there is a 20% chance that the point chosen at random will lie on bg.
To find the probability that a point chosen at random will be on the line segment bg, we need to consider the length of bg in relation to the length of the entire line segment ak.
Let us assume that ak is a straight line segment, and bg is a smaller segment that lies entirely within it. To find the probability, we need to divide the length of bg by the length of ak.
Let the length of bg be x and the length of ak be y. Then the probability that a point chosen at random will be on bg is:
Probability = Length of bg / Length of ak
Probability = x / y
However, we need to be careful here. If we choose a point anywhere on ak, it may not necessarily lie on bg. There are an infinite number of points on ak, but only one segment bg. Therefore, the probability we are looking for is actually the ratio of the lengths of bg to ak.
So, if we know the lengths of bg and ak, we can find the probability by dividing them. For example, if bg is 2 units long and ak is 10 units long, the probability of choosing a point on bg is:
Probability = 2 / 10
Probability = 0.2 or 20%
In this case, there is a 20% chance that the point chosen at random will lie on bg.
In conclusion, the probability of a point chosen at random on ak being on bg is directly proportional to the length of bg in relation to the length of ak. Therefore, we need to find the ratio of the lengths of the two line segments to determine the probability.
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what is the probability a point is chosen at random on ak and then the point will be on bg. dont forget to reduce the products?
HELP ME ASAP!!! YOU WILL BE BRAINLIEST
We can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability.
What is probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
The theoretical probability of rolling a 5 on a fair die is 1/6, which means that if the die is rolled many times, we would expect to see a 5 about 1/6 of the time.
For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:
experimental probability = number of 5's rolled / number of trials
experimental probability = 25/100
experimental probability = 0.25
So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.
For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:
experimental probability = number of 5's rolled / number of trials
experimental probability = 30/200
experimental probability = 0.15
So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.
Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.
On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.
Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.
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We might say that Maya's experimental probabilities oscillate about the theoretical probability, but after more trials, the experimental probabilities ought to converge to the theoretical probability.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
A fair die has a theoretical probability of rolling a 5 of 1/6, therefore if the die is rolled several times, we can anticipate seeing a 5 roughly 1/6 of the time.
For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:
experimental probability = number of 5's rolled / number of trials
experimental probability = 25/100
experimental probability = 0.25
So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.
For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:
experimental probability = number of 5's rolled / number of trials
experimental probability = 30/200
experimental probability = 0.15
So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.
Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.
On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.
Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.
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list all symmetry groups that are the symmetry groups of quadrilaterals and for each group sketch a quadrilateral
The quadrilaterals which have both line and rotational symmetry of order more than 1 are square, and rhombus
Symmetry is a fundamental concept in mathematics and geometry. It refers to the property of a shape that remains unchanged when it is transformed in a certain way.
Now, let's talk about quadrilaterals that have both line and rotational symmetry of order more than 1. One example of such a quadrilateral is a square.
Another example of a quadrilateral with both line and rotational symmetry of order more than 1 is a rhombus. A rhombus is a type of quadrilateral where all four sides are equal in length, and opposite angles are equal.
In summary, a square and a rhombus are examples of quadrilaterals that have both line and rotational symmetry of order more than 1.
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Complete Question:
Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Find the standard normal area for each of the following (LAB)Round answers to 4 decimals
The answer of the standard normal area for each of the following questions are given below respectively.
What is standard normal area?Standard normal area refers to the area under the standard normal distribution curve, which is a normal distribution with a mean of 0 and a standard deviation of 1.
a. P(1.24<Z<2.14) = 0.0912
b. P(2.03 <Z<3.03) = 0.0484
c. P(-2.03 <Z<2.03) = 0.9542
d. P(Z > 0.53) = 0.2977
Note: The standard normal distribution is a continuous probability distribution with mean 0 and standard deviation 1. The area under the curve represents probabilities and can be calculated using a standard normal distribution table or a calculator with a normal distribution function.
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Complete the recursive formula of the arithmetic s -17,-8, 1, 10, .... a(1) = -17 a(n) = a(n − 1)+
Answer:
The common difference between consecutive terms in the sequence is 8 (since -17 + 8 = -9, -9 + 8 = -1, -1 + 8 = 7, and so on). Therefore, the recursive formula for this arithmetic sequence is:
a(1) = -17
a(n) = a(n-1) + 8 for n >= 2
This formula says that the first term in the sequence is -17, and each subsequent term is found by adding 8 to the previous term.
