How do you find the Y intercept of a system of equations?.

Answers

Answer 1

Set x = 0 and solve for y to find the y-intercept. The main point will be (0,y).

The point on the line where it intersects the y axis is known as the y intercept.

In analytic geometry, a y-intercept or vertical intercept is a point where the graph of a function or relation intertwines the y-axis of the coordinate system, with the horizontal axis representing a variable x and the vertical axis representing a variable y. As a result, these points satisfy the x = 0 condition.

An intercept is a point on the y-axis through which the slope of a line passes. It is the y-coordinate of a y-axis point at which a straight line or a curve interferes. This is represented by the straight line equation,

y = mx+c,

where m denotes the slope and c is the y-intercept

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Related Questions

the radius of the big circle is 6 inches long and the diameter of the small circle is 8 inches long. find the area of the shaded region.

Answers

[tex]20\pi in^{2}[/tex] is the area of the shaded region of the radius of the big circle is 6 inches long and the diameter of the small circle is 8 inches long.

What do you name a circle?

The circle is a closed, two-dimensional object in which all points inside the plane are equally spaced out from the center. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is rotationally symmetric about the center for all angles.

The shaded area is the portion of the bigger circle that is not included in the smaller circle, assuming that the 8-inch diameter circle is entirely contained inside the 6-inch radius circle.

Therefore, the shaded area equals the large circle's area less the small circle's area.

The little circle has a radius of 4 inches since its diameter is 8 inches, so

[tex]A_{Shaded} = A_{l} - A_{s} \\A_{Shaded} = \pi 6^{2} - \pi 4^{2} \\A_{Shaded} = 36\pi - 16\pi \\A_{Shaded} = 20\pi in^{2}[/tex]

So, Area = [tex]20\pi in^{2}[/tex]

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When two angles and an included side of one triangle are congruent to the corresponding pieces of another triangle?.

Answers

When 2 angles and an included side of 1 triangle are congruent to the corresponding piece of another triangle, it is said to be in ASA or AAS congruency

What is ASA congruency?

According to the Angle-Side-Angle Postulate (ASA), two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

And as seen in the figure to the right, we prove that triangle ABC is congruent to triangle DEF by the Angle-Side-Angle Postulate.

What is AAS congruency?

Contrarily, the Angle-Angle-Side Postulate (AAS) states that two triangles are congruent if their respective non-included sides are congruent with two angles from one triangle and two angles from another.

And as seen in the figure to the right, we prove that triangle ABC is congruent to triangle PQR by the Angle-Angle-Side Postulate.

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Which congruence theorems can be used to prove?.

Answers

The Side-Angle-Side rule is used to demonstrate the congruent theorem of a particular collection of triangles.

How may Abda Adbc be demonstrated using a congruence theorem?

The two sides and included angle of ABDA are therefore equivalent to ABDC's two sides and included angle. According to the SAS Triangle Congruence Theorem, the triangles are congruent.

Does AAA support congruence?

Knowing merely angle-angle-angle (AAA) is insufficient because it can result in triangles that are similar but not congruent. There are four shortcuts that can be used to check whether two triangles are congruent.

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an airline offers a certain flight once per day that usually contains about 250250250 passengers. the flight offers seats in first class (most expensive), business class, and economy class (least expensive). the airline wants to survey 500500500 passengers of this flight about their overall satisfaction. the passengers will be selected using a cluster random sample where each flight is a cluster. Why might the airline choose a cluster random sample instead of a simple random sample in this setting?

Answers

The airline might choose cluster random sampling in this case.

Cluster Sampling:

It is a sampling method where the entire population under study is divided into homogeneous groups called clusters. The clusters are externally homogeneous and internally heterogeneous.

Simple Random Sampling:

It is a sampling technique where every unit in the population has an equal chance of being selected in the sample and the samples are selected at random. The airline wants to survey 500 passengers on this flight about their overall satisfaction. The passengers will be selected using a cluster random sample where each flight is a cluster.

Cluster sampling involves fewer resources for sampling compared to simple random sampling.

Here, the population under study is people travelling the flight which is externally homogeneous.

