Answers
Okay, here we have this:
Considering the provided expression, we are going to simplify it, so we obtain the following:
539.A:
Then by properties of exponents we get the following:
[tex]\begin{gathered} 216^{\frac{1}{3}} \\ =(6^3)^{\frac{1}{3}} \\ =6^{\frac{3}{3}} \\ =6^1 \\ =6 \end{gathered}[/tex]Finally we obtain that the given expression is equal to 6.
Related Questions
A funky 6-sided die with faces labeled 1, 2, 3, 4, 5, and 6 has a chance of 1/12 landing on each face and a 1/24 chance of landing on each edge. When Kira rolls the die, if it lands on a face, she records the number on top. If she lands on an edge, she records the sum of the two numbers on top. If Kira rolled the die infinitely many times and averaged the result, what is the expected value of the number recorded?
Answers
From the statement, we know that there are two possible scenarios:
A) Kira rolls the die and gets a face with a 1, 2, 3, 4, 5 or 6.
• The probability of this event is P(A) = 1/12.
,• Kira will write the number of the face in this case.
B) Kira rolls the die and gets an edge.
• The probability for this event is 1/24.
,• Kira will write the sum of the numbers that share the top edge.
,• There are multiple values for the result of the sum.
We must take into account that:
• 1 and 5 are on opposite faces,
,• 2 and 3 are on opposite faces,
,• 4 and 6 are on opposite faces.
The possible values of the sum and the forms to get it are:
0. 3, = 1 + 2 → P(B'_1) = 1/24
,1. 4, = 1 + 3 → P(B'_2) = 1/24
,2. 5, = 1 + 4 → P(B'_3) = 2/24
,3. 6, = 2 + 4 → P(B'_4) = 2/24
,4. 7, = 1 + 6 = 2 + 5 = 3 + 4 → P(B'_5) = 3/24
,5. 8, = 2 + 6 = 3 + 5 → P(B'_6) = 2/24
,6. 9, = 3 + 6 = 4 + 5 → P(B'_7) = 2/24
,7. 11, = 5 + 6 → P(B'_9) = 1/24
We have 8 possible results for the sum.
---------------------
Now, we want to know the value of the expected value of the numbers recorded by Kira.
By definition, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.
The expected value of the number recorded by Kira will be:
[tex]E=\sum_{i\mathop{=}1}^6A_i\cdot P(A_i)+\sum_{i\mathop{=}1}^8B_i\cdot P(B_i)[/tex]Where:
• A_i represents the result of event A_i and P(A_i) its probability,
,• B_i represents the result of event B_i and P(B_i) its probability.
Using the data from above, we compute each of the sums.
A) For the first sum, we take into account that each event A_i has the same probability:
[tex]\sum_{i\mathop{=}1}^6A_i\cdot P(A_i)=(1+2+3+4+5+6)\cdot\frac{1}{12}=\frac{7}{4}=1.75.[/tex]B) For the second sum, we use each of the values of the sum and the probabilities of each sum:
[tex]\begin{gathered} \sum_{i\mathop{=}1}^8B_i\cdot P(B_i) \\ =3\cdot\frac{1}{24}+4\cdot\frac{1}{24}+5\cdot\frac{1}{24}+6\cdot\frac{1}{24}+7\cdot\frac{3}{24}+8\cdot\frac{2}{24}+9\cdot\frac{2}{24}+11\cdot\frac{2}{24}=\frac{95}{24}. \\ \end{gathered}[/tex]Summing the results of each sum, we get the following result for the expected value:
[tex]E=\frac{7}{4}+\frac{95}{24}=\frac{42}{24}+\frac{95}{24}=\frac{137}{24}\cong5.71.[/tex]AnswerThe expected value for the number recorded is 137/24 or approximately 5.71.
Find the compound amount and interest on 40,000 naira at 15% for 2 years
Answers
Answer: 52900 Naira
Step-by-step explanation:
1) Use the equation A = P(1+r/n)^nt
A = Ammount
(Starting Cash) P = 40,000
(Intrest rate) R = 15%
(Number of periods) n = N/A
(Time) t = 2
2) Make an equation
A = 40,000(1+15%)^2
3) Solve the equation.
A = 40,000(1+0.15)^2
A = 40,000(1.15)^2
A = 40,000(1.3225)
A = 52900
Clare follow the same workout cycle each time she goes to the gym. First, she runs for 1/3 of an hour. Then, she lifts weights for 1/6 of an hour. If Clare has 1 1/2 hours to spend at the gym, how many times can she go through her workout cycle?