(please mark my answer as brainliest)
Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation.
The result of the division in ordinary decimal notation is 300.
Scientific notation, also known as standard form or exponential notation, is a method of expressing very large or very small numbers in a compact and standardized way.
To perform the indicated operation, we need to divide 0.00036 by 0.0000012.
First, let's express both numbers in scientific notation
0.00036 = 3.6 x 10^(-4)
0.0000012 = 1.2 x 10^(-6)
Now we can divide the two numbers and simplify
3.6 x 10^(-4) / 1.2 x 10^(-6) = (3.6 / 1.2) x 10^(-4-(-6)) = 3 x 10^(2)
Finally, we can convert this result back to ordinary decimal notation
3 x 10^(2) = 300
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The given question is incomplete, the complete question is:
Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation. 0.00036/0.0000012
Does the expression 56x+40y-48z=8(7x+5y-6z)
For all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.
Explain expression using an example.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.
Indeed, for all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.
We can simplify both sides of the equation to understand why:
56x + 40y - 48z = 8(7x + 5y - 6z)
56x + 40y - 48z = 56x + 40y - 48z
As we can see, the equation is true for all values of x, y, and z because both sides are identical.
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y=4(x+5)^2+16 can you help me
To solve this equation, begin by expanding the parentheses.
y = 4x² + 40x + 100 + 16
Then, collect like terms on the left hand side.
y = 4x² + 40x + 116
Finally, rearrange the equation to get y on the left side.
4x² + 40x - (y - 116) = 0
The final answer will be a quadratic equation.
Given two points (x1, y1) and (x2, y2) in the cartesian plane, show that the slope
m of a line is of the form
m =y2 − y1÷x2 − x1
assuming that x2≠ x1
therefore, we have shown that: [tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})[/tex] assuming that x2 ≠ x1.
What is slope?Slope refers to the measure of steepness of a line or a curve. In mathematics, slope is usually denoted by the letter "m" and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on a line.
The formula for calculating the slope between two points (x1, y1) and (x2, y2) on a line is:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})[/tex]
by the question.
To finds the slope of a line passing through two points (x1, y1) and (x2, y2), we use the slope formula:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})[/tex]
This formula represents the change in y divided by the change in x between the two points.
Now, assuming that x2 ≠ x1, we can simplify the formula as follows:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})*(1/1)[/tex]
Multiplying the numerator and denominator by 1, which in this case is (x2 - x1) / (x2 - x1), we get:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})*(x_{2}-x_{1})/(x_{2}-x_{1})[/tex]
Simplifying the numerator, we have:
[tex]m= (y_{2} -y_{1} )/(x_{2}-x_{1})/[(x_{2}-x_{1})*1][/tex]
The term (x2 - x1) cancels out, leaving us with:
[tex]m=(y_{2}-y_{1} /1[/tex]
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change these fractions to decimals 1/35
Answer:
Step-by-step explanation:
Consider the following algebraic statements and determine the values of x for which each statement is true.
8=-|x|
Answer:
This is false.
Step-by-step explanation:
Since absolute value bars change negatives into positives and positive into themselves (positives) we can put the example:
[tex]-|8|\\[/tex]
When we remove the absolute value bars, 8 will still equal 8. But, we have a negative, therefore the 8 has a negative after being simplified with absolute value.
x = -8, not positive 8.
Answer:
Ther are no values of x that would make this statement true. There is no solution.
Step-by-step explanation:
here are the factors of sixteen and twenty. click the factors that are common to both numbers. (choose 3)
The common factors of sixteen and twenty are 1, 2, and 4.
The factors of sixteen are 1, 2, 4, 8, and 16. The factors of twenty are 1, 2, 4, 5, 10, and 20. The factors that are common to both numbers are 1, 2, and 4.
To calculate the factors of sixteen, we can start by dividing sixteen by two until we cannot divide any further. We can start with sixteen divided by two, which equals eight. Eight divided by two equals four. Four divided by two equals two. Two divided by two equals one. As we can see, the factors of sixteen are 1, 2, 4, 8, and 16
To calculate the factors of twenty, we can start by dividing twenty by two until we cannot divide any further. We can start with twenty divided by two, which equals ten. Ten divided by two equals five. Five divided by two equals two. Two divided by two equals one. As we can see, the factors of twenty are 1, 2, 4, 5, 10, and 20.The common factors of sixteen and twenty are 1, 2, and 4. This can be determined by comparing the two lists of factors. As we can see, 1, 2, and 4 are present in both lists.
