Three vertices of DEFG are D(1, 1), E(5, 2), and F(1, 8). Find the coordinates of the remaining vertex.

Example of dependent events and independent events and their probabilities are as given below.

1. a. Two independent events that I know the probability of are:

Rolling a fair die and getting a 4 (probability of 1/6)

Flipping a fair coin and getting heads (probability of 1/2)

b. I know these events are independent because the outcome of one event does not affect the outcome of the other event. The outcome of rolling a die does not affect the outcome of flipping a coin, and vice versa.

c. The probability of both events occurring is (1/6) × (1/2) = 1/12

2a. Two dependent events:

i. Drawing a red card from a deck of cards and then drawing another card (without replacement)

ii. Drawing a red ace and then drawing another red card (without replacement)

b. I know these events are dependent because the outcome of the first event affects the outcome of the second event. The probability of the second event depends on the outcome of the first event.

c. These dependent events might require a different method for calculating the probability of both events occurring, such as conditional probability.

The probability of both events occurring would be P(A and B) = P(A) × P(B|A)

where P(A) is the probability of the first event and P(B|A) is the probability of the second event given that the first event has occurred.

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The area of the given triangle is 45 square units.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

In the given triangle, measure of the side base is 10 units and height is 9 units.

Here, area of a triangle = 1/2 ×10×9

= 45 square units

Therefore, the area of a triangle is 45 square units.

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The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.

What is the ratio?

A ratio is a mathematical comparison of two or more quantities. It is used to show the relationship between the sizes of different quantities or amounts. It is typically expressed as a ratio of two numbers, such as 24:2, with a colon separating the numbers.

The ratio of miles to hours is 24 to 2. This can also be written as 24:2 or 12:1. It means that for every 24 miles, 2 hours are required to travel that distance.

Hence, The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.

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Step-by-step explanation:

Let’s use the equation: 3|2x-1|-8=-14

3(|2x−1|)−8=−14

Step 1: Add 8 to both sides.

3(|2x−1|)−8+8=−14+83(|2x−1|)=−6

Step 2: Divide both sides by 3.3. (|2x−1|)3=−63|2x−1|=−2

Step 3: Solve Absolute Value. |2x−1|=−2

No solutions. (Absolute value cannot be less than 0.)

Pre-algebra is a primary branch of algebra designed to prepare students for a standard high school algebraic course

Real number system, linear connections, functions, linear equations, systems of equations, geometric concepts such as transformations, Pythagorean Theorem and angle relationships, and scatter plots are all studied.You will learn about and investigate subjects such as integers, order of operations, algebraic expressions, one and two-step equations, proportions, percents, probability, geometry, and linear equations in Pre-Algebra.

Pre-algebra classes are intended to prepare pupils for a typical algebraic curriculum in high school. Integers, fractions, square roots, step equations, linear equations, and decimals are introduced to students. They will also learn how to use variables to solve basic problems.

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f(1) = -1

Quadratic equations form the shape of a parabola, which looks like a U-shape.

Graph

To find f(1) we need to find the y-value when x = 1. To do this, we can just look at the graph. Find where on the graph x = 1, then look for where the graph intersects this value. This graph has an x value of 1 when y = -1. We can see this at the coordinate point (1,-1). Thus, f(1) = -1.

Equation

We can also solve this using the equation of the function. This function is represented by f(x) = x² - 2. Now, to find f(1), plug 1 in for x.

This also shows that f(1) = -1.

A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

y = 5000x - 250

y = 5000 * 0.29 - 250

y = 1200

A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.

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Answer: We can use the concept of conditional probability to find the probability that a student who passed the first test also passed the second. Conditional probability is the