Given that the hoop makes one complete oscillation in 2s, this implies that the period of oscillation is 2s
Then,
T = 2s
Let the Mass of the thin hoop be M
Let the Radius of the hoop be R
The moment of inertial of a hoop is
I = MR²
The period of a physical pendulum of small amplitude is given by
T = 2π √(I / Mgd)
Where,
T is the period in seconds
I is the moment of inertia in kgm²
M is the mass of the hoop
g is the acceleration due to gravity
g = 9.8m/s²
d is the distance from the rotational axis to the center of gravity
Therefore, d = R
Then, applying the formula
T = 2π √ (I / MgR)
So, we know that
I = MR²
Then,
T = 2π √( MR² / MgR)
T = 2π √(R/g)
Make R the subject of the formula
Square both sides
T² = 4π²(R/g)
T²g = 4π²R
Then, R = T²g / 4 π²
Since g = 9.8m/s² and T= 2s
R = 2² × 9.8 / 4π²
R = 0.993m
Then, the radius of the hoop is 0.993m
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an angle measures 84 degrees, and a circle is centered at the angle's vertex. the subtended arc along this circle is how many times as long as 1/360th of the circle's circumference?
The measure of this angle is 172°.
Circumference: Any shape's circumference establishes the path or boundary that encircles it. To put it another way, the circumference and perimeter both refer to the length of a shape's outline.
When two of its rays pass through the endpoints of an arc, line segment, or other section of a curve, the angle is subtended by that arc, line segment, or other section of the curve.
From the information provided.
The circle's 1/360th circumference measures 0.5 cm in length.
Total circumference of circle now will be
360*0.5cm
= 180cm
However, if a 360° angle is equivalent to a circumference of 180 cm;
Then, an angle that subtends with 86 cm long will be:
=(86/180)*360
=172°.
Therefore, the measure of this angle is 172°
Given Question is incomplete complete question here
A circle is centered at the vertex of an angle, and the angle's rays subtend an arc that is 86 cm long. 1/360th of the circumference of the circle is 0.5 cm long. What is the measure of this angle in degrees?
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40% of the students like music, and 12% of the students like music and dance.what percent of those that like music also like dance?
the students that like music also like dance is 30%.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
40% of the students like music
12% of the students like music and dance.
p(A)=0.4
p(A∩B)=.12
p(A|B)= p(A∩B)/p(A)
=0.4/0.12= 0.3
Hence the students that like music also like dance is 30%.
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-16 5/8-(13 3/8) please help
Answer:
-30
Step-by-step explanation:
Your welcome.
each square of the three by three grid is painted so that the whole picture has at least the two lines of symmetry indicated. each grid square is painted one solid color. what is the maximum number of colors that could have been used?
3 colors are the maximum that can be used.
What is square?
Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
each square of the three-by-three grid is painted so that the whole picture has at least the two lines of symmetry indicated.
each grid square is painted one solid color
Based on the symmetry lines the groups that must be the same color are
{1,3,7,9}
{2,4,6,8}
and {5}
Hence, 3 colors are the maximum that can be used.
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Three times a number, minus nine, equals six times six, divided by four. In the box, type an equation to represent this situation. Use capital X for the variable and a small x to show multiplication. Show division with a slash (/). Do not add any spaces.
Answer:
Answer:
3X-9=(6x6)/4
Step-by-step explanation:
a boat travels 42 miles upstream in 3 hours looking for a lost diver. it then travels downstream 70 miles in 2 hours. write a system to represent the situation. then find the speed of the boat and the speed of the current. use b for boat and c for current.
The system of equations for the given situation are 14=b-c ; 35=b+c and the speed of boat is 24.5 miles/hr and speed of current is 10.5 miles/hr.
Given,
Distance covered by boat in upstream in 3 hours = 42 miles
Distance covered by boat in downstream in 2 hours = 70 miles.
Let
speed of boat in still water be 'b'
speed of current of stream be 'c'
we know that distance=speed x time
If the boat is moving upstream, the current (which is 'c' miles per hour) will push against it, reducing the boat's speed by 'c' miles per hour. The boat's resulting speed (as it travels upstream) is 'b-c' miles per hour. If, on the other hand, the boat is travelling downstream, the current will push it faster, increasing the boat's speed by 'c' miles per hour. The boat's downstream speed is 'b+c' miles per hour as a result.
Then the system of equations will be
distance while going upstream ,
distance=speed x time
42=(b-c)(3)
14=b-c....i
distance while going downstream,
70=(b+c)(2)
35=b+c....ii
solving eq. i and eq. ii
14=b-c
35=b+c
------------
49=2b
b=24.5
Substitute in eq. i,
14=24.5-c
c=24.5-14
c=10.5
Thus, the boat's speed is 24.5 miles per hour and the current's speed is 10.5 miles per hour.