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Complete question
What are the common factors of sixteen and twenty ?
Can someone pls help me it would mean so much to me
Answer: y = 3x-2 (for first question)
Step-by-step explanation:
Equation of the line: y = mx+c. For A, it passes through (0, -2) and has a gradient of 3. So, you substitute the values inside the equation.
x = 0
y = -2
m = 3
-2 = 0+c
c= -2
ans: y = 3x-2
Use the same method to complete the rest of the questions. GL
Note: I am just a student, if I get this wrong I hope someone corrects me, thanks
the answer is supposed to be 799 & 7188, but I don't know how to get there
Doing simple algebra with the two summations we can see that:
[tex]\Sigma x = 799\\\\\Sigma x^2 = 7,188[/tex]
How to find the values of the two summations?First, we know that there are 97 passengers, and we know that the summation:
[tex]\Sigma (x - 5) = 314[/tex]
Where x represents the weights.
Then we can rewrite that sum as:
[tex]\Sigma (x - 5) = \Sigma x - 97*5[/tex]
And replace that in the original equation to get:
[tex]\Sigma x - 97*5 = 314\\\Sigma x = 314 + 5*97 = 799[/tex]
So that is the first summation, now let's get the second one, we can rewrite the summation as:
[tex]\Sigma (x - 5)^2 = \Sigma x^2 - 10x +25 \\\\\Sigma x^2 - \Sigma 10x + \Sigma 25[/tex]
Where remember we have 97 terms, and the summation is equal to 1623, then:
[tex]\Sigma x^2 - \Sigma 10x + 25*97 = 1623[/tex]
Now we can replace the second term by the thing we found earlier:
[tex]\Sigma x^2 - 10\Sigma x + 25*97 = 1623\\\\\Sigma x^2 - 10*799 + 25*97 = 1623\\\\\Sigma x^2 = 1623 + 10*799 - 25*97\\\\\Sigma x^2 = 7,188[/tex]
That is the answer.
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Pls help !! I will mark brainilest
Answer:
m = -1
Step-by-step explanation:
may not be accurate, I haven't done this in a while
Answer:
-1y−y1=m(x−x1)
y−6=−1(x+5)
y−6=−1x+(−1×5)
y−6=−1x+−5
y−6=−1x−5
y=−1x−5+6
y=−1x+1
y=−x+1
m=−1
b=1
Step-by-step explanation: Hope this helps!! Mark me brainliest!
Is this figure a polygon dont answer if you don’t know the answer
Polygon - a plane figure with at least three straight sides and angles, and typically five or more.
Answer:
No
Step-by-step explanation:
Since a polygon has straight sides, with 3 or more, it cannot be a polygon since one side is curved.
please help me with 4 math questions
Using linear negative association, According to the all four parts correct options are D ;A ;D ;D respectively
What is linear negative association?The slope of a line expresses a great deal about the linear relationship between two variables. If the slope is negative, there is a negative linear relationship, which means that as one variable increases, the other variable decreases. If the slope is zero, one increases while the other remains constant.
The first answer to the question is option D
The second answer to the question must be option A
Option D must be chosen for the third question.
Option D must be selected for Question 4.
Solution:
1.
square of 3 is 9
3 to the power of negative 2 is 1/ 9
cube of 3 is 27
3 to the negative power 3 is 1/27
2.
cylinder volume =πr²h
Given value
pi =3.14
r=5
h=10
Volume=3.14×5²×10
cylinder volume =785m³
3.
When a point is rotated 90 degrees anticlockwise about the origin, it becomes the point (x,y) (-y,x).
The coordinates of Point N are (4, 3)
N' will be the new coordinates (-3, 4)
As a result, the y-coordinate of N' is 4.
4.
Option D must be selected for Question 4.
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(-2) to the second power - (-28) divided by 7
Answer:
≈ 4.57
Step-by-step explanation:
(-2) ^ 2 = 4
4 - (-28) = 4 + 28 = 32
32/7 ≈ 4.57
Can someone actually see if I got this answer correct please
Instead of 2.00 as mentioned in the question, the semester GPA is 1.38. Please double-check your calculations or provide more details if you made an error when reporting your grades or computing your GPA.
