The given function is f(x) = -0.82x² + 17x + 0.273. The area bounded by the function f(x) = -0.82x² + 17x + 0.273, the z-axis, and the lines x = 2 and x = 8 is given by:∫[2, 8] [-0.82x² + 17x + 0.273] dx= [-0.82 * (x³/3)] + [17 * (x²/2)] + [0.273 * x] |[2, 8]= -0.82 * (8³/3) + 17 * (8²/2) + 0.273 * 8- [-0.82 * (2³/3) + 17 * (2²/2) + 0.273 * 2]= -175.4132 + 507.728 + 2.184 - [-3.4717 + 34 + 0.546]= 357.4712.
Thus, the area bounded by the function f(x) = -0.82x² + 17x + 0.273, the z-axis, and the lines x = 2 and x = 8 is 357.4712 square units (rounded to 2 decimal places).
Therefore, the area is 357.47 square units (rounded to 2 decimal places).
Answer: 357.47 square units.
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Suppose that, in an alternate universe, the possible values of m
l
are the integer values including 0 ranging from −l−1 to l+1 (instead of simply −l to +l ). How many orbitals would exist in each of the following subshells? A. p subshell B. d subshell Which atomic orbitals have values of n=3 and I=1 ?
A. In the alternate universe, the p subshell would have 5 orbitals.
B. In the alternate universe, the d subshell would have 10 orbitals.
In the alternate universe where the possible values of mℓ range from -l-1 to l+1, the number of orbitals in each subshell can be determined.
A. For the p subshell, the value of l is 1. Therefore, the range of mℓ would be -1, 0, and 1. Including the additional values of -2 and 2 from the alternate universe, the total number of orbitals in the p subshell would be 5 (mℓ = -2, -1, 0, 1, 2).
B. For the d subshell, the value of l is 2. In the conventional universe, the range of mℓ would be -2, -1, 0, 1, and 2, resulting in 5 orbitals. However, in the alternate universe, the range would extend to -3 and 3. Including these additional values, the total number of orbitals in the d subshell would be 10 (mℓ = -3, -2, -1, 0, 1, 2, 3).
Therefore, in the alternate universe, the p subshell would have 5 orbitals, and the d subshell would have 10 orbitals.
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13
25
Which expression represents the volume, in cubic units,
of the composite figure?
n(5)(13) — —n (5³-)(12)
π(5²)(13) — π (5²)(25)
π(5²)(13) +- π7 (5²)(12)
π(5²) (13) + ¹7 (5²) (25)
The expression that represents the volume of the composite figure is \(\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)\). The correct option is the third option \(\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)\)
Calculating VolumeFrom the question, we are to determine the expression that represents the volume of the composite figure
The composite figure consist of a cylinder and a cone
∴ Volume of the composite figure = Volume of the cylinder + Volume of the cone
Volume of a cylinder = \(\pi r^{2} h\)
Where r is the radius
and h is the height of the cylinder
Volume of a cone = \(\frac{1}{3} \pi r^{2} h\)
Where r is the radius
and h is the height of the cone
Consider the composite figure
For the cylinder part
r = 5
h = 13
For the cone part
r = 5
h = 25 - 13 = 12
Thus,
Volume of the composite figure = \(\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)\)
Hence, the expression that represents the volume of the composite figure is \(\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)\). The correct option is the third option \(\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)\)
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The width of a rectangle is 38 centimeters. The perimeter is at least 692 centimeters. Write an inequality that represents all possible values for the length of the rectangle. Then solve the inequality.
Answer:
See bolded / underlined / italicized below -
Step-by-step explanation:
This is a great question!
If x were the length of this rectangle, then we could conclude the following,
2( 38 ) + 2( x ) > 692,
As you can see there is a greater than sign present, as the perimeter is at least 692 centimeters. In this case the perimeter is given to be at least 692 centimeters, but can also be calculated through double the width and double the length together. And of course we are given the width to be 38 cm -
2( 38 ) + 2x > 692,
76 + 2x > 692,
2x > 616,
x > 308
Solution = Length should be at least 308 cm
( The attachment below is not drawn to scale )
find the area of a non shaded area
Line A’B’ is the translated image of line AB. Which could be the coordinates of A’ and B’?
To determine the specific coordinates of A' and B' after the translation, we would need the translation vector information or more details about the direction and magnitude of the translation.
To determine the coordinates of A' and B' after translating line AB, we need to know the translation vector or the direction and magnitude of the translation. Without that information, we cannot provide specific coordinates for A' and B'.
However, I can explain how a translation works and how you can find the coordinates of A' and B' given a translation vector.
