Question 6 of 10
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ACDE AOPQ?
Check all that apply.
AA
A. AAS
B. ASA
C. LL
OD. HL
E. LA
F. SAS
Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.
what is triangle ?Having three straight sides and three angles where they intersect, a triangle is a closed, two-dimensional shape. It is one of the fundamental geometric shapes and has a number of characteristics that can be used to study and resolve issues that pertain to it. The triangle inequality theory states that the sum of a triangle's interior angles is always 180 degrees, and that the longest side is always the side across from the largest angle. Triangles can be used to solve a wide range of mathematical issues in a variety of disciplines and can be categorised based on the length of their sides and the measurement of their angles.
given
We can use the following congruence theories or postulates based on the data in the diagram:
A. ASA
B. AAS
C. LL (corresponding angles hypothesis)
F. SAS
Therefore, A, B, C, and F are the proper responses as the congruence theories or postulates based on the data.
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Given that x + 1/2 = 5, what is 2*x^2 - 3x + 6 - 3/x +2/x^2
pls help me soon
Sure, let's solve this step-by-step:
First, we need to solve for x in the equation x + 1/2 = 5.
We can do this by subtracting 1/2 from both sides, giving us x = 4 1/2.
Now, we can substitute x = 4 1/2 into the equation 2*x^2 - 3x + 6 - 3/x +2/x^2.
We can simplify the equation by multiplying both sides by x^2, giving us:
2*x^2 - 3x + 6 - 3/x +2 = 10*x^2 - 3x + 6.
Now, we can combine all of the terms with x:
10*x^2 - 6x + 6 = 0.
Finally, we can solve the equation using the quadratic formula:
x = 3/5 or x = 2.
Therefore, the answer to the equation is 10*(3/5)^2 - 6(3/5) + 6 = 4.8, or 10*2^2 - 6(2) + 6 = 16.
Let the Universal Set, S, have 158 elements. A and B are subsets of S. Set A contains 67 elements and Set B contains 65 elements. If Sets A and B have 9 elements in common, how many elements are in neither A nor B?
There are 92 elements in A but not in B.
What are sets?In mathematics, a set is a well-defined collection of objects or elements. Sets are denoted by uppercase symbols, and the number of elements in a finite set is denoted as the cardinality of the set enclosed in curly braces {…}.
Empty or zero quantity:
Items not included. example:
A = {} is a null set.
Finite sets:
The number is limited. example:
A = {1,2,3,4}
Infinite set:
There are myriad elements. example:
A = {x:
x is the set of all integers}
Same sentence:
Two sets with the same members. example:
A = {1,2,5} and B = {2,5,1}:
Set A = Set B
Subset:
A set 'A' is said to be a subset of B if every element of A is also an element of B. example:
If A={1,2} and B={1,2,3,4} then A ⊆ B
Universal set:
A set that consists of all the elements of other sets that exist in the Venn diagram. example:
A={1,2}, B={2,3}, where the universal set is U = {1,2,3}
n(A ∪ B) = n(A – B) + n(A ∩ B) + n(B – A)
Hence, There are 92 elements in A but not in B.
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Write an equation in slope-intercept form for the line that passes through (3,-10) and (6,5).
Answer:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
m = (5 - (-10)) / (6 - 3) = 15/3 = 5
Now that we have the slope, we can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1)
Substituting the values of m, x1, and y1, we get:
y - (-10) = 5(x - 3)
Simplifying and rearranging the equation, we get:
y + 10 = 5x - 15
y = 5x - 25
Therefore, the equation of the line passing through (3,-10) and (6,5) in slope-intercept form is y = 5x - 25.
Step-by-step explanation:
#trust me bro
Mia has a collection of vintage action figures that is worth $190. If the collection appreciates at a rate of 6% per year, which equation represents the value of the collection after 5 years?
The equation that represents the value of the collection after 5 years is:
Value of collection after 5 years = 190 x (1 + 0.06)^5
Explanation:
To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).
