What is the width of a rectangle with a length of
5/6 feet and an area of 2 square​ feet?

Answer:

Step-by-step explanation:

s + at = F

at = F - s

t = (F - s)/a

x/a + y/b = 1

x/a = 1 - y/b

a(x/a = 1 - y/b)

x = a - ay/b

Answer:

its b on edge 2022

Step-by-step explanation:

\(\sqrt{2^{4} } *\sqrt{5}\)

Answer:

Step-by-step explanation:

165 times

Answer:

4≤x same as x ≥ 4

Step-by-step explanation:

First you need to apply the distributive property.

That means 2 times -3 and positive 5

The inequality should look like this:

-6+10+2≥-4(x-2)-3

You should then do the same but on the other side keeping the -6+10+2 the same and undisturbed

Should look like this:

-6+10+2≥-4x+8-3

After, solve all of it

Should be simplified to this:
6 ≥ -4x+5

Now subtract 5 from both sides

6-5 ≥ -4x

1 ≥ -4x

Since we are dividing the inequality rule said that we shall flip the sign if dividing or multiplying by a negative number.  

So the answer should look like this:

x ≥ 4

Answer:

Step-by-step explanation:

1. Since we know that Lila wants to use 1 cup of pretzels, we can multiply 1/2 x 1/2, which is 1.

2. Now that we multiplied 1/2 by 1/2, we have to multiply 1 1/4 by 1/2.

So 5/4 x 1/2 is 5/8.

3. Lila will need 5/8 cups of raisins.

A sample statistic handles the parameter it is intended to estimate so when target population and indeed the sampled population are equal.

Data gathering, organization, analysis, interpretation, as well as presentation are all topics covered in the field of statistics. It is customary to start with a statistical population or perhaps a statistical model to be investigated when using statistics to solve a scientific, industrial, or social problem.

To sum up, the five reasons to studying statistics are to be able to do research efficiently, to read and assess journal articles, to even further develop critical thinking and analytical skills, to behave as an informed consumer, and to be aware of when you need to seek outside statistical support.

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Answer:

32 = 2^5 and 16=2^4.......

Answer:

Formula 1 Racing

Step-by-step explanation:

The length of the arc intercepted by a central angle of π/6 radians in a circle with a radius of 16 inches is approximately 8.4 inches.

To find the length s of the arc intercepted by a central angle of π/6 radians in a circle with a radius of 16 inches, we can use the formula for the length of an arc:

where s is the arc length, r is the radius of the circle, and θ is the central angle in radians.

Plugging in the values, we have:

Now, we can calculate the length of the arc:

Rounding to the nearest tenth, the length of the arc intercepted by a central angle of π/6 radians in a circle with a radius of 16 inches is approximately 8.4 inches.

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Answer:

C 61,705

Step-by-step explanation:

10.9% of 35,000 = 3,815

3,815 x 7 = 26,705  (interest is added per year and 3,815 is the interest amount)

35,000 + 26,705 = 61,705 ( the original loan plus the interest for 7 years)

Answer:

(66.3-14.62)/0.6-0.22

(51.68)/0.6-0.22

(51.68/0.6)-0.22

(86.14667)-0.22

85.92667

Answer:

The answer is A actually. D is wrong

Step-by-step explanation:

Answer: its A got it right

Step-by-step explanation:

Since the rectangle's shorter side is half as long as its longer side, its top left vertex is (0,a).

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To find the y-coordinate, repeat the previous step while adhering to a horizontal line.

Here,

Let x be the length and y be the width,

y=x/2

x=2a

y=a

The top left vertex=(0,a)

The top left vertex is (0,a) as shorter side of the rectangle is half the length of the longer side.

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The closest integers to 44 are 43 and 45.

To complete the statement using the integers closest to the number in the middle, we need to determine the middle number in a sequence or set of numbers. However, the given prompt only provides the number "44" without any context or additional information.

If we assume that the number "44" is part of a sequence or set, we would need more information to determine the middle number and complete the statement accurately.

Without additional context or information, it is not possible to provide a specific answer or complete the statement. Please provide more details or clarify the question to assist further.

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(A) The total population of deer after 4 years is approximately 153,000.

(B) 64,000 deer would be present after 5 years.

(a) The total population of deer after 4 years can be predicted using the given model as T = 70,000(1+0.7)^4. Solving this equation, we get T ≈ 153,33. Therefore, the total population of deer after 4 years is approximately 153,000.

(b) If the initial population of deer is 30,000 and the growth rate is 0.11, then the total population of deer after 5 years can be calculated as T = 30,000(1+0.11)^5. Solving this equation, we get T ≈ 63,531. Therefore, approximately 64,000 deer would be present after 5 years.

