there is no polygon that satisfies the given conditions.
Why it is and what is a Polygon?
Let the number of sides of the polygon be n.
We know that the sum of angles of an n-sided polygon is (n-2) × 180 degrees.
In this polygon, two angles are 100 degrees each, and the remaining (n-2) angles are 130 degrees each.
So, we can set up an equation:
2 × 100 + (n-2) × 130 = (n-2) × 180
Simplifying this equation, we get:
200 + 130n - 260 = 180n - 360
Solving for n, we get:
50n = 100
n = 2
However, a polygon with only 2 sides is not possible.
Therefore, there is no polygon that satisfies the given conditions.
A polygon is a 2-dimensional geometric figure that is formed by connecting a finite number of line segments to create a closed shape. These line segments are called sides of the polygon. The sides of a polygon only intersect at their endpoints, and the endpoints of each side are called vertices. A polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, and a polygon with more than four sides is generally referred to by its number of sides (e.g. a pentagon has five sides, a hexagon has six sides, etc.).
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ASA, SSS, SAS
Define each postulate and give a well written and visual example of each term.
Include as much detail as possible
Answer:
In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.
ASA Postulate:
ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.
SSS Postulate:
SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.
SAS Postulate:
SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.
Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.
Answer:
They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent
Step-by-step explanation:
and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
11. Figure EFGH is a parallelogram. Find the length of Line FG.
The length οf line FG is 12 cm, If Figure EFGH is a parallelοgram.
What is parallelοgram?A parallelοgram is a type οf quadrilateral with twο pairs οf parallel sides. The οppοsite sides οf a parallelοgram are equal in length and parallel tο each οther.
Since EFGH is a parallelοgram, we knοw that the οppοsite sides are parallel and equal in length. Therefοre, the length οf line FG is equal tο the length οf line EH.
We can find the length οf EH by using the Pythagοrean theοrem οn right triangle EFG:
[tex]EF^2 + FG^2 = EG^2[/tex]
Since EF = 5 cm, EG = 13 cm, and angle FEG is a right angle (as οppοsite angles in a parallelοgram are equal), we can sοlve fοr FG:
[tex]FG^2 = EG^2 - EF^2[/tex]
[tex]FG^2 = 13^2 - 5^2[/tex]
[tex]FG^2 = 144[/tex]
[tex]FG = \sqrt{(144)[/tex]
[tex]FG = 12 cm[/tex]
Therefοre, the length οf line FG is 12 cm.
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Assume that the int variables a, b, c, and low have been properly declared and initialized. The code segment below is intended to print the sum of the greatest two of the three values but does not work in some cases.
if (a > b && b > c)
{low = c;}
if (a > b && c > b)
{low = b;}
else
{low = a;}
System.out.println(a + b + c - low);
The variable is not initialized, it will have a default value associated with its data type.
To print the sum of the greatest two of the three values in the given code segment, the code must be corrected by introducing curly braces that help enclose the second if statement such that it can execute properly in cases where it is necessary. If the second if statement is not enclosed in curly braces, then the else statement will execute the code that is present inside of it. Thus, only a will be assigned to low. The corrected code segment should be:if (a > b && b > c) {low = c;}if (a > b && c > b) {low = b;} else {low = a;}System.out.println(a + b + c - low);For a better understanding of this code, let's discuss variables, declared, and initialized.What are variables?A variable is a memory location that stores a data value. Variables in Java are declared by assigning a data type to them. The value stored in the memory location can be changed throughout the program execution.What is initialization in Java?Initialization in Java refers to assigning a specific value to a variable during its declaration. The value may be provided by the user, entered via keyboard, or assigned to a constant. If a variable is not initialized, it will have a default value associated with its data type.
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Consider the decay function d(x)=850(0. 94)x. Describe the characteristics of the functions
The decay function d(x) is an exponential function with an initial value of 850, a decay factor of 0.94, and a rate of decay that increases as x increases. The function has a horizontal asymptote at y=0, and its domain is all real numbers while its range is (0, 850].
The decay function d(x) can be described by the following characteristics:Exponential Decay: The function d(x) is an exponential function because it has a constant base (0.94) raised to a variable exponent (x).