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Help please! It’s for an assignment. My grade is low and I need to bring it up
Answer:
Step-by-step explanation:
i think it is 74
50 points decreased by 26%
step by step
Answer:
37
Step-by-step explanation:
50*26%
50-(50*26%)
oliver saves 10% of his weekly earnings for living expenses. he usually makes $520 each week. This week made 10% more. oliver incorrectly claims that he has $520 left for spending money oliver this week. Calculate the amount of spending money has left for this week. What error did likely make?
Answer:
Step-by-step explanation:
10% of $520 is $52, so that's what Oliver usually saves each week.
This week he earned 10% more, which is $52. $520 + $52 = $572
10% of $572 is $57.20
His pay minus his living expenses is $572 - 57.20
He has $514.80 to spend
Since 10% of $520 is $52 and that's what he usually saves, it looks like he just went with that instead of adding the $52 to the $520 and then deducting 10%
4. 32, 16, 8, ___ ___ ___
Rule: _____________
Answer:
32, 16, 8, 4, 2, 1
Step-by-step explanation:
32, 16, 8, 4, 2, 1
Rule: Divide by 2 the previous number
A triangle has vertices a(-2, 3), b(0, 0), and c(1, 2). What are the coordinates of the vertices if the triangle is reflected over the y-axis and then dilated by a scale factor of 2?.
The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.
Define scale factor.The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Given
In line with the posed question.
Triangle ABC's vertices are A(-2, 3), B(0, 0), and C. (1, 2).
As we are aware,
The x-coordinates of each point must be negative while keeping the y-value constant in order to reflect a triangle over the y axis.
As a result, when triangle ABC is mirrored across the y-axis, its vertices are
A'(2,3)
B'(0, 0)
C'(-1, 2)
The vertices of the triangle will also change when it is dialated by a scale factor of 2.
A'(4, 6)
B'(0, 0)
And, C'(-2, 4)
The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.
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true or false: a) every unitary operator u : x ! x is normal. b) a matrix is unitary if and only if it is invertible.
True, Every normal unitary operator u: x! x exists.
False, An if only if it is invertible, a matrix qualifies as unitary.
What is the matrix?
A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix, are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.
Here, we have
a. Every unitary operator U:X→X is normal as an operator A is unitary if A*A = AA* = I and an operator is normal if A*A = AA*.
Hence, every unitary operator u: x → x is normal.
b. A unitary matrix is always invertible but an invertible matrix need not be unitary. An invertible matrix A is unitary if A⁻¹ = A*
Hence, it is not true.
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alina wants to make keepsake boxes for her two best friends. she doesn't have a lot of money, so she wants to make each box described so that it holds as much as possible with a limited amount of material. for eliza, alina wants to make a rectangular box whose base is twice as long as it is wide. this box will be lined on the entire inside with velvet and in addition the outside of the top of the box is to be lined in velvet. if alina has 300 square inches of velvet, how can she make eliza's box so that it holds as many keepsakes as possible? find the width (w), length (l), and height of the box in inches. (round your answers to three decimal places.)
The width, length and height of the box is 12.247 inch, 24.494 inch, 73.482 inch respectively.
We have given that Alina wants to make a rectangular box whose base is twice as long as it's wide and alina has 300 square inches of velvet.
i.e A = l × w
it s given that l = 2w
∴ A = 2w²
⇒ 300 = 2w²
w² = 150
w = 12.247 inch
i.e. l = 2w
l = 2(12.247)
l = 24.494 inch
Therefore length of the box is 24.494 inch and width is 12.247 inch.
Now we have to find height of the box.
For the height of rectangle we know the formula
i,e, Height = [tex]\frac{P}{2}[/tex] - w
where P is perimeter
we will first find perimeter of rectangle.
Therefore P = 2(l + w)
P = 2(24.494 + 12.247)
P = 2(36.741)
P = 73.482 inch
Hence the height of the rectangle is 73.482 inch.
Therefore the Eliza's box that Alina make has width 12.247 inch, length 24.494 inch and height 73.482 inch.
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The vertices of a quadrilateral are a(-3,-1), b(1,5), c(5,5), and d(5,-1). Select the statement that represents this quadrilateral.
B. Due to the fact that ABCD has at least two parallel sides in one pair.
The y-coordinates of the two points A(-3, 1) and D(5, 1) are identical.
Then
The x-axis and the line AD are parallel.
As opposed to that,
The y-coordinates of the two points B(1,5) and C(5,5) are identical.
Then
The x-axis and the line BC are perpendiculars.
We discover:
• AD lies along the x-axis.
BC is perpendicular to the x-axis.
Therefore
AD / BC
Conclusion:
Due to the fact that ABCD contains at least two parallel sides in one pair.
