The reflected triangle be R'S'T'
coordinate of R' is (-7, 3) , S' is (-5, -6) and T' is (2, -2)
What is Reflection ?Reflection is a sort of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. For instance, Triangle P has been reflected to become Triangle Q on the line x = 4 x= 4 x= 4.
A flip is a geometric movement that involves turning an item over in a straight line to create a mirror image. The distance between each point on an item and its corresponding point on the picture is equal. A reflection is another name for a flip.
The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x.
So, the coordinate of RST is
R(-3, 7), S(6,5), T(2, -2)
The reflected triangle be R'S'T'
coordinate of R' is (-7, 3) , S' is (-5, -6) and T' is (2, -2)
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After reflection along the line y is x, the image of the point (5, -3) is (-3, 5).
What is a reflection of the point?It is the representation of the point that is situated in the opposite direction of the specified point.
Given
The reflecting line is y = x at the point (5,-3).
The image's center will therefore be about on the line y = x.
If x = 5, then y will have the value of 5.
The value of x will be x = -3 for y = -3.
Consequently, the image's purpose is (-3, 5).
After reflection along the line y is x, the image of the point (5, -3) is (-3, 5).
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What is the YYY intercept of y =- 3 7xy − 3 − 7x?
After solving, the y-intercept of line7x−y+3=0 is 3.
In the given question, we have to find the y-intercept of 7x−y+3=0.
The general equation of line is y = mx + c, where m is the slope of line and c is the y-intercept of the line.
We express the following equation in slope-intercept form, which is to obtain the slope and y-intercept.
To find the y-intercept of 7x−y+3=0 we firstly convert the equation in the form y = mx + c.
7x−y+3=0
We firstly isolate the y.
subtract y on both side, we get
y = 7x + 3
When we compare the equation by y = mx + c
So, c = 3
Hence, the y-intercept of 7x−y+3=0 is 3.
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The complete question is:
What is the y-intercept of 7x−y+3=0?
How do you draw an inverse relation graph?
To see the points of draw an inverse graph.
Choose some points on the given relation (graph).Interchange the x and y coordinates of each point to get new points.Plot all these new points and join them by a curve which gives the graph of the inverse relationship.Now, According to the question:
Inverse Relation of a Graph
If a relation is given as a graph, then its inverse is obtained by reflecting it along the line y = x. This is because the inverse of a relation is nothing but the interchanged ordered pairs of the given relation. To graph the inverse of a relation that is given by a graph,
Choose some points on the given relation (graph).Interchange the x and y coordinates of each point to get new points.Plot all these new points and join them by a curve which gives the graph of the inverse relationship.Learn more about Inverse graph at:
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Which expressions are equivalent to - 7z+(-2.5) + 3.5z + 4y - 1.5?
Select all that apply.
A. 4 + 4y + 3.5z
B. -3.5z + 4y -4
C. -4+4y+(-3.5z)
D. 4y-4-3.5z
E. 4y +(-3.5z)-2.5
Answer:
The answer is option B
Step-by-step explanation:
-7z - 2.5 + 3.5z + 4y - 1.5
- 3.5 z + 4y - 4 (B)
// in case you are wondering the reason i got -2.5 is + sign outside and the - sign inside = -2.5
// Basically I just combined the like terms and solved it
The polynomial (x – 2)(x^2 + 1) – x(x – 3) can be written in the form: ax^3 + bx^2 + cx + d where a, b, c, and d are constants. What are the values of a, b, c, and d? Show your work. .
The values of a, b, c, and d in the polynomial ( x - 2 )( x² + 1 ) - x( x - 3 ) in the form of the form ax³ + bx² + cx + d are 1, -3, 4 and -2 respectively.
What are the values of a, b, c, and d?Given the expression in the question;
( x - 2 )( x² + 1 ) - x( x - 3 )
To simplify, apply distributive property
( x - 2 )( x² + 1 ) - x( x - 3 )
x( x² + 1 ) - 2( x² + 1 ) - x( x - 3 )
x( x² ) + x(1 ) - 2( x² ) + (-2)( 1 ) - x( x ) - (-x)3
x³ + x - 2x² - 2 - x² + 3x
Collect and add like terms
x³ - 2x² - x² + x + 3x - 2
x³ - 3x² + 4x - 2
Comparing to the form ax³ + bx² + cx + d
a = 1
b = -3
c = 4
d = -2
Therefore, the values of a, b, c, and d are 1, -3, 4 and -2 respectively.
