X= root 6^2 + 10^2
X=2 root 34
So, x is 11.66 to 2d.p
(root means square root)
Hope this helps!
Answer:
x = 11.66
Step-by-step explanation:
Hello!
We can use the Pythagorean theorem to solve for the hypotenuse.
Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
a = legb = legc = hypotenusePlug the values of 6 and 10 into the formula to solve.
Find the Hypotenuse[tex]a^2 + b^2 = c^2[/tex][tex]6^2 + 10^2 = c^2[/tex][tex]36 +100 = c^2[/tex][tex]136 = c^2[/tex][tex]c = \sqrt{136[/tex][tex]c \approx 11.66[/tex]The hypotenuse is approximately 11.66.
The sides of triangle ∆ABC have lengths of 3 cm, 8 cm, and 10 cm. If the smallest side of a similar triangle ∆XYZ has a length of 12 cm, what must be the length of the longest side of ∆XYZ?
The length of the longest side of ∆XYZ will be 40 cm. Then the correct option is A.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The sides of triangle ∆ABC have lengths of 3 cm, 8 cm, and 10 cm. If the smallest side of a similar triangle ∆XYZ has a length of 12 cm.
Let 'x' be the length of the longest side. Then the equation is given as,
x / 10 = 12 / 3
Simplify the equation, then we have
x / 10 = 12 / 3
x / 10 = 4
x = 40 cm
The length of the longest side of ∆XYZ will be 40 cm. Then the correct option is A.
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The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 85%, interpret the likelihood of randomly selecting a terrier from the shelter. Likely Unlikely Equally likely and unlikely This value is not possible to represent probability of a chance event
The interpretation of the likelihood of randomly selecting a terrier from the dog shelter where terriers are 85% is A. Likely.
What is probability?Probability refers to the chance or likelihood of an expected event occurring when there are many possible chances.
Probability is depicted as a fractional value lying between zero and one when it is not 100% uncertain or certain.
Thus, since the percentage of terriers in the dog shelter is 85%, it is 85% likely that one selects a terrier.
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Answer: A: Likely.
Step-by-step explanation:
Find the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually.
A. 270
B. $135
C. $3000
D. $4.5
Answer:
A) 270
Step-by-step explanation:
Interest = principle x time x rate
Interest = 3000 x 2 x .045 4.5% = .045 as a decimal
Interest = 270
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on orange.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on yellow.
The statement about probability that is true is that the probability of landing on purple is equal to the probability of landing on yellow. That is option D
What is probability?Probability is defined as the possible outcome of an event which may likely or unlikely occur.
The total number of sections with different colours = 8
Sections 1 and 8 are purple.
Sections 2 and 3 are yellow.
Sections 4, 5, and 6 are blue.
Section 7 is orange
The probability of landing on purple is equal to the probability of landing on yellow. That is;
probability of landing a purple = 2/8 = 1/4
Probability of landing a yellow = 2/8 = 1/4
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30 POINTS!!
whats 1 + 1 ?
Answer:2
Step-by-step explanation:1+1=2
Answer: 2
Step-by-step explanation:
1
+
1
____
2
A line passing through the point (0, 4) has a slope of-2. Write the equation of the line in point-slope form.
Answer:
[tex]y-4=-2(x-0)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope (m) of -2, and contains the point (0,4).
We want to write the equation of the line in point-slope form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
SolvingSince we are already given the slope, we can immediately plug it into the formula.
Substitute -2 as m.
[tex]y-y_1=-2(x-x_1)[/tex]
Now, let's label the values of our points to avoid confusion and mistakes.
[tex]x_1=0\\y_1=4\\[/tex]
Substitute into the formula.
[tex]y-4=-2(x-0)[/tex]
Topic: point-slope form
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Jase uses a rope as the circumference of a circle on the playground. If the rope is 6 meters long, what is the area of the circle in square
meters? Use x = 3. 14. Round to the nearest hundredth as necessary.
Answer:
279.05649m³
Step-by-step explanation:
Circumference = 2πr
6 = 2πr
6/2π = r
r = 9.424777961
Area = πr²
Area = π(9.424777961²)
Area = 279.05649m³
-8r-3(-6-5r)=8-5(4-2r)
Answer:
the answer I got was 18 over 1657
Step-by-step explanation:
its a fraction so the numerator is 18 and the denominator is 1657
A cylinder with base radius of 4 cm and a height of 7 cm is removed from the cuboid.