Therefore, the equation for the value of the collection after 5 years is:
Value of collection after 5 years = 190 x (1 + 0.06)^5
This can also be written as:
Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)
Therefore, the value of the collection after 5 years is $246.90.
Answer: 254.26
Step-by-step explanation:
Expand and simplify completely
[tex]x(x+(1+x)+2x)-3(x^2-x+2)[/tex]
Answer:
x² + 4x - 6
Step-by-step explanation:
x(x + (1 + x) + 2x) - 3(x² - x + 2) ← simplify parenthesis on left
= x(x + 1 + x + 2x) - 3(x² - x + 2)
= x(4x + 1) - 3(x² - x + 2) ← distribute parenthesis
= 4x² + x - 3x² + 3x- 6 ← collect like terms
= x² + 4x - 6
Type the correct answer in each box. Assume π = 3.14. Round your answer(s) to the nearest tenth. 90° 30° In this circle, the area of sector COD is 50.24 square units. The radius of the circle is units, and m AB is units.
Therefore, the length of segment AB is approximately 7.4 units.
What is area?Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width.
Here,
To find the radius of the circle, we can use the formula for the area of a sector:
Area of sector = (θ/360) x π x r²
where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is approximately 3.14.
We're given that the area of sector COD is 50.24 square units and the central angle of the sector is 90°. So we can plug in these values and solve for r:
50.24 = (90/360) x 3.14 x r²
50.24 = 0.25 x 3.14 x r²
r² = 50.24 / (0.25 x 3.14)
r² = 201.28
r = √201.28
r ≈ 14.2
Therefore, the radius of the circle is approximately 14.2 units.
Next, we need to find the length of segment AB. Since AB is a chord of the circle, we can use the formula:
AB = 2 x r x sin(θ/2)
where θ is the central angle of the sector in degrees, r is the radius of the circle, and sin() is the sine function.
We're given that the central angle of sector COD is 30°. So we can plug in this value and the radius we found earlier to solve for AB:
AB = 2 x 14.2 x sin(30/2)
AB = 2 x 14.2 x sin(15)
AB ≈ 7.4
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Find the value of X using the picture below.
Answer:
x = 7
Step-by-step explanation:
The two angles are equal so the opposite sides are equal.
5x-2 =33
Add two to each side.
5x-2+2 = 33+2
5x=35
Divide by 5
5x/5 =35/5
x = 7
Parts A-D. What is the value of the sample mean as a percent? What is its interpretation? Compute the sample variance and sample standard deviation as a percent as measures of rotelle for the quarterly return for this stock.
The sample mean is 2.1, the sample variance is 212.5% and the standard deviation is 14.57%
What is the sample mean?a. The sample mean can be computed as the average of the quarterly percent total returns:
[tex](11.2 - 20.5 + 13.2 + 12.6 + 9.5 - 5.8 - 17.7 + 14.3) / 8 = 2.1[/tex]
So the sample mean is 2.1%, which can be interpreted as the average quarterly percent total return for the stock over the sample period.
b. The sample variance can be computed using the formula:
[tex]s^2 = sum((x - mean)^2) / (n - 1)[/tex]
where x is each quarterly percent total return, mean is the sample mean, and n is the sample size. Plugging in the values, we get:
[tex]s^2 = (11.2 - 2.1)^2 + (-20.5 - 2.1)^2 + (13.2 - 2.1)^2 + (12.6 - 2.1)^2 + (9.5 - 2.1)^2 + (-5.8 - 2.1)^2 + (-17.7 - 2.1)^2 + (14.3 - 2.1)^2 / (8 - 1) = 212.15[/tex]
So the sample variance is 212.15%. The sample standard deviation can be computed as the square root of the sample variance:
[tex]s = \sqrt(s^2) = \sqrt(212.15) = 14.57[/tex]
So the sample standard deviation is 14.57%.