Initial Value: The initial value of the function d(x) is 850, which represents the value of the function when x=0.
Decay Factor: The decay factor of the function d(x) is 0.94, which is less than 1. This means that as x increases, the function decreases and approaches zero, but never reaches zero.
Rate of Decay: The rate of decay of the function d(x) is determined by the value of the decay factor, which is 0.94. The closer the decay factor is to 1, the slower the rate of decay. Conversely, the closer the decay factor is to 0, the faster the rate of decay.
Asymptote: The function d(x) has a horizontal asymptote at y=0. This means that as x becomes very large, the function approaches but never touches the x-axis.
Domain and Range: The domain of the function d(x) is all real numbers, and the range is (0, 850]. This means that the function outputs a positive value less than or equal to 850, but never outputs zero.
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suppose that a point is chosen uniformly at random from within a unit circle let (x,y) denote the coordinates of the randomly chosen point.
The probability of the chosen point uniformly at random from within a unit circle is 1/π.
Suppose that a point is chosen uniformly at random from within a unit circle.
Let (x,y) denote the coordinates of the randomly chosen point.
The coordinates of the randomly chosen point (x, y) on the unit circle can be given by:
x = cos(θ)y = sin(θ) where θ is the angle between the positive x-axis and the line segment connecting the origin to the point (x, y).
The probability density function for this situation is given by:
p(x,y) = {1/(πr^2)} for 0≤x^2 + y^2 ≤ r^2 and p(x,y) = 0 elsewhere
where r is the radius of the unit circle. For this situation, r = 1.
So, we can say that the probability of selecting a point in a unit circle is given by:
Probability (0≤x^2 + y^2 ≤ 1) = 1/(π*1^2) = 1/π.
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The height off the ground, in feet, of a squirrel leaping from a tree branch is given by the function H(x) = –16x*2 + 24x + 15, where x is the number of seconds after the squirrel leaps. How many seconds after leaping does the squirrel reach its maximum height?
A.
1. 33 s
B.
0. 50 s
C.
0. 75 s
D.
1. 00 s
Answer:
C. 0.75 s
Step-by-step explanation:
Given a squirrel's height is defined by H(x) = -16x² +24x +15, you want to know the value of x when the height is a maximum.
VertexThe x-coordinate of the vertex of y = ax² +bx +c is x=-b/(2a). For the given function, we have a=-16 and b=24, so the x-value at the vertex is ...
x = -b/(2a) = -24/(2(-16)) = 24/32 = 3/4
x = 0.75
The squirrel reaches its maximum height 0.75 seconds after leaping.
Two trapezoids have areas of 432cm^2 and 48cm^2. Find the ratio of similarity
If two trapezoids have respective surface areas of [tex]432cm^2 and 48cm^2[/tex], their similarity ratio is 3:1.
The ratio of the areas of similar figures is the square of the ratio of their corresponding side lengths.
Let's denote the ratio of similarity between the two trapezoids by "k".
The area of the first trapezoid is [tex]432 cm^2[/tex], and the area of the second trapezoid is [tex]48 cm^2[/tex].
Therefore, we can set up the equation:
(k * side length of first trapezoid)^2 / (k * side length of second trapezoid)^2 = 432/48
Simplifying the right-hand side of the equation gives:
(k * side length of first trapezoid)^2 / (k * side length of second trapezoid)^2 = 9
We can simplify the left-hand side of the equation by canceling out the "k" terms:
(side length of first trapezoid)^2 / (side length of second trapezoid)^2 = 9
Taking the square root of both sides gives:
(side length of first trapezoid) / (side length of second trapezoid) = 3
Therefore, the ratio of the corresponding side lengths of the two trapezoids is 3:1. Since the ratio of similarity is the square of the ratio of corresponding side lengths, we have:
k = (side length of first trapezoid) / (side length of second trapezoid) = 3/1 = 3
So, the ratio of similarity between the two trapezoids is 3:1.
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What is true about angle APD?
Angle APD is opposite to angle APC. Angle APD is supplementary (adds up to 180 degrees) to angle CPB.