The remaining solid is to be painted on all its surfaces. Find the area that will be covered in paint.
the total area will be covered in the paint will be 2143.9cm²
What is cylinder?
Two parallel, identical bases connected by a curving surface form a 3D solid shape known as a cylinder. Similar to a disc in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases. Perpendicular distance is the measurement separating the two bases, and it is denoted by the letter "h," which stands for height. The distance between the two circular bases' centers and outer edges is known as the cylinder's radius and is denoted by the letter "r". A rectangle and two circles combine to form the cylinder.
A cylinder with base radius of 4 cm and a height of 7 cm is removed from the cuboid.
Volume of cuboid is = 16*15*24 = 5760 cm³
Volume of the cylinder = π r² h = π* 4² *7 = 351.85 cm³
So the surface area of the cylinder = 2π r h = 2*π*4*7 = 175.9 cm²
Total area of the cuboid = 2(240+360+384) = 1968
Toatl area = 1968+175.9 = 2143.9cm²
So the total area will be covered in the paint will be 2143.9cm²
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Energy is generated from solar & wind power. Solar power must be at most 6 units/day or the panels will burn out. Wind must be strong enough to power 1 unit/day or else the turbines won’t turn. The wind power must be less than twice the solar power less one, or the batteries won’t charge properly.
Find the optimal production of wind and solar that will maximize overall power output.
The optimal production of wind and solar that will maximize overall power output is 3 units/day of solar power and 2 units/day of wind power.
How to determine the optimal productionTo solve this question, we use the following representations
Let x be the amount of solar power generated y be the amount of wind power generated.So, the objective function is to maximize z = x + y, which represents the overall power output.
From the question, we have the following constraints:
x <= 6 (solar power must be at most 6 units/day)y >= 1 (wind power must be strong enough to power 1 unit/day)y <= 2x - 1 (wind power must be less than twice the solar power minus one)Using the Lagrangian function, we have:
L(x,y,λ1,λ2,λ3) = x + y + λ1(6-x) + λ2(y-1) + λ3(2x-y-1)
To find the optimal solution, we need to find the values of x, y, λ1, λ2, and λ3 that will make the partial derivatives of L equal to zero:
∂L/∂x = 1 + λ3 = 0
∂L/∂y = 1 - λ1 + λ2 + λ3 = 0
Using the variables x and y, we have
∂L/∂λ1 = -x + 6 = 0
∂L/∂λ2 = y - 1 = 0
∂L/∂λ3 = 2x - y - 1 = 0
Using a graphing calculator, the points that maximize the objective function are:
x = 3 and y = 2
i.e.
Power output is 3 units/day of solar power and 2 units/day of wind power.
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7x^2-10=-17 solve by taking square root
The solution to the equation 7x² - 10 = -17 is x = i
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
7x^2-10=-17
Express the equation properly
So, we have the following representation
7x² - 10 = -17
Add 10 to both sides of the equation
This gives
7x² = -7
Divide both sides by 7
x² = -1
Take the square roots
x = √-1
Rewrite as
x = i
Hence, the solution is x = i
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to earn an A in a course, a boy must have a final average of at least 88%. on the first four examinations, he as grades of 85%, 91%, 81%, and 83%. if the final examination counts as two grades, what must be get on the final to earn an A in the course?
He must get at least 97% on the final examination to earn an A in the course.
What must be get on the final to earn an A in the course?To earn an A in a course, a boy must have a final average of at least 88%. On the first four examinations, he had grades of 85%, 91%, 81%, and 83%. If the final examination counts as two grades, the final grade must be at least 91% to earn an A in the course. The total of all five grades must be equal to or greater than 88%. To calculate this, the four grades must first be added together to get the total of the first four grades. In this case, the total is 340. The final grade must then be calculated to get the total of all five grades to equal or exceed 88%.To find the final grade, the 340 must be divided by five, since the final counts as two grades. The result of this calculation is 68. This number must then be added to the final grade to reach a total of 88%. The final grade must therefore be at least 20 points higher than the 68, so 91% or higher. Therefore, to earn an A in the course, the boy must get at least 91% on the final examination, since this counts as two grades.To learn more about weighted average refer to:
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3. Gary's Gardens and Peter's Produce sell carrots in bulk. The table shows how much Peter's Produce
charges for carrots. The graph shows how much Gary's Gardens charges for carrots. For one pound
of carrots, how much more does Gary's Gardens charge than Peter's Produce?