The people travelling in the flight are classified into three groups namely first class (most expensive), business class, and economy class (least expensive) which is internally heterogeneous. More number of persons can be included in the survey which acts as a good representative of the entire population. Thus, cluster sampling is suitable for this study. Simple random sampling may result in an unequal number of persons in each class if the persons are surveyed at random. So, cluster sampling better suits the scenario than simple random sampling.

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A length of a rectangle i 370mm correct to 2 ignificant figure the width i 19. 4mm correct to 1 decimal place. What the lower bound of the area of the rectangle?

Answers

The lower bound of the area of the rectangle is  7062.75 [tex]mm^{2}[/tex].

What is the Lower bound and Upper bound?

Lower Bounds - The lowest value that would be utilized to round a number to the previously estimated value is known as the lower bound.

Upper Bounds - The lower value that would be used to round a number to the next expected value is known as the upper bound.

Given, length = 370 mm

           width = 19.4 mm

First, we consider length = 370 mm, then

The upper bound for length = 375 mm

And, the lower bound = 365 mm

Second, we consider  width = 19.4 mm, then

The upper bound for width = 19.45 mm

And, the lower bound = 19.35 mm

So, the area of the given rectangle is:

Area =  length * width

Using lower bounds dimensions for both length and width, then

Area = 365*19.35 [tex]mm^{2}[/tex]

        = 7062.75 [tex]mm^{2}[/tex]

Therefore, the lower bound of the area of the rectangle is  7062.75 [tex]mm^{2}[/tex]

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A rug i to be placed in a 9 ft. By 12 ft. Room in uch a way that a uniform trip of flooring will remain
uncovered on all four ide of the rug. If the area covered by the rug i exactly half the area of the
room, what are the dimenion of the rug?

Answers

The rug has a dimension of 6 by 9 yards.

What is a dimension?

In everyday language, a dimension is a measurement of an object's length, width, and height, such as a box. The concept of dimension in mathematics is a continuation of the ideas that a line is one dimension, a plane is two dimensions, and space is three dimensions.

Dimensions include things like width, depth, and height. Three geometric objects have one dimension each: a line, a square, and a cube.

Solution Explained:

Given in question

Area of the room = 9*12=108 yards^2

Area of 1/2 the room = 180/2 = 90 yards^2

So according to the question, the rug covers half the room so we form the equation and we simplify,

(9-2X)(12-2X)=54

108-24X-18X+4X^2=54

4X^2-42X+108-54=0

4X^2-42X+54=0

(2X-18)(2X-3)=0

2X-3=0

2X=3

X=3/2

X=1.5

(9-2*1.5)(12-2*1.5)=54

(9-3)(12-3)=54

6*9=54

54=54

The rug has dimensions of 6 by 9 yards.

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Starlin's goal is to spend less than $415 on a trip. So far, he has spent $25 on gas for his car. He will spend $100 each day on other expenses.
Let d represent the number of days for Starlin's trip.
Drag and drop the answer into the box to correctly complete the statement.
response - correct
Starlin's trip must last fewer than ___ days.
4

Answers

Answer: less than 4 days

Step-by-step explanation:

415 - 25 = 390

if ur spending 100 each day then

day 1 = 290

day 2 = 190

day 3 = 90

he needs to spend less than 4 days

Write a linear function for the data in each table using function notation.
x 1, 2, 3, 4
y 4, 10, 16, 22

x 1, 2, 3, 4
y 1.5, 4, 6.5, 9

Answers

The linear functions of the tables are y = 6x - 2 and y = 2.5x - 1

How to determine the linear equation of the tables?

Table 1

From the table, we have the following points that can be used in our computation:

(x, y) = (1, 4)  and (2, 10)

The equation of the line is then calculated using the following equation

y = m(x - x₁) + y₁

Where

m = slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation, so, we have the following representation

So, we have

m = (10 - 4)/(2 - 1)

Evaluate

m = 6

Recall that

y = m(x - x₁) + y₁

So, we have

y = 6(x - 1) + 4

So, we have

y = 6x - 6 + 4

Evaluate

y = 6x - 2

Table 2

From the table, we have the following points that can be used in our computation:

(x, y) = (1, 1.5)  and (2, 4)

The equation of the line is then calculated using the following equation

y = m(x - x₁) + y₁

Where

m = slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation, so, we have the following representation

So, we have

m = (4 - 1.5)/(2 - 1)

Evaluate

m = 2.5

Recall that

y = m(x - x₁) + y₁

So, we have

y = 2.5(x - 1) + 1.5

So, we have

y = 2.5x - 2.5+ 1.5

Evaluate

y = 2.5x - 1

Hence, the linear function is y = 2.5x - 1

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a single card is drawn from a standard deck of 52 cards. what are the odds against drawing a card with a number less than 5?

