The statement "If ∠1 and ∠2 form a linear pair; ∠1 and ∠3 are supplementary, then ∠2 = ∠3" is proved.
If the sum of two angles is 180 then they are called supplmentary angles of each other.
If one straight line meets another straight line at a point, then two adjoint angles at that point on that line is called Linear angles to each other.
Here given that ∠1 and ∠2 are linear to each other.
From property of the linear angles we know that the sum of linear angles is 180.
Therefore, ∠1 + ∠2 = 180
So, ∠2 = 180 - ∠1 .........(1)
Also it is given that, ∠1 and ∠3 are supplementary angles.
So, ∠1 + ∠3 = 180
Therefore, ∠3 = 180 - ∠1.....(2)
Comparing (1) and (2) we get,
∠2 = ∠3 = 180 - ∠1
Therefore, ∠2 = ∠3, proved
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Suppose that a classroom has 4 light bulbs. The probability that each individual light bulbs work is 0. 6. Suppose that each light bulb works independently of the other light bulbs. What is the probability that none of the 4 light bulbs work?.
Answer:
0.0256 or 16/625 or 2.56%
Step-by-step explanation:
The problem states that each light bulb operates independently of the other, so the probability doesn't change for each light bulb based on how many other light bulbs are working.
The probability of each light bulb working is 0.6 out of 1. However, we want the probability of it being broken.
1 - 0.6 = 0.4
This is the probability of one light bulb being broken. But there are 4 lightbulbs.
We can multiply 0.4 by itself 4 times, as the probability stacks.
0.4 * 0.4 * 0.4 * 0.4 = 0.0256 (Also achieved by raising 0.4 to the power of 4)
To get the percentage, multiply it by 100. 2.56%
0.4 is equal to 40% or 40/100. If you simply, that fraction is equal to 2/5
2/5 * 2/5 * 2/5 * 2/5 = 16/625 (Also achieved by raising 2/5 to the power of 4)
2. Write an inequality representing the total cost of your purchase. (3 points)
a. Each pound of fruit costs $4. Write an expression that shows the total cost of
the fruit. Use the variable you identified in question 1.
CLOSE
Answer:
4f
Step-by-step explanation:
I am using the variable f for fruit. Each pound of fruit costs $4, so the total will be 4 * the number of pounds of fruit.
Statistics from 2003 to 2013 indicated that, in the United States, women were earning approximately ______ cents for every dollar earned by men.
The answer for the fill in the blank is 80
Statistics from 2003 to 2013 indicated that, in the United States, women were earning approximately ___80___ cents for every dollar earned by men.
A transitional matrix answers two questions: Where did people who are now in each job category come from, and _____.
A transitional matrix answers two questions:
Where did people who are now in each job category come from,
and where did people who were in each job category go?
The term "transition matrix" is used in various contexts of mathematics. In linear algebra, it is sometimes used to represent changes in a coordinate matrix. In Markov chain theory, it is used as an alias for a stochastic matrix, a matrix that describes a transition.
The transition matrix P is regular if there are only positive entries in the power of P. If the transition matrix is regular, a Markov chain is a normal Markov chain. For example, if you take the power of the matrix D in succession, the entry for D will always be (or will be) positive.
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What is the length of the circles radius?
Answer: D. 8 cm.
Step-by-step explanation:
[tex]l_{arc}=\frac{26}{9}\pi \ cm\ \ \ \ \Theta=65^0 \ \ \ \ \ r=?\\\boxed {l_{arc}=2\pi r*\frac{\Theta^0}{360^0} }\ \ \ \ \ \Rightarrow\\\boxed {r=\frac{{l_{arc}}*360^0}{2\pi *\Theta} }.\\r=\frac{\frac{26}{9}*\pi *360^0 }{2\pi *65^0} =\frac{13*360^0}{9*65^0} =\frac{40}{5}=8 \ (cm).[/tex]
Which equation has a graph that is a parabola with a vertex at (–2, 0)?
The equation of the parabola which has a vertex at (-2,0) is; y = x² +4x +4.
What is the equation of the parabola with vertex (-2,0)?From the task content, it follows that the vertex of the of the parabola described by the graph in discuss is given by the point; (-2,0).
Hence, the vertex form of the equation is;
y = (x-(-2))² +0
Hence, the equation is; y = x² +4x +4.
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Answer: B
Step-by-step explanation:
Edge 2023
Find side x, giving your answer to 1 decimal place.
7 cm
81°
X
40°
In the given diagram, the value of the side labelled x is 10.8 cm
Law of sinesFrom the question, we are to determine the value of side x
Using the law of sines
In any given triangle XYZ,
[tex]\frac{x}{sinX}=\frac{y}{sinY}=\frac{z}{sinZ}[/tex]
Thus,
In the given triangle,
[tex]\frac{x}{sin81^\circ} =\frac{7}{sin40^\circ}[/tex]
∴ [tex]x=\frac{7 \times sin81^\circ}{sin40^\circ}[/tex]
x = 10.75599
x ≈ 10.8 cm
Hence, the value of the side labelled x is 10.8 cm
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Bethany wants to estimate the value of (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14). Which statement about the estimate is true?