Exponential growth is a mathematical concept that describes how a quantity increases exponentially over time. In this case, the deer population is growing exponentially with a given rate of growth. The equation T = 70,000(1+0.7)^4 is used to calculate the total population of deer after 4 years. Similarly, the equation T = 30,000(1+0.11)^5 is used to calculate the total population of deer after 5 years, given the initial population and growth rate. The solutions to these equations are approximations rounded to the nearest thousand, and they provide estimates of the expected deer population in the future.

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From the angle of elevation in trigonometry, the distance that the snake need to launch in order to catch the frog is equals to the 1.078 feet.

We have a snake which looks to catch the frog. Angle of elevation when sanke look the frog on a log = 28°

Distance between sanke and bottom of log = 2 feet

We have to determine the distance that snake need to launch in order to catch the frog. If we consider scenario on drawing, it form a right angled triangle with one angle 28° and Adjective side = 2 feet. To calculate the opposite side, using tangent trigonometry ratio,

\(tan(\theta) = \frac{opposite \: side}{adjacent \: side} \)

Substitute all known values in above formula,

\(tan(28°) = \frac{opposite \ side}{2} \)

=> opposite side = 2 feet × tan(28°)

=> opposite side = 2 × 0.5317094 = 1.078 feet

Hence, required value is 1.078 feet.

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Given ƒ : [0, 1] → R is integrable and f(x) ≥ 0 for all x = [0, 1].