Answers

If a single card is drawn from a standard deck of 52 cards, the probability it will be a card with a number less than 5 is 4/13.

Probability measures how likely an event occurs. The probability of an event A is defined as:

P(A) = number of ways A can occur / total possible outcomes

In the given problem, let an ace card is considered as 1. Then, for each suit of cards, the card numbers which are less than 5 are cards number: 1, 2, 3, 4.

There are 4 suits, hence:

number of ways the event can occur = 4 x 4 = 16

total possible outcomes = 52

Therefore,

P(<5) = 16/52 = 4/13

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Answer:14/52

Step-by-step explanation:

What is the slope of y =- 4x 10?.

Answers

The slope of the line y = - 4x + 10 is -4.

What is slope?

The slope of any line can be calculated using any two distinct points lying on the line. It is defined as the change in y coordinate with respect to the change in x coordinate of that line.

The net change in y coordinate is Δy, while the net change in the x coordinate is Δx, then the slope

                    m = Δy/Δx = dy/dx.

Here, we are given the line y = - 4x + 10

Differentiating the equation of line with respect to x, we get

                  dy/dx = - 4

slope m = dy/dx = -4.

Therefore, the slope of the line was found to be -4.

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NOTE : The question given here is not complete. The complete question is given below.

Question: What is the slope of y = - 4x + 10?.

What determines where the graph will cross the x-axis?.

Answers

The graph will cross the x-axis if the multiplicity of the real root is odd.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)

(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)

(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)

(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.

The graphs: (a) black, (b) red, (c) green

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Solve x2−x−3=0 by completing the quare. If the olution are real rational number, lit from leat to greatet eparated by a comma. If the olution are not real number, write your anwer in the form a ± bi. If the olution are irrational, write your anwer in implified radical form, uing ± to expre both olution

Answers

The solution of the equation x²-x -3 = 0 are x = (1±√13) /2.

What is an equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Here we are given the equation x²-x -3 = 0 ---(i) which is a quadratic equation which we can solve using Sri Dharacharya Method.

Sri Dharacharya Formula:   For a quadratic equation ax² + bx + c = 0

The value of x is x= (-b ± [tex]\sqrt{b^{2}-4ac }[/tex]) /2a.

Using this formula in (i), we get

     x = (-(-1) ± [tex]\sqrt{(-1)^{2} -4*1*(-3)}[/tex]) /2*1

⇒  x = (1±√13) /2.

The solution of the equation are irrational which are x = (1±√13) /2.

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there are twelve gymnasts, among whom are lia, bella, and priscilla. there is going to be world cup competition. a team comprised of 5 gymnasts should be send to participate in the competition. how many ways can this be done so that the team includes exactly two gymnast from {lia, bella, priscilla}?

Answers

Number of ways 5 gymnasts participate including exactly two from Lia , Bella , Priscilla is equal to 252.

As given in the question,

Total number of gymnasts = 12

Number of gymnasts to be participates = 5

Condition:

Exactly two gymnasts from Lia , Bella , Priscilla

Number of ways 5 gymnasts participates

= ⁹C₃ × ³C₂

= ( 9!)/ ( 9 - 3)! 3! × 3!/ ( 3-2)! 2!

= [( 9× 8 ×7 × 6!)/ 6! ( 3× 2× 1)] × ( 3 × 2!)/ 2!

= [( 9× 8 ×7)/ ( 3× 2× 1)] × 3

= 252

Therefore, the number of ways 5 gymnast can participate out of 12 with the given condition is 252.

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a construction company is considering submitting bids for two contracts. it will cost the company \$10{,}000$10,000dollar sign, 10, comma, 000 to prepare and submit the bids, and if won, each bid would produce \$50{,}000$50,000dollar sign, 50, comma, 000 of income to the company. the company estimates that it has a 10\, percent chance of winning any given bid.