Gary's Gardens
Peter's Produce
Weight (pounds) Cost (dollars)
12
16
28
3.
4
7
Cost (dollars)
50
45
40
35
30
25
15
10
5
10
20
30
40 50 60
Weight (pounds)
70
2
8
100
Therefore , the solution of the given problem of unitary method comes out to be $ 4 for garry and $ 1.33 for peter.
What is a unitary method, exactly?To accomplish a task through using unitary procedure, multiply the number of a tiny slice by two after first determining its size. The unit technique, to put it simply, is used to isolated a programmed object from either a specific set or set of sets. For illustration, 40 pens would cost 400 pounds ($1.01), or Rs. It's feasible that one nation will have complete control over the technique used to do this. Almost all living things have a unique characteristic. It can integrate and reciprocate in equal measure (mathematics, algebra).
Here,
Given :
Garry charges for one carrot for :
=> 12/3
=> $ 4
Peter charges for one carrot :
=> 20/15
=> 4/3
=> $ 1.33
Therefore , the solution of the given problem of unitary method comes out to be $ 4 for garry and $ 1.33 for peter.
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Pls help me to find the answer!
Answer:
Step-by-step explanation:
13x+16
Lets simplify this step by step
5(2x+2)+3x+6
Distribute:
=(5)(2x)+(5)(2)+3x+6
=10x+10+3x+6
Combine Like Terms:
=10x+10+3x+6
=(10x+3x)+(10+6)
=13x+16
13x+16
The following is a function, true or false?
It is TRUE that the given image represents the function.
What is a function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Initially, functions represented the idealized relationship between two changing quantities.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
So, the given image represents a function and it is a kind of many-to-one function.
Therefore, it is TRUE that the given image represents the function.
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1×(
–
0.3÷
–
0.5–0.9)
Write your answer as an integer or a decimal. Do not round.
Using PEDMAS the value of 1×(-0.3÷0.5-0.9) is -0.3
What is PEDMAS ?PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete.
In the expression 1×(-0.3÷ -0.5-0.9) we solve what is in the parentheses first and we must follow the rules in the parentheses.
So we deal with the division first
1× ( 0.6-0.9)
1× -0.3 = -0.3
Therefore the value of the expression 1×(-0.3÷0.5-0.9) is -0.3.
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how many more feet of bricks does sofia need? move numbers to the boxes to show the answer
According to the line-plot Sofia needed 10(3/4) more feet of bricks.
What is the line-plot?
A line plot is a graph that shows data as checkmarks or dots across a number line, indicating the frequency of each value.
In the line plot the horizontal line is showing the values of the size in feet of the bricks say 'l'.
The number of vertically aligned crosses at a given value of 'l', indicates the length of bricks for which the 'l' is needed in the project.
Follow the formula - l × n (number of crosses) = total bricks in feet
0/4 × 0 = 0
1/4 × 2 = 2/4
2/4 × 4 = 8/4
3/4 × 3 = 9/4
1 × 6 = 6
To obtain the total size in feet add all the values -
L = 2/4 + 8/4 + 9/4 + 6
L = (2 + 8 + 9 + 24)/4
L = 43/4
L = 10(3/4)
Therefore, the feet of bricks required is 10(3/4).
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3+4 (r-6)=3(2+2r) 7r show work please
By solving the equation The answer is -27+17r .Because the Given question is a Equivalent Equation
Explanation3+4(r-6)= 3(2+2r)+7r
3+4r-24=6+6r+7r
3-6-24+4r+6r+7r
-24+17r
What is equivalent Equation?Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
If two equations have the same solution, they are equivalent.
Equations that are equivalent can be created by adding, subtracting, multiplying, and dividing by the same number on either side of the equal sign.
Distribute the coefficients Combine any like term on both side.Arrange the term in same order.If all the terms in two expressions are same then the equations are equivalent.How to Solve an Equation in StepsFinding the value of the variable that makes the equation's condition true is the goal of equation solving. The subsequent actions are carried out while keeping the equation balanced on both sides in order to isolate the variable. By repeating this, LHS and RHS finally remain equal, and the equilibrium is maintained throughout.
