An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
What is nilpotent matrix?A nilpotent matrix in linear algebra is a square matrix N such thatfor some positive integer kk. The index of occasionally the degree of the smallest such k A nilpotent transformation, more generally speaking, It is a linear transformation of a vector space such that Lk=0 for some positive integer. Both of these ideas are specific examples of the more basic idea of nilpotence, which is applicable to rings' constituent parts.acc to our question-
When n=1, the only 1×1 nilpotent matrix is (0). Thus U={(0)} and it is a subspace of VIn this case, we prove that the set U of all 2×2 nilpotent matrices is not a subspace of V.The set U is not a subspace because it is not closed under addition as the following example shows.Hence,An matrix A is a nilpotent matrix if there exists a positive integer k such that Ak is the zero matrix.
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4. A triangle has two sides measuring 8 cm and 15 cm. Write an inequality to represent the possible lengths of the third side.
Answer:
7 < x < 23
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the interval
difference of 2 sides < x < sum of 2 sides , that is
15 - 8 < x < 15 + 8
7 < x < 23
Describe the characteristics of each set of numbers
that make up the set of integers.
Positive and negative numbers are included in the category of integers, which is distinct from decimals and fractions.
What in math is an integer?
A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.There are numerous types of numbers, including integers, whole numbers, rationals , real numbers, and natural numbers. Positive and negative numbers are included in the category of integers, which is distinct from decimals and fractions. It has the following qualities:
Numbers below zero are considered negative numbers.
In the set of integers, zero is included.
There are overlaps between the number categories.
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You have 84,000 grams of a radioactive kind of tellurium. How much will be left after 75
minutes if its half-life is 25 minutes?
grams
Answer:
10,500 g
Step-by-step explanation:
Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 25 minutes. After 75 minutes, then, the amount of radioactive atoms is halved three times. Therefore:
1st half-life: [tex]84000\text{ g}\div{2}=42000\text{ g}[/tex]
2nd half-life: [tex]42000\text{ g}\div{2}=21000\text{ g}[/tex]
3rd half-life: [tex]21000\text{ g}\div{2}=10500\text{ g}[/tex]
The bottom of a 5.5-meter ladder is 3.3 meters from the base of a wall, and it just reaches the bottom of a window in the wall. If the window is 1 meter high, what is the distance from the top of the window to the base of the wall?
The distance from the top of the window to the base of the wall is 5.4 m.
According to the question,
We have the following information:
The bottom of a 5.5-meter ladder is 3.3 meters from the base of a wall, and it just reaches the bottom of a window in the wall. And the window is 1 meter high.
Now, we know that the ladder, wall and base will make a right-angled triangle. We can use Pythagoras theorem to find height of the wall.
(Pythagoras theorem: square of hypotenuse = sum of squares of base and height)
Let's take height of the wall to be h meters.
[tex]h^{2}[/tex] = [tex](5.5)^{2} -(3.3)^{2}[/tex]
[tex]h^{2}[/tex] = 30.25-10.89
19.36
h = √19.36
h = 4.4 m
Now, the distance from the top of the wall window to the base of the wall is:
4.4 + height of the window
4.4+1
5.4 m
Hence, the distance from the top of the window to the base of the wall is 5.4 m.
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What are the solutions to the equation?
Finding the value of the given equation's unknown variables is a step in the equation-solving process. The value of the variable satisfies the requirement that the two expressions are equal and is called the solution of that equation.
What Does Solving Equations Mean?Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. When a condition on variable guarantees that two expressions in the variable have the same value, it qualifies as an equation.
The variable's value for which the equation holds true is referred to as the equation's solution If the LHS and RHS are switched, an equation doesn't change. The answer is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are working with, we can solve it. There are several types of equations, including linear, quadratic, rational, and radical ones.
When a linear equation has one variable, there is only one solution; when there are two variables, there are two solutions. A quadratic equation's solution yields two roots. To solve an equation, a variety of techniques and steps are used.