How many credit hours are there in three?Students must devote approximately 135 hours (45 x 3) of class, instructional, and independent time to a three credit unit course. Students who enroll in a course for four credit hours must dedicate around 180 (45 x 4) hours to it, split between in-class and out-of-class work.
You must first translate each letter grade using the common 4.0 scale into its equivalent numerical number before you can determine your semester GPA:
A = 4.0
B = 3.0
C = 2.0
D = 1.0
F = 0.0
E = 0.0 (equivalent to F)
Then, you can use the formula:
(Total grade points) / GPA (total credit hours)
Using this formula, we can calculate your semester GPA as follows:
FYE 105: F (0.0) x 3 credit hours = 0.0 grade points
MAT 150: E (0.0) x 3 credit hours = 0.0 grade points
ENG 101: D (1.0) x 3 credit hours = 3.0 grade points
BIO 112: A (4.0) x 3 credit hours = 12.0 grade points
BIO 113: B (3.0) x 1 credit hour = 3.0 grade points
Total grade points = 0.0 + 0.0 + 3.0 + 12.0 + 3.0 = 18.0
Total credits earned is 13 (3 + 3 + 3 + 3 + 1)
GPA = 18.0 / 13 = 1.3846
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6TH GRADE MATH IS THIS CORRECT??
Answer:
Step-by-step explanation:
y2-y1/x2-x1
-7-(-19)/-2-1
12/-2
-6
The slope is -6
CAN SOMEONE PLEASE HELP thank you so so much please!!!
Step-by-step explanation:
try this option, all the details are in the attachment.
6TH GRADE MATH, What is the y intercept in the equation y= 4x - 8??
Graph the function.
f(x) = 3/5x -5
Use the Line tool and select two points to graph.
Answer:
see attached
Step-by-step explanation:
You want to graph the function f(x) = 3/5x -5.
GraphFor graphing purposes, it is convenient to choose values of x that result in integer values of y. In this case, the multiplier of x (the slope) has a denominator of 5, so it is convenient to choose x-values that are multiples of 5.
For x = 0, y = 3/5·0 -5 = -5
For x = 5, y = 3/5·5 -5 = 3 -5 = -2
Suitable points for your plot are (0, -5) and (5, -2). These are shown in the attachment.
Part A
Use GeoGebra to graph points A, B, and C to the locations shown by the ordered pairs in the table. Then join each pair of
points using the segment tool. Record the length of each side and the measure of each angle for the resulting triangle.
Location
A(3,4), B(1,1).
C(5.1)
A(4.5), B(2.1).
C(7.3)
—————-
AB=
BC=
AC=
Answer:
Step-by-step explanation:
Answer:
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]
Step-by-step explanation:
Step 1Place points A, B and C on the coordinate grid.
Alternatively, type the following into the input field as 3 separate inputs:
Triangle 1
A = (3, 4)B = (1, 1)C = (5, 1)Triangle 2
A = (4, 5)B = (2, 1)C = (7, 3)Step 2Use the Segment tool to join each pair of points.
Alternatively, type Segment( <Point>, <Point> ) into the input field (replacing <Point> with the letter name of the point) to create a segment between two points.
Record the length of each side.
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&AB&BC&AC\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&3.61&4&3.61\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&4.47&5.39&3.61\\\cline{1-4}\end{array}[/tex]
Step 3Use the Angle tool to measure each angle in the resulting triangle.
Alternatively, type Angle(Polygon(A, B, C)) into the input field to create all interior angles.
Record the measure of each angle.
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\sf Location&m \angle A&m \angle B&m \angle C\\\cline{1-4}\vphantom{\dfrac12} A(3,4),\;B(1,1),\;C(5,1)&67.38^{\circ}&56.31^{\circ}&56.31^{\circ}\\\cline{1-4}\vphantom{\dfrac12} A(4,5),\;B(2,1),\;C(7,3)&82.87^{\circ}&41.63^{\circ}&55.49^{\circ}\\\cline{1-4}\end{array}[/tex]
Note: All measurements have been given to the nearest hundredth (2 decimal places).
6.) The sum of two numbers is 45.
The larger number y is 6 less than twice the smaller number
a.
Write a system of linear equations.
What is the smaller number?
Answer:
x= 13 =smaller number
Step-by-step explanation:
let x=smaller number
y=2x-6=larger number
x+y=45
x+2x-6=45 (equation)
3x=39
x=13
Answer:
[tex]x = 13[/tex] ..... smaller number
and
[tex]y = 32[/tex] ....... larger number
Step-by-step explanation:
Greetings!!!