Addition property of equality: Add the same number to both the sides. If a = b, then a + c = b + cSubtraction property of equality: Subtract the same number from both sides. If a = b, then a - c = b - cMultiplication property of equality: Multiply the same number on both sides. If a = b, then ac = bcDivision property of equality: Divide by the same number on both sides. If a = b, then a/c = b/c (where c ≠ 0)We separate the variable on one of the sides of the equation after applying this approach of systematic balancing, which entails a series of identical mathematical operations on both sides of the equation. The final step is the solution of the equation.
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Which statement describes the solution of the equation rounded to the nearest tenth?
A) The solution is greater than 10.5 and less than 11.
B) The solution is less than 1.5 and greater than 1.
C) The solution is less than -10 and greater than -10.7.
D) The solution is greater than -1.5 and less than -1.
PLEASE ANSWER ONLY IF YOU KNOW!! I need help w this!!
The solution is greater than -1.5 and less than -1.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
convert mixed fractions into improper fractions, then to decimal
14 2/5 = 72/5 = 14.4
11 1/8 = 89/8 = 11.125
Thus, the equation becomes:
14.4x+6.55= -11.125x-2.45 + 17 x
=> 14.4x + 11.125x - 17x = -6.55 -2.45
=> 8.525x = -9
=> x = -9 / 8.525 = -1.055
solution of the equation rounded to the nearest tenth = -1.1
Thus, The solution is greater than -1.5 and less than -1.
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Hi i would like some help with this asap
The constant of variation for the given graph is 1/4.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.
Given that the equation of the line in the graph is a direct variation equation.
Direct variation equations are of the form,
y = k x, where k is a constant number called constant of variation.
We have to find the value of k.
y = k x is an equation in slope intercept form where k is the slope and the value of y intercept is 0, since the line passes through origin (0, 0).
It is enough to find the slope of the given line.
Take two points from the graph, let it be (4, 1) and (-4, -1).
Slope = (-1 - 1) / (-4 - 4) = -2 / -8 = 1/4
The value of k is 1/4.
Hence the value of constant of variation is 1/4.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
Division Line
3 1 /6 divided by 3
Answer:
[tex]\frac{19}{18}=1\frac{1}{18}[/tex]
Step-by-step explanation:
[tex]3\frac{1}{6}\div3=\frac{19}{6}\div3=\frac{19}{6}*\frac{1}{3}=\frac{19}{18}=1\frac{1}{18}[/tex]
A rate is a type of ratio that has both terms expressed in different units.
The statement that a rate is a type of ratio that has both terms expressed in different units is true.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A rate is a type of ratio that has both terms expressed in different units.
This is true.
Example:
The unit rate of running a distance of 5 km in 4 hours.
Rate = 5km/4 hours
Unit rate = (5/4) km / 1 hour
Thus,
A rate is a type of ratio that has both terms expressed indifferent unit is true.
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evaluate function expressions
The given function expressions is 24f + 14g
What is meant by expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. Mathematical expressions are sentences having a minimum of two numbers or variables, at least one arithmetic operation, and a mathematical concept. Let's examine the proper way to write expressions. A mathematical expression for this sentence is x/2 + 6. The components of an expression are integers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases.Given,
-3 × f (-8) + 7 × g(2)
= -3f (-8) + 7g (2)
Simplifying the above equation,
= -3f (-8) = 24f
= 7g (2) = 14g
Then we get,
= 24f + 14g
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Help solve the equation please!!
Answer:
you forgot the question
Step-by-step explanation:
Before the 1936 US president election, a popular poll predicted that Alfred Landon would
The correct option is a. Bias from undercoverage, is best description of the term bias.
Define the term bias from undercoverage?When you remove a portion of the population from your sample, undercoverage bias develops.
Sample isn't any longer indicative of the intended population as a result. This kind of study bias can affect non-probability sampling designs.Undercoverage bias as well as nonresponse bias may appear to be identical, but they differ greatly.