Also suppose f f(x) dx = 0.Prove that there is at least one value x € [0, 1] with ƒ(x) = 0.a) Given any values a, b with 0 ≤ a < b ≤ 1, and given any ɛ > 0, there exist a', b' with 0 ≤ a ≤ a' < b′ ≤ b ≤ 1 such that supæ¤[a'‚b'] ƒ(x) ≤ ɛ.Proof:Let I be the closed interval I = [a, b]. Since ƒ(x) ≥ 0 for all x in [0,1], we have ∫[a,b] ƒ(x) dx ≥ 0.The lower bound of the interval implies the existence of a non-negative number M such that ƒ(x) ≤ M for all x in I. Hence,∫[a,b] ƒ(x) dx ≤ M ∫[a,b] dx = M(b-a)Thus, for every interval I, we have∫I ƒ(x) dx ≤ M|I|Here, |I| denotes the length of the interval I. Also, we know that f is integrable on [0,1] and given ɛ > 0, there exists a partition P of [0,1] such thatU(ƒ, P) - L(ƒ, P) < ɛHere, U(ƒ, P) and L(ƒ, P) denote the upper and lower Riemann sums, respectively, corresponding to the partition P.Let a, b be given such that 0 ≤ a < b ≤ 1. Let I = [a, b]. Then I can be written as a union of two subintervals J, K where J = [a, (a + b)/2], K = [(a + b)/2, b]. By the above inequality, we have∫J ƒ(x) dx ≤ M|J|, ∫K ƒ(x) dx ≤ M|K|Adding both the equations and applying the triangle inequality, we get ∫I ƒ(x) dx ≤ M|J| + M|K|Hence, U(ƒ, P|I) - L(ƒ, P|I) ≤ M|J| + M|K|Here, P|I denotes the partition of I corresponding to the partition P. We haveU(ƒ, P|I) - L(ƒ, P|I) ≤ M|J| + M|K| < M(b - a) = M|I|We know that f is integrable on [0,1], which means that for every positive ε, there is a partition Pε of [0,1] such that U(ƒ, Pε) - L(ƒ, Pε) < εGiven ε > 0, we can apply this result to each of the two subintervals J and K. This gives us partitions PJ and PK of J and K respectively, such thatU(ƒ, PJ) - L(ƒ, PJ) < ε/2, U(ƒ, PK) - L(ƒ, PK) < ε/2Define a' = min{pj : j ∈ PJ} and b' = max{pk : k ∈ PK}It follows that 0 ≤ a ≤ a' < b' ≤ b ≤ 1 and supæ¤[a'‚b'] ƒ(x) ≤ U(ƒ, PJ) + U(ƒ, PK) - L(ƒ, PJ) - L(ƒ, PK) < εHence, given any values a, b with 0 ≤ a < b ≤ 1, and given any ɛ > 0, there exist a', b' with 0 ≤ a ≤ a' < b′ ≤ b ≤ 1 such that supæ¤[a'‚b'] ƒ(x) ≤ ɛ.b) We will now show that there is at least one value x € [0, 1] with ƒ(x) = 0. To do this, we will apply part (a) iteratively with ε = 1/n for every positive integer n, to obtain nested intervals [a1, b1] ⊆ [a2, b2] ⊆ [a3, b3] ⊆ … with sup_{[an,bn]} ƒ(x) ≤ 1/n for each n.Let I1 = [0, 1]. Since ƒ(x) ≥ 0 for all x in [0, 1], we have∫[0,1] ƒ(x) dx ≥ 0The lower bound of the interval implies the existence of a non-negative number M1 such that ƒ(x) ≤ M1 for all x in I1. Let ε = 1. By part (a), there exist a1, b1 with 0 ≤ a1 < b1 ≤ 1 such that sup_{[a1,b1]} ƒ(x) ≤ 1. Let I2 = [a1, b1]. Since ƒ(x) ≥ 0 for all x in [0, 1], we have∫[a1,b1] ƒ(x) dx ≥ 0The lower bound of the interval implies the existence of a non-negative number M2 such that ƒ(x) ≤ M2 for all x in I2. Let ε = 1/2. By part (a), there exist a2, b2 with a1 ≤ a2 < b2 ≤ b1 such that sup_{[a2,b2]} ƒ(x) ≤ 1/2. Let I3 = [a2, b2]. Since ƒ(x) ≥ 0 for all x in [0, 1], we have∫[a2,b2] ƒ(x) dx ≥ 0The lower bound of the interval implies the existence of a non-negative number M3 such that ƒ(x) ≤ M3 for all x in I3. Let ε = 1/3. By part (a), there exist a3, b3 with a2 ≤ a3 < b3 ≤ b2 such that sup_{[a3,b3]} ƒ(x) ≤ 1/3. Let I4 = [a3, b3]. Since ƒ(x) ≥ 0 for all x in [0, 1], we have∫[a3,b3] ƒ(x) dx ≥ 0The lower bound of the interval implies the existence of a non-negative number M4 such that ƒ(x) ≤ M4 for all x in I4. Let ε = 1/4. By part (a), there exist a4, b4 with a3 ≤ a4 < b4 ≤ b3 such that sup_{[a4,b4]} ƒ(x) ≤ 1/4. Let I5 = [a4, b4]. Since ƒ(x) ≥ 0 for all x in [0, 1], we have∫[a4,b4] ƒ(x) dx ≥ 0The lower bound of the interval implies the existence of a non-negative number M5 such that ƒ(x) ≤ M5 for all x in I5. Continue this process to obtain a nested sequence of intervals I1 ⊆ I2 ⊆ I3 ⊆ …, where In = [an, bn] and sup_{In} ƒ(x) ≤ 1/n for each n.Since ƒ(x) ≥ 0 for all x in [0, 1], we have∫[0,1] ƒ(x) dx ≥ ∫In ƒ(x) dxSince ƒ(x) is integrable on [0,1], we have∫[0,1] ƒ(x) dx = 0It follows that∫In ƒ(x) dx ≤ ∫[0,1] ƒ(x) dx = 0for each n.Since ƒ(x) ≥ 0 for all x in [0, 1], we have 0 ≤ ∫In ƒ(x) dx ≤ 1/nfor each n.Since ∫In ƒ(x) dx ≤ 1/n for each n, we have ƒ(x) = 0 for each x in the intersection of the intervals In. Since the intervals In are nested and have non-zero length, the intersection of the intervals In is non-empty. Therefore, there is at least one value x € [0, 1] with ƒ(x) = 0.

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This contradicts the fact that ∫0¹ ƒ(x) dx = 0, since for any n we have ∫an b n ƒ(x) dx ≥ supä[an, b n] ƒ(x) × (b n - an) ≥ (1/n) × (b n - an), and hence ∫0¹ ƒ(x) dx = limn→∞ ∫anbn ƒ(x) dx ≥ limn→∞ (1/n) × (b n - an) > 0, which is a contradiction. Therefore, there must exist at least one value x € [0, 1] with ƒ(x) = 0.

(a) To show that there exist a', b' such that supæ¤[a', b'] ƒ(x) ≤ ɛ, we use proof by contradiction, which implies that there is no such a', b'. That is to say, for any a', b', sup æ¤[a', b'] ƒ(x) > ɛ.

We first pick any arbitrary ɛ > 0 and let a0 = a and b0 = b. Then divide the interval [a0, b0] into two subintervals [a1, (a0 + b0)/2] and [(a0 + b0)/2, b1] such that the supremum of ƒ(x) on the first subinterval is greater than ɛ/2, and the supremum of ƒ(x) on the second subinterval is greater than ɛ/2. Let (a2, b2) be the subinterval that has a larger supremum than the other. Repeating this process, we construct the nested sequence of intervals in this way: [a0, b0] → [a1, b1] → [a2, b2] → ... Let (an) and (b n) be the corresponding sequences of endpoints.