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Determine whether each of these functions from {a,b,c,d} to itself is bijection if it is than find f -¹.
f(a)=b, f(b)=a, f(c)=d, f(d)=c
f(a)=a, f(b)=b, f(c)=c, f(d)=d
Only function (a) is one-to-one.
What is a one-one function?A mathematical function with individuality known as an injective function, injective, or one-one function never translates discrete components of its domain to equivalent elements of its codomain. We can say that each element of the codomain is only a representation of a single element in the domain.acc to our question-
If every element of the range of the function corresponds to exactly one element of the domain, then the function is called one-to-one.
The elements of a function are
A = {a,b,c,d}
Therefore, this function is one-to-one.
(b).f (a) = b, f (b) = b, f (c) = d, f (d) = c.
Here, the value of function is b for x=a and x=b. For two domains the functions has same range.
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on the grid,draw the graph of y=2x-3 for values of x from -3 to 5
The graph of the equation y = 2x - 3 at the interval of -3 to 5 is attached below.
Graph:
Graph means the diagram that shows the variation of a variable in comparison with that of one or more other variables.
Given,
Here we have the equation y = 2x - 3
Now, we need to plot the graph of the given equation at the interval of -3 to 5..
To plot the graph for the given function,
The given interval is taken as the value of x and we have to calculate the value of y from it,
Now, we have to take the given interval -3, -2, -1, 0, 1, 2, 3, 4, 5 are the samples value for x.
So, we have to apply the values on the equation,
Then we get the value of the function as,
x = -3 => y = 2(-3) - 3 = -6 - 3 = 9
x = -2 => y = 2(-2) - 3 = -4 - 3 = -7
x = -1 => y = 2(-1) - 3 = -2 - 3 = -5
x = 0 => y = 2(0) - 3 = 0 - 3 = -3
x = 1 => y = 2(1) - 3 = 2 - 3 = -1
x = 2 => y = 2(2) - 3 = 4 - 3 = 1
x = 3 => y = 2(3) - 3 = 6 - 3 = 3
x = 4 => y = 2(4) - 3 = 8 - 3 = 5
x = 5 => y = 2(5) - 3 = 10 - 3 = 7
The completed table is attached below.
Now, we have to plot the graph through the derived table, then we get the graph like the following.
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at 9:30 am andrew left exeter for portsmouth, cycling at 12 mi/h. at 10:00 am stacy left portsmouth for exeter, cycling at 16 mi/h. the distance from exeter to portsmouth is 20mi.find the time they meet
Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.
How to solve this problem?
Stacey and Andrew in the mentioned problem will meet in a time frame only when the both have travelled equal distances in respect to another.
Given, speed at which Andrew was travelling = 12 mi/h
Speed at which Stacey was travelling = 16 mi/h
Let the time taken by Stacey be = t hours
Therefore, the time taken by Andrew = (t + 0.5) hours
When Stacey overtakes Andrew, they must have covered the same distance, therefore:
16t = 12×(t + 0.5) ⇒ 16t = 12t + 6 ⇒ 4t = 6 ⇒ t = 6/4 ⇒ t = 3/2 ⇒ t = 1.5
Therefore, Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.
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Each bag of grass seed covers 55 square
yards. How many bags of grass seed will
Sasha need to purchase to cover her
backyard?
38 yd
28 yd
The area of Sasha's backyard is 1064 yard square. So the number of bags required would be 20.
What is area?
The measurement that expresses the size of a region on a plane or curved surface is called area. It's S.I. unit is m².
Main Body:
The area of Sasha's backyard = 38*28
= 1064 yd square
Now 1 bag covers 55 yd square
so, bag required for 1064 yd = 1064/55
= 19.3 approximately
Therefore the amount of required bags are 20.
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Hong made $153 for 9 hours of work.