Answers
Clare can go 3 times for her workout cycle
How to calculate the number of work out cycle ?Clare follows the same workout cycle each time she goes to the gym
She spends 1 1/2 hour at the gym
First, she runs 1/3 of an hour
After that, she lifts 1/3 of an hour
The first step is to convert to minutes
60 mins = 1 hour
1/2 × 60
= 30
30 + 60
= 90 mins
convert 1/3 to mins
1/3 × 60
= 20 mins
convert 1/6 to mins
1/6 × 60
= 10 mins
Total mins= 20 + 10
= 30 mins
The number of workout cycles can be calculated as follows
= 90/30
= 3
Hence Clare can go 3 times for her workout cycle
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(-2,-3), (4,3) in point slope form
Answers
Answer: y + 3 = 1 ⋅ (x + 2)
Step-by-step explanation:
The table below represents an exponential function, g, that has been vertically shifted from the parent function, f(x) = 2x.
x 0 1 2 3 4
g(x) -11 -10 -8 -4 4
Determine the size of the shift from function f to function g. Then, plot the points of a function that is shifted only half as much as g from the parent function, f. Use the same x-values as used in the table for function g.
Drawing Tools
Select
Point
PLS SHOW GRAPH
Answers
The size of the shift from function f to function g is 12 units down
How to calculate the size of the shift?The table of values is given as
x 0 1 2 3 4
g(x) -11 -10 -8 -4 4
From the question, we understand that the function g(x) is an exponential function
The parent function of an exponential function in this case, is represented as
f(x) = 2^x
When represented on a table of values, we have
x 0 1 2 3 4
f(x) 1 2 4 8 16
So, we have
x 0 1 2 3 4
f(x) 1 2 4 8 16
g(x) -11 -10 -8 -4 4
Notice that the difference between the values of f(x) and g(x) is 12
This means that
g(x) = f(x) - 12
So, we have
g(x) = 2^x - 12
Hence, the size of the shift is 12 units down
See attachment for the graphs of f(x) and g(x)
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5. Solve for x using any method you'd like. Round to the hundredth. Show all your work. (2 points each) C. 5x^5 + 16 = 41
Answers
x = 1.37 after solving the given equation.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.So, the equation here is: 5x⁵ + 16 = 41
Now, solve the equation normally as follows:
5x⁵ + 16 = 415x⁵ = 41 - 165x⁵ = 25x⁵ = 25/5x⁵ = 5Now, take the roots on both sides and solve as follows:
x⁵ = 5x = [tex]\sqrt[5]{5}[/tex]In decimal form:
x = 1.37972966Therefore, x = 1.37 after solving the given equation.
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The width of a garden is 19.5 feet, and the perimeter of the garden is 84 feet. What is the area of the garden?
Answers
Rectangular garden has sides:
width, length, width, length
The perimeter is sum of all the 4 sides.
So, we can say:
84 = 2w + 2l
Where
w is width
l is length
Width is 19.5, so we find length:
84 = 2(19.5) + 2l
84 = 39 + 2l
2l = 45
l = 22.5 feet
Now, area is given by:
Area = length * width
Area = 22.5 * 19.5 = 438.75 sq. ft.
Find an equation for the perpendicular bisector of the line segment whose endpoints are ( 8 , − 1 ) (8,−1) and ( 4 , − 9 ) (4,−9).
Answers
The equation of the perpendicular bisector of the line segment is y = - (1 / 2) · x - 2.
What is the equation of the perpendicular bisector of a line segment?
In this problem we find a line segment whose endpoints are known and we need to determine the equation of the line perpendicular such that the segment is partitioned into two segments of equal length. Now we present the procedure. First, determine the coordinates of the midpoint:
M(x, y) = 0.5 · (8, - 1) + 0.5 · (4, - 9)
M(x, y) = (6, - 5)
Second, determine the slope of the line segment:
m = [- 9 - (- 1)] / (4 - 8)
m = (- 8) / (- 4)
m = 2
Third, calculate the slope of the bisector:
m' = - 1 / m
m' = - 1 / 2
Fourth, determine the intercept of the bisector:
b = y - m' · x
b = - 5 - (- 1 / 2) · 6
b = - 5 + 3
b = - 2
The equation of the perpendicular bisector of the line segment is y = - (1 / 2) · x - 2.
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help me please
The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
Answers
The water pressure on a submerged object is given by P = 64d, then the value d is 10.5 feet.
a. D = P/64 is the solution to the formula's "d" subject.
b. The depth of a submerged object at a pressure of 672 pounds per square foot is 10. 5 feet.
What is a function?A function can be defined as an expression, law or rule that shows the relationship between two variables.