Answers

The expected value of the number of bids and profit are 0.2 and $220000

How to determine the expected value of the number of bids and profit?

The possible question is added as an attachment


From the complete question, we have the following table of values

X (Number of bids)    0            1                   2

M = Profit               -$10000    $40000    $90000

Probability               0.81           0.18         0.01

Expected value of the number of bids

This is calculated as

E(x) = Sum of the products of the number of bids and the probability

This is represented as

E(x) = 0. * 0.81+1 * 0.18 + 2 * 0.01

Evaluate the products

E(x) = 0 + 0.18 + 0.02

Evaluate the sum

E(x) = 0.2

Expected value of the profit

This is calculated as

E(x) = Sum of the products of the number of profits and the probability

This is represented as

E(x) = 0 * -10000 + 1 * 40000 + 2 * 90000

Evaluate the products

E(x) = 0 + 40000 + 180000

Evaluate the sum

E(x) = 220000

Hence, the expected profit is $220000

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During a football eaon one team cored 23 goal more than another between them they cored 135 goal how many goal did each team core

Answers

The number of goals scored by one team is 56 and the other team scored 79 goals.

What are the linear equations in two variables?

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.

Let the number of goals scored by one team be 'x' and the number of goals scored by the other team be 'y'

One team scored 23 goals more than another team

                        y = x + 23 --------(I)

And both teams scored 135 goals in total, so

                        x + y = 135 ------(II)

ut the value of y = x + 23 in equation (II), we get

                    x + x + 23 = 135

                   2x = 135 - 23

                    x = 112/2

                    x = 56

then y = 79.

Hence, the number of goals scored by one team is 56 and the other team scored 79 goals.

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which of the following is true for a relation? entities in a column vary as to kind. the order of the columns is important. the order of the rows is unimportant. more than one column can use the same name.

Answers

The true statement for the relation is, the order of rows is unimportant.

What is row and column?

A row is an arrangement of items that are put next to or horizontally. A vertical split of items based on category is known as a column. The arrangement is in a left to right direction. The set-up is vertical, from top to bottom.

A table's rows are individual groups of connected data. Rows and columns are found in tables in relational databases (also known as records and fields, respectively).

Consider the given statements,

Entities in a column vary as to kind.

The order of the columns is important.

The order of the rows is unimportant.

More than one column can use the same name.

From the given statements, the true statement for the relation is, the order of rows is unimportant.

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The graph of f(x) |x] is reflected across the y-axis and
translated to the left 5 units. Which statement about the
domain and range of each function is correct?

A. Both the domain and range of the transformed
function are the same as those of the parent function.

B. Neither the domain nor the range of the transformed
function are the same as those of the parent function.

C. The range of the transformed function is the same as
the parent function, but the domains of the functions
are different.

D. The domain of the transformed function is the same
as the parent function, but the ranges of the functions
are different.

Answers

Answer:

A. Both the domain and range of the transformed function are the same as those of the parent function.

Step-by-step explanation:

Parent absolute value function:

[tex]f(x)=|x|[/tex]

Graph of the parent absolute value function:

Line |y| = -x where x ≤ 0Line |y| = x where x ≥ 0Vertex at (0, 0)

Therefore:

The domain of the parent function is unrestricted: {-∞, ∞)The range of the parent function is restricted: [0, ∞)

If function f(x) is reflected across the y-axis:

[tex]\implies f(-x)=|-x|[/tex]

The reflection does not change the graph as the parent function is symmetric about the y-axis.

If function f(x) is translated to the left 5 units:

[tex]\implies f(x+4)=|x+4|[/tex]

The domain remains unrestricted and the range remains [0, ∞).

Therefore, both the domain and range of the transformed function are the same as those of the parent function.

a boat travels upstream for 36 miles in 4 hours and returns in 3 hours traveling downstream in a river. what is the rate of the boat in still water and the rate of the current?

