Which triangle has hypotenuse GF?
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Otriangle AFG
O triangle BFG
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The triangle which has hypotenuse GF include the following: C. triangle EFG.
What is a triangle?In Mathematics and Geometry, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is a right angle?In Mathematics and Geometry, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.
By critically observing the image (see attachment), we can reasonably infer and logically deduce that triangle EFG has hypotenuse GF because it is opposite the right angle (90 degrees).
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Complete Question:
Which triangle has hypotenuse GF?
triangle AFG
triangle BFG
triangle EFG
triangle DFG
tables that show a proportional relationship between x and y/ x,y 2,6,3,9,4,12/ 1,5,4,8,12,16
The ratio of y to x is not constant for each pair of values, we cannot conclude that the relationship between x and y is proportional.
Define constant?
A constant is a fixed value or quantity that does not change in a particular context or situation.
The tables you provided appear to show a proportional relationship between x and y. Specifically, the ratio of y to x is constant for each pair of values. We can confirm this by computing the ratios:
For the first table:
Ratio of y to x for the pair (2,6): 6/2 = 3
Ratio of y to x for the pair (3,9): 9/3 = 3
Ratio of y to x for the pair (4,12): 12/4 = 3
Since the ratio of y to x is constant for each pair of values, we can conclude that the relationship between x and y is proportional.
Similarly, for the second table:
The ratio of y to x for the pair (2, 1): 1/2 = 0.5
The ratio of y to x for the pair (4, 8): 8/4 = 2
The ratio of y to x for the pair (12, 16): 16/12 = 4/3
Hence, the ratio of y to x is not constant for each pair of values, we cannot conclude that the relationship between x and y is proportional.
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The complete question is in the attached image.
the product for (3x+2)(2x+4)
Answer:
6x^2+16x+8
Step-by-step explanation:
it is handwritten in the photo
in 2019 the average credit score for mortgage loans purchased by fannie mae was 749. in 2022 a sample of 20 mortgages were randomly selected and it was found that the average credit score was 740 with a sample standard deviation of 25. assume the data was normally distributed. compute a 90% confidence interval for the 2022 average credit score. is the data categorical or quantitative? what is the point estimate? what is the critical value? (round to 3 decimal places) what is the standard error? (round to 3 decimal places) what is the margin of error? (round to 3 decimal places) based on the 90% confidence interval for the 2022 average credit score, have the credit scores decreased since 2019? (yes or no) i would like to obtain a 90% confidence interval using the data above, within plus-or-minus 3. what sample size would i need?
You would need a sample size of at least 138.32 to obtain a 90% confidence interval with a margin of error of plus or minus 3.
To determine whether the credit scores have decreased since 2019, we need to compare the 2019 average credit score of 749 with the lower bound of the 2022 confidence interval of 730.343. Since 730.343 is lower than 749, we can conclude that there is evidence to suggest that the credit scores have decreased since 2019.
Finally, if you want to obtain a 90% confidence interval with a margin of error of plus or minus 3, you can use the formula for the sample size n =
=> (z² x s²) / (E²),
where z is the critical value, s is the estimated standard deviation from a previous study or pilot sample, and E is the desired margin of error.
Since s is unknown in this case, we can use a conservative estimate of 50 for the standard deviation.
Therefore, n = (1.725² x 50²) / (3²) = 138.32.
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los 2tercios de la suma de dos numeros son 74 y los 3quintos de su diferencia 9
If the 2 thirds of the sum of two numbers are 74 and the 3 fifths of their difference 9, the two numbers are 63 and 48.
Let x and y be the two numbers. Then we have two equations based on the given information:
2/3(x+y) = 74 ... (1)
3/5(x-y) = 9 ... (2)
To solve for x and y, we can start by isolating one variable in terms of the other from one of the equations. For example, from equation (1), we have:
x + y = (3/2) * 74
x + y = 111
Next, we can substitute this value of (x + y) into equation (2) and solve for the other variable:
3/5(x - y) = 9
x - y = 15
Now we have two equations with two variables:
x + y = 111
x - y = 15
Solving for x and y by adding the two equations gives:
2x = 126
x = 63
Substituting this value of x into either equation gives:
y = 48
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Complete question is:
The 2 thirds of the sum of two numbers are 74 and the 3 fifths of their difference 9. Find the two numbers.