Given the role as;
P = 64d
Where;
P stands for pressure in pounds per square foot.
The object's depth, d, is expressed in feet.
Now let's center the formula on the variable "d."
Both sides of the equation are divided by the variable "d64-based "'s coefficient. This is carried out so that the variable can stand on its own.
We have.
P/64 = 64d/64
d = P/ 64
If there is pressure, P is equivalent to 672 pounds per square foot.
When the value of the variable is inserted into the formula, we obtain;
d = P/64
Then,
d = 672/64
Discover the quotient.
d = 10. 5 ft.
Therefore,
The water pressure on a submerged object is given by P = 64d, then the value d is 10.5 feet.
a. D = P/64 is the solution to the formula's "d" subject.
b. The depth of a submerged object at a pressure of 672 pounds per square foot is 10. 5 feet.
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25. Susan is an electrician. She charges $75 for each repair appointmentand an additional $42 for each hour needed during the appointmentto make the repair. The expression shown can be used to calculate thetotal charge, in dollars, for each repair appointment,75 + 421where: h = the number of hours Susan works on a repair duringthe appointmentWhat is the total charge, in dollars, for a repair appointment if Susanworks for 6 hours?
Answers
Given:
Charge for each repair = $75
Additional charge per hour = $42
The expression is used to calculate the total charge, in dollars, for each repair appointment:
75 + 42h
Let h represent the number of hours Susna works during an appointment.
To find the total charge if Susan works for 6 hours, substitute 6 for h in the expression and evaluate.
Thus, we have:
h = 6
75 + 42h
75 + 42(6) = 75 + 252 = 327
Therefore, the total charge in dollars if Susan works for 6 hours is = $327
ANSWER:
$327
Where is the function f(x) = 2/6x^3 not differentiable?
Answers
at X= 0 the function f(x) = 2/6x^3 is not differentiable
Since 1/0 cannot be differentiated and the denominator will become zero when x=O, the function is not defined. Sharp points, cusps, and discontinuities in the graph indicate that a function is "not differentiable." Additionally, it implies that at that same location, we can draw an endless number of tangents. There is therefore no special tangent at that place. Even at x=0, the provided function is not defined. (If you plug in x=0, you get (1/0), which is undefined and leaves you with nothing to do.)) Only after a function is clearly defined at a certain moment do we discuss its continuation. And only if the function is continuous at the place do we talk about differentiability.
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5) Roland has a basket of 24 fruits. If 3) out of 8 of these fruits are oranges, how many oranges are in Roland's basket? a) 5 b) 8 c) 9 d) 15
Answers
Answer:
The answer would be C or 9.
Step-by-step explanation:
Figure out how many times 8 can fit into 24.(That would be 3 times) Then multiply 3 by the number of times 8 fit into 24 and get to your answer! (Please let me know if I am wrong)
Answer:
[C] 9
Step-by-step explanation:
Given:
Roland has a basket of 24 fruits. If 3 out of 8 of these fruits are oranges, how many oranges are in Roland's basket?
Solve:
" 3 out of 8 " is the same things as "⅜"
Therefore,
24 × ⅜
Now solving 24 × ⅜:
24 is the same as 24/1 since 24 divided by 1 is 24.
Hence, the problem will be like this:
[tex]\frac{24}{1}\times\frac{3}{8}[/tex]
Multiply the numerators together (24 x 3 = 72) and multiply the denominators together (1 x 8 = 8) and make it into one fraction like so:
[tex]\frac{72}{8}[/tex]
Now we have to find the GCF: GCF = Greatest Common Factor;
The greatest common factor of 72 and 8 is 8.
Dividing the numerator and the denominator by its greatest common factor to get:
[tex]\frac{9}{1}[/tex]
Convert the improper fraction above to a whole number to get the answer:
[tex]\frac{9}{1}=9[/tex]
Hence, there are 9 oranges in Roland's basket.
As a result, [C] 9 is the correct answer.
Kavinsky~
fill in the missing number to form equivalent fraction
20/?=?/6=10/?=?/900=8/12
Answers
Missing numbers are 30, 4, 30 and 300.
What is equivalent fraction?Equivalent fractions are those that, despite their visual differences, reflect the same value. You will have consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces. Two or more fractions that are equal despite having dissimilar numerators and denominators are said to be equivalent. Every time, the fraction is written as "one half" in its simplest form.
