(272 m) / (769 km/h) x (1 h/3600 s) = 0.0095 s
1. Convert km/h to m/s: 769 km/h x (1000 m/1 km) x (1 h/3600 s) = 213.6 m/s
2. Divide the distance to travel (272 m) by the rate (213.6 m/s): 272 m / 213.6 m/s = 0.0095 s
The airplane's speed on this certain flight is 769 kilometers per hour. In order to calculate how long it will take to cover a distance of 272 meters, we must first convert the speed to meters per second. 769 kilometers per hour is equivalent to 213.6 meters per second. Once we have the rate, we can divide the distance by the rate, which is 272 meters divided by 213.6 meters per second. This calculation yields a result of 0.0095 seconds. Therefore, the airplane will take 0.0095 seconds to cover 272 meters.
The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.
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Write the first five terms of the sequence that is represented by the recursive function
f(1) =3
f(n) = f(n-1) = 4, where n is an integer and n > 1.
The first five terms of the arithmetic sequence are given as follows:
3, -1, -5, -9, -13.
How to model the arithmetic sequence?An arithmetic sequence is a sequence for which the difference between consecutive terms is constant, being called common difference d.
The recursive definition is given as follows:
f(n) = f(n - 1) + d.
For this problem, the definition is given as follows:
f(n) = f(n - 1) - 4.
Meaning that the common difference is of 4, and hence each term is obtained subtracting the first term by 4, starting with the first term given by f(1) = 3.
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Kevin hiked up Lamb's Canyon in 3 hr and then ran back down in 2 hr. His speed running downhill was 1.8 mph greater than his speed hiking uphill. How far up the canyon did he hike?
Kevin hiked (blank) mi up the canyon.
Kevin hiked up Lamb's Canyon with the goal of making it to the top.
How far up the canyon did he hike?To solve it, you need to set up two equations - one for hiking and one for running.Let x be the distance Kevin hiked up the canyon.
For hiking: 3 hr = x / h
For running: 2 hr = (x + 1.8) / r
Where h is the speed at which Kevin hiked uphill and r is the speed at which he ran downhill.Solving the two equations for x yields:
x = (3h * r) / (h + r)
To find the distance Kevin hiked up the canyon, you need to plug in the values for h and r.Therefore, Kevin hiked (3h * r) / (h + r) mi up the canyon.
For the distance that Kevin hiked uphill, the equation would look like this:Distance = (x mph) * (3 hr)
For the distance that Kevin ran downhill, the equation would look like this:Distance = (x + 1.8 mph) * (2 hr)
We can combine these two equations by setting them equal to each other and solving for x. We get:(x mph) * (3 hr) = (x + 1.8 mph) * (2 hr)
Solving for x, we get x = 2.4 mph.
Now that we know x, we can plug it back into our original equation for the distance that Kevin hiked uphill. We get:Distance = (2.4 mph) * (3 hr) = 7.2 mi. Therefore, Kevin hiked 7.2 mi up the canyon.To learn more about to find the distance refer to:
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how to solve 9x-3y=5 & 2x -3y=7 using the elimination method
The solution to the system of equations 9x - 3y = 5 and 2x - 3y = 7 is (-2/7, -53/21)
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Given the equations:
9x - 3y = 5 (1)
2x - 3y = 7 (2)
To solve by elimination method, subtract equation 2 from 1, hence:
7x = -2
Dividing by 2:
x = -2/7
Put x = -2/7 in equation 2:
2(-2/7) - 3y = 7
y = -53/21
The solution is (-2/7, -53/21)
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The local coffee shop ran a summer special. With the purchase of an $8.75 reusable mug, the cost of a coffee would only be $1.95 per cup for every visit through out the entire month. If Bre spent a total of $41.90 in the month of July, how many cups of coffee did she purchase?
PLS HELP
Answer: X = 17
Step-by-step explanation:
8.75 + 1.95x = 41.9
1.95x = 41.9 - 8.75
1.95x = 33.15
x = 33.15/1.95
x = 17
Some values of functions f, g, h, and k are provided in the table on the right.
Find a possible equation of each function Verify your results with a graphing
calculator table. (HINT Use linear or exponential equations]
The equation of function f is f(x) =?
Without any values of the functions f, g, h, and k, it is not possible to find the equation of each function. The equation of a function can be determined by analyzing the values of the function. Based on the given values, a possible equation can be found and then verified by plotting the points on a graph and seeing if they align with the equation.
It's important to note that the equation can be a linear or exponential equation but it's impossible to determine it without any values.
) draw a chord that goes between points a and b. 2) identify how many points along the curve have a tangent line parallel to the chord through . watch for rules about when there are and aren't tangent lines to the curve.
There are no points along the curve that have a tangent line parallel to the chord through A and B.
1) The chord between points A and B is a straight line connecting those two points.