A water sprinkler sends water out in a circular pattern. What is the area formed by the water pattern if it can spray out 14 feet in any direction? Use 3.14 for x.
The area formed is about square feet.
(Type an integer or a decimal.)
The area formed by the water pattern of a sprinkler that can spray out 14 feet in any direction is about 615.44 square feet.
Explain the term area.
Area is the measure of the size of a two-dimensional surface or region, usually measured in square units. It is the amount of space enclosed by a flat shape or the surface of an object. The area of a shape can be calculated using formulas based on its dimensions and geometry.
According to the given information
The formula for calculating the area of a circle is A = πr² where A is the area and r is the radius of the circle. In this case, r = 14 feet and π = 3.14 so A = 3.14 x (14)² = 615.44 square feet
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I need some help on this question would really appreciate it
The equation of the line in slope - intercept form, given the two points, would be D. y = - 10 / 3 x - 2 / 3.
How to find the slope - intercept form ?First, write out the points on the graph to be ( -2, 6 ) and ( 1, - 4 ) .
The slope would be:
= (change in y) / (change in x)
= (-4) - 6 / 1 - (-2)
= - 10 / 3
Use a point to find the y - intercept in the form:
y = mx + b
6 = - 10 / 3 ( - 2 ) + b
b = - (2/3)
The equation then is :
y = - 10 / 3 x - 2 / 3
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Harden is building shelves for his comic book collection. He has a piece of wood that is 3.5 feet long. After cutting four equal pieces of wood from it, he has 0.6 feet of wood left over.
Part A: Write an equation that could be used to determine the length of each of the four pieces of wood he cut
Part B: Explain how you know the equation from part A is correct
Part C: Solve the equation from Part A. Show every step of your work.
The length of each piece of wood is 0.725 feet.
We are given that the Length= 3.5feet
Now,
This is a word problem that can be solved by using algebra and arithmetic.
Part A: Let x be the length of each of the four pieces of wood he cut. Then, according to the problem, we have:
4x + 0.6 = 3.5
This is the equation that could be used to determine the length of each piece of wood.
Part B: We know the equation from part A is correct because it represents the total length of the wood before and after cutting. The left side of the equation is the sum of the lengths of the four pieces of wood and the leftover piece of wood. The right side of the equation is the original length of the wood. Since cutting does not change the total length of the wood, these two sides must be equal.
Part C: To solve the equation from part A, we need to isolate x by using inverse operations. We get:
4x + 0.6 = 3.5 4x = 3.5 - 0.6 (subtract 0.6 from both sides) 4x = 2.9 x = 2.9/4 (divide both sides by 4) x = 0.725
Therefore, by the algebra the answer will be 0.725 feet.
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A translation is shown on the grid below.
On a coordinate plane, triangle A B C has points (negative 4, 2), (negative 4, negative 2), (negative 1, negative 2). Triangle A prime B prime C prime has points (1, 5), (1, 1), (4, 1).
Which are true statements about the translation? Select 3 options.
A : The sides of the image and pre-image are congruent.
B : The image is turned 90°.
C : The angles in the image are different from the angles in the pre-image.
D: The image is a slide of the pre-image.
E: The image has a different shape than the pre-image.
F: Each point has moved in a different direction.
G: each point has moved the same number of units.
please answer asap thxxx :}
The correct statements regarding a translation are given as follows:
A : The sides of the image and pre-image are congruent.
G: each point has moved the same number of units.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The side lengths are not changed, hence the image and the pre-image are congruent. The angle measures are also not changed, hence the image and the pre-image are similar, and the shapes also remain constant.
For a translation, the movements have to be:
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HELP!! determine asymptotes, intercepts, and multiplicities!!