Let the two numbers be X and Y
[tex]x + y = 45........ \:equation \: 1[/tex]
The larger number is y and is 6 less than twice the smaller number. which means:-
[tex](y - 6) = 2x........... \: equation \: 2[/tex]
so, now solve for y. from equation 2
[tex]y - 6 = 2x \\ y = 2x + 6[/tex]
Substitute equation 1 into equation 2
[tex]x + y = 45 \\ x + (2x + 6) = 45 \\ 3x + 6 = 45 \\ 3x = 45 - 6 \\ 3x = 39....divide \: both \: sides \: by \: 3 \\ x = 13[/tex]
To solve for y substitute x into the first equation
[tex](13) = + y = 45 \\ y = 45 - 13 \\ y = 32[/tex]
Finally, to be more sure make a cross check
[tex]y - 6 = 2x \\ 32 - 6 = 2(13) \\ 26 = 26[/tex]
If you have any questions tag it on comments
Hope it helps!!!
From the given graph, how many students worked at least 10 hours per week?
Answer:
39.
Step-by-step explanation:
From the group of 10-14 hours worked per week, 8 students.
From the group of 15-19 hours worked per week, 4 students.
From the group of 20-24 hours worked per week, 12 students.
From the group of 25-29 hours worked per week, 8 students.
From the group of 30-34 hours worked per week, 4 students.
And finally, from the group of 35+ hours worked per week, 3 students.
So, 8+4+12+8+4+3 = 39 students.
Simplify without calculator: (-5) (7)+4×5 (Show all calculations)
Step-by-step explanation:
this is the answerrr
without calculator
i need help solving for these
Answer:
multiply them fro your answer
PLEASEE HELP!
Draw an angle that is 150 degrees.
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to draw an angle that is 150}^{\circ}.[/tex]
[tex]\textsf{We will need a Protractor to draw this angle.}[/tex]
[tex]\large\underline{\textsf{To Draw an Angle with a Protractor;}}[/tex]
[tex]\textsf{First, notice a point at the bottom of the Protractor. This is where we will start.}[/tex]
[tex]\textsf{Draw a Straight Line from the point to the 0}^{\circ} \ \textsf{mark.}[/tex]
[tex]\textsf{Secondly, use a ruler to carefully draw a straight line towards the 150}^{\circ} \ \textsf{mark.}[/tex]
[tex]\textsf{Note that some Protractors may be different from others. Similar steps should apply.}[/tex]
[tex]\textsf{Refer to the picture. It represents what the angle should look like afterwards.}[/tex]
To do :-
To draw a angle of 150° .Instruments required:-
A pair of compasses ,A ruler ,A pencil ,and a protactorSteps of construction:-
Draw a line segment of desired length.Taking a point on the line , draw a semicircle using a compass .Taking G as centre cut an arc on the semicircle mark the point of intersection as I .Taking I as centre cut another arc on the semicircle , mark it as point J .Taking J and I as center, cut an arc such that both the arcs intersect each other, mark it as point D .Join C and D .Taking F as centre again cut an arc on the semicircle, mark it as point E .Join E and C .Using a protactor you can check whether the angle formed is 150° or not .Hence angle ECB represents 150° .
Precaution:- do not change the arm length of the compass.
and we are done!
What is the meaning of "isometries"?
Answer:
"permutations that preserve distances"
Step-by-step explanation:
You want to know the meaning of "isometries" in the given discussion of dihedral groups.
The wording of the paragraph tells you the meaning:
"isometries ... are permutations that preserve distances."
__
Additional comment
Often, writing that introduces an unfamiliar word will describe the meaning of that word. Here, the meaning is described, along with several examples (translations, rotations, reflections).
The word isometry has its origin in ancient Greek. The prefix "iso-" means "equal", and "-metry" comes from metron, meaning "measure." Effectively, an isometry is a transformation that preserves measures.
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For the given statements for domain and range, option 3 and option 4 are correct answers.
What is domain and range?The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. With functions, we enter various numbers, and the output is a new set of numbers. The two essential characteristics of functions are domain and range. A function's domain and range are its constituent parts.
The domain of the function are all the input values while the range are the output values of the function for the given input.
In the given options, option 3 and 4 are correct as the functions have the same input but not the same output.
That is, they have the same domain, all real numbers, but not the same range.
Hence, for the given statements for domain and range, option 3 and option 4 are correct answers.
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