A translation involves shifting an object or a line by a certain distance in a specific direction. The translation vector represents this direction and magnitude.
If we have a translation vector (dx, dy), the coordinates of A' and B' can be found by adding the translation vector to the coordinates of A and B, respectively.
A' = (Ax + dx, Ay + dy)
B' = (Bx + dx, By + dy)
Here, (Ax, Ay) and (Bx, By) represent the coordinates of points A and B, respectively.
So, to determine the specific coordinates of A' and B' after the translation, we would need the translation vector information or more details about the direction and magnitude of the translation.
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Find the slope of the line through P and Q. P(0, 0), Q(10, 2) Find the slope of the line through P and Q. P(3, -3), Q(-1, 6)
Slope of the line through P1 and Q1 is 1/5.Slope of the line through P2 and Q2 is -9/4.
Given:P1(0, 0), Q1(10, 2)P2(3, -3), Q2(-1, 6)
To find: Slope of the line through P and Q.
To find the slope of the line through two points P(x1,y1) and Q(x2,y2) we use the formula:
Slope = (y2 - y1) / (x2 - x1)
Using the formula:
Slope of line through P1 and Q1
Slope = (y2 - y1) / (x2 - x1) = (2 - 0) / (10 - 0) = 2 / 10 = 1 / 5
Slope of line through P2 and Q2
Slope = (y2 - y1) / (x2 - x1) = (6 - (-3)) / (-1 - 3) = 9 / (-4)
Thus. slope of the line through P1 and Q1 is 1/5.Slope of the line through P2 and Q2 is -9/4.
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Use the properties of radicals to simplify the expression. Explain
Answer: you didn’t even say please
explanation: why don’t you ask your mother you make me sad
- m/3 = -4
find the answer for m with work provided
Answer:
m = 12
Step-by-step explanation:
\(-\frac{m}{3} =-4\\\)
→ Multiply both sides by 3
\({-m} =-12\\\)
→ Multiply both sides by -1
m = 12
A dump truck bar 1/3 of a ton of rocks on the 1st beat trip when half of a ton on the 2nd trip and forfeits of a tone on the 3rd trip what was the total way of the rock.
Answer: 1/30
Step-by-step explanation:
Here's the correct question:
A dump truck brought 1⁄3 of a ton of rock on the first trip, 1⁄2 of a ton on the second trip, but on the third trip, had to take back 4⁄5 of a ton. What was the total weight of the rock left at the construction site?
To calculate the the total weight of the rock left at the construction site goes thus:
= 1/3 + 1/2 - 4/5
The lowest common multiple of 3,2 and 5 is 30. Therefore, we'll make the fractions have a common denominator.
= 1/3 + 1/2 - 4/5
= 10/30 + 15/30 - 24/30.
= 1/30
A band expects to put 15 songs on their next CD. The band writes and records 60% more songs than they expect to put on the CD. During the editing process, 75% of the songs are removed. How many songs will there be on the final CD?
Answer: 6
Step-by-step explanation:
From the question, we are informed that a band expects to put 15 songs on their next CD and that the band writes and records 60% more songs than they expect to put on the CD. Therefore, the total songs will be:
= 15 + (60% × 15)
= 15 + (0.6 × 15)
= 15 + 9
= 24 songs.
During the editing process, 75% of the songs are removed. The total number of songs that will be there on the final CD will be:
= 24 - (75% × 24)
= 24 - (0.75 × 24)
= 24 - 18
= 6
6 songs will be there on the final CD.
Answer:
21
Step-by-step explanation:
You fottt
This math my graduation depends on it
In an arithmetic sequence, consecutive terms have a fixed distance d between them. If a₁ is the first term, then
2nd term = a₂ = a₁ + d
3rd term = a₃ = a₂ + d = a₁ + 2d
4th term = a₄ = a₃ + d = a₁ + 3d
and so on, up to
nth term = \(a_n = a_{n-1} + d = a_{n-2} + 2d = a_{n-3} + 3d = \cdots = a_1 + (n-1)d\)
so that every term in the sequence can be expressed in terms of a₁ and d.