c. To construct a 95% confidence interval for the population variance, we can use the chi-square distribution with degrees of freedom n - 1 = 7. The upper and lower bounds of the confidence interval can be found using the chi-square distribution table or calculator, as follows:
upper bound = (n - 1) * s^2 / chi-square(0.025, n - 1) = 306.05
lower bound = (n - 1) * s^2 / chi-square(0.975, n - 1) = 91.91
So the 95% confidence interval for the population variance is (91.91, 306.05).
d. To construct a 95% confidence interval for the standard deviation (as percent), we can use the formula:
lower bound = s * √((n - 1) / chi-square(0.975, n - 1))
upper bound = s * √((n - 1) / chi-square(0.025, n - 1))
Plugging in the values, we get:
lower bound = 6.4685%
upper bound = 20.1422%
So the 95% confidence interval for the standard deviation (as percent) is (6.4685%, 20.1422%).
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When expressions of the form (x −r)(x − s) are multiplied out, a quadratic polynomial is obtained. For instance, (x −2)(x −(−7))= (x −2)(x + 7) = x2 + 5x − 14.
a. What can be said about the coefficients of the polynomial obtained by multiplying out (x −r)(x − s) when both r and s are odd integers? when both r and s are even integers? when one of r and s is even and the other is odd?
b. It follows from part (a) that x2 − 1253x + 255 cannot be written as a product of two polynomials with integer coefficients. Explain why this is so.
a.(1) When both r and s are odd integers, the quadratic polynomial obtained by multiplying out (x - r)(x - s) will have a coefficient of 1 for x^2 term, and both the coefficient of x term and constant term will be odd integers.
(2) When both r and s are even integers, the polynomial obtained by multiplying out (x - r)(x - s) will also have a coefficient of 1 for x^2 term, but the coefficient of x term and constant term will be even integers.
(3) When one of r and s is even and the other is odd, the polynomial obtained by multiplying out (x - r)(x - s) will have a coefficient of 1 for x^2 term, the coefficient of x term will be an odd integer, while the constant term will be an even integer.
b. x^2 - 1253x + 255 cannot be written as a product of two polynomials with integer coefficients.
a. When both r and s are odd integers, the product (x − r)(x − s) will have a coefficient of 1 for x^2 term, and both the coefficient of x term and constant term will be odd integers. This is because the sum of two odd integers and the product of two odd integers is also an odd integer.
When both r and s are even integers, the product (x − r)(x − s) will also have a coefficient of 1 for x^2 term, but the coefficient of x term and constant term will be even integers. This is because the sum of two even integers and the product of two even integers is also an even integer.
When one of r and s is even and the other is odd, the product (x − r)(x − s) will have a coefficient of 1 for x^2 term, and the coefficient of x term will be an odd integer, while the constant term will be an even integer. This is because the sum of an odd and even integer is an odd integer, and the product of an odd and even integer is an even integer.
b. If x^2 - 1253x + 255 can be written as a product of two polynomials with integer coefficients, then we can write it as (x - r)(x - s) where r and s are integers. From part (a), we know that both r and s cannot be odd integers since the coefficient of x term would be odd, but 1253 is an odd integer. Similarly, both r and s cannot be even integers since the constant term would be even, but 255 is an odd integer. Therefore, one of r and s must be odd and the other must be even. However, the difference between an odd integer and an even integer is always odd, so the coefficient of x term in the product (x - r)(x - s) would be odd, which is not equal to the coefficient of x term in x^2 - 1253x + 255. Hence, x^2 - 1253x + 255 cannot be written as a product of two polynomials with integer coefficients.
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find the following answer
According to the Venn diagram the value of [tex]n(A ^ C \cap B ^ C) = {3}[/tex] so the number of elements in that set is 1.
What is Venn diagram ?
A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. It is usually represented as a rectangle or a circle for each set and the overlapping areas between them, showing the common elements that belong to more than one set. Venn diagrams are widely used in mathematics, logic, statistics, and computer science to visualize the relationships between different sets and help solve problems related to set theory.