Undercoverage bias happens when certain demographic members are completely left out of the questionnaire survey you utilise for your investigation.When some of the respondents you chose to be included in your sample don't answer, nonresponse bias develops.For the stated question-
Roosevelt received support from lower-income voters and ultimately won with 62% of the vote, one of the biggest margins of victory in US presidential election history.
Thus, this clearly shows the bias from undercoverage.
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The complete question is-
Before the 1936 US presidential election, a popular poll predicted that Alfred Landon would comfortably win against Franklin D. Roosevelt. The poll randomly sampled people from sources like telephone and car registration records, but the country was in an economic crisis, so many voters without those luxuries were not included in the poll. Voters with lower incomes favored Roosevelt, who ultimately won with 62%, percent of the vote—one of the largest margins of victory ever in a US presidential election. Which type of bias does this scenario best describe?
a. Bias from undercoverage
b. Bias from using voluntary response
c. Response bias
d. Nonresponse bias
Help help help help help help
Answer: [tex]B. \frac{2}{7} -\frac{2}{k}[/tex]
Step-by-step explanation:
The function p, where p (z) = -2² +14z - 40, models the profit from Lindsey's store, in thousands of dollars, after a months of opening the store.
Part A
Based on the function, when did Lindsey's store have a profit of zero dollars?
Enter your answers in the empty boxes to correctly complete the sentence.
The store had $0 profit first in month
and then in month
Part B
When did the store have its maximum profit, and what was the profit?
Enter your answers in the empty boxes to correctly complete the sentence.
The maximum profit of $
occurred in month
The store had $0 profit first in month 4 and then in month 10
The maximum profit of $1000 occurred in month 7
When the store has $0 profitThe function is given as
p(z) = -z² + 14z - 40
Next, we set p(z) = -z² + 14z - 40 = 0 and then solve for z.
So, we ha
-z² + 14z - 40 = 0
Rewrite as
z² - 14z + 40 = 0
Factorize
(z - 10)(z - 4) = 0
Solve for z
z = 10 and z =4
So the store had a profit of zero dollars in month 4 and then in month 10
Maximum profitHere, we calculate the vertex using
x = -b/2a = -14/2*-1 = 7
Plugging this value into the function, we get:
p(7) = -7² + 14*7 -40 = 49-98+40 = 1
so the maximum profit was $1000 and it occurs in the month 7.
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Use the table to write a linear function that relates y to x .
From the table given a linear function that relates y to x is y = -7.
What is point - slope form of line?
The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
The point - slope form of line is y - y1 = m(x - x1).
From the given table of values we have to find the linear function that relates y to x.
First to find the slope.
Slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-7-(-7)}{0-(-2)} = \frac{0}{2} = 0[/tex]
Now consider the point - slope form of line,
y - y1 = m(x - x1).
y - (-7) = 0(x - 0)
y + 7 = 0
y = -7
Hence, from the table given a linear function that relates y to x is y = -7.
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Which of the following is expected if the null hypothesis is true for an analysis of variance?
a. SS (between) should be about the same size as SStotal
b. SS (between) should be about the same size as SSwithin
c. MS (between) should be about the same size as MStotal
d. MS (between) should be about the same size as MSwithin
The null hypothesis is true for an analysis of variance -MS (between) should be about the same size as MS within. Option (d) is the correct answer.
If the null is true, MS between and MS within should be about the same since they are both estimates of the same quantity (variance).
The null hypothesis is a characteristic arithmetic theory that suggests that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.
The null hypothesis in statistics defines that there is no difference between groups or no relationship between variables.
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Triangle 2 and triangle 3 were created by drawing an altitude in triangle 1. What is the relationship between the green highlighted
segment in triangle 2 and the blue highlighted segment in triangle 1?
A. The highlighted segments are corresponding sides of triangles 1 and 3.
B. The highlighted segments are corresponding sides of triangles 2 and 3.
C. The highlighted segments have no corresponding relationship.
D. The highlighted segments are congruent.
The relationship between the green highlighted segment in triangle 2 and the blue highlighted segment in triangle 1 is D. The highlighted segments are congruent.
What are congruent segments ?Congruent segments are segments in different shapes that have the same length and angle. In other words, they are identical to each other even though they are in different shapes.
The green highlighted segment in triangle 2 and the blue highlighted segment in triangle 1 are congruent segments because the blue highlighted segment was segment the green highlighted segment was derived from which is why they are the same.
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