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Does anyone know this?
Answer:
Area = 50
Step-by-step explanation:
x2 = 36
x = 6
36 + 6 + 6 + 1 + 1 =50
the small squares = 1
How much water, in ounces, do you drink on average per day? Let Y be the amount of water, in ounces, a randomly selected student drinks on average per day. Y is a (continuous or discrete)?
If Y represents the amount of water a randomly selected student drinks per day, it follows that the variable Y in this scenario is a discrete variable.
What is the difference between a discrete and continuous variable?A discrete variable is a variable that takes on distinct, countable values while- A continuous variable on the other hand, is one which takes on any value within a range, and the number of possible values within that range is infinite.
Hence, since it is possible to put a count to the amount of water one drinks per day, it follows that variable, Y in this scenario is discrete.
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you invest a total of $5000 between two saving accounts. account A pays 2% annual interest and account B pays 4% annual interest. after one year, you have earned a total of $135 in interest. How much did you invest in each account
The Investment in Account A is 1750, Investment in Account B is 3250
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Given;
The total investment = 5000
Let the amount invested in account A be x
Therefore, the amount invested in account B = 5000-x
In Account A, rate of interest = 4% per year
Thus, interest earn in one year
= x*4*1/100
= 4x/100
Now, The interest in account B = 2% per year
Thus, the interest earn in one year
= (5000-x)*2*1/100
= 2(5000-x)/100
Therefore, total interest;
(x*4*1/100)*((5000-x)*2*1/100)
(2x+10000)/100=35
x=1750
Hence, investment with interest in account A and account B will be $1750 and 5000-1750 = $3250
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Hal’s Hardware and Sal’s Supermarket are both selling light bulbs.
Answer:
hibb
Step-by-step explanation:
kjnbbibubjkbibubjbkmbb
Answer:Hal's Hardware and Sal's Supermarket are both retail stores that sell light bulbs. Hal's Hardware specializes in hardware and home improvement items, while Sal's Supermarket is a grocery store that also sells household items. Both stores likely carry a variety of light bulb types, including incandescent, LED, and fluorescent bulbs, in different wattages and sizes. The prices and selection of light bulbs may vary between the two stores, with Hal's Hardware potentially having a wider selection and more specialized options while Sal's Supermarket may have more affordable prices.
It's also possible that Hal's Hardware would have a more knowledgeable staff that could provide customer service and technical assistance on the products, whereas Sal's Supermarket may focus more on providing a convenient shopping experience.
It's important to note that both stores are likely to have different target audiences, promotions, and sales strategies. Therefore, a consumer might want to check both stores for the best deal on the type of light bulbs they need.
Step-by-step explanation:
a coral reef is 3 kilometers due south of its closest point along a straight shoreline. a visitor is staying in a tent that is 14 kilometers east of that point. the visitor is planning to go from the tent to the coral reef. suppose the visitor runs at a rate of 12 kmph and swims at a rate of 1 kmph. how far should the visitor run to minimize the time it takes to reach the coral reef? round to two decimal places.
3.6miles the visitor have to run to minimize the time it takes to reach the coral reef.
How do you find the time in math?Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.The equation for calculating time is [Time = Distance ÷ Speed].Seconds, minutes, hours, days, weeks, months, and years are the fundamental units of time. To determine the time of day, we use seconds, minutes, and hours; to determine the date, we use days, months, and years. The smallest units of time are seconds, minutes, and hours, while the larger ones are days, months, and years.Correct question :
A visitor is staying in a cabin that is 3 miles west of the closest point on a shoreline to a coral reef. The coral reef is 2 miles due south of the shoreline. The visitor plans to travel from the cabin to the coral reef by running and swimming. If the visitor runs at a rate of 7 mph and swims at a rate of 2 mph, how far should the visitor run to minimize the time it takes to reach the coral reef
Given data :
distance of tent from the closest point on shore-line, d=3miles.
distance between shoreline point and coral reef, x=2miles
The shortest distance (say l) that the visitor runs towards the reef in order to swim a minimum distance which takes least time.
∴ l² = d² + x²
l = [tex]\sqrt{3^{2} +3^{2} }[/tex]
l = 3.6 miles
Now on reaching at the shore at this point the visitor will have to swim the least distance due east to reach coral reef.