2) There are no points along the curve that have a tangent line parallel to the chord through A and B, since the chord is a straight line and the curve is curved.
1) To draw the chord between points A and B, you must use a straight line to connect those two points.
2) Since the chord is a straight line and the curve is curved, there are no points along the curve that have a tangent line parallel to the chord through A and B.
To draw the chord between points A and B, draw a straight line connecting those two points. However, since the chord is a straight line and the curve is curved, there are no points along the curve that have a tangent line parallel to this chord. This is due to the fact that tangent lines only exist at points where the curve changes direction, and the chord is a straight line, not affected by the curvature of the curve. Therefore, there are no points along the curve that have a tangent line parallel to the chord through A and B.
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Identify the pattern in the list of numbers. Then use this pattern to find the next number. 5,7,12,19,31,50
The next number in the sequence is 81.
The pattern in the list of numbers is that each number is the sum of the previous two numbers in the sequence. It is a Fibonacci sequence.
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1.
So, to find the next number, we add the two last numbers of the sequence:
50 + 31 = 81
Therefore, the next number in the sequence is 81.
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There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple?
According to the information, the probability that the next pice of fruit out of the bag will be an apple is 0.66.
How to calculate the probability that the next piece of fruit out of the bag will be an apple?To calculate the probability that the next piece of fruit out of the bag will be an apple we have to perform the following mathematical operation:
We have to calculate how many fruits there are in the bag.
4 apples, 3 peaches, and 2 plums less 2 plums and 1 peach = 4 apples, 2 peaches.So, we have 4 apples and 2 peaches, so we have 6 fruits in total. Now, we have to divide the number each fruit in the bag by the total number of fruits as shown.
4 / 6 = 0.66
2 / 6 = 0.33
According to the above, the probability that the next pice of fruit out of the bag will be an apple is 0.66.
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what is the y-intercept in the following equation y=-4x-5
Answer:
y intercepts : (0, -5)
Step-by-step explanation:
hope it helps<3Answer:
(0,-5)
Step-by-step explanation:
please help. solve the inequality
Answer:
x ≤ - 2 ; 0 ≤ x ≤ 7
Step-by-step explanation:
x ≤ - 2
0 ≤ x ≤ 7
Which expression is the least absolute value ?
|-28|
|-1|
|6|
|15|
Answer:
|-28|
Step-by-step explanation:
-28 is the least value in the expression given
One of the legs of a right triangle measures 11 cm and the other measures 14 cm
The measure of hypotenuse of the triangle whose sides are given would be = 17.80cm
How to find the hypotenuse of triangle?The formula used to calculate the hypotenuse of a triangle is the Pythagorean formula= C²= a² + b²
Where c = hypotenuse = ?
a² = 11 cm
b² = 14 cm
Substitute the given values into the formula to find hypotenuse.
c² = 11² + 14²
c² = 121+196
c² = 317
C = √317
C = 17.80cm.
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Complete question:
One of the legs of a right triangle measures 11 cm and the other leg measures 14 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
when performing an addition or subtraction calculation, significant figures in the calculated result are dictated by the decimal places of the measured numbers. the calculated result should have choose... the measured number in the calculation with the fewest
The number with the fewest Decimal point will determine the number of significant figures in the calculated result.
The significant figures in the estimated result of an addition or subtraction calculation are determined by the decimal places of the measured values. This is so that the computed result can accurately reflect the precision of the measurement, which is shown by the decimal points in the measured values. Therefore, in the calculation with the fewest decimal places, the calculated result should have the same number of decimal places as the measured value. The result should have two decimal places, for instance, if one number has two decimal places and the other has four. By doing this, it is ensured that the result is not given a higher level of precision than the measured data utilized in the computation warrant.
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Is 4.259462364423... Rational or irratioL
(a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use μ 20−39 −μ 60 and older.)Interpret the interval. O We cannot draw a conclusion from the given information. O We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval. O We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval. O We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.
We have a 95% confidence interval around the real average height of younger women being greater than that of older women.
What is meant by real average?You will make the same amount of money if you earn $50,000 this year as you did last year. The purchasing power you previously had will be impacted if inflation changes. The cost of things increases by 2% if inflation does as well. An estimated $54,132 is the annual take-home pay for the average American worker. According to location, education level, and other criteria, salaries might vary widely. Along with net worth and assets, income is a crucial component of your total financial wellness. A reference base period's average hourly wage rate expressed in USD. It demonstrates how much merchandise and services one hour of labour can acquire. Real wage rate is calculated as follows: 100% x (current-year nominal wage rate / current-year CPI).To learn more about real average, refer to:
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A tumor is injected with 0.6
grams of Iodine-125, which has a decay rate of 1.15%
per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t
days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60
days.
Enter the exact answer.
Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c*exp(h)
or c*ln(h)
.