At the same rate, how many hours would he have to work to make $187?
hours
X
Answer:
11 hours
Step-by-step explanation:
153 divided by 9 (which is 17) 17$ per hour so add 17 and 17 together which would be 34 and add it to 153 which would be 187$ he worked 2 more hours so in total he worked 11 hours.
and i know that was a bad explanation but its whatever hope this helped.
help meeeeeeeeeeeeeeeeee please
Answer:
try using the Pythagorean theorem
Step-by-step explanation:
hypotenuse ² = Opposite ² +Adjacent ²
where hypotenuse is the side facing the right angle sign;(x+3)
what fraction multiplied by 31/27 equals 1
Answer: 27/31 is the answer
Step-by-step explanation:
31/27 x 27/31 = 1 because 27/31 is the recprical
Answer:x = 31/27 = 1.148
Step-by-step explanation:
What is 5.2E11 in standard form
The standard form of 5.2E11 using the set scientific notation and rules is 311345.5369.
What is a standard form in mathematics?The standards for putting mathematical elements in standard form make it easier for anyone to read, write, and interact with them. The standard form is the most popular approach to representing a mathematical element.
In mathematics, the standard form is the most prevalent way of describing a specific element. Every element in arithmetic is represented in a standard form, from enormous numbers to little integers, or equations to lines.
A standard form is a method of writing a particular mathematical notion, such as an equation, or expression, in a way that adheres to specified criteria. The standard form is used to portray very big or very small numbers in a succinct manner.
The standard form of 5.2E11 using the set scientific notation and rules is:
311345.5369.
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A bowling alley charges $15 per game. Customers are also charged an additional $3 to rent bowling shoes.
Which statement is true, based on the given description?
The description shows a linear relationship, but not a proportional relationship.
The description shows a linear relationship and a proportional relationship.
The description does not show a linear relationship or a proportional relationship.
The description shows a proportional relationship, but not a linear relationship.
The statement that is true on the bowling alley charges and the additional cost for renting bowling shoes is The description shows a linear relationship, but not a proportional relationship.
What is a linear relationship?In a linear relationship, the values of the two variables can be drawn on a graph such that they form a line. There would often be a y-intercept and then a slope or a constant rate of change. In this case the constant rate of change is the $15 per game and the additional cost to rent bowling shoes is the y-intercept. This is therefore a linear relationship.
A proportional relationship would have a constant rate of change but there would be no y - intercept. As there is a y - intercept in this scenario, this is not proportional.
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Answer: A: The description shows a linear relationship, but not a proportional relationship.
annual revenue for corning supplies grew by 5.5% in 2007; 1.1% in 2008; -3.5% in 2009; -1.1% in 2010; and 1.8% in 2011. what is the mean growth annual rate over this period? round your answer to four decimal places. do not round intermediate calculations.
The mean yearly growth rate for this period is 0.0036.
Define annual growth rate.The average annualized return of a portfolio, asset, or cash flow over time is known as the average annual growth rate, or AAGR. The basic arithmetic mean of a set of returns is used to calculate AAGR.
The change in a measurement's value over a year is known as the annual growth rate (AGR).
The sum of the growth rates for each year divided by the total number of years yields the mean growth annual rate.
Where the annual growth rate is calculated as follows: 5.5 + 1.1 - 3.5 - 1.1 + 1.8 = 3.8%
And the total number of years is 5.
Then ,
The average annual growth rate for this time period is = 3.8/5
Over this time span, the average yearly growth rate was 0.76%.
Make a decimal conversion
= 0.76% = 0.0076
Therefore, the mean yearly growth rate for this period is 0.0036.
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The range of f(x) = |x| is y ≥ 0. If a < 0 and b ≠ 0 for g(x) = a|x| + b, what is the range of function g?
The range of the function g, given the premises for f(x) = |x| and a < 0 while b ≠ 0 is; the set of all real numbers.
Range of a functionIt follows from the task content that the range of the function g(x) = a|x| + b is to be determined given the parameters as in the task content.
Since the function f(x) = |x| has a range of y ≥ 0, and a is a negative number ( < 0), it therefore means that the a|x| is always a number less than 0 (<0).