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a plane flew at a constant speed and traveled 762762762 miles in 555 hours. how many miles would the plane travel in 333 hours at the same speed? miles
The plane travel 457657656.894 miles in 333 hours at the same speed.
The plane is travelling at a speed of 762762762 miles in 555 hours.
Considering that the plane traveled 762762762 miles in 555 hours.
If I write that as a fraction it is 762762762mi/555hours.
I can make this a unit rate by saying,
762762762 / 555 = 762762762 ÷ 555= 1374347.318.
This means plane is travelling at a speed of 152.4 miles in an hour.
So distance travelled by plane in 333 hours can be find out
By using,
Distance = speed x time
=1374347.318 x 333
=457657656.894
So plane travel 457657656.894 miles in a span of 333 hours.
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How many exercises are in class 10 polynomials?
In class 10 mathematics chapter 2 (Polynomials), there are 4 exercises.
'What are polynomials?'
Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.
The Greek words "polynomial" and "nominal" are the origins of the word polynomial, which is translated as "many phrases" when combined. There is no limit to the number of terms that a polynomial can have.
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a coin that is cm in diameter is tossed onto a by grid of squares each having side length cm. a coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position. given that the coin lands in a random position so that no part of it is off the grid, what is the probability that it is in a winning position?
The probability that it is in a winning position will be 0.8036.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A coin that is 2 cm in diameter is tossed onto a grid of squares each having a side length of 4 cm. A coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position.
Then the probability of winning is calculated as,
P = [a² - πd² / 4] / (a²)
P = [4² - 3.14 x 2² / 4] / (4²)
P = (16 - 3.14) / 16
P = 0.8036
The probability that it is in a winning position will be 0.8036.
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The figure shows the dimensions of a city park in feet.
Part B: The city plans to cover the park with grass. One square of grass covers 60 square feet. How many squares of grass will need to be ordered to fill the entire park?
A. 18 squares
B. 21 squares
C. 20 squares
D. 19 squares
Jayden is making frozen dog treats for his puppy Spot. He mixes 1 quart of yogurt, 10 fluid ounces of peanut butter, and 6 fluid ounces of honey. Then, he freezes the mixture in ice cube trays. Each tray holds 16 fluid ounces of treats. How many trays of dog treats does Jayden make?
Jaden produces four trays in total.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Jayden is making frozen dog treats for his puppy Spot. He mixes 1 quart of yogurt, 10 fluid ounces of peanut butter, and 6 fluid ounces of honey. Then, he freezes the mixture in ice cube trays.
Since 1 quarts = 32 fluid ounces
The total quantity of a mixture (in ounces) = 32 + 10 + 6
The total quantity of a mixture (in ounces) = 48
Since Each tray holds 16 fluid ounces of treats.
Thus the total number of trays Jayden makes = 48/ 16
the total number of trays Jayden makes = 4
Therefore, the total number of trays Jaden makes is 4.
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What is a 180 degree angle called?
Angles that are 180 degrees (θ = 180°) are known as straight angles.
A straight angle is a 180-degree angle in mathematics. Straight refers to the fact that it appears as a straight line. Angles are formed when two rays are linked end to end, according to the definition of angles in mathematics.
As a result, the two rays of the 180-degree angle are subtended in the opposite direction, where the rays are united at the ends.
In radians, the 180-degree angle is measured in pi (π). To point the opposite way, the straight angle changes the direction. A 180-degree is also considered supplementary.
Thus, Angles that are 180 degrees (θ = 180°) are known as straight angles.
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what point do we get when we rotate $(3,2\sqrt 3)$ around the point $(2,\sqrt 3)$ by $60^\circ$ counterclockwise?
The new point we will get P([tex]1,2\sqrt{3}[/tex]) when we rotate the point [tex](3,2\sqrt 3)[/tex] around the point (2, [tex]\sqrt{3}[/tex]) by 60⁰ counterclockwise.
Rotating point A [tex](3,2\sqrt 3)[/tex][tex](3,2\sqrt 3)[/tex] around point O[tex](2,\sqrt 3)[/tex] by 60⁰ counterclockwise.