6. It's kind of hard to tell, but it looks like you're given a₁₃ = -53 and a₃₅ = -163.
We have
a₁₃ = a₁ + 12d = -53
a₃₅ = a₁ + 34d = -163
Solve for a₁ and d. Eliminating a₁ and solving for d gives
(a₁ + 12d) - (a₁ + 34d) = -53 - (-163)
-22d = 110
d = -5
and solving for a₁, we get
a₁ + 12•(-5) = -53
a₁ - 60 = -53
a₁ = 7
Then the nth term is recursively given by
\(a_n = a_{n-1}-5\)
and explicitly by
\(a_n = 7 + (n-1)(-5) = 12 - 5n\)
7. We do the same thing here. Use the known terms to find a₁ and d :
a₁₉ = a₁ + 18d = 15
a₃₈ = a₁ + 37d = 72
⇒ (a₁ + 18d) - (a₁ + 37d) = 15 - 72
⇒ -19d = -57
⇒ d = 3
⇒ a₁ + 18•3 = 15
⇒ a₁ = -39
Then the nth term is recursively obtained by
\(a_n = a_{n-1}+3\)
and explicitly by
\(a_n = -39 + (n-1)\cdot3 = 3n-42\)
8. I won't both reproducing the info I included in my answer to your other question about geometric sequences.
We're given that the 1st term is 3 and the 2nd term is 12, so the ratio is r = 12/3 = 4.
Then the next three terms in the sequence are
192 • 4 = 768
768 • 4 = 3072
3072 • 4 = 12,288
The recursive rule with a₁ = 3 and r = 4 is
\(a_n = 4a_{n-1}\)
and the explicit rule would be
\(a_n = 3\cdot4^{n-1}\)
If you divided 58 objects into sets of 10, how many sets of 10 could you make, and how many are left over?
Answer:
5 SETS OF 10 WE CAN MAKE, 8 OBJECTS WILL LEFT.
Step-by-step explanation:
Answer:
We can Make 5 sets of 10 and have 8 left over :)
Step-by-step explanation:
we have 58 objects and we make them into sets of 10
1 set=10
1 set 2 set 3 set 4 set 5 set | 1 one 2 one 3 one 4 one 5 one 6 one 7 () () () () () | one 8 one
can i get brainliest
please help asap I need help I am being timed
Stereo Inc. sells a stereo system for $400 down and monthly payments of $90 for the next 4 years. If the interest rate is 2.75% per month, find:
a) The cost of the stereo.
Answer = $
b) The total amount of interest paid.
Answer = $
a) The cost of the stereo system is $4,760.
b) The total amount of interest paid is $1,760.
To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.
To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.
In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.
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The standard or typical average difference between the mean number of seats in the 559 full-service restaurants in delaware (µ = 99.2) and one randomly selected full-service restaurant in delaware is:
The standard deviation of the sampling distribution of the sample mean would be approximately 2.8284
To determine the standard deviation of the sampling distribution of the sample mean, we will use the formula;
σ_mean = σ / √n
where σ is the standard deviation of the population that is 20 and n is the sample size (n = 50).
So,
σ_mean = 20 / √50 = 20 / 7.07
σ_mean = 2.8284
The standard deviation of the sampling distribution of the sample mean is approximately 2.8284 it refers to that the sample mean would typically deviate from the population mean by about 2.8284, assuming that the sample is selected randomly from the population.
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The complete question is;
Another application of the sampling distribution of the sample mean Suppose that, out of a total of 559 full-service restaurants in Delaware, the number of seats per restaurant is normally distributed with mean mu = 99.2 and standard deviation sigma = 20. The Delaware tourism board selects a simple random sample of 50 full-service restaurants located within the state and determines the mean number of seats per restaurant for the sample. The standard deviation of the sampling distribution of the sample mean is Use the tool below to answer the question that follows. There is a.25 probability that the sample mean is less than
If a+b+c = 9 and ab+bc+ca = 40, find a^2 + b^2 + c^2
Explanation
By definition.
\(\begin{gathered} (a+b+c)^2=a^2+b^2+c^2+2((ab)+(bc)+(ac)) \\ \end{gathered}\)so
Let
\(\begin{gathered} (a+b+c)=9 \\ ab+bc+ac=40 \\ \text{now, replace} \end{gathered}\)\(\begin{gathered} (a+b+c)^2=a^2+b^2+c^2+2((ab)+(bc)+(ac)) \\ 9^2=a^2+b^2+c^2+2(40) \\ 81=a^2+b^2+c^2+80 \\ \text{subtract 80 in both sides} \\ 81-80=a^2+b^2+c^2+80-80 \\ 1=a^2+b^2+c^2 \end{gathered}\)hence
\(a^2+b^2+c^2=1\)I hope this helps you
If p = 20 and q = 30, evaluate the following expression:
p+q/5
Answer:
10
Step-by-step explanation:
20+30/5
=10
Which equation matches the graph? A. y-2=3(x-2) B. y-2=3(x+2) C. y+2=-3(x+2) d. y-2=-3(x-2)
Answer:
There's no graph
Step-by-step explanation:
according to the u.s. census bureau, 19.1% of u.s. households are in the norheast. in addition 4.4% of u.s households earn $75,000/year or more and are located in the northeast. determine the probability that a randomly selected u.s. household earns more than $75,000/year, given that the household is located in the northeast.