Answer:
In the numerator:
2x^2 + 3x - 20 = (2x - 5)(x + 4)
- no asymptotes
- x-intercept is at x = 2.5 (since there is a hole at x = -4)
- y-intercept is at y = -5
what value of z divides the standard normal distribution so that half the area is on one side and half is on the other? round your answer to two decimal places. if you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the space key. note: selecting a cell will return the value associated with the column and row headers for that cell.
The value of z that divides the standard normal distribution so that half the area is on one side and half is on the other is 0.00.
To understand this better, let's visualize the standard normal distribution. The graph of the standard normal distribution is a bell-shaped curve that is symmetrical around the mean of 0.
When we say that half the area is on one side and half is on the other, we mean that the area under the curve to the left of the z-score is equal to the area under the curve to the right of the z-score.
Since the standard normal distribution is symmetric, this occurs when the z-score is equal to 0.00. At this point, the area to the left of 0.00 is 0.50 (or 50%), and the area to the right of 0.00 is also 0.50 (or 50%).
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C. The painting American Gothic by
Grant Wood is rectangular in shape
and measures 29"in height and 25"
in width. A reproduction is made
where each dimension is some
fraction of the original dimension. If
the reproduction has 1/9 of the
original area, what is the width of
the reproduced piece?
the width of the reproduced piece is 2.78 inches.
Now, we first need to find the original area of the painting.
Since, The original area is,
= 29 inches x 25 inches
= 725 square inches
Now. we know that the reproduction has 1/9 of the original area, which means that the area of the reproduction is:
= 725 square inches / 9
= 80.56 square inches
Hence, for the width of the reproduced piece, we need to find the width of a rectangle whose area is 80.56 square inches, given that the height is 29 inches which remains constant in the reproduction.
Hence, We can use the formula for the area of a rectangle,
Area = length x width
In this case, we know the area is, 80.56 square inches)
and the length is, 29 inches
Thus, we can solve for the width:
80.56 square inches = 29 inches x width
width = 2.78 inches
Thus, the width of the reproduced piece is 2.78 inches.
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Directions: Rewrite each of the following using the powers of 10.
1) 79 x 10 =
2) 15 x 100 =
3) 22 x 1,000 =
4) 15 x 1,000 =
5) 83 x 102 =
6) 23 x 102 =
7) 72 x 102 =
8) 4 x 102 =
9) 75 x 102 =
10) 55 x 102 =
11) 81 x 103 =
12) 3 x 103 =
13) 81 x 103 =
14) 85 x 103 =
15) 98 x 10⁻1 =
16) 86 x 10⁻3 =
17) 65 x 10⁻2 =
18) 19 x 103 =
19) 3.49 x 109 =
20) 2.79 x 108 =
21) 8.42 x 107 =
22) 7.32 x 106 =
23) 3.84 x 105 =
24) 4.12 x 104 =
FUN FACTS:
103 = ONE THOUSAND
106 = ONE MILLION
109 = ONE BILLION
1012 = ONE TRILLION
1015 = ONE QUADRILLION
1018 = ONE QUINDRILLION
1021 = SEXTILLION
1024 = SEPTILLION
1027 = ONE OCTILLION
1030 = ONE NONILLION
The values of each number using power 10 is shown below.
1. 79 x 10
= 790
2. 15 x 100
= 1500
3. 22 x 1,000
= 22,000
4. 15 x 1000
= 15,000
5. 83 x 102
= 8,466
6. 23 x 10²
= 2300
7. 72 x 10²
= 7200
8. 4 x 10²
= 400
9. 75 x 10²
= 7500
10. 55 x 10²
= 5500
11. 81 x 10³
= 81,000
12. 3 x 10³
= 3000
13. 85 x 10³
= 85, 000
14. 98 x [tex]10^{-1[/tex]
= 9.8
15. 86 x [tex]10^{-3[/tex]
= 0.086
16. 65 x [tex]10^{-2[/tex]
= 0.65
17. 19 x 10³
= 19,000
18. 3.49 x [tex]10^{9[/tex]
= 349,000,000,000
19. 2.79 x [tex]10^{8[/tex]
= 27,900,000,000
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a data analyst creates a histogram to share in a presentation. what are histograms used to demonstrate?1 pointhow two or more values contrast and comparehow much each part of something makes up the wholehow often data values fall into certain rangeshow data has changed over time
Histograms are primarily used to demonstrate how often data values fall into certain ranges. So, option 3 is correct.