Let us get point P as result.
so, assuming O is the center of a circle which has radius = r
r = [tex]\sqrt{(2-3)^2 + (\sqrt{3}-2\sqrt{3})^2 }[/tex]
or r = 2
And point A and P(x,y) are on the circumference of the circle.
so, the coordinates of point P(x,y) will as follows
x = Oₓ + (Aₓ-Oₓ)cosθ - (Ay-Oy)sinθ
or x = 2 + (3-2)cos60⁰ - [tex]\sqrt{3}[/tex]sin60⁰ = 2+1/2-3/2 = 1
And y = Oy + (Aₓ-Oₓ)sinθ + (Ay-Oy)cosθ
y = [tex]\sqrt{3}[/tex] + [tex]\sqrt{3} /2[/tex] + [tex]\sqrt{3} /2[/tex] = [tex]2\sqrt{3}[/tex]
so, P([tex]1,2\sqrt{3}[/tex]}
Therefore, the new point we will get P([tex]1,2\sqrt{3}[/tex]) when we rotate the point [tex](3,2\sqrt 3)[/tex] around the point (2, [tex]\sqrt{3}[/tex]) by 60⁰ counterclockwise.
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silmutaneous equation
Step-by-step explanation: Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.
What is the average speed of a train Travelling 240 km in 4 hours?
The average speed of a train travelling 240 km in 4 hours is 60 km/h.
Distance = 240 km
Time = 4 hours
Speed = Distance/Time
Speed = 240 km/4 hours
Speed = 60 km/h
The average speed of a train is calculated by dividing the total distance travelled by the total time taken to travel that distance. In this case, the train has travelled a total distance of 240 km in 4 hours. We can calculate the average speed of the train by dividing 240 km by 4 hours. This gives us an average speed of 60 km/h. This means that the train travelled an average speed of 60 km/h for the entire journey. This speed is the average speed of the train, which means that it could have been travelling faster or slower than this at different times during the journey.
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A bridge connecting two cities separated by a lake has a length of 3961 miles .
Use the table of facts to find the length of the bridge in yards.
Round your answer to the nearest tenth.
If the bridge connecting two cities separated by a lake has a length of 3961 miles, using the table, the length of the bridge in yards is 6971360
How to convert miles into yards?You should understand that 3 feet makes 1 yard
The given parameter that will help us to solve the problem is
12 inches = 1 foot
3 feet = 1 yard
36 inches = 1 yard
5280 feet = 1 mile
1760 yards = 1 mile
But the given length is 3961 miles to be converted to yards
This implies that (1760 * 3961) miles will give you
6971360 yards
Conclusively, 6971360 yards make 3961 miles
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jacob and elizabeth are 210 feet apart when they begin walking directly toward one another. jacob travels at a constant speed of 2.5 feet per second and elizabeth travels at a constant speed of 4.5 feet per second. let t represent the number of seconds that have elapsed since jacob and elizabeth started walking toward one another. write an expression in terms of t that represents the number of feet jacob has traveled since he started walking toward elizabeth.
The number of feet Jacob has traveled since he started walking toward Elizabeth is 2.5t .
Let the distance between Jacob and Elizabeth is 210 feet
Distance = speed x time
Jacob is walking at the constant speed of 2.5 feet per second
and Elizabeth is walking at a constant speed of 4.5 feet per second
Let the distance traveled by jacob be x and distance traveled by Elizabeth be (210 - x)
Let t be time passed when they both started walking towards each other
So the time taken by Jacob to cover x amount of distance is t
so by formula Distance = speed x time
x = 2.5 x t
So number of feet jacob has traveled since he started walking toward elizabeth is 2.5t.
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
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15 POINTS HELP MEEEEEE!!!!!!
The distance between the points (2, 4) and (5, -2) is 3√5 units.
How to find the distance between points?The distance between the point (2, 4) and (5, -2) using Pythagoras theorem can be calculated as follows:
Using Pythagoras's theorem,
c² = a² + b²
where
a and b are the other legsc is the hypotenuseTherefore,
d = √(y₂ - y₁)² + (x₂ - x₁)²
using (2, 4) and (5, -2)
x₁ = 2
x₂ = 5
y₁ = 4
y₂ = -2
Hence,
d = √(-2 - 4)² + (5 - 2)²
d = √(-6)² + (3)²
d = √36 + 9
d = √45
d = √9 × 5
Therefore,
distance = 3√5 units
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1. In Luguru Academy, each lesson in lower primary and upper primary classes lasts 30 minutes and 40 minutes respectively. The first time the two bells ring at the same time, the pupils go out for a tea break if lessons of the whole school start at 8:30am. a) At what time does tea break start? b) How many upper primary lessons take place before break? 2. A bottle contained 6 litres of milk. Malimoto took of the remainder. How much milk remained in the bottle? 3. An irregular pentagon has the following four interior angles 110°, 108° 135°, and 152°. Determine the value of the exterior angle adjacent to the fifth interior angle. 4. A candidate scores 45, x and y percent in an interview, what is his average score?