The value will be greater than 1 because 4.296 times 10 Superscript 11 is a very large number and multiplication always increases the size of a number.
The value will be greater than 1 because 4 times 2 = 8 and 8 is larger than 1.
The value will be less than 1 because (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14) will be a negative number. All negative numbers are less than one.
The number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1.
The statement that is true about the estimate is that the number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1 (option D).
How to estimate an exponential function?According to this question, Bethany wants to estimate the value of (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14).
This expression can be mathematically written as:
(4.296 × 10¹¹) (1.8614 × 10-¹⁴)
The result of this expression is 7.996 × 10-³, which is value less than 1.
Therefore, the number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1.
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Please help!! Which of the following graphs shows a parabola with a vertex of (1,-9) and solutions of (-2,0) and (4,0)?
The graphs show a parabola with a vertex that has Roots are -2 and 4.
We have given that,
vertex of (1,-9) and solutions of (-2,0) and (4,0).
What is the formula for the roots?
y=k*(x+2)(x-4)
Vertex = (1,-9) is a point of the parabola
-9=k*(1+2)(1-4) implies k=1
Equation of the parabola is y=(x+2)(x-4).
The graphs show a parabola with a vertex that has Roots are -2 and 4.
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Alden is registering for classes next semester. he uses the quantitative reasoning process to decide between two teachers, dr. alvarez, and dr. bareno . he speaks to 17 friends that previously took the course from dr. alvarez and also speaks to 18 friends that took it from dr. bareno. eight of his friends said they highly recommend dr. alvarez. eleven of his friends highly recommend dr. bareno.
Based on quantitative reasoning, Alden should take the classes from Dr. Baeno in his next semester.
Quantitative Reasoning Behind Choosing Dr. Baeno
Alden talked to 17 friends that previously took course from Dr. Alvarez.
Eight out of 17 friends recommended Dr. Alvarez.
∴ The fraction of his friends in favor of Dr. Alvarez = 8/17
Also, Alden talked to 18 friends who took course from Dr. Baeno.
Eleven out of 18 friends recommended Dr. Baeno.
∴ The fraction of his friends in favor of Dr. Baeno = 11/18
Making Comparison
Now, since we know that,
11/18 > 8/17
The capacity for using knowledge and mathematics to address problems in the real world is known as quantitative reasoning.
Hence, applying quantitative reasoning, we can infer that it is more favorable for Alden to take classes from Dr. Baeno.
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In the following diagrams calculate the
sides marked with letters x and y.
All dimensions are in cm.
Answer:
x=7.48 cm, y=6.94
Step-by-step explanation:
Start by finding the value of x.
Using the Pythagorean Theorem, [tex]13^{2}+x^{2} =15^{2}[/tex]
[tex]169+x^{2} =225\\x^2=56\\x=\sqrt{56}\\x=2\sqrt{14}[/tex]
Using this, we can again use the Pythagorean Theorem to find the value of y.
[tex]2.8^{2} +y^{2} =(2\sqrt{14} )^{2} \\7.84+y^{2} =56\\y^{2} =48.16\\y=\sqrt{48.16}[/tex]
(I rounded to two decimal places, not sure what is required here)
x=7.48 cm
y=6.94 cm
A circle has a center at Left-parenthesis 8 comma 2 right-parenthesis.. The point Left-parenthesis 3 comma 7 right-parenthesis. is on the circle. What is the area of the circle to the nearest tenth of a square unit?
The area of the circle is 157.14 square unit.
What is a Circle ?A circle is a round shaped figure , whose all points lie in the same plane and the distance between the center and any point on the circle is same.
It is given that , For Circle
Center is ( 8 , 2)
Point on the circumference is ( 3 , 7)
The distance between these point will give the radius
r = [tex]\rm \sqrt { (3-8)^2 + ( 7-2)^2[/tex]
r = √50 unit
The area of the circle is given by
A = π r²
A = π * (√50 )²
A = π * 50
A = 50 π
A = 157.14 square unit
Therefore the area of the circle is 157.14 square unit.
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Try It #2
A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was36,800. Assume this trend continues.
b. Identify the year in which the population will reach 54,000.
Answer:
The year in which population will be 54000, is 2020.
Step-by-step explanation:
In the question, it is given that the city's population is growing linearly. In 2008 , population was 28200 and in 2012 , it is 36800 .
It is required to identify the year in which population will be 54000 . equation.
Step 1 of 2
The population in 2008 was 28200 and in 2012 it was, 36800 .