Histograms are graphical representations of a dataset's distribution, with the data separated into intervals or "bins" and the frequency of values falling into each bin represented as bars.
Histograms can be used to find the trends and the specific information in the data for the help of data analyst. They are especially useful for huge datasets when the distribution of values from a simple list may be difficult to understand. Although histogram could be used for more than two data types and but this is not there natural purpose. Hence option option 3 is correct choice.
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Complete question - A data analyst creates a histogram to share in a presentation. what are histograms used to demonstrate?
1. how two or more values contrast and compare
2. how much each part of something makes up the whole
3. how often data values fall into certain ranges
4. how data has changed over time.
Angle A is …. Than 90°. Angle B is …… than 90°
Answer:
Angle A° is less than 90°
Angle B° is less than 90°
Step-by-step explanation:
Angle A° = Angle B° = 45°
find the area and perimeter
The area and perimeter of the shape are 370mm² and 90mm respectively.
What is area and perimeter?Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.
Perimeter is the addition of the sides of the shape.
Therefore, the perimeter of the shape = 15+15+30+30 = 30+60 = 90mm
The area of the shape = area of the whole shape - area of the cut out
area of the whole shape = l×w
= 30×15 = 450mm²
area of the cut out =l×w
8× 10 = 80mm²
area of the shape = 450-80
= 370mm²
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plsss help!!
Which list is ordered from least to greatest?
L) 72.14
M) 723.99
N) 7.323
0) 7.358
P) 91.34
A) M,L,P,N,O
B) N,O,P,L,M
C) N,O,L,P,M
D) L,M,P,N,O
Answer:
C
Step-by-step explanation:
7.3<7.4<72.14<91.34<723.99
if integrate f(x) dx = 1/3 * x ^ 3 - 2x ^ 2 + 3x - 5 then the value of f(-2) = ...
please
Integrating and evaluating the function gives f(x) = 1/12x⁴ - 2/3x³ + 3/2x² - 5x and f(2) = -8
Integrating and evaluating the functionFrom the question, we have the following parameters that can be used in our computation:
∫ 1/3x³ - 2x² + 3x - 5 dx
The rule of integration is
x^n = x^(n + 1)/(n + 1)
using the above as a guide, we have the following:
∫ 1/3x³ - 2x² + 3x - 5 dx = 1/12x⁴ - 2/3x³ + 3/2x² - 5x
So, we have
f(x) = 1/12x⁴ - 2/3x³ + 3/2x² - 5x
Next, we are to calculate f(2)
This means that x = 2
So, we have
f(2) = 1/12(2)⁴ - 2/3(2)³ + 3/2(2)² - 5(2)
Evaluate
f(2) = -8
Hence, the value of f(2) is -8
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There are 5 men and 6 women interviewed for a job. One of the candidates will be offered the job. Find the probability that the job is offered to a man. Convert the fraction to a decimal. Round to three decimal places.
The calculated probability that the job is offered to a man is 0.455
Finding the probability that the job is offered to a man.From the question, we have the following parameters that can be used in our computation:
There are 5 men and 6 women interviewed for a job.
This means that
Men = 5
Women = 6
The probability that the job is offered to a man is
P = men/Total
So, we ave
P = 5/11
Evaluate
P = 0.455
Hence, the probability is 0.455
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An employee receives a 2% raise once per year. If the employee’s initial salary is $61,900.00, what will the employee’s salary be after 7 years?
An employee receives a 2% rise once every year. If an employee's starting salary is $61,900.00, salary after seven years will be $71,103.64.
We will calculate the salary for each year till 7th year.