However, the possible values of constant, b include all real numbers except 0.
On this note, the function g(x) = a|x| + b has a range which is the set of all real numbers. This is so because, g(x) > 0 when a|x| < b and g(x) < 0 when a|x| > b.
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Please solve the equation
[tex]5 {}^{2x + 1} - 26(5 {}^{x} ) \: + 5 = 0[/tex]
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
[ log 5 = 0.69 ]
[ log 26 = 1.41 ]
The formula for log [tex]x^n[/tex] = n log x
The value of x is 0.043
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
[tex]5^{2x + 1} - 26(5^x) + 5 = 0[/tex]
[tex]5^{2x + 1} + 5 = 26(5^x)[/tex]
The formula for log [tex]x^n[/tex] = n log x
Taking logs on both sides.
log [tex](5^{2x + 1} + 5)[/tex] = log [tex]26(5^x)[/tex]
log [tex]5^{2x + 1}[/tex] + log 5 = log 26 + log [tex]5^{x}[/tex]
(2x + 1) log 5 + log 5 = 1.41 + x log 5
[ log 5 = 0.69 ]
[ log 26 = 1.41 ]
(2x + 1) x 0.69 + 0.69 = 1.41 + 0.69x
1.39x + 0.69 + 0.69 = 1.41 + 0.69x
0.70x = 1.41 - 1.38
x = 0.03 / 0.70
x = 0.043
Thus,
The value of x is 0.043
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Which of the following best describes the ordered pairs listed below? (-2, -1), (1, -4), (5, -8), (9, -12) A. function only B. both a relation and a function C. relation only D. neither a relation nor a function
Since each input is mapped to only one output, the best description of the ordered pairs is given by:
B. both a relation and a function.
When does a relation represents a function?
A relation represents a function if each value of the input is mapped to only one value of the output.
For a point in the format (x, y), we have that:
=> x is the input.
=> y is the output.
=> The meaning is that the input x is mapped to the output y.
For this problem, the points are given as follows:
(-2, -1), (1, -4), (5, -8), (9, -12)
Each input is mapped to only one input, that is, there are no repeated values of x, hence the best description of the ordered pairs is given by:
B. both a relation and a function.
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simplify
2-5-(6/2+1)
Answer:
-7
Step-by-step explanation:
6/2=3
3+1= 4
2-5= -3
-3-4= -7
6/2+1= 4
2-5-4= -7
*Do what is in the parenthesis first!!*
What is cos 60°?
A.1
B. √3/2
C. √3
D.1/2
E.1/√2
F.1/√3
Answer:
The trigonometric functions, sin, cos and tan for an angle are the primary functions. The value for cos 60 degrees and other trigonometry ratios for all the degrees 0°, 30°, 45°, 90°, 180° are generally used in trigonometry equations. These trigonometric values are easy to memorize with the help trigonometry table.
Cos 60 Degree Value
In a right-angled triangle, the cosine of ∠α is a ratio of the length of the adjacent side (base) to the ∠α and its hypotenuse, where ∠α is the angle formed between the adjacent side and the hypotenuse.
Cos 60 Degree value
Cosine α = Adjacent Side / Hypotenuse
Cos α = AC / AB
Cos α = b / h
Now, to find the value of cos 60 degrees, let us consider, an equilateral triangle ABC as given below:
Cos 60 Degree
Here, AB = BC = AC and AD is perpendicular bisecting BC into two equal parts.
As we know, cos B = BD/AB
Let us consider the length of each side as 2 units, such as AB = BC = AC = 2 units and BD = CD = 1 unit.
Therefore, the value of cos 60° = BD/AB = ½
In the same way, we can write the value of sin 60° and tan 60° by evaluating the required sides.
In right triangle ABD, by Pythagoras theorem:
AB2 = AD2+ BD2
22 = AD2 + 12
AD2 = 22 -12
AD2 = 4 – 1
AD2 = 3
AD = √3
Now, we have got all the sides of triangle ABD.