The equation relating population and year is,
[tex]$$\begin{aligned}&y-28200=\left(\frac{36800-28200}{2012-2008}\right)(x-2008) \\&y-28200=\left(\frac{8600}{4}\right)(x-2008) \\&y-28200=2150(x-2008)\end{aligned}$$[/tex]
Step 2 of 2
The year in which population will be 54000 , can be determined by substituting 54000 for y,
[tex]54000-28200=2150(x-2008)$\\ $25800=2150(x-2008)$\\ $x-2008=12$\\ $x=2020$[/tex]
On a coordinate plane, 2 lines are shown. Line P Q has points (negative 5, 3) and (5, 1). Line R S has points (negative 4, negative 2) and (0, negative 4).
Which statement best explains the relationship between lines PQ and RS?
They are parallel because their slopes are equal.
They are parallel because their slopes are negative reciprocals.
They are not parallel because their slopes are not equal.
They are not parallel because their slopes are negative reciprocals.
Considering the slope of the lines, their relationship is given as follows:
They are not parallel because their slopes are not equal.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.In this problem, their slopes are given as follows:
mPQ = (1 - 3)/(5 - (-5)) = 3/10.mRS = (-4 - (-2))/(0 - (-4)) = -1/2.Different slopes, multiplication different of -1, hence the correct option is given by:
They are not parallel because their slopes are not equal.
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Answer:
C. They are not parallel because their slopes are not equal.
Find the length of the arc on a circle with a radius of 20 inches intercepted by a
central angle of 138°. Round to the nearest hundredth.
Answer:
48.2 metres
Step-by-step explanation:
Find the circumference of the circle, then ...
Explanation:
Circumference =2πr=2π(20)=40π meters
Arc Length =central∠360o×(Circumference)=138360×40π
=463π≈48.2 meters
hope that helps
The length of the arc of the circle is 48.2 meters.
What is the length of the arc of the circle?The arc length formula for a circle is times the radius of a circle. Arc length ( [tex]\theta[/tex] x r) is a way to express the arc length formula in radians.
The length of the arc is calculated as:-
Circumference =2πr=2π(20)=40π meters
Arc Length = Central ∠360° × (Circumference)
Arc Length =138360×40π
Arc length =463π ≈ 48.2 meters
Therefore, the length of the arc of the circle is 48.2 meters.
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The given figure shows the intersection of plane Swith a square pyramid
The shape of the cross section is a square. The correct option is the D. SQUARE
Cross sectionFrom the question, we are to determine shape of the cross-section formed.
A cross-section is seen when a three-dimensional image is cut by a plane.
The given figure is a square pyramid.
In the given diagram, plane S is a square. The intersection of plane S with the square pyramid gives square cross-section as shown in the figure.
Thus, the shape of the cross section is a square.
A shows a parallelogram
B shows a triangle
C shows a trapezoid
D shows a square
Hence, the shape of the cross section is a square. The correct option is the D. SQUARE
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help me and u will get 100 points at the end
Answer:
x > 0 and y < 2
Step-by-step explanation:
By definition the inverse of a function is simply, when the domain and range are swapped. So if the domain of g(x) is x < 2 and y > 0, then the inverse will have these swapped. So x > 0 and y < 2
Geometry question, I need help with this.
1st transformation: A vertical translation of the figure down by 8 units
2nd transformation: Shows a reflection on both axis and vertical translation up the plane by 8 units
Transformation of coordinatesTransformation is a way of changing the position of an object on an xy-plane.
For the translation
(x, y)-> (x, y-8)
It shows a vertical translation of the figure down by 8 units while the translation;
(x, y - 8) -> (-x, -y)
shows a reflection on both axis and vertical translation up the plane by 8 units
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The fraction closest to 4/5 is
A.2/3
B.7/9
C.8/11
D.5/8
Answer:
It would be C
Step-by-step explanation:
The fraction equal to 4/5 is 8/10 so closest to 8/10 is 8/11
what is 1/3 into a quotient?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Keep in mind:}[/tex]
[tex]\large\textbf{When you hear or see the word \boxed{quotient} in mathematics}\\\large\textbf{usually it means the RESULT/ANSWER of a division}\\\large\textbf{equation.}[/tex]
[tex]\huge\textbf{Assuming:}[/tex]
[tex]\mathbf{\dfrac{1}{3}}[/tex]
[tex]\mathbf{\dfrac{1\leftarrow \boxed{\mathsf{dividend}}}{3\leftarrow \boxed{\mathsf{divisor}}} = result \leftarrow \boxed{\mathsf{quotient}}}[/tex]
[tex]\mathbf{1 \leftarrow \boxed{\rm{dividend}} \div 3 \leftarrow \boxed{\rm{divisor}} = result\leftarrow \boxed{\rm{quotient}}}[/tex]
[tex]\uparrow\huge\textbf{Simplify \& you'll have the quotient}\uparrow[/tex]
[tex]\mathbf{Quotient \rightarrow 0.333333333}[/tex]
[tex]\mathbf{Quotient \approx 0}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{0}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a \$7.50$7.50dollar sign, 7, point, 50 delivery fee and \$14$14dollar sign, 14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under \$60$60dollar sign, 60.