Using LCM, the pupils go out for a tea break at 10.30 a.m, Using property of pentagon, The value of the exterior angle adjacent to the fifth interior angle is 145°.
How do I figure out LCM?Step 1: Use the repeated division method to identify the prime factors of the supplied numbers.
Write the numbers in exponent form in step two. Only those prime factors' product with the highest power should be sought.
Step 3: The LCM of the provided numbers is the product of these factors with the highest powers.
a) Find the moment when two bells will ring simultaneously.
In 30 minutes, the first bell rings.
The second bell will ring in 40 minutes, and classes will begin at 8:30. LCM of 30, 40, equals 120 minutes.
Bath bells sound at the same time at 8.30 a.m. plus 2 hours after 120 minutes, which is 10.30 a.m.
b) 40 + 40 + 40 = 120 minutes
∴ 3 classes will take place before break in upper primary.
An irregular pentagon has the following four interior angles 110°, 108° 135°, and 152°. Determine the value of the exterior angle adjacent to the fifth interior angle.
Sum of angles of pentagon = 540°
⇒ 110° + 108° + 135° + 152 + x = 540
⇒ x = 35
The value of the exterior angle adjacent to the fifth interior angle is 180 - 35 = 145°
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What is the number and types of solutions of the quadratic equation x² 7x 12 0?
The number of solutions of the quadratic equation x² 7x 12 0 is two, and the types of solutions are real and distinct.
x2 - 7x - 12 = 0
(x - 6)(x + 2) = 0
x - 6 = 0 or x + 2 = 0
x = 6 or x = -2
Therefore, the number of solutions of the quadratic equation x2 7x 12 0 is two, with real and distinct solutions of x = 6 and x = -2.
The quadratic equation x² 7x 12 0 can be solved by factoring. After factoring the equation, we get
(x - 6)(x + 2) = 0.
This equation can be simplified further to x - 6 = 0 or x + 2 = 0. Solving for x in each equation, we get x = 6 and x = -2. This means that the number of solutions of the quadratic equation x² 7x 12 0 is two, with real and distinct solutions of x = 6 and x = -2. The solutions of the quadratic equation can be used to find the x-intercepts of the graph of the equation, which can be used to graph the equation.
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find L on JK such that JK:JL = 4:1 if J(-3,5) and K(1,-10)
L on JK such that JK : JL = 4:1 if J(-3,5) and K(1,-10) is: [-2, 5/4]. This can be solved using the section formula.
What is section formula?In order to get the location of a point that splits a line segment connecting two points into two sections with a length ratio of m:n, the section formula is utilised. The Section formula is used in coordinate geometry to determine whether a line segment is divided internally or externally by a point. To determine a triangle's centroid, in center, and ex-center, apply this formula. It is used in physics to identify equilibrium locations, the mass center of systems, and other concepts.
JK : JL = 4 : 1
That means JL = 1 and LK = 3
Now, (x₁, y₁) = (-3, 5)
(x₂, y₂) = (1, -10)
from above data, m = 1 and n = 3
Next, applying By section formula, we get:
= [(mx₂ + nx₁)/ (m + n) , (my₂ + ny₁)/ (m + n)]
= [(1 × 1 + 3× -3)/ (1 + 3) , (1×(-10) + 3 × 5)/ (1 + 3)]
= [-8/4 , 5/4]
= [-2, 5/4]
so, L = [-2, 5/4]
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the general manager, marketing director, and 3 other employees of company a are hosting a visit by the vice president and 2 other employees of company b. the eight people line up in a random order to take a photo. every way of lining up the people is equally likely.
The probability that the maid of honor is in the leftmost position is 0.00034.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.
The probability is classified into theoretical probability and experimental probability.
We have to find the probability that the maid of honor is in the leftmost position.
There is no case, where it generally manages its next groom is = 7 and it will be arranged in the 2, that can be arranged in 2! ways. So, the total number of ways are: 7*2 = 14
∴ The required probability = 14/8! = 1/2880 = 0.00034
Thus, the probability that the maid of honor is in the leftmost position is 0.00034.
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The probability that the maid of honor is in the leftmost position is 0.00034.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.