Sin 60° = AD/AB = √3/2
Tan 60° = AD/BD = √3 / 1 = √3
We can also write the value of cos 60 degrees in decimal form as:
cos 60° = 1/2 = 0.5
Also, we can write the values of sine, cosine and tangent with respect to all the degrees in a table.
Let us draw a table with respect to degrees and radians for sine, cosine and tangent functions.
Angle in Degrees 0 30 45 60 90 180 270 360
Angle in Radians 0 π/6 π/4 π/3 π/2 π 3π/2 2π
Sin 0 1/2 1/√2 √3/2 1 0 -1 0
Cos 1 √3/2 1/√2 1/2 0 -1 0 1
Tan 0 1/√3 1 √3 ∞ 0 ∞ 0
Unit Circle in Trigonometry
It is possible to give the values of trigonometric ratios with respect to radians equivalent to degrees, in case of a unit circle, whose radius is equal to one. The radian for a unit circle is denoted by π. In the below figure, the angle values are represented in degrees instead of radians.
Cos 60 Degree graph
You have learned about cos 60 degrees value along with other degree’s values here now. Also, the derived values for sin and tan with respect to degrees and radians. In the same way, we can find the values for other trigonometric ratios like secant, cosecant and cotangent.
Let us see some example where we can use the value of cos 60 degrees.
Example 1: Find the value of cos 60° + sin 30°.
Solution:
cos 60° + sin 30°
= cos 60° + sin (90° – 60°)
= cos 60° + cos 60°
= (1/2) + (1/2)
= (1 + 1)/2
= 2/2
= 1
Alternatively, cos 60° + sin 30° = (1/2) + (1/2) = (1 + 1)/2 = 2/2 = 1
Example 2: Calculate: 2 sin 60° – 4 cos 60°
Solution:
We know that, sin 60° = √3/2 and cos 60° = 1/2
Thus, 2 sin 60° – 4 cos 60° = 2(√3/2) – 4(1/2)
= √3 – 2
therefore it 3/2
Step-by-step explanation: Peace Out.... Have a good day
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0.000007328 rounded to the nearest millioneth,the numbers is about
When the numerical data (number) 0.000007328 is rounded to the nearest millionth, the number is about 0.000007.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsTen thousandthsHundred thousandthsMillionths.UnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.Based on the numerical data (number) provided above, the place value of seven (7) is millionth and it would be rounded up as seven (7) because the next number on its right (3) is less than five (5) and as such, it can seven (7) rounded up to eight (8).
In this context, we can reasonably infer and logically deduce that 0.000007 is a numerical data (number) that represents millionth based on the place value of seven (7).
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the hypotenuse of a triangle is 4x one of the legs . the other leg in 3(sqrt 5 units. find the length of the hypotenus?
The length of the hypotenuse is 4√3 units.
Given that hypotenuse is 4 times the length of one leg of a triangle. So here we can assume that length to be x. Hence the hypotenuse length is 4x. To calculate hypotenuse we have the formula a²=b² + c², where b and c are two sides of the triangle and a is the hypotenuse. If we put these values in the formula we get,
16x² = x² + (3√5)²
15x² = 45
x² = 3
x = ±√3
Since length cannot be negative, the final value of x = √3, and since the length of the hypotenuse was 4x, the final value of the hypotenuse is 4√3.
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Which of the coordinate pairs below are separated by a vertical
distance of greater than 6 units? Select all that apply.
A) (5.1, -3.3) and (5.1, 3.4)
B) (-1, 2.6) and (-1, -4.2)
C) (3.7, 2.2) and (3.7, -3.4)
D) (6, 1.5) and (6, -2)
Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.
Given that,
The coordinate pairs separated by a vertical distance of greater than 6 units is to be determined.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
here,
(A)
Since the x coordinate is the same in all the pairs, distance on the y axis can only be calculated.