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This is for edmentum 75 POINTS!! Modeling with Functions
Monica and Shanna are saving the money they earn from their after-school jobs to go on a school trip. Monica starts with $20 and then saves $14 each week. Shanna's savings are shown in the table.
Identify the function types that would best model Monica's and Shanna's total savings.
Select the correct answer from each drop-down menu.
options are: Linear, quadratic, and exponential
The function are Linear that would best model Monica's and Shanna's total savings.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Monica and Shanna are saving the money they earn from their after-school jobs to go on a school trip.
Here, Monica starts with $20 and then saves $14 each week. Shanna's savings are shown in the table.
Hence, The function for Monica is,
⇒ y = 20 + 14x
Where, x is number of weeks and y is total cost.
And, For Shanna's;
The equation is find as;
Two points from table are (0, 0) and (1, 18)
Hence, The equation is,
⇒ y - 0 = (18 - 0) / (1 - 0) (x - 0)
⇒ y = 18x
Thus, Both function for best model Monica's and Shanna's total savings is Linear function.
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Mr. Jones needs to build a fence in his backyard to keep their dog safe. The length of the fence should be at least 60 ft, and the distance around should be no more than 260 ft. Which system of inequalities and graph represent the possible dimensions of the pen?
The system of inequalities that represents the possible dimensions of the pen is given as follows:
x ≥ 60.y > 0.x + y ≤ 130.The graph of the system is given by the image given at the end of the answer.
How to built the system of inequalities?The first step in building the system of inequalities is identifying the variables, which are given as follows:
Variable x: length of the pen.Variable y: width of the pen.The length of the fence should be at least 60 ft, hence:
x ≥ 60.
The distance around should be no more than 260 ft, hence, considering the perimeter of the fence:
2x + 2y ≤ 260
x + y ≤ 130.
The dimensions cannot be negative, hence another restriction needed is:
y > 0.
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The sale price for an item is $72, the discount is 64% off, what is the original price???
Answer: The original price is 200$
Step-by-step explanation:
original price = 100 percent
100-64=36
36% =72
100%= x
use cross multiply
36x=100*72
36x=7200
x=200
The original price is 200$
Answer:$200
Step-by-step explanation:
$72 is 100-64 or 36% if the original price.
First, we convert the percentage into a decimal number.
So, 0.36.
Next we divide that by $72
The answer is $200
Does anybody know the answers to the Carnegie skills practice on pages 39 to 41 I need help it's due tomorrow
the general convention is to reject a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect. True or False
The general convention is to reject a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect. This is False.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
After a performing a test, scientists can reject the null hypothesis meaning there is a definite, consequential relationship between the two phenomena
In this case, the convention is to accept a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect.
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When θ = 28° , which equation can be ued to find the ditance from point A to point B?
Equation which is used to find the distance between the given points A and B for the given θ = 28° is equal to AB = x cos28°.
Diagram is attached.
As given in the question,
Diagram is attached.
Given angle θ = 28°
Hypotenuse = x
Two points A and B is on the base
Base - length = AB
In the given triangle,
Equation represents the distance between two points is:
cosθ = base / hypotenuse
⇒ cos 28° = AB / x
⇒ AB = x cos 28°
Therefore, the equation used to represent the distance between two point A and B is equal to AB = x cos28°.
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Which of the following could be the length of the third side of a triangle with side lengths 2 feet and 10 feet?
Answer:
Below
Step-by-step explanation:
Due to the triangle side length rule, these two sides added together must be greater than the third side
so the third side could be 11 10 9
8 -7-6-5-4-3-2-1 will not work because 2 + these sidelengths do not sum to greater than the third side 10
a program admissions coordinator wanted to know if the math placement test given to a certain cohort of students was an indicator on how well they would perform on their first exam. she records the scores of their placement test and first exam below. is there a correlation between these measures? placement exam 1 11 49 27 71 7 60 33 85 28 80 23 75 20 61 48 100 35 71 26 81
Yes, there is a correlation between these measures. The higher the placement exam score, the higher the student's score on their first exam tends to be. For example, students with placement exam scores of 11 and 49 had first exam scores of 27 and 71 respectively, indicating that the higher the placement exam score, the higher the first exam score.
What does the word "measure" mean?A measure in mathematics is a generalization of the ideas of length, area, and volume. Measures are sometimes referred to as "mass distributions" informally. A measure, in more exact terms, is a function that gives numbers to particular subsets of a given set. This quantity is described as the set's measure.
What are some measures' examples?To measure length or distance, this system employs inches, feet, yards, and miles. Volume or capacity are expressed in fluid ounces, cups, pints, quarts, or gallons. In ounces, pounds, and tons, weight or mass is expressed.