Describe Supplementary Angles?In geometry, two angles are called supplementary angles if the sum of their measures is equal to 180 degrees. In other words, if two angles are placed adjacent to each other so that they share a common vertex and a common side, and the non-common sides form a straight line, then these angles are supplementary.
For example, if angle A and angle B are supplementary, then their measures are such that A + B = 180 degrees. Therefore, if angle A measures 120 degrees, then angle B measures 60 degrees.
It is important to note that supplementary angles do not have to be adjacent or even on the same line. As long as the sum of their measures equals 180 degrees, they are considered supplementary.
When two lines AB and CD intersect at point P, the angles formed are related in several ways. Specifically:
Angle APD is opposite to angle APC.
Angle APD is supplementary (adds up to 180 degrees) to angle CPB.
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please help me .Solve this question.
9-9÷9÷9-9÷9
Answer:
71/9
Step-by-step explanation:
please help me .Solve this question 9-9÷9÷9-9÷9
9 - 9 : 9 : 9 - 9 : 9 =
9 - 1 : 9 - 1 =
9 - 1/9 - 1 =
8/9 - 1 =
(81 - 1 - 9)/9 =
71/9
a market sells five kinds of cups, 4 kinds of saucers, and 2 kinds of spoons. How many ways are there to buy two objects of different types? WILL GIVE BRAINLIST
Answer:
Step-by-step explanation:
To solve this problem, we need to determine the number of ways to choose two objects of different types from the given sets.
We can start by computing the number of ways to select two objects from each of the three sets, and then add these numbers together. Since we must choose two different types, we cannot choose two objects from the same set.
The number of ways to choose two cups is:
C(5,2) = 5! / (2! * (5-2)!) = 10
The number of ways to choose two saucers is:
C(4,2) = 4! / (2! * (4-2)!) = 6
The number of ways to choose two spoons is:
C(2,2) = 1
Since we must choose two different types, we need to multiply the number of ways to choose two objects from different sets. There are three sets to choose from, so we need to choose two of them as follows:
3 choices of sets * number of ways to choose two objects from each set = 3 * (10 + 6 + 1) = 51
Therefore, there are 51 ways to buy two objects of different types from the given sets of cups, saucers, and spoons.
What is a coterminal angle of 22 times pi over 3 question mark
[tex]\cfrac{22\pi }{3}\implies \cfrac{(3)(7)\pi +\pi }{3}\implies 7\pi +\cfrac{\pi }{3}\implies 6\pi +\pi +\cfrac{\pi }{3}[/tex]
so the angle is really 3 revolutions plus another π plus a little bit more. Check the picture below.
How can you show solidarity and dicipline in projecting our environment
Showing solidarity and discipline in protecting our environment requires collective effort and a willingness to change our behavior and attitudes towards the environment. Here are some ways in which we can show solidarity and discipline in protecting our environment:
Educate ourselves and others about environmental issues and their impact on our planet and communities.
Reduce, reuse, and recycle waste by properly disposing of garbage, avoiding single-use plastics, and using eco-friendly products.
Conserve resources like water and energy by taking shorter showers, turning off lights and electronics when not in use, and using public transportation or carpooling.
Plant trees, flowers, and other vegetation to improve air quality, provide shade, and prevent erosion.
Support environmental causes and organizations through volunteering, donating, and spreading awareness.
By taking these actions, we can demonstrate our solidarity and discipline in protecting our environment, and inspire others to join us in making a positive impact on the planet.
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What is the length of side x in the triangle below?
Answer: x = 8.7
Step-by-step explanation:
You are given the reference angle: 60°, the hypotenuse and the leg of which to find.
X is opposite in reference to 60° and you are given the hypotenuse.
Sine works with the hypotenuse and the opposite: sin∅ = opp/hyp
sin(60°) = x/10
To figure out x, you must transpose, to make x the subject. X is being divided by 10, so to undo that you must multiply, and what you do to one side, you must do to the next to balance the equation.
10 x sin(60) = x/10 x 10
= X = sin(60) x 10
sin(60) = 0.866
X = 0.866 x 10
X = 8.66
You can round off to one decimal place or leave the answer as is.