According to the question:
To solve this problem, we first need to understand the notation used.
n(A) denotes the set A and the numbers within the braces {} indicate the elements in set A. For example, n(A)={7,4,3,9} means that the set A contains 7, 4, 3, and 9.
n(AnB) denotes the intersection of sets A and B, i.e., the elements that are common to both A and B. For example, n(AnB)={4,3} means that the sets A and B have 4 and 3 in common.
^ denotes intersection of sets
cap denotes the intersection of sets
Now, we need to find the elements that are common to sets A and C, and sets B and C. We can do this by taking the intersection of A and C, and the intersection of B and C, and then taking the intersection of the two resulting sets.
[tex]n(A ^ C) = n(A \cap C) = {3,9}[/tex]
[tex]n(B ^ C) = n(B\cap C) = {3,5}[/tex]
Now, we take the intersection of [tex]n(A ^ C)[/tex] and [tex]n(B ^ C)[/tex]:
[tex]n(A ^ C \cap B ^ C) = {3}[/tex]
Therefore, the answer is 1.
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Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch. I need help
D: Please !!!!
Answer:
We can use the formula for the area of a rectangle to solve this problem. Let's assume that the length of the top of the bookcase is L and the width is b. Then, we can write:
L × b = 300
Solving for b, we get:
b = 300 / L
Since we don't know the length L, we cannot find the exact value of b. However, we can use the given information to make an estimate. Let's say that the length of the bookcase is 60 inches. Then, we have:
b = 300 / 60 = 5
So, if the length of the bookcase is 60 inches, the width needs to be at least 5 inches to accommodate Bria's soap carving collection. However, if the length is different, the required width will also be different.
what is 8 x 1 ????????????
Answer:8
Step-by-step explanation:8x1=8
19. Hockey Game Two families go to a hockey game. One family purchases two adult tickets and four youth tickets for $28. Another family purchases four adult tickets and five youth tickets for $45.50. Let x represent the cost in dollars of one adult ticket and let y represent the cost in dollars of one youth ticket. a. Write a linear system that represents this situation. b. Solve the linear system to find the cost of one adult and one youth ticket. c. How much would it cost two adults and five youths to attend the game?
Subtract 1/9 - 1/14 and give answer as improper fraction if necessary.
Answer:
To subtract 1/9 - 1/14, we need to find a common denominator. The smallest number that both 9 and 14 divide into is 126.
So, we will convert both fractions to have a denominator of 126:
1/9 = 14/126
1/14 = 9/126
Now we can subtract them:
1/9 - 1/14 = 14/126 - 9/126
Simplifying the right-hand side by subtracting the numerators, we get:
5/126
Therefore, 1/9 - 1/14 = 5/126 as an improper fraction.
Answer:
1/9-1/14
=14-9/9*14
=5/126
= 25 1/5
Match the definition:HistogramBinDescriptive StaticsMeanMedianModeStandard deviationA. The scatter around a central pointB. is a measure of a data’s variabilityC. is a graph of the frequency distribution of a set of dataD. values calculated from a data set and used to describe some basic characteristics of the data setE. a group in a histogramF. the middle value of a sorted set of dataG. is the most commonly occurring value in a data set
The matches of Histogram, Bin, Descriptive Statistics, Mean, Median and Standard Deviation are C, E, D, A, F, G and B respectively.
The Match the definition are given.
Histogram - C). is a graph of the frequency distribution of a set of data
Bin - E). a group in a histogram
Descriptive Statistics - D). values calculated from a data set and used to describe some basic characteristics of the data set
Mean - A). The scatter around a central point
Median - F). the middle value of a sorted set of data
Mode - G). is the most commonly occurring value in a data set
Standard Deviation - B). is a measure of a data’s variability
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The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.
n(A)=
The cardinality of set A, n(A) = 29
What is cardinality of a set?The cardinality of a set is the total number of elements in the set
Given the Venn diagram here shows the cardinality of each set. To find the cardinality of set A, n(A), we proceed as follows.