Answer:
The exponential model representing the amount of Iodine-125 remaining in the tumor after t days would be:
Iodine-125(t) = 0.6 * e^(-0.0115t)
To find the amount of Iodine-125 that would remain in the tumor after 60 days, we would plug in t = 60 into the model:
Iodine-125(60) = 0.6 * e^(-0.0115(60))
= 0.6 * e^(-0.69)
= 0.6 * 0.5032
= 0.3019
So after 60 days, there would be approximately 0.3019 grams of Iodine-125 remaining in the tumor.
If I helped you, could you please make my answer best?
HELP!!! You go out to dinner and the bill comes to $40.94. How much should you tip if you want the tip to be 15.0% of the bill? Express the dollar amount to the nearest cent
Answer: 6.14for the tip
Step-by-step explanation:
Answer:
$6.14
Step-by-step explanation:
Well, first step is to divide 15.0% by $40.94.
Then you get 6.141
Translate that to money, rounding off, you get:
$6.14!
I hope this helps! Great to be of service to you!
ara sells apples at a farmers market she begins the day with 35 1/2 pounds of apples she sells half of the apples in the mornning 4/19 of the apples in the afternoon and 1/4 of the apples in the evening how many pounds of apples dose she have left
Using mathematical operations, Ara's remaining pounds of apples are 1.405 pounds.
What are mathematical operations?The four basic mathematical operations are addition, subtraction, division, and multiplication.
In this situation, we applied the mathematical operations of multiplication, addition, and subtraction to determine the difference (or the quantity of apples left) between the quantity brought to the market and the quantity sold.
The total quantity of apples = 35¹/₂ pounds
The quantity sold in the morning = ¹/₂ of 35¹/₂ pounds = 17.75 pounds
The quantity sold in the afternoon = ⁴/₁₉ of 35¹/₂ pounds = 7.47 pounds
The quantity sold in the evening = ¹/₄ of 35¹/₂ pounds = 8.875 pounds
The total quantity sold = (¹/₂ + ⁴/₁₉ + ¹/₄) = ³⁶/₃₈ of 35¹/₂ pounds = 34.095 pounds
The remaining pounds of apples = 1.405 pounds (35.5 - 34.095)
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what is the angle between the given vector and the positive direction of the x-axis? (round your answer to the nearest degree. i + sqrt (15) j
The angle between the given vector and the positive direction of the x-axis is found by taking the inverse tangent of the vector components. The angle is equal to arctan(i/sqrt(15)) = 90°.
The angle between the given vector and the positive direction of the x-axis is found by taking the inverse tangent of the vector components. The angle is equal to arctan(i/sqrt(15)) = 90°.
90°
The angle between the given vector and the positive direction of the x-axis is found by taking the inverse tangent of the vector components. The angle is equal to arctan(i/sqrt(15)) = 90°.
The angle between the given vector with components i and sqrt(15) j and the positive direction of the x-axis is equal to arctan(i/sqrt(15)) = 90°. To calculate this angle, we take the inverse tangent of the components of the vector, which is equal to 90°. This angle is then rounded to the nearest degree, resulting in an angle of 90° between the two.
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Use the converse of the Pythagorean theorem to determine whether the triangle is
right, obtuse or acute.
9 m
15 m
10 m
The given triangle is obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The triangle's longest side measures 15 units in length.
Compare the sum of the squares on the other two sides to the square that is the length of the longest side.
The square of the longest side is 15², which equals 225.
9² + 10² = 181 square units make up the sum of the squares on the other two sides.
Thus, 181 < 15².
As a result, the triangle is an obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.
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Find the area of the circle, given the square has an area of [tex]144 cm^{2}[/tex]. Leave your answer in terms of π.
A) 24π [tex]cm^{2}[/tex]
B) 144π[tex]cm^{2}[/tex]
C) 36π[tex]cm^{2}[/tex]
The area of this inscribing circle is 36π cm².
What are the dimensions of a square?The area of a square is a product of it's any two sides or a product of diagonals divided by two. If side has a length a then diagonal is a√2.
The perimeter of a square is the sum of the lengths of all the sides.
We know area of a square is side².
Given, The area of this square is 144 cm².
We know 12×12 is 144.
Therefore, The length of the sides of this square is 12 cm.
We know a circle inscribed in a square has a diameter that is equal to the side of a square.
Therefore, The diameter of this circle is 12 and hence radius is 12/2 = 6 cm.
We also know that the area of a circle is πr².
Therefore, The area of this circle is π(6)² cm².
= 36π cm².
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find $53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} 1\frac{2}{3} \right)$. express your answer as a mixed number.
The result of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex] is[tex]$-56\frac{13}{20}$[/tex]
A mixed number is a combination of a whole number and a fraction, like [tex]3\frac{1}{2}[/tex], expressing numbers greater than one whole unit. It can be converted to an improper fraction.