X = 8.7 (1 d.p)
Place the three sets of conditions in order. Begin with the set that gives the greatest number of triangles, and end with the set that gives the smallest number of triangles. Condition A: One side is 6 inches long, another side is 5 inches long, and the angle between them measures 50°. Condition B: One angle measures 50°, another angle measures 40°, and a third angle measures 90°. Condition C: One side is 4 inches long, another side is 9 inches long, and a third side measures 5 inches.
The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.
What is triangle inequality theorem?According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.
The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.
Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.
Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.
Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.
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PLEASE HELPP!! i’ve been struggling with this problem for the past 30 min.. lessons about polynomials.
Answer:
39.77 -> 39 or 40, depending on rounding
Step-by-step explanation:
Since 2002-1992 is 10. T would equal 10. At that point, it would be a gesture of plugging in 10 whereever you see a "t" and solve for both
A video receives-16 pints and 33 points in one day. How many members voted
Answer:49
Step-by-step explanation:
Answer your answer and show all the steps that you used to solve this problem in the space provided use the 30° - 60° - 90° triangle theorem to find the answer
The value of x is 8 inches.
To find the value of x, we can use the property of similar triangles that states that the corresponding sides of similar triangles are in proportion. Specifically, we can set up the proportion:
4/10 = x/20
We can then cross-multiply to get:
4 * 20 = 10 * x
Simplifying this equation gives us:
80 = 10x
Dividing both sides by 10, we get:
x = 8
Therefore, the value of x is 8 inches.
In summary, we used the property of similar triangles and set up a proportion involving the corresponding sides of the two triangles. By cross-multiplying and simplifying, we were able to find the value of x.
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Complete Question:
Enter your answer and show all the steps that you use to solve this problem in the space provided.
On the left triangle, the shorter side is labeled 4 inches and the longer side is labeled 10 inches. On the right triangle, the shorter side is labeled x inches and the longer side is labeled 20 inches.
The two triangles above are similar. Find the value of x. Be sure to explain your steps.
write an equation of the line that passes through (1 3) and has a slope of 5/4
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{ \cfrac{5}{4}}(x-\stackrel{x_1}{1}) \\\\\\ y-3=\cfrac{5}{4}x-\cfrac{5}{4}\implies y=\cfrac{5}{4}x-\cfrac{5}{4}+3\implies {\Large \begin{array}{llll} y=\cfrac{5}{4}x+\cfrac{7}{4} \end{array}}[/tex]
the radius of a circle is increasing at a rate of 4 cm/s. how fast is the area of the circle increasing after 10 seconds? g
Answer:
A = 1600π cm²
Step-by-step explanation:
Pre-SolvingWe are given that a circle's radius increases 4 cm every second.
We want to know how large the area of the circle is after 10 seconds.
SolvingWe first need to find how large the radius will be.
We know the proportion of the rate increase / time; for every 1 second, the rate increases by 4 cm.
We can write this as a proportion:
[tex]\frac{4 cm}{1 s} = \frac{x}{10s}[/tex]
We can cross multiply to get:
4 cm * 10 s = x * 1 s
Divide both sides by 1 s
(4 cm * 10 s) / (1 s) = 40cm = x
So, after 10 seconds, the radius will be 40cm.
We aren't done yet though, remember that the question wants us to find the area of the circle.
The area can be calculated using the equation A = πr², where r is the radius.
We can substitute 40 as r in the equation to get:
A = πr² = π * (40)² = 1600π cm²
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 5 inches.
(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
(b) If a random sample of eight 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the mean is larger for the x distribution.
The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
The probability in part (b) is much higher because the mean is smaller for the x distribution.
The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
The probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793 and the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057 and the probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
What do you mean by normally distributed data?
In statistics, a normal distribution is a probability distribution of a continuous random variable. It is also known as a Gaussian distribution, named after the mathematician Carl Friedrich Gauss. The normal distribution is a symmetric, bell-shaped curve that is defined by its mean and standard deviation.
Data that is normally distributed follows the pattern of the normal distribution curve. In a normal distribution, the majority of the data is clustered around the mean, with progressively fewer data points further away from the mean. The mean, median, and mode are all the same in a perfectly normal distribution.