Answers

Answer:

rate of the boat is 10.5 and the rate of the current is 1.5

Step-by-step explanation:

Distance = rate x time

Let r = rate of the boat

Let c = current

Upstream:

Rate: r -c

Time: 4 hours

Distance: 36

36 = 4(r-c)  Divide both sides of the equation by 4

9 = r - c

Downstream:

Rate: r + c

Time: 3 hours

Distance: 36

36 = 3(r+c)  Divide both sides by 3

12 = r -c

Combine the two bold equations:

9 = r - c

12 = r + c

21 = 2r  Divide both side's by 2

10.5 = r This is the rate of the boat.

Rate of the current:

4(10.5 - c) =36

42 - 4x = 36  Subtract 42 from both sides

-4x = -6  Divide both sides by -4

x = 3/2 or 1.5

helpppppppppppppppppp

Answers

Answer:

E

Step-by-step explanation:

We just need the last two clues. Since they said it is a line (4th clue) it could only be B, C, or E. But then, the last clue says the domain is -7. Now for almost all lines the domain is 'all real numbers'. All kinds of diagonal lines and also horizontal lines, the domain is all real numbers. Only vertical lines have a domain that is a single value. Graph E is a line that has the domain -7.

HELP!! (this is a math problem about angles)

Answers

Answer:

Below

Step-by-step explanation:

angle 1 + 120 = straight line = 180    so angle 1 = 60°

angles 1  3  4  7   are all equal

angle 2 = 120° = angles 5 and 6

A diatance from school to priyanthas house is 700m and the distance from scool to lasntha house is 1km 300 m. find the ratio of the distance

Answers

Answer:

well 700m is 2296.59 feet

and 1km is 3280.84 feet

and 300m is 984.252 feet

Step-by-step explanation:

hope this helps :)

find an equation for the parabola that has its vertex at the origin and satisfies the given conditions. opens upward with focus 6 units from the vertex

Answers

The equation of parabola that open upwards with focus 6 units is x²=24y.

A parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. A parabola is a curve where any point at an equal distance from a fixed point  (the focus) and a fixed straight line (the directrix).

A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface is also Parabola.

The general equation of Parabola is given by

y = a(x-h)²+ k

where (h,k) is the vertex of parabola.

And the equation of parabola open upward is,

(x-h)² = 4a(y-k)

where (h,k) is vertex and a is focus unit.

⇒ (x-0)² = 4(6)(y-0)

⇒ x² = 24y

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HELP QUICK PLEASE THANK YOU

Answers

To make a volume of 320mL mixture that contains 8% vinegar, use 64mL of the first brand and 256mL of the second brand.

How to solve simultaneous equation word problems?

Let F be the volume of the first brand and let S be the volume of the second brand.

Now, we want the total mixture to be 320mL so: F + S = 310

Also, you want the total mixture to contain 12% vinegar so:

0.08F + 0.13S = 0.12(320)

Now, we can solve the system of equations using substitution method.

F + S = 320   -----(1)

0.08F + 0.13S = 0.12(320)   -----(2)

F = 320 - S      [solve 1st equation for F]

0.08(320 - S) + 0.13S = 0.12(320)     [substitute into 2nd equation]

25.6 - 0.08S + 0.13S = 38.4

0.05S = 12.8

S = 256 mL

F + 256 = 320     [substitute answer for S back into original equation]

F = 320 - 256

F = 64 mL

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Help please I’ve been stuck on this for 1 week

Answers

The equation 5x - (3 - 2x) = -(-x- 7) + 6x is an equation with no solution. It simplifies to 0 = 10

How to simplify an equation with no solution?

An equation with no solution is a type of equation that is never true, no matter what we replace the variable with e.g.  6x + 10 = 6x - 10. This equation has no solution because is no value that will ever satisfy this type of equation

Given:  the equation 5x - (3 - 2x) = -(-x- 7) + 6x

5x - (3 - 2x) = -(-x- 7) + 6x

Clear the parenthesis:

5x - 3 + 2x = x + 7 + 6x

Add/subtract like terms:

7x -3 = 7x + 7

Collect like terms:

7x -7x = 7 + 3

0 = 10

Since 0 is not equal to 10, therefore this expression has no solution

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Is it possible to construct a triangle with lengths of its sides as 3cm 4cm 8cm?.