Given that the household is located in the northeast, there is a 0.230 probability that the randomly chosen US household makes more than $75,000.
Given info;
19.1% of US households, according to the US Census Bureau, are in the Northeast. Additionally, 4.4% of households in the US earn $75,000 or more annually and are situated in the northeast.
let, A represents the U.S. households in the Northeast.
B represents the U.S. households earning $75,000 or more.
To determine the probability that a randomly selected US household earns more than $75,000/year, given that the household is located in the northeast.
P(A) = 19.1% = 0.191
P(A ∩ B) = 4.4% = 0.044
P(B I A) = P(A ∩ B) / P(A)
= 0.044 / 0.191
= 0.230
Hence, the probability that a randomly selected US household earns more than $75,000/year, given that the household is located in the northeast is 0.230.
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Evaluate ∫ (x - y z - 2) ds where c is the straight-line segment x = t, y = (1 - t), z = 1, from (0, 1, 1) to (1, 0, 1).
The evaluated integral ∫(x - yz - 2) ds is equal to √(2) * [t²/2 - 3t] + C, where C is the constant of integration.
Let's denote the parametric equations for the line segment as follows: x = x(t) y = y(t) z = z(t)
Since we are given the points (0, 1, 1) and (1, 0, 1) as the endpoints of the line segment, we can determine the equations for x(t), y(t), and z(t) by interpolating between these two points.
For the x-coordinate, we observe that it varies linearly from 0 to 1 as t ranges from 0 to 1. Therefore, we can set: x(t) = t
For the y-coordinate, it decreases linearly from 1 to 0 as t increases from 0 to 1. Hence, we have: y(t) = 1 - t
The z-coordinate remains constant at 1 throughout the line segment, so we can set: z(t) = 1
The arc length ds can be calculated using the formula:
ds = √(dx/dt² + dy/dt² + dz/dt²) dt
To find dx/dt, dy/dt, and dz/dt, we differentiate the parametric equations x(t), y(t), and z(t) with respect to t, respectively.
dx/dt = 1 dy/dt = -1 dz/dt = 0
Now we substitute these derivatives into the arc length formula to get: ds = √(1² + (-1)² + 0²) dt ds = √(2) dt
Finally, we can rewrite the integral in terms of t and substitute the expression for ds: ∫(x - yz - 2) ds = ∫(t - (1 - t) * 1 - 2) √(2) dt = ∫(t - 1 + t - 2) √(2) dt = ∫(2t - 3) √(2) dt
To evaluate this integral, we can integrate term by term:
= √(2) * [t²/2 - 3t] + C
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PLS HELP!! NO LINKS!! WILL MARK YOU BRAINLIEST!!
Answer:
(d) -11
Step-by-step explanation:
The sum of the acute angles of a right triangle is 90°. (That makes the sum of all angles be 180°, as it is for any triangle.)
65° +(36 +x)° = 90°
x = 90 -101 . . . . . . . . divide by °, subtract 101
x = -11
Theorem: There are three distinct prime numbers less than 12 whose sum is also prime. Select the sets of numbers that show that the existential statement is true. a. 3, 9, 11 b. 3, 7, 13 c. 2, 3, 11 d. 5, 7, 11 e. 3, 5, 11
The sets of numbers that satisfy the theorem are:
d. 5, 7, 11
e. 3, 5, 11
How to satisfy the theorem?Find three distinct prime numbers less than 12 that has sum is also prime. We can check each set of numbers given in the options to see if they satisfy the theorem.
a. 3, 9, 11
Sum = 23 (not prime)
Does not satisfy the theorem.
b. 3, 7, 13
Sum = 23 (not prime)
Does not satisfy the theorem.
c. 2, 3, 11
Sum = 16 (not prime)
Does not satisfy the theorem.
d. 5, 7, 11
Sum = 23 (prime)
Satisfies the theorem.
e. 3, 5, 11
Sum = 19 (prime)
Satisfies the theorem.
Therefore, the sets of numbers that satisfy the theorem are d and e.
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write the point-slope form of the equation that represents the line that passes through the point (-1,6) and has a slope of -3
Answer:
y-6=-3(x+1)
Step-by-step explanation:
y-y1=m(x-x1)
y-6=-3(x-(-1))
y-6=-3(x+1)
Can someone please help me
Answer:
Hence corre ctophon is (A)
Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic? w(w – 2) = 48 w(w 2) = 48 2w(w – 2) = 48 2w(w 2) = 48.