Calculating the given probabilities :
(a) The probability that an 18-year-old man selected at random is between 70 and 72 inches tall can be found by standardizing the values and using the standard normal distribution table. First, we find the z-scores for 70 and 72 inches:
[tex]z-1 = (70 - 71) / 5 = -0.2[/tex]
[tex]z-2 = (72 - 71) / 5 = 0.2[/tex]
Then, we use the table to find the area between these two z-scores:
[tex]P(-0.2 < Z < 0.2) = 0.0793[/tex]
So the probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793.
(b) The mean height of a sample of eight 18-year-old men can be considered a random variable with a normal distribution. The mean of this distribution will still be 71 inches, but the standard deviation will be smaller, equal to the population standard deviation divided by the square root of the sample size:
[tex]\sigma_x = \sigma / \sqrt{n} = 5 / \sqrt{8} \approx 1.7678[/tex]
To find the probability that the sample mean height is between 70 and 72 inches, we standardize the values using the sample standard deviation:
[tex]z_1 = (70 - 71) / (5 / \sqrt{8}) \approx -1.7889[/tex]
[tex]z_2 = (72 - 71) / (5 / \sqrt{8}) \approx 1.7889[/tex]
Then, we use the standard normal distribution table to find the area between these two z-scores:
[tex]P(-1.7889 < Z < 1.7889) \approx 0.9057[/tex]
So the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057.
(c) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. When we take a sample of eight individuals, the variability in their heights is reduced compared to the variability in the population as a whole. This reduction in variability results in a narrower distribution of sample means, with less probability in the tails and more probability around the mean. As a result, it becomes more likely that the sample mean falls within a given interval, such as between 70 and 72 inches.
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During the day, 25 trains pulled into the subway station. Of those trains, 14 were full.
Find the experimental probability that the next train that pulls into the station is full
The experimental likelihood that probability the incoming train will be fully occupied is 0.56, or 56%.
What is the simplest method for resolving probability?It's simple to calculate the likelihood of a simple event occurring by adding the probabilities together. Your overall odds to win something, for instance, are 10% + 25% = 35% if your chances of winning $10 or $20, respectively, are 10% and 25%, respectively.
In this instance, 14 of the 25 arriving trains were completely full.
The following train's likelihood of being full is determined by the proportion of full trains to all other trains.
14/25 are in favor of the upcoming train being fully loaded.
The likelihood that the following train will have every seat taken is 0.56, or 56%.
Which four rules of probability are there?It either happens or it doesn't, according to the four significant rules of probability. The chance of an event occurring when the probability of it not occurring is put together is always 1. The same principles apply to empirical probability.
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How does the standard deviation of the sampling distribution of all possible sample means (for a fixed sample size n) from a population compare numerically to the standard deviation of the population?
The standard error of the mean is defined as the standard deviation of the sampling distribution of all potential sample means drawn from a population.
The standard error is also known as the standard deviation of the sampling distribution.
The standard deviation of the population is known as the population standard deviation.
The population standard deviation is an estimate of the amount of variation or dispersion of the values in the population.
It represents the average distance of the values from the mean of the population.
The standard deviation of the sampling distribution of all possible sample means (for a fixed sample size n) from a population is lower than the standard deviation of the population.
The standard deviation of the sampling distribution of all possible sample means is a measure of the variation of the sample means around the population mean.
The sample means are less variable than the individual observations in the population; therefore, the standard deviation of the sample means is lower than the standard deviation of the population.
In general, the standard error is given by:
$$SE = \frac{{{\sigma _p}}}{{\sqrt n }}$$
where, σp represents the population standard deviation and n represents the sample size.
The standard deviation of the sampling distribution is lower than the population standard deviation.
The standard deviation of the sampling distribution is dependent on the sample size n.
As the sample size increases, the standard deviation of the sampling distribution decreases.
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In triangle JKL, m/J = (8x+6)°, m/K = (2x + 2)°, and m/L= (4x + 4)°. Find
m/L.
The value of the angle m<L is 52 degrees
How to determine the value
Following the side angle theorem of triangles, we have that the sum of the angles in a given triangle is equal or equivalent to 180 degrees.