Given Data
20/?=?/6=10/?=?/900=8/12
Fraction which is given
[tex]\frac{8}{12}[/tex]
= [tex]\frac{2}{3}[/tex]
As they are equivalent fraction, so their simplest form will be equal
Let the missing numbers be x
1) [tex]\frac{20}{x}[/tex]
= [tex]\frac{20}{30}[/tex]
2) [tex]\frac{x}{6}[/tex]
= [tex]\frac{4}{6}[/tex]
3) [tex]\frac{10}{x}[/tex]
= [tex]\frac{10}{30}[/tex]
4) [tex]\frac{x}{900}[/tex]
= [tex]\frac{600}{900}[/tex]
Missing numbers are 30, 4, 30 and 300.
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What’s the answer to this question
Answers
The value of (fg)(6) is -6x³ + 72x² + 72x - 864 after doing the mathematical operations.
What do we mean by mathematical operations?A mathematical function called an operation, also known as an "operand" or "argument," transforms zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The operations that are most frequently studied are unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication.An operation of arity zero also referred to as a nullary operation, is a constant.The mixed product is an illustration of an operation of arity 3, also referred to as a ternary operation.So, f(x) = x² - 12 and g(x) = 12 - x.
Then, (fg)(6) will be:
[(x² - 12)(12 - x)]6[x²(12 - x) - 12(12 - x)]6[12x² - x³ - 144 + 12x]6-6x³ + 72x² + 72x - 864Therefore, the value of (fg)(6) is -6x³ + 72x² + 72x - 864 after doing the mathematical operations.
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Translate the sentence into an equation.
Four more than the quotient of a number and 8 equals 9.
Use the variable x for the unknown number
Answers
Answer:
(x / 8) + 4 = 9
Step-by-step explanation:
follow the instructions of the question and then write the values
Are these rational numbers?
1) -1098.15
2) -2,784.75
Answers
Yes, these -1098.15 and -2,784.75 are rational numbers.
Rational number is the one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively
What is a rational numbers?A rational number is the one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer (e.g., 5 = 5/1) and, for instance, the number 3/7 are rational numbers. Boldface Q, also known as blackboard bold, is typically used to signify the set of all rational numbers, also known as "the rationals," the field of rationals, or the field of rational numbers.
Real numbers are those that are sensible. The rational real numbers are those whose decimal expansion either ends after a finite number of digits (for instance, 3/4=0.75) or eventually starts to repeatedly repeat the same finite sequence of digits (9/44=0.204545454). This assertion is accurate not just in base 10, but also in every other integer base, such as the binary and hexadecimal ones
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417 x 25 in partly product?
Answers
ANSWER
10425
EXPLANATION
We want to multiply the numbers given by using product of parts.
To do this, we will split the number into hundred, tens and units. That is:
[tex](400\text{ + 10 + 7) }\cdot\text{ 25}[/tex]So that will be:
[tex]\begin{gathered} (400\cdot\text{ 25) + (10 }\cdot\text{ 25) + (7 }\cdot\text{ 25)} \\ =\text{ 10000 + 250 + 175} \\ =\text{ 10425} \end{gathered}[/tex]That is the answer.
(a) For each pool, write an expression for the amount of water in the
gool after x minutes
Two pools are being filled with water. To start, the first pool had 817 liters of water and the second pool was empty. Water is being added to the first pool at a
rate of 19 liters per minute water is being added to the second pool at a rate of 38 liters per minute.
Leta be the number of minutes water has been added.
Amount of water in the first pool (In liters) =
Amount of water in the second pool (in liters) =
(b) Write an equation to show when the two pools would have the
same amount of water
Answers
(a) Amount of water in the first pool (In liters) = (817 + 19x) liters
Amount of water in the second pool (in liters) = 39x liters
(b) An equation to show when the two pools would have the same amount of water is 817 + 19x = 38x.
Given:
For the First Pool :
Initial amount of water in the Pool = 817 liters
Water is being added to the first pool at a rate of 19 liters per minute.
Amount of water added after x minutes = 19x
So, Total amount of water after x minutes = (817 + 19x) liters
For the Second Pool:
It was empty initially.
Water is being added to the second pool at a rate of 38 liters per minute.
Amount of water added after x minutes = 38x
So, Total amount of water after x minutes = 38x liters
Now to determine an equation to show when the two pools would have the same amount of water.
817 + 19x = 38x
38x - 19x = 817
19x = 817
x = 817/19
x = 43 minutes
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Question
Given that the terminal side of angle 0 goes through the point (-4, 3), find csc(0).
Answers
Answer: -4/3
Step-by-step explanation:
[tex]\csc \theta=\frac{1}{\sin \theta}=\frac{1}{-3/4}=-4/3[/tex]
Select all the correct answers.
Which functions have a range of {ye R |-∞0 < y < ∞0}?