Answers

Answer:

Step-by-step explanation:

Yes it is possible you start with one side worth 4 cm and the other two move on to the next

Can you help me find me the equation both please

Answers

Step-by-step explanation:

the standard form is (x - h)² = 4p(y - k), where the focus is (h, k + p) and the directrix is y = k - p.

the vertex is exactly in the middle between focus and directrix, and is therefore (h, k) = (0, 0).

therefore, p = 9.

(x - 0)² = 4×9×(y - 0)

x² = 36y

y = 1/36 x²

Use your newly gained natural deduction skills to solve the following problems. In each problem, the arrow symbol means the same thing as the horseshoe symbol in the preceding chapter.1).1. F ∨ (D → T)2. ~F3. D/T2).1. P → (G → T)2. Q → (T → E)3. P4. Q/G → E3).1.~X → [~X → (Y → X)]2.~X /~Y4).1.K → (L → M)2.M ∨K3.~M /~L5).1. ~S→D2. ~S v (~D→K)3.~D/K

Answers

1. F v (D → T)

2.  V F

3. D

∴ T

4. D → T (Disjunctive syllogism 1,2)

5. T          ( Modus Ponens 3,4)

2. P → (cu → T)

2. Q → (T → E)

3. P

4. Q

∴ Cu → E

5. Cu → T  (modus ponens 1,3)

6. T → E  ( modus ponens 2,4)

7. Cu → E (Hypothetical syllogism 5,6)

3. 1. ~ X → [~X → (y → X)]

   2. ~ X

   ∴ ~ y

  3. ~X → (y → X)   (modus ponens 1,2)

  4.  y → X              ( modus ponens 2,3)

  5. ~ y                     ( modus tollens 2,4)

4. 1. k → (L→m)

    2. m v k

    3. ~m

    ∴ ~L

    4. K   (disjunctive syllogism 2,3)

    5. L → m  (modus ponens 1,4)

    6. ~ L    (modus tollens 3,5)

5. 1. ~S → D

   2. ~S v (~D→K)

   3. ~ D

∴ K

  4. ~(~S)   (Modulas tollens 1,3)

  5. S          ( Double nojection 4)

  6. ~D→K (Disjunctive syllogism 2,5)

  7. K         (Modus ponenes 3,6)

Hence we get the required answer.

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tammy works as a tutor for an hour and as a waitress for an hour. this month, she worked a combined total of hours at her two jobs.

Answers

Answer:

What is the question?!

Step-by-step explanation:

at the terminal of a certain airline, records disclose that 10% of their flights arrive early, 70% arrive on time, 12% arrive somewhat late, and 8% arrive very late. use the formula for the multinomial distribution to determine the probability that in six randomly selected flights, one will arrive early, three will arrive on time, two will be somewhat late, and none will be very late. express your answer as a decimal rounded to 2 decimal places.

Answers

The required probability by using multinomial distribution is 0.03.

The multinomial distribution is the kind of probability distribution used in finance to assess factors like the likelihood that a company would declare earnings that are greater than anticipated while rivals report disappointing results. In a multinomial distribution, a process has a set of k potential outcomes (X1, X2, X3,..., Xk) and corresponding probabilities (p1, p2, p3,..., pk) such that Σpi = 1. Due to the certainty of one of the outcomes, the probabilities must add up to 1.

Given that at the terminal of a certain airline, records disclose that 10% of their flights arrive early, 70% arrive on time, 12% arrive somewhat late, and 8% arrive very late.

Multinomial probability P = [ n! / ( n1! * n2! * ... nk! ) ] * ( p1n1 * p2n2 * . . . * pknk )

= [ 6! / ( 1! x 3! x 2! x 0! ) ] * ( 0.10^1 x  0.70^3 x 0.12^2 x 0.08^0)

=60*0.000494

=0.02964

Therefore the required probability = 0.03

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What is congruent example?.

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The concept and examples of congruence are described below.

What is congruent?

The word 'congruent' signifies 'precisely equivalent' concerning shape and size. In any event, when we turn, flip, or pivot the shapes, they stay equivalent. For instance, draw two circles of similar range, then cut them out and put them on each other.

Example of congruent angle in geometry:

congruent angles have a similar point measure. For instance, an ordinary pentagon has five sides and five points, and each point is 108 degrees. No matter what the size or size of a customary polygon, the points will constantly be compatible.

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