From the information given, we have that;
m/J = (8x+6)°m/K = (2x + 2)° m/L= (4x + 4)°Now, equate the angles to 180 degrees, we have;
m<J + m<K + m<L =180
substitute the values into the equation
8x + 6 + 2x + 2 + 4x + 4 = 180
collect the like terms, we have;
8x + 2x + 4x = 180 - 12
add or subtract the values
14x = 168
Make 'x' the subject
x = 12
For m<L = 4x + 4 = 4(12) + 4 = 52 degrees
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Key Takeaways of Cross Tab and Scatter plots (Reflecting on visual models)
- We can develop insights and knowledge about our world from manipulating and visualizing data, in particular by finding patterns
- When investigating two columns of data we can observe patterns different values move together (are correlated). We cannot know for certain the cause of the correlation.
Key takeaways of Cross Tab and Scatter plots (Reflecting on visual models):
We can develop insights and knowledge about our world by manipulating and visualizing data, in particular by finding patterns. Cross Tab is a powerful method of data analysis that helps to compare the relationship between two or more variables. The scatter plot is one of the most effective tools to visualize two-variable data.
Scatter plots: A scatter plot is a graph in which two variables are plotted against each other, with the horizontal axis representing one variable and the vertical axis representing the other. Each point in the scatter plot represents a pair of values for the two variables being plotted. When analyzing a scatter plot, we can look for patterns, relationships, or correlations between the two variables.Cross Tab: Cross tab is a popular data analysis tool that helps to determine the relationship between two or more variables. In cross-tabulation, a table is created with one variable displayed along the rows and the other variable displayed along the columns. The resulting table shows the number of occurrences of each combination of values for the two variables.The main takeaways from cross-tabulation and scatter plots include:
Cross Tab and Scatter plots can help us to find patterns and relationships between variables.The analysis of scatter plots can help us to identify trends, clusters, and outliers.Cross Tab helps us to identify the relationship between two or more variables by displaying the data in a table format.In conclusion, both cross-tabulation and scatter plots are effective tools for data analysis that can help to identify patterns and relationships between variables. When investigating two columns of data we can observe patterns of different values that move together (are correlated). We cannot know for certain the cause of the correlation.
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Write an explicit rule for the recursive rule. a1=8,
an=an−1−12
Answer:
[tex]a_{n}[/tex] = 20 - 12n
Step-by-step explanation:
the explicit rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
a recursive rule has the form
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
given recursive rule
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 12 : a₁ = 8
then a₁ = 8 and d = - 12
explicit rule is therefore
[tex]a_{n}[/tex] = 8 - 12(n - 1) = 8 - 12n + 12 = 20 - 12n
The solution of the differential equation y apostrophe minus y over x equals y squared is a. y equals fraction numerator 1 over denominator open parentheses c over x minus x over 2 space close parentheses end fraction b. y equals 1 plus c e to the power of x c. y equals c x minus x ln x d. y equals c over x minus x over 2 e. y equals fraction numerator 1 over denominator c x minus x ln x end fraction
The solution of the differential equation is
a. b. c. d. e.
The given differential equation is y' - (y/x) = y²Where y is a function of x.
The solution of the given differential equation is given below Option (e) y = (1/c) (x - x ln x)
y' - (y/x) = y²
We first check whether the given differential equation is a Bernoulli differential equation. It is not a Bernoulli differential equation. Hence we cannot directly solve the given differential equation.
Using the integrating factor method, we get
Integration factor, I(x) = e^(∫(1/x)dx) = e^(ln x) = x
1. Multiplying the integrating factor to the given differential equation, we get
x y' - y = x y²
This is a linear differential equation with variable coefficients.