Salary after 1 year = Original salary × (100 + raise)/100
= 61,900 × (100+2)/100
= 61,900 × 102/100
= $63,138
Salary after second year = salary after first year × 1.02
= 63,138 × 1.02
= $ 64,400.76
Salary after third year = salary after second year × 1.02
= 64,400.76 × 1.02
= $ 65,688.78
Salary after fourth year = salary after third year × 1.02
= 65,688.78 × 1.02
= $ 67,002.55
Salary after fifth year = salary after fourth year × 1.02
= $ 67,002.55 × 1.02
= $ 68,342.60
Salary after sixth year = salary after fifth year × 1.02
= $ 68,342.60 × 1.02
= $ 69,709.45
Salary after seventh year = salary after sixth year × 1.02
= $ 69,709.45 × 1.02
= $ 71,103.64
So, the final salary after seven years after all the increments will be $ 71,103.64
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could you please help with thses two? ill mark brilientest
Answer:
Cylinder problem:
28.26 = 3.14(r^2)(9)
28.26 = 28.26(r^2), so r = 1 cm
Trapezoid problem:
Since we have similar trapezoids, the side lengths of WXYZ are each 5 times the side lengths of ABCD.
60/12 = 5, so b = 5 × 10 = 50 inches
A group of physical education majors was discussing the height of female runners and whether female runners tended to be tall, on the average. They decided to estimate the mean height of female runners. A sample of 12 runners showed a sample mean height of 65.80 inches and a sample standard deviation of 1.95 inches. Assume the population is approximately normal. Construct a 90% confidence interval for the mean of the population of female runners from which the 12 runners were selected.a) What is the left boundary of the confidence interval? Round your answers to two decimal placesb) What is the right boundary of the 90% confidence interval? Round your answers to two decimal places
Therefore, the 90% confidence interval for the mean height of the population of female runners is (64.77, 66.83) inches.
A confidence interval is a range of values that provides an estimate of the unknown population parameter with a certain level of confidence. The confidence level represents the percentage of times that the true population parameter will be contained within the interval, based on repeated sampling.
a) Using a t-distribution with 11 degrees of freedom (n-1), and a 90% confidence level, the t-value is 1.796.
The left boundary of the confidence interval is:
65.80 - (1.796 * (1.95 / √(12))) = 64.77 inches (rounded to two decimal places)
b) The right boundary of the confidence interval is:
65.80 + (1.796 * (1.95 / √(12))) = 66.83 inches (rounded to two decimal places)
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X~N(570, 103). Find the z-score corresponding to an observation of 470.A. 0.97 B. -0.97 C. 0.64 D. -0.64
Option B To find the z-score corresponding to an observation of 470, we use the formula: z = (x - μ) / σ
where x is the observation, μ is the mean, and σ is the standard deviation. Substituting the values given in the question, we get: z = (470 - 570) / 10.1489.
z = -9.84, Therefore, the z-score corresponding to an observation of 470 is -0.97, which is option B.
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. Sal Khan invented it.
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Which of the following is NOT a solution to the system of inequalities? (3, 1) (0, 5) (1, 4) (1, 3)
The point that is not a solution of the system of inequalities is (3, 1).
How to identify the solutions of the system of inequalities?A point is a solution of the system of inequalities only if it lies in the shaded region (the green one) or in top of the solid line (this would be the line with negative slope).
Then from the given points the ones that are solutions are:
(1, 3) (it lies on the shaded region)
(1, 4) (it lies in the shaded region)
(0, 5) (it lies in the shaded region)
Then the anser is the remaining one (3, 1), that is not a solution.
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I need this done right now please write the equation
Answer:
y = -6x +3
Step-by-step explanation:
You want the slope-intercept equation matching the given graph.
GraphThe line on the graph crosses the y-axis at the marked point (0, 3). Another point is marked at (1, -3), which is 1 unit right and 6 units down.
The first point tells you the y-intercept (b) is +3.
The second point tells you the slope (m) is rise/run = -6/1 = -6.
Then the point-slope equation is ...
y = mx + b
y = -6x +3
<95141404393>
in how many ways can 4different prizes be givn to any 4 of 10 people if no person receives more than 1 prize?