The probability is classified into theoretical probability and experimental probability.
We have to find the probability that the maid of honor is in the leftmost position.
There is no case, where it generally manages its next groom is = 7 and it will be arranged in the 2, that can be arranged in 2! ways. So, the total number of ways are: 7*2 = 14
∴ The required probability = 14/8! = 1/2880 = 0.00034
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find the area of shaded regions below. give your answer as a completely simplified exact values in terms of pi
The area of the shaded portion is 36pi cm² -72
What is a segments?A segment of a circle is part of the circle cut off by the chord. A chord is a straight line that touches a circle at two points. Do well also to understand that a chord is a straight line touching two points on the circumference of a circle.
A circle's area is calculated as pi*r², so a semicircle is pi*r² / 2, and a quarter circle is pi*r² / 4.
We have a quarter circle of radius 12, of which the area is pi*(12² / 4) = 36pi.
In conclusion, this means that the shaded area is 36pi - 72.
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how many lines can pass through a given pair of two distinct points?
Answer: Only one line can pass through two distinct points.
Choose the most accurate relationship between ∠1 and ∠2. A horizontal line is shown with a ray extending upward from a point near the center of the line. A second line runs diagonally from the lower left to the upper right, intersecting the line at the point of origin of the upward pointing ray. The angle formed by the two lines below the horizontal line on the left is labeled 1. The angle formed just left of the horizontal line and upward pointing ray is labeled 2. The angle just right of the upward ray formed by the upward ray and diagonal line is labeled 4. The angle formed just right of the diagonal line and above the horizontal line is labeled 5. The angle formed below the horizontal line and just right of the diagonal line is labeled 6. A. adjacent B. linear pair C. supplementary D. vertical
The relation between angles ∠1 and ∠2 will be the adjacent angles. Then the correct option is A.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The property of angles are as follows:
Two angles are said to be supplementary angles if their sum is 180 degrees.When two lines intersect, then their opposite angles are equal.If the total of two angles is 180 degrees, they are said to be linear angles.In math, two points are nearby in the event that they have a typical side and a typical vertex.The relation between angles ∠1 and ∠2 will be the adjacent angles. Then the correct option is A.
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The complete question is attached below.
Point-slope form
Complete the point-slope equation of the line through (-2, 6) and (1, 1).
Use exact numbers.
y-6=
The point slope equation of the line from the given points (-2, 6) and
(1, 1) is 3y+5x = 8 .
What is equation of straight line ?
The equation of straight line as follows , y = mx+b .
where m is the slope .
Given ,
To find the point slope equation of the line
from the given points (-2, 6) and (1, 1).
First we have to find slope,
so slope = y2-y1 / x2-x1
This is (1-6)/(1-(-2)) = -5/3
Now that you know the slope you can use that for the point-slope equation
The point-slope equation is y-y1 = m(x-x1). If we start with y-6, the x value is -2 (from our point (-2,6)
y-6 = -5/3 (x-(-2))
y-6 = -5/3 (x+2)
3(y-6) = -5(x+2)
3y - 18 = -5x -10
3y+5x = 18-10
3y+5x = 8
Hence, The point slope equation of the line from the given points (-2, 6) and (1, 1) is 3y+5x = 8 .
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Solve the following system of equations for all three variables.
9x+4y+6z= -8
9x+4y+6z= -5
x-8y+8z= -6
There is no solution for the system of equations because the determinant of A is zero.
What are matrices?A matrix is an array of rows and columns containing numbers, symbols, or expressions that is rectangular in shape.
In linear algebra, matrices describe linear mappings and enable explicit computations. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices.
Given the equations,
9x + 4y + 6z = -8
9x + 4y + 6z = -5
x - 8y + 8z = -6
solving by matrix method,
A = [tex]\left[\begin{array}{ccc}9&4&6\\9&4&6\\1&-8&8\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}-8\\-5\\-6\end{array}\right][/tex]
X = [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]
X = A⁻¹B
for A⁻¹, calculate the determinant of A
|A| = [tex]\left|\begin{array}{ccc}9&4&6\\9&4&6\\1&-8&8\end{array}\right|[/tex]
|A| = 9(32 + 48) - 4(72 - 6) + 6(-72 - 4)
|A| = 720 - 264 - -456
|A| = 0
since |A| is zero there are no solutions for the equation.
Hence there are no solutions for a system of equations.
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