Since the cardinality of a set is the total number of elements in the set, then cardinality of set A , n(A) = 9 + 8 + 3 + 9
= 29
So, n(A) = 29
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in one of his experiments conducted with animals, thorndike found that cats learned to escape from a puzzle box:
In one of his experiments conducted with animals, Thorndike found that cats learned to escape from a puzzle box is increased gradually
To quantify the learning process, Thorndike used a mathematical formula known as the Law of Effect equation. The equation is:
B = f(log S1/S2)
where B represents the strength of the behavior, S1 represents the satisfaction of the positive consequence, and S2 represents the degree of frustration or negative consequence.
In the context of Thorndike's puzzle box experiment, the Law of Effect equation can be used to describe how the cat's behavior changed over time as it learned to escape the puzzle box more quickly and efficiently. Initially, the cat's behavior was weak because it did not know which actions would lead to a positive outcome.
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The windows to a Tudor-style home create many types of quadrilaterals. Use the picture of the window below to answer the following questions.
Please help me I will give literally anything
a. Determine which type of quadrilaterals you see. Name these quadrilaterals using the labeled vertices.
b. What properties of quadrilaterals would you have to know to identify the parallelograms in the picture? Be specific as to each type of parallelogram by using the properties between sides, angles, or diagonals for each.
Answer:
I'd be happy to help!
a. From the picture of the window, we can identify the following quadrilaterals:
Rectangle: ABCD (all angles are right angles and opposite sides are parallel and congruent)
Parallelogram: EFGH (opposite sides are parallel and congruent)
Trapezoid: BCGH (at least one pair of opposite sides are parallel)
b. To identify the parallelograms in the picture, we would need to know the following properties of parallelograms:
Opposite sides are parallel and congruent
Opposite angles are congruent
Diagonals bisect each other
Using these properties, we can identify the following parallelograms in the picture:
Parallelogram EFGH: Opposite sides EF and GH are parallel and congruent, and opposite sides EG and FH are also parallel and congruent. Additionally, angles E and G are congruent, and angles F and H are congruent.
Rectangle ABCD: Opposite sides AB and CD are parallel and congruent, and opposite sides AD and BC are also parallel and congruent. Additionally, angles A and C are congruent, and angles B and D are congruent. The diagonals AC and BD bisect each other, meaning that they intersect at their midpoints.
Step-by-step explanation:
help I’ll give brainliest ^•^ just question (7) thanks!!
Answer:
To shift the graph of f(x) = |x| to have a domain of [-3, 6], we need to move the left endpoint from -6 to -3 and the right endpoint from 3 to 6.
A translation to the right by 3 units will move the left endpoint of the graph of f(x) to -3, but it will also shift the right endpoint to 6 + 3 = 9, which is outside the desired domain.
A translation to the left by 3 units will move the right endpoint of the graph of f(x) to 3 - 3 = 0, which is outside the desired domain.
A translation upward or downward will not change the domain of the graph, so options B and D can be eliminated.
Therefore, the correct answer is C g(x) = x - 3. This translation will move the left endpoint to -3 and the right endpoint to 6, which is exactly the desired domain.
Show your solution ( 3. ) C + 18 = 29
Answer:
Show your solution ( 3. ) C + 18 = 29
Step-by-step explanation:
To solve the equation C + 18 = 29, we want to isolate the variable C on one side of the equation.
We can start by subtracting 18 from both sides of the equation:
C + 18 - 18 = 29 - 18
Simplifying the left side of the equation:
C = 29 - 18
C = 11
Therefore, the solution to the equation C + 18 = 29 is C = 11.
PLS HELP I WILL MARK BRAINILEST
Answer:
Let's assume the original price of the stock was x.
When the company announced it overestimated demand, the stock price fell by 40%.
So, the new price of the stock after the first decline was:
x - 0.4x = 0.6x
A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.
So, the new price of the stock after the second decline was:
0.6x - 0.6(0.6x) = 0.24x
Given that the current stock price is $2.40, we can set up the equation:
0.24x = 2.40
Solving for x, we get:
x = 10
Therefore, the stock was originally selling for $10.
exercise 2.4.3 in each case, solve the systems of equations by finding the inverse of the coefficient matrix.