That is, an ≤ an+1 < bn+1 ≤ bn. Then we have supä[an, bn] ƒ(x) > ɛ for all n. This contradicts the fact that ƒ is integrable, and hence there exists a', b' such that supæ¤[a', b'] ƒ(x) ≤ ɛ. (b) Suppose for the sake of contradiction that ƒ(x) > 0 for all x. By part (a), we can find a sequence of nested intervals [a1, b1] ⊇ [a2, b2] ⊇ [a3, b3] ⊇ ... such that supæ¤[an, bn] ƒ(x) ≤ 1/n for all n. Since ƒ(x) > 0 for all x, we have limn→∞ supä[an, bn] ƒ(x) = 0 by the squeeze theorem.

However, this contradicts the fact that ∫0¹ ƒ(x) dx = 0, since for any n we have ∫an b n ƒ(x) dx ≥ supä[an, b n] ƒ(x) × (b n - an) ≥ (1/n) × (b n - an), and hence ∫0¹ ƒ(x) dx = limn→∞ ∫an b n ƒ(x) dx ≥ limn→∞ (1/n) × (b n - an) > 0, which is a contradiction. Therefore, there must exist at least one value x € [0, 1] with ƒ(x) = 0.

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Answer:

Step-by-step explanation:

To convert 20 cm to meters, we divide by 100, because 1 meter = 100 centimeters.

So, 20 cm = 20/100 m = 0.2 m

To convert 0.2 m to meters in the lowest form, we divide by 15, because 1 meter = 15 units.

So, 0.2 m = 0.2/15 m = 0.013 m

So the final answer is 0.013 m.

Answer: \(84\)

Step-by-step explanation:

Using the formula for the area of a trapezoid, the area is \(A=\frac{1}{2}(7)(10+14)=84\)

Answer:

x = 15

Step-by-step explanation:

10x - 30 and 3x + 15 are same- side interior angles and sum to 180° , so

10x - 30 + 3x + 15 = 180 , that is

13x - 15 = 180 ( add 15 to both sides )

13x = 195 ( divide both sides by 13 )

x = 15

Step-by-step explanation:

The partial derivatives ∂T/∂U and ∂U/∂T are approximately -7.548 and -6.416 respectively.

To calculate the partial derivatives ∂T/∂U and ∂U/∂T using implicit differentiation of the equation (TU−V)² ln(W−UV) = ln(13), we'll differentiate both sides of the equation with respect to T and U separately.

First, let's find ∂T/∂U:

Differentiating both sides of the equation with respect to U:

(2(TU - V)ln(W - UV)) * (T * dU/dU) + (TU - V)² * (1/(W - UV)) * (-U) = 0

Since dU/dU equals 1, we can simplify:

2(TU - V)ln(W - UV) + (TU - V)² * (-U) / (W - UV) = 0

Now, substituting the values T = 3, U = 4, V = 13, and W = 65 into the equation:

2(3 * 4 - 13)ln(65 - 3 * 4) + (3 * 4 - 13)² * (-4) / (65 - 3 * 4) = 0

Simplifying further:

2(-1)ln(53) + (-5)² * (-4) / 53 = 0

-2ln(53) + 20 / 53 = 0

To express this fraction in symbolic notation, we can write:

∂T/∂U = (20 - 106ln(53)) / 53

Substituting ln(53) = 3.9703 into the equation, we get:

∂T/∂U = (20 - 106 * 3.9703) / 53

= (20 - 420.228) / 53

= -400.228 / 53

≈ -7.548

Now, let's find ∂U/∂T:

Differentiating both sides of the equation with respect to T:

(2(TU - V)ln(W - UV)) * (dT/dT) + (TU - V)² * (1/(W - UV)) * U = 0

Again, since dT/dT equals 1, we can simplify:

2(TU - V)ln(W - UV) + (TU - V)² * U / (W - UV) = 0

Substituting the values T = 3, U = 4, V = 13, and W = 65:

2(3 * 4 - 13)ln(65 - 3 * 4) + (3 * 4 - 13)² * 4 / (65 - 3 * 4) = 0

Simplifying further:

2(-1)ln(53) + (-5)² * 4 / 53 = 0

-2ln(53) + 80 / 53 = 0

To express this fraction in symbolic notation:

∂U/∂T = (80 - 106ln(53)) / 53

Substituting ln(53) = 3.9703 into the equation, we get:

∂U/∂T = (80 - 106 * 3.9703) / 53

= (80 - 420.228) / 53

= -340.228 / 53

≈ -6.416

Therefore, the partial derivatives are:

∂T/∂U = -7.548

∂U/∂T = -6.416

Therefore, the values of ∂T/∂U and ∂U/∂T are approximately -7.548 and -6.416, respectively.