The equation which John solve to find w, the greatest width in centimeters he can use for the mosaic, is w(w + 2) = 48.
What is the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
\(A=a\times b\)
Here, (a)is the length of the rectangle and (b) is the width of the rectangle
The area of the tile is 48 square cm. John wants to make the mosaic with this tile having the length 2 cm longer than the width.
Let suppose the width of the rectangle mosaic is w cm. Thus the length of it is,
\(l=w+2\)
As the area of a rectangle is the product of its length and width and Tte area of the tile is 48 square cm. Thus,
\(48=(w+2)\times w\\48=(w+2)w\\\)
The equation which John solve to find w, the greatest width in centimeters he can use for the mosaic is
\(w(w + 2) = 48\)
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Answer:
B. w(w + 2) = 48
Step-by-step explanation:
I just took the quiz.
Have the day you deserve :)
the following data set shows the number of children in each household in anmol's neighborhood. 0, 0, 2, 1, 2, 8, 3, 0, 00,0,2,1,2,8,3,0,00, comma, 0, comma, 2, comma, 1, comma, 2, comma, 8, comma, 3, comma, 0, comma, 0 what is the range of children in these households?
The range of children in these households is from 0 to 8, as those are the minimum and maximum values in the data set. The range indicates the spread of the data, and in this case, it shows that there is a wide range of children in Anmol's neighborhood, from households with no children to households with 8 children.
To find the range of children in Anmol's neighborhood, we need to identify the highest and lowest numbers in the data set and then subtract the lowest from the highest. Here's the step-by-step explanation:
1. Organize the data set: 0, 0, 2, 1, 2, 8, 3, 0, 0, 0, 2, 1, 2, 8, 3, 0, 0
2. Identify the highest number of children in a household: 8
3. Identify the lowest number of children in a household: 0
4. Subtract the lowest number from the highest number: 8 - 0
The range of children in the households in Anmol's neighborhood is 8.
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Approximate −12 + √32 the square root of thirty-two to the nearest tenth.
−6.3
−5.7
5.7
6.3
The correct option for the approximate value of -12 + √32 is -6.3 to the nearest tenth.
What is an approximation?An approximation is anything that is similar, but not exactly equal, to something else.
The given expression is −12 + √32
The value of √32 is given as 5.656
Since,after decimal 6 to the right of 5 is greater than 5
To the nearest tenth, we can write as 5.66
∴ √32 = 5.66
For the required value of the expression we can write,
−12 + √32
Put the value of √32 = 5.66
Putting values in expression we have,
-12 + √32 = -12 + 5.66
Solving them
⇒ -12 + √32 = -6.34
Hence,the approximate value of -12 + √32 is -6.3 to the nearest tenth.
So, the correct option is -6.3.
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For trapezoid WXYZ shown below, points U and V are the midpoints of the legs. Use this information to find UV, the length of the mid segment.
Given:
\(\begin{gathered} WX=x+7 \\ ZY=6x+5 \\ UV=8x-3 \end{gathered}\)\(\begin{gathered} UV=\frac{1}{2}(WX+ZY) \\ 8x-3=\frac{1}{2}(x+7+6x+5) \\ 2(8x-3)=(7x+12) \\ 16x-6=7x+12 \\ 16x-7x=12+6 \\ 9x=18 \\ x=\frac{18}{9} \\ x=2 \end{gathered}\)\(\begin{gathered} \text{Length of the midsegment=8x-3} \\ =8(2)-3 \\ =16-3 \\ =13 \end{gathered}\)13 is the final answer.
a cylinder with a height of 17 centimeters and a radius of 8 centimeters is filled with water. if the water is then poured into the rectangular prism shown, will it overflow? write an argument that can be used to defend your solution.
Answer:
The volume of a cylinder is calculated by multiplying the area of the base by the height. The area of the base of a cylinder is πr², where r is the radius of the cylinder. In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm². The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.
The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters. The volume of the rectangular prism is 1620 cm³.
Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.
Here is an argument that can be used to defend this solution:
The volume of the cylinder is calculated by multiplying the area of the base by the height.
The area of the base of a cylinder is πr², where r is the radius of the cylinder.
In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm².
The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.
The volume of a rectangular prism is calculated by multiplying the length, width, and height.
In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters.
The volume of the rectangular prism is 1620 cm³.
Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.
Step-by-step explanation:
cuanto es la raiz cuadrada de 123
Answer:
11.0905365064
11.1 (rounded)
Step-by-step explanation:
\(\sqrt{123} =11.090\)
Answer:
Step-by-step explanation:
11.0905365064