(5.1, -3.3) and (5.1, 3.4)
y = 3.4 - (-3.3)
y = 6.7
Similarly distance,
(B) y = 6.8
(C) y = 5.6
(D) y = 3.5
Thus, Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.
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you want to know the opinions of american school teachers about establishing a national test for high school graduation. you obtain a list of the members of the national education association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. by the deadline, 1347 teachers return the questionnaire. the population is
The list of the members of the national education association is the Population.
Given, that a list of the members of the national education association is obtained and the questionnaire is mailed to 2500 teachers chosen at random from the list.
1347 teachers from those 2500 teachers return the questionnaire.
So, as we know that
A population is the group that you want to draw conclusions about.
Here, we want to know the opinions of American school teachers about establishing a national test.
So, The list of the members of the national education association is the Population.
Also, 1347 responses which we got is the sample.
Hence, The list of the members of the national education association is the Population.
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cosec 2A + cosec 4A = cot A - cot 4A
The given expression is proved by the necessary changes.
cosec 2A + cosec 4A = cot A - cot 4A
Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A
Taking LHS :
⇒Cosec 2 A + Cot 4 A
⇒Cosec 2 A + ( Cot 2 A )2
⇒Cosec 2 A + ( Cosec 2 A - 1 )2 ( we know:1+ Cot 2 θ = Cosec 2 θ )
⇒Cosec 2 A + Cosec 4 A + 1 - 2 Cosec 2 A
⇒ Cosec 4 A + 1 - Cosec 2 A
⇒ Cosec 4 A + 1 - ( 1 + Cot 2 A)
⇒ Cosec 4 A + 1 - 1 - Cot 2 A
⇒ Cosec 4 A - Cot 2 A
or cosec2A+cosec4A=cotA-cot4A
Hence Proved.
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let x represent one number and let Y represent another number.
The sum of two numbers is -7.
If one number is subtracted from the other, their difference is 11.
Use the given conditions to write a system of equations.
Solve the system and find the numbers
Answer:
c I got you ok answer c
Step-by-step explanation:
bc I got this correct
Answer:
Its D, x+y=-7;x-y=11. Also Part 2 is 2,-9
Step-by-step explanation:
Just did it Pearson 2022
Find the equation to represent the volume of
a cylinder with diameter 10 and height of 2x.
The volume of a cylinder is 50πx
We know that
The volume (V) of a cylinder is,
V = πr²h
where
r is the radius of the cylinder
h is the height of the cylinder
From the question, we have
a cylinder with diameter 10 and height of 2x.
r = 10/2 =5
V = πr²h
V = π*5²*2x
V = 50πx
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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if we want to create a 95% confidence interval for a population proportion with a margin of error (m) of 0.099, what sample size is necessary? use the simplified formula (n
For the specified requirements, 97 sample size are required.
Given that,
Confidence Interval = 95
Margin of error (m) =0.099
We know , to find Sample size for estimating a population proportion
n = (Z*/m)² P(1-P)
where , m is margin of error
P is estimated proportional value.
If we have no preconceived of the value of the population proportion
, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.
for a 95% confidence interval ,
Z* = 1.960 , m=0.099
Using equation we get
n = (1.96/0.099)²(0.5)( 1 - 0.5 )
By solving,
n = 97.02≅ 97
The necessary sample size is 97
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8 Write an equation of the line passing through the point (-7,-6) with slope m = 4
the wheels on Kiran's bike are 64 inches in circumference. How many times doo the wheels rotate if Kiran rides 300 yards ?
Answer:
169 times
Step-by-step explanation:
We know that the circumference of Kiran's bike wheel is 64 inKiran rides total distance of 300 yardsTo find number of rotations made by wheel...
Know that 1 yard = 36 in
300 yards = 36 x 300 = 10800 in
Number of rotation = Total distance covered by wheel ÷ Circumference of wheel
Number of rotations = 10800 ÷ 64 = 168.75 ≅ 169
Therefor, the wheel rotates = 169 times
Hope this helps! :)