The inverse of the coefficient matrix is A^-1 = [-2 2]. The solution to the system of equations is x = -1 and y = 1/5.
To solve the system of equations:
2x + 2y = 1
2x - 3y = 0
We can write this system in matrix form as:
[2 2] [x] [1]
[2 -3] [y] = [0]
The coefficient matrix is:
[2 2]
[2 -3]
To find the inverse of the coefficient matrix, we can use the following formula:
A^-1 = (1/|A|) adj(A)
where |A| is the determinant of A and adj(A) is the adjugate of A.
The determinant of the coefficient matrix is:
|A| = (2)(-3) - (2)(2) = -10
The adjugate of the coefficient matrix is:
adj(A) = [-3 2]
[-2 2]
Therefore, the inverse of the coefficient matrix is:
A^-1 = (1/-10) [-3 2]
[-2 2]
Multiplying both sides of the matrix equation by A^-1, we get:
[x] 1 [-3 2] [1]
[y] = -10 [-2 2] [0]
Simplifying the right-hand side, we get:
[x] [-1]
[y] = [1/5]
Therefore, the solution to the system of equations is:
x = -1
y = 1/5
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_____The given question is incomplete, the complete question is given below:
solve the systems of equations by finding the inverse of the coefficient matrix. a. 2x+2y=1 2x-3y-0
The pens in a box are repackaged equally into 9 packs. Each pack has more than 15 pens.
1. Find an inequality to represent n, the possible number of pens in the box.
2. Explain why you chose this inequality.
Therefore, the possible number of pens in the box is p, where p is greater than 135.
What is inequality?Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.
Inequalities are mathematical expressions that compare two values using the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). To solve an inequality, you need to isolate the variable (the unknown quantity) on one side of the inequality symbol and determine the range of values for which the inequality holds true.
Here are some general steps to solve an inequality:
Simplify both sides of the inequality as much as possible. This may involve combining like terms, distributing terms, or factoring.Get all the variable terms on one side of the inequality symbol and all the constant terms on the other side. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol.Solve for the variable by isolating it on one side of the inequality symbol. If the variable has a coefficient, divide both sides of the inequality by that coefficient.Write down the solution as an inequality. If you have solved for x, the solution will be in the form of x < a or x > b, where a and b are numbers.Check your solution by testing a value in the original inequality that is within the range of the solution. If the inequality holds true for that value, then the solution is correct. If not, then you may need to recheck your work or adjust your solutionby the question.
Let's say there are 'p' pens in the box. Each pack has more than 15 pens, so we can write the inequality:
p/9 > 15
Multiplying both sides by 9, we get:
p > 135
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Could you please solve this one.
The proof that the lines CD and XY are parallel is shown below in paragraghs
How to prove the lines CD and XY are parallelGiven that
∠CAY ≅ ∠XBD
This means that the angles CAY and XBD are congruent angles
The above means that
The angles ∠AYX & ∠ACD correspond to the angle ∠CAYThe angle ∠BXY & ∠BDC corresponds to the angle ∠XBDBy the corresponding angles, we have
∠BXY = ∠AYX
∠ACD = ∠BDC
By the congruent angles above, the following lines are parallel
Line AC and BX
Line AY and BD
Line CD and XY
Hence, the lines CD and XY are parallel
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Help me find the value of x
Answer:
x = 30
Step-by-step explanation:
We know
The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.
2x + 3x + 10 = 160
5x + 10 = 160
5x = 150
x = 30
the figure below shows the change of a population over time. which statement best describes the mode of selection depicted in the figure?
The statement that best describes the mode of selection depicted in the figure is (b) Directional Selection, changing the average color of population over time.
The Directional selection is a type of natural selection that occurs when individuals with a certain trait or phenotype are more likely to survive and reproduce than individuals with other traits or phenotypes.
In the directional selection of evolution, the mean shifts that means average shifts to one extreme and supports one trait and leads to eventually removal of the other trait.