There are 210 ways we can give 4 different prizes to any 4 of 10 people if no person receives more than 1 prize.
To calculate the number of ways we can do this, we can use the formula for combinations. The formula for the number of ways to choose r objects from a set of n objects is:
ⁿCₓ = n! / x!(n-x)!
where n! represents the factorial of n, which is the product of all positive integers up to n.
5! = 5 x 4 x 3 x 2 x 1 = 120.
In this problem, we want to choose 4 people from a set of 10, so we can use the formula:
¹⁰C₄ = 10! / 4!(10-4)!
Simplifying this expression, we get:
¹⁰C₄ = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)
¹⁰C₄ = 210
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PLEASE HELP THIS IS THE BIGGEST GRADE ALL YEAR
Li is playing a board game in which the number of spaces that she moves is dependent upon the number that she rolls on a number cube. For instance, if she rolls a 4, then she moves 4 spaces.
Li is currently on space 13 and she needs to reach space 40 to win the game, Li wrote an inequality to determine the fewest number of rolls it would take her to win the game.
13÷6x ≥ 40
A. Examine the inequality above that describes Li's current situation. Describe the meaning of each number and variable in the inequality.
What is the meaning of the 13?
What is the meaning of the 6?
What is the meaning of x?
What is the meaning of the 40?
B. Solve the inequality for x and graph the solution on a number line.
C. Explain the meaning of your solution within the context of the problem.
13 is the y-intercept, which is the initial number of space.
6 is the slope, which means the number of spaces is increasing by 6.
x represent number of rolls.
40 the minimum number of spaces required to win the game.
The fewest number of rolls it would take Li to win the game is 0.054 rolls.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about Li's current situation, we have the following inequality:
13 ÷ 6x ≥ 40
13/6x ≥ 40
13 ≥ 240x
x ≤ 0.054
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Q1.
Draw and label the axis of symmetry for the given object and image.
The axis of symmetry for the given object and image is added as an attachment
Drawing and labeling the axis of symmetryFrom the question, we have the following parameters that can be used in our computation:
The object and the image
By definition, the axis of symmetry is any line that divides a shape and its image into symmetrical parts i.e. into identical shapes and sizes
In this case, the axis of symmetry would be a vertical line that divides both triangles in to identical figures
Using the above definition as a guide, we can draw the axis of symmetry for the object and image & then label it AB
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In statistics, a series of random events in which the probability of a given event is determined only by its predecessors is known as a "chain" named after what Russian mathematician?
In statistics, a series of random events in which the probability of a given event is determined only by its predecessors is known as a "chain". This concept is attributed to the Russian mathematician Andrey Markov, and such chains are commonly referred to as Markov chains.
Markov chains have important applications in many areas of science and engineering, including physics, economics, genetics, and computer science. They are used to model a wide range of phenomena, including the behavior of financial markets, the spread of diseases, the performance of computer networks, and the evolution of populations.The basic idea behind a Markov chain is that the future state of the system depends only on the current state, and not on any previous states. The probability of transitioning from one state to another is determined by a transition matrix, which specifies the probabilities of moving from one state to another in a single time step.
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Jackie is using spherical beads to to create a border around a picture frame. Each bead has a diameter of 1.5 millimeters. It will take a total of 360 beads to create the border. What is the approximate total volume of the beads that form the border of the picture frame?
Answer:
Step-by-step explanation:
The diameter of each bead is 1.5 millimeters, which means the radius of each bead is 0.75 millimeters (since radius = diameter/2).
The volume of a sphere is given by the formula V = (4/3)πr^3.
Substituting the radius of each bead into the formula, we get:
V = (4/3)π(0.75)^3 ≈ 1.7671 cubic millimeters
To find the total volume of the 360 beads used to create the border of the picture frame, we can simply multiply the volume of one bead by the total number of beads:
Total volume = 360 × 1.7671 ≈ 635.76 cubic millimeters
Therefore, the approximate total volume of the beads that form the border of the picture frame is about 635.76 cubic millimeters.