The inequality that can be used to represent the situation is 7.50 + 14x ≤ 60 where x ≤ 3.75
InequalityDelivery fee = $7.50Cost of each pizza = $14Budget = $60Number of pizza = x7.50 + 14x ≤ 60
14x ≤ 60 - 7.50
14x ≤ 52.50
x ≤ 52.50 / 14
x ≤ 3.75
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What is the gradient of the graph shown?
Answer:
gradient = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
calculate the gradient m using the gradient formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 2) ← 2 points on the line
m = [tex]\frac{2-0}{0-(-6)}[/tex] = [tex]\frac{2}{0+6}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.03. If 476 are sampled, what is the probability that the sample proportion will be less than 0.04
The probability that the sample proportion will be less than 0.04 is 0.8995 or 89.95%.
The true proportion (p) is given to be 0.03.
Therefore, Mean (μ) = p = 0.03.
The standard error of sampling distribution can be calculated using the formula σ = √[{p(1 - p)}/n], where n, is the sample size, that is, n = 476.
Therefore, σ = √[{0.03(1 - 0. 03)}/476] = 0.00782.
Since, np = 14.28 and n(1 - p) = 461.72 are both greater than 5, we assume the sample is normally distributed.
Since, we are asked to find the probability that the sample proportion is less than 0.04, we using our calculator, enter as following:
Normalcdf(-100000000,0.04,0.03,0.00782), which gives us the value 0.8995 or 89.95%.
Thus, the probability that the sample proportion will be less than 0.04 is 0.8995 or 89.95%.
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Please help me. Due today. Please show work so I can get it correct!!!!
Applying the inscribed angle theorem, the value of x in the circle is: 126°.
What is the Inscribed Angle Theorem?According to the inscribed angle theorem, the measure of the inscribed angle, 63° is one-half of the measure of central angle, x, as shown in the circle given.
Therefore, we would have the following equation:
1/2(x) = 63
x = 2(63)
x = 126°
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PLEASE QUICKLY!!!
The length of a rectangular frame is represented by the expression 3x + 6, and the width of the rectangular frame is represented by the expression 3x + 4. Write an equation to solve for the width of a rectangular frame that has a total area of 120 square inches.
The width of the rectangle is 10 inches
How to determine the width?The given parameters are:
Length = 3x + 6
Width = 3x + 4
Area = 120
The area of a rectangle is
Area = Length * Width
So, we have:
(3x + 6) *(3x + 4) = 120
Expand
9x^2 + 12x + 18x + 24 = 120
Evaluate the like terms
9x^2 + 30x - 96 = 0
Using a graphing calculator, we have:
x = 2
Substitute x = 2 in Width = 3x + 4
Width = 3 * 2 + 4
Evaluate
Width = 10
Hence, the width of the rectangle is 10 inches
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Factor out the GCF. Use the distributive property to write an equivalent
expression for 8d-16f.
The equivalent expression for the given expression is 8(d - 2f)
Greatest common factor (GCF)From the question, we are to factor out the GCF
The given expression is
8d - 16f
The GCF of the terms in the expression is 8.
∴ 8d - 16f = 8(d -2f)
The factored form of the expression is 8(d - 2f)
Hence, the equivalent expression for the given expression is 8(d - 2f)
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please answer algebra question. will mark brainliest
answers:
1. 9
2. 12
3. 18
4. 36 sq cm
Answer:
9 sq cm
Step-by-step explanation:
If you join the two triangles it will become a square of side 3cm.
3cm * 3cm = 9cm squared.
Hope you have a nice day :)
Any questions please comment.
please help me asap thank you so so much u are so amazing!!
Answer:
7.76
Step-by-step explanation:
0.22×20=4.4
3.36(base amount ,average of the others)+4.4=7.76
Jeanie is picking out clothing from her closet. She has 5 pairs of pants, 6 shirts, and 4 pairs of shoes to choose from. How many different ways can she arrange her outfit for the day?
Enter the total number of outcomes in the box, without units
What is the sum of a° + c°?
300°
120°
230°
240°
Answer:
300°
Step-by-step explanation:
Given from the diagram:
Angle a° = 180° (Single angle on a straight line)
Angle c° + 60° = 180° (Sum of angles on a straight line)
Angle c° = 180° - 60° = 120°
Angle a° + c° = 180° + 120° = 300°
Answer:
a + c = 300°
Step-by-step explanation:
a = 180°
c = 180° - 60° = 120°
a + c = 180° + 120° = 300°