The standard form of the linear differential equation with variable coefficients is given below:
y' + p(x) y = q(x) where p(x) = -1/x and q(x) = x y²
2. Multiplying the integrating factor, we get x y' - y = x y²
3. Multiplying the integrating factor x on both sides, we get x² y' - xy = x³ y²
4. Differentiating both sides with respect to x, we get
2xy' + x² y'' - y - 2x y' = 3x² y y'
On simplifying, we getx² y'' + 3x y' - 2y = 0
This is a homogeneous differential equation. We substitute y = ux, where u is a function of x. On substituting we getx² u'' + 2x u' = 0
5. On simplifying, we get u' = -c/x²
6. On integrating, we get u = c/x + d where c and d are arbitrary constants.
Substituting u = y/x, we get y/x = c/x + d
Hence the solution of the given differential equation is y = c - x ln x
where c = 1
The correct option is (e).Option (e) y = (1/c) (x - x ln x)
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Find the mean, variance, and standard deviation for each of the values of n and p when the conditions for the binomial distribution are met. Round your answers to three decimal places as needed. Part 1 out of 4 n = 295, p = 0.21
The mean, variance, and standard deviation for n = 295 and p = 0.21 by using binomial distribution are
61.95, 48.8125, and 6.988, respectively.
The binomial distribution, which is a type of probability distribution, is used to calculate the probability of a certain number of successes (or failures) in a given number of trials. The mean, variance, and standard deviation of a binomial distribution can be calculated using the following formulas:
Mean (μ) = np
Variance (σ²) = npq
Standard deviation (σ) = √(npq)
Where n is the number of trials, p is the probability of success in a single trial, and q is the probability of failure in a single trial (q = 1 - p).
Part 1 out of 4: n = 295, p = 0.21
Using the formulas above, we can calculate the mean, variance, and standard deviation for this binomial distribution.
Mean (μ) = np
= 295 × 0.21 ⇒61.95
Variance (σ²) = npq
= 295 × 0.21 × 0.79 ⇒ 48.8125
Standard deviation (σ) = √(npq)
⇒ √(48.8125) = 6.988
Therefore, the mean, variance, and standard deviation for n = 295 and p = 0.21 are 61.95, 48.8125, and 6.988, respectively.
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Joseph paints ornaments for a school play. Each ornament is made up of two identical cylinders, as shown. All surfaces of each cylinder must be painted. How many cans of paint does he need to paint 75 ornaments?
PLEASE HELP ME BIG GRADE!!!!!!!!!
Number of cylindrical cans of paint does he need to paint 75 ornaments is 20.
What is the Surface Area of a Cylinder?The total area that the cylinder's curved surface and round bases enclose is referred to as its surface area. The cylinder's total surface area consists of the curving surface as well as the areas of the two bases, each of which is shaped like a circle. A cylinder is a 3D solid object made up of two circular bases connected by a curving face.
Surface Area of Cylinder = 2πrh+2πr²
where , r is radius of cylinder=4.6cm
H is height of cylinder=2*6.5cm=13cm
A=2×π×4.6×13+2×π×4.6²≈508.68668cm²
Total Number of cans of paint needed to paint 75 ornaments=75×508.68668
/1900=20.
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5. Find x and h.
x =
h =
Using pythagoras' theorem in the right-angled triangle
x = 3 andh = 3√3What is a right-angled triangle?A right-angled triangle is a polygon with 3 sides in which one angle is a right angle
Now, since we have 3 triangles, using Pythagoras' theorem in all three triangles, we have
h² + (12 - x)² = 12² - 6² (1)
Also, h² + x² = 6² (2)
So, h² + (12 - x)² = 12² - 6²
h² + (12 - x)² = 144 - 36
h² + (12 - x)² = 108 (3)
From equation (2), h² = 36 - x²
Substituting this into equation (3), we have that
h² + (12 - x)² = 108 (3)
36 - x² + (12 - x)² = 108 (3)
Expanding the brackets, we have that
36 - x² + 144 - 24x + x² = 108
36 + 144 - 24x = 108
180 - 24x = 108
-24x = 108 - 180
-24x = -72
x = -72/-24
x = 3
Since h² = 36 - x²
h = √(36 - x²)
So, substituting the value of x = 3 into the equation, we have that
h = √(36 - x²)
h = √(36 - 3²)
h = √(36 - 9)
h = √27
h = 3√3
So,
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3x^2-2x+1 when x is 4
Answer: I got 29
Step-by-step explanation:
You would plug in 4 in all the spots where the x's are and then solve the problem