F(x)=x^2+7x-9
F(x)=-4x+11
F(x)=2/3X-8
F(x)=2^x+3
F(x)=-(x+1)^2-4
Answers
Answer: [tex]f(x)=-4x+11[/tex] and [tex]f(x)=\frac{2}{3}x-8[/tex]
Step-by-step explanation:
All linear functions with unrestricted domains have a range of all real numbers.
Select the three equations that pass through the points (–4, –16) and (5, 2):
y + 4 = 2(x – 16)
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)
Answers
The equation of line passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The standard form for linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
The equation of line passing through (5, 2) and (-4, -16) is:
y - 2 = [(-16-2)/(-4-5)](x - 5)
y - 2 = 2(x - 5)
y = 2x - 8
y + 16 = 2(x + 4)
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what is the fraction if the denominator is 8
Answers
Step-by-step explanation:
1/8, 2/8, 3/8, 4/8, etc...
Which graph represents the solution to the inequality 2(b + 2) < 24?
number line with open point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing right
number line with open point at 10 with arrow pointing right
Answers
The solution to the inequality shows that the circle will be on 10 and pointing to the left.
Solving inequalityInequality are expressions not separates by an equal sign.
Given the inequality expression below:
2(b + 2) < 24
Expand
2b + 4 < 24
2b < 24 - 4
2b < 20
Divide both sides by 2
2b/2 < 20/2
b < 10
Hence the number line with open point at 10 with arrow pointing left.
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Question 1 options:
Is the relation in this set of points a function?
{(-2, 6) , (4, 5) , (3, -3) , (6, 9), (4, -4)}
State whether the statement is true of false.
1. The relation is a function.
2. An element from the domain is paired with more than one element from the range.
Answers
Answers:
FalseTrue================================================
Explanation:
Focus on (4,5) and (4,-4)
The input x = 4 leads to simultaneous outputs y = 5 and y = -4 at the same time. This is not allowed in a function. For a function to be possible, each input x must lead to exactly one y output.
Therefore, this given relation is not a function.
-----------
Domain = set of possible x inputs
Range = set of possible y outputs
The statement "An element from the domain is paired with more than one element from the range" basically means we have an x value paired with more than one y value. Therefore, this statement is true since I mentioned (4,5) and (4,-4) earlier.
Answer:
This answer is correct!
I need help with functions
Answers
The defition of a function is a mathematical correspondence that assigns exactly one element of one set to each element of the same or another set.
So, Your ques
Fine the unknown quantity in the following percent problem using the formal RxB=A. Round your answer to two decimal places, if necessary.
50% of what number is 60?
Answers
Answer:
120
Step-by-step explanation:
You want to find a number such that 50% of it is 60, using the formula R×B = A.
Percent relationAn amount is found by multiplying the rate by the base. That is described by the formula ...
R × B = A
Here, we're given the amount and the rate, and we want to find the base. We can fill in the given numbers and solve for B.
50% × B = 60
B = 60/0.50 . . . . . . divide by the rate
B = 120 . . . . . . . simplify
50% of 120 is 60.
Given the two rectangles below. Find the area of the shaded region?
Answers
Answer:
Step-by-step explanation:
34 units.
James bought a plant and planted it in a pot near a window in his house. The initial height of the plant was 6 inches and it grew at a rate of 3 inches per month. Make a table of values and then write an equation for H, in terms of t, representing the height, in inches, of the plant t months after James bought the plant.
Answers
initial height = 6
Rate of growth = 3 inches per month
Table:
Month height 1
96+3(3) = 91
2 6 + 3 (2)=12
3 6+3 (3) = 15
Apply the formula:
H = H0 + rt
Where:
H0 = initial growth
r = growing rate
t= number of months
Replacing:
H(t) = 6 + (3 t)
need help asap!!
Q: The length of a pipe in a panpipe L, in ft, is inversely proportional to its pitch p, in hertz. The inverse variation is modeled by the equation p = 497/L. Find the length of pipe required to produce a pitch of 220 Hz.
Answers
Answer:
hajajJzjzjzjzjzjzkzkzkzkzksk
eatmyass
The length of pipe required to produce a pitch of 220 Hz is 2.26 feet.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
The length of a pipe in a panpipe L, in ft, is inversely proportional to its pitch p, in hertz.
The inverse variation is modeled by the equation p = 497/L.
The length of pipe required to produce a pitch of 220 Hz,
= 497/220
= 2.26 feet
Therefore, the length is 2.26 feet.
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please help!!!!!!!!!
Answers
Answer:
I believe the first one
Step-by-step explanation:
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