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Calculate The Partial Derivatives ∂T/∂U And ∂U/∂T Using Implicit Differentiation Of (TU−V)² ln(W−UV) = Ln(13) at (T,U,V,W)=(3,4,13,65).

(Use symbolic notation and fractions where needed.) ∂/∂T= ∂T/∂=

Answer:

what

Step-by-step explanation:

which questions you are telling there is no question to answer you!!

65% of the club members voted for Aldo as President.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

It is expressed by:

Percentage = (value / total value) * 100%

where;

value = 13

total value = 20

Percentage = (13 / 20) * 100%

Percentage = 65%

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Note that where the above conditions exists with regard to the geometric ratios, the sum of the antecedents is approximately 445.31.

Let the three continuous geometric ratios be a, ar, and ar^2, where a is the first term and r is the common ratio. Then the equality can be written as:

a/ar + ar/ar² + ar² = 3/4

Simplifying this equation, we get:

1/r + r + r² = 3/4

Multiplying both sides by 4r², we get:

4r + 4r³ + 4r⁴ = 3r²

Rearranging, we get:

4r⁴ + 3r² - 4r = 0

We can factor this equation as:

r(4r³ - 4r² + 3) = 0

Since r cannot be zero, we must solve the cubic equation:

4r³ - 4r² + 3 = 0

Using a numerical method or a computer program, we can find that one real root of this equation is approximately 0.8202.

Now that we know the value of r, we can use the difference between the largest and minor consequent to find the value of a. The largest consequent is ar², and the minor consequent is a, so we have:

ar² - a = 120

Substituting r = 0.8202, we get:

a(0.8202)² - a = 120

Simplifying, we get:

a = 120 / (0.6721)

a ≈ 178.63

Finally, we can calculate the sum of the antecedents:

a + ar + ar² = 178.63 + (178.63)(0.8202) + (178.63)(0.8202)²

Summing these terms, we get:

a + ar + ar² ≈ 445.31

Therefore, the sum of the antecedents is approximately 445.31

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Translation:

If the sum of the ratios of an equality of 3 continuous geometric ratios is 3/4, calculate the sum of antecedents. Consider that the difference between the largest and minor consequent is 120

Answer: 3g - 5 = 19 ; 8 pounds

Step-by-step explanation:

Given that :

Difference between weight of 3 gallons of a liquid and a brick that weighs 5 pounds = 19 pounds.

Mathematically,

Let one gallon of the liquid = g

Hence,

(3 × g) - 5pounds = 19 pounds

3g - 5 = 19

The weight of one gallon(g) of the liquid equals :

From the expression above :

3g - 5 = 19

3g = 19 + 5

3g = 24

Divide both sides by 3

3g/3 = 24 /3

g = 8 pounds

Hence, weight of 1 gallon of the liquid is 8 pounds.

(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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All the area measure units should have square above them.

Hence, option A, C, D is correct.

Answer:

a) c) d)

Step-by-step explanation:

Length is a one-dimensional measure, therefore it is measured in single units.

⇒ m

⇒ cm

⇒ ft

The area of a shape is a two-dimensional quantity (e.g. length × width), therefore it is measured in square units.

⇒ m × m = m²

⇒ cm × cm = cm²

⇒ ft × ft = ft²

The volume of a shape is a three-dimensional quantity (e.g. length × width × height), therefore it is measured in cubic units.

⇒ m × m × m = m³

⇒ cm × cm × cm = cm³

⇒ ft × ft × ft = ft³

Therefore,

For the given dimension the volume of the metal piece will be 3680 mm³.

In terms of geometry, it is known as the six-faced hexahedron. Three dimensions make up its form.

It is given that, this diagram shows the dimensions of a metal piece used in a machine.

We have to calculate the volume of the metal piece.

A cuboid's volume is calculated by multiplying its three dimensions (width, length, and height) together.

The volume of the horizontal cuboid:

V =  l × b × h

V= 30 ×8 × 8

V= 1920 mm³

The volume of the vertical cuboid:

breadth = 10 mm

Length = 14+8 = 22 mm

Height = 8 mm

V =  l × b × h

V = 22 × 10 × 8

V=  1760 mm³

The volume of the metal piece is obtained as,

= 1920 + 1760

= 3680 mm³

Volume of metal piece  = 3680 mm³

Thus, the volume of the metal piece will be 3680 mm³.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

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