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Find the probability that a randomly selected car from this sample had 222 doors or 444 doors.
A car is selected from random sample of 100 cars,
a) The events for which the selected car has 2 doors and 4 doors are mutually exclusive event ;
i.e P(A ∩ B) = 0.
b) The probability that a randomly selected car from this sample had 2 doors or 4 doors is 0.77..
Mutually exclusive event :
A and B are mutually exclusive if they cannot occur at the same time. This means that A and B have no common result and P(A and B) = 0.
We have given a Venn diagram which consists the cars have sunroof , 2 doors and 4 doors.
Firstly we need to understand the Venn diagram properly for determining the required probability values.
From Venn diagram ,
Total number of cars in sample = 100
Cars with sunroof only = 13
Number of cars with 2 doors only = 14
Number of cars with 4 doors only = 25
Number of cars with sunroof and 2 doors = 18
Number of cars with sunroof and 4 doors = 20
a) let us consider two events A and B
A : car with two doors
B : car with four doors
As we see in Venn diagram,
the number of cars with 4 doors and 2 door, n(A∩B) = 0 => P(A and B) = 0
so, by definition of mutually exclusive event
A and B are are mutually exclusive events.
b) Probability that car with 2 doors, P(A)
= favourable outcomes for A / total outcomes
= 14+18/100 = 32/100
Probability that car with 4 doors, P(B)
= favourable cases for B/ total outcomes
= 25+20/100 = 45/100
Probability that randomly selected car from this sample had 2 doors or 4 doors = P( A or B)
= P(A) + P(B) = 77/100 = 0.77
Hence, the required probability is 0.77..
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Complete question:
Two-way tables, Venn diagrams, and probability Sunroof 13 10 18 20 14 25 2 doors 4 doors In this sample, are the events "2 doors" and "4 doors" mutually exclusive? Choose 1 answer A Yes O No Find the probability that a randomly selected car from this sample had 2 doors or 4 doors. O of 4
What happens to an image after a dilation?
After dilation, the shape of the image and preimage will be same, but the size will be different
The dilation is the one form of transformation, that will change the size of the original figure, but the shape of the figure remains same
Consider a triangle and dilating the triangle by a scale factor of 3
The scale factor 3 means the size of the original image will enlarge by three times of the original size .
Still the shape of the triangle will be same, but the size of the triangle changed according to the dilation
Therefore, size of the image will change, but the shape will not change
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sergio read the first 18 pages of a novel in 2 hours what is the unit rate at which he is reading plss help asap tysm <3
The answer will be (9)
Step-by-step explanation:
The first step to dividing fractions of 18 divide 2 than (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators.
If Sergio read 18 pages of novel in 2 hours, than he's only reading 9 pages at a time than the next!
Plssss need help
Don’t understand
Evaluate the expression for the given value of the variable. 49 + 1/8y, y= -1/2
Answer:
48 and 15/16
Step-by-step explanation:
49+1/8(-1/2)
49+(-1/16)
48 and 15/16
The required value of the expression is 3 when substituting the value of -1/2 for y.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question as:
49 + 1/8y
To evaluate the expression, we need to substitute the value of -1/2 for y. Doing this gives us:
⇒ 49 + 1/8(-1/2)
⇒ 49 + (-1/16)
Simplifying the expression further gives us:
⇒ 49 - 1/16
⇒ (16 × 3 + 1 - 1)/16
⇒ 48/16
Apply the division operation, and we get
⇒ 3
Therefore, the final value of the expression is 3.
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Write the fraction as a percent. 18/20=
Answer:
90%
Step-by-step explanation:
Do 18 divided by 20 you get 0.9 which equals 90% since the 9 is in the tens place.
PLEASE HELP ME!!!
Jack ran mile and Roy ran mile.
a. What benchmark fractions can be used to estimate how much farther Roy
ran than Jack?
b. Using the benchmark fractions, what is a reasonable estimate for the
difference between the two distances?
c. What is the actual difference?
Answer:
C
Step-by-step explanation:
If they both ran a mile its the same thing I think
What is the equation of the line that passes through (- 1/3 and has a slope of 2?
The equation of a line that passes through [tex](-1,3)[/tex] and has a slope [tex]2[/tex] is [tex]y=2x+5[/tex]
The equation of the line passes through the point is [tex](-1,3)[/tex]
One point and the slope are given, we will use one point form i.e.
[tex]y=mx+c.....(1)[/tex]
The point [tex](-1,3)[/tex] satisfies the equation and the slope is [tex]2[/tex]
Plug in these values in (1)
[tex]3=2(-1)+c\\3=-2+c\\c=3+2\\c=5[/tex]
Plug in the value of slope and c is
The equation becomes [tex]y=2x+5[/tex]
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