To find the solution of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex]
We can first simplify the inner parenthesis
[tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right)=53\cdot(-1\frac{1}{10})=-53\frac{11}{10}$[/tex]
Then simplify the denominator, The denominator is the bottom part of a fraction, which represents the total number of parts in the whole. It is used to indicate the size of the fraction's unit or whole. It is also used to divide the numerator (top part of a fraction) by in order to determine the fraction's value.
[tex]$2\frac{3}{4} - 1\frac{2}{3} = \frac{11}{4} - \frac{5}{3} = \frac{44}{12} - \frac{20}{12} = \frac{24}{12} = 2$[/tex]
Now we can divide -53 and 11/10 by 2
[tex]$-53\frac{11}{10} \div 2 = -53\frac{11}{20} = -\frac{1133}{20} = -56\frac{13}{20}$[/tex]
So, the answer is [tex]$-56\frac{13}{20}$[/tex]
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Given the following probabilities for choosing 2 marbles from a bag of 10 marbles, determine if the events are dependent or independent.
P(blue) = 3/10 , P(green) = 1/5 , and P(blue and green) = 3/100
probabilities for choosing 2 marbles from a bag of 10 marbles is Dependent events
Given the following probabilities for choosing 2 marbles from a bag of 10 marbles are:-
P(blue) = 3/10, P(green) = 1/5, P(blue and green) = 3/100
We know the fact that two event are independents if we have following:-
P(X and Y) = P(X) times P(Y)
For this problem, we must have P(blue and green) = P(blue) times P(green).
P(blue and green) = (3/10) * (1/5) = 3/50
But given P(blue and green) = 3/100
Since we have 3/100 ≠ 3/50
Hence, the events are not independent events.
So, they are dependent events.
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There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple? (Give your answer as a fraction in simplest form.)
The probability that the next fruit out of the bag is an apple is P = 4/5
How to find the probability?We want to fnind the probability of randomly selecting an apple from the bag, where we assume that all the fruits have the same probability of being randomly selected.
Remember that the probability is equal as the quotient between the number of apples and the total number of fruit on the bag.
Originally, there are:
4 apples.3 peaches2 plums.The checkout person takes 2 plums and 1 peach, so now there are:
4 apples.1 peach.For a total of 4 + 1 = 5 fruits
Then the probability of randomly grabing an apple is:
P = 4/5
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NEED HELP ASAP Select from the drop-down menu to correctly complete the statement.
The product of 7 and 58 is
Choose...
because 58 is less than 1.
Drop downs: greater than 7
less than 7
equal to 7
The product of 7 and ⁵/₈ is less than 7 because ⁵/₈ is less than 1
How to find the product of fractions?We want to find the product of 7 and ⁵/₈.
Now, this will be expressed as;
7 * ⁵/₈.
Now, we are multiplying a whole number by a proper fraction that is less than 1 and as such, it means that the product will be lesser than 7 simply because ⁵/₈ is less than 1.
Thus;
7 * ⁵/₈ = 35/8
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Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
A. Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
B. Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
C. Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
D. Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The correct option regarding the probabilities for Sandy's is given as follows:
A. Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
How to obtain the probability?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
For the theoretical probability, the outcomes are considering without any experiment, while for an experimental probability the outcomes are taken from previous experiment.
This means that for a large number of trials, these probabilities should be very close, meaning that the correct option is given by option A.
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Its A...............
Step-by-step explanation:
The GDP in Canada is $1.65 trillion. The rate of
inflation is 2.5%. If the population of Canada is
36,732,000, find the per capita GDP in this country.
per capita GDP = $ [?]
Round to the nearest hundredth.
Enter
PH
The per capita GDP can be calculated by dividing the total GDP by the population.
How is this calculated?$1.65 trillion (GDP) / 36,732,000 (population) = $45,073.58 (per capita GDP)
This means that, on average, each person in Canada has a GDP of $45,073.58. However, it's important to note that this number doesn't necessarily reflect the distribution of wealth within the country. It's just a way of measuring the overall economic output of a country on a per person basis.
Additionally, it's worth noting that this number only takes into account the GDP and population at the time of the calculation. The inflation rate of 2.5% would increase the GDP but not the population so it's not considered in this calculation
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can you help me with my math today
Find the surface area of the soild.
The surface area of the square pyramid shown is 466.56 in²
What is an equation?An equation is an expression showing the relationship between numbers and variables.
The shape shown is a square pyramid with 5 surfaces. The surface area is the sum of each individual area surface. It is given as:
Surface area = base² + 4(1/2 * base * height)
base = 10.8 in, height = 16.2 in, hence:
Surface area = 10.8² + 4(1/2 * 10.8 * 16.2) = 466.56 in²
The surface area of the solid is 466.56 in²
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