In this case, one end of the extreme-phenotypes which means that the dark-brown rats are being selected for. So, over the time, the average color of the rat population will change.
Therefore, the correct option is (b).
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The given question is incomplete, the complete question is
The figure below shows the change of a population over time. which statement best describes the mode of selection depicted in the figure?
(a) Disruptive Official, favoring the average individual
(b) Directional Selection, changing the average color of population over time
(c) Directional selection, favoring the average individual
(d) Stabilizing Selection, changing the average color of population over time
According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800.
(a) What is the probability that a household in Maryland has an annual income of $90,000 or more? (Round your answer to four decimal places.)
(b) What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.)
The required probability that a household in Maryland with annual income of ,
$90,000 or more is equal to 0.3377.
$50,000 or less is equal to 0.2218.
Annual household income in Maryland follows a normal distribution ,
Median = $75,847
Standard deviation = $33,800
Probability of household in Maryland has an annual income of $90,000 or more.
Let X be the random variable representing the annual household income in Maryland.
Then,
find P(X ≥ $90,000).
Standardize the variable X using the formula,
Z = (X - μ) / σ
where μ is the mean (or median, in this case)
And σ is the standard deviation.
Substituting the given values, we get,
Z = (90,000 - 75,847) / 33,800
⇒ Z = 0.4187
Using a standard normal distribution table
greater than 0.4187 as 0.3377.
P(X ≥ $90,000)
= P(Z ≥ 0.4187)
= 0.3377
Probability that a household in Maryland has an annual income of $90,000 or more is 0.3377(rounded to four decimal places).
Probability that a household in Maryland has an annual income of $50,000 or less.
P(X ≤ $50,000).
Standardizing X, we get,
Z = (50,000 - 75,847) / 33,800
⇒ Z = -0.7674
Using a standard normal distribution table
Probability that a standard normal variable is less than -0.7674 as 0.2218. This implies,
P(X ≤ $50,000)
= P(Z ≤ -0.7674)
= 0.2218
Probability that a household in Maryland has an annual income of $50,000 or less is 0.2218.
Therefore, the probability with annual income of $90,000 or more and $50,000 or less is equal to 0.3377 and 0.2218 respectively.
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Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
NOTE: Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the 30°-60°-90° Triangle Theorem to find the answer.
The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.
What is Triangle theorem?The 30°-60°-90° Triangle Theorem states that in such a triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the product of the length of the hypotenuse and the square root of 3 divided by 2.
Using this theorem, we can write:
y = hypotenuse
Opposite of 30° angle = 5 = hypotenuse/2
Opposite of 60° angle = x = hypotenuse × (√(3)/2)
Solving for the hypotenuse in terms of y from the first equation, we get:
hypotenuse = 5×2 = 10
Substituting this value into the third equation, we get:
x = 10 × (√(3)/2) = 5 × √(3)
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During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 131°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T=-0.005x^2+0.45x+125. Will the temperature of the part ever reach or exceed 131°F? Use the discriminant of a quadratic equation to decide.
answer options
1. No
2. Yes
From the discriminant of the give quadratic equation, the temperature of the machine will part after 50 minutes of operation.
Will the temperature of the part ever reach or exceed 135°F?The given equation that models the temperature of the machine is;
T = -0.005x² + 0.45x + 125
Let check if there's a value that exists for T = 135
Putting T = 135 in the given equation,
135 = -0.005x² + 0.45x + 125
We can simplify this to;
0.005x² - 0.45x + 10 = 0
From the general form of quadratic equation which is ax² + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.
The discriminant of this quadratic equation is given by:
D = b² - 4ac
= (-0.45)² - 4(0.005)(10)
= 0.2025 - 0.2
= 0.0025
The discriminant of the equation is positive which indicates we have two roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.
We can also find the roots of the quadratic equation using the formula:
[tex]x = (-b \± \sqrt(D)) / 2a[/tex]
Substituting the values of a, b, and D, we get:
[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]
Taking the positive value, we get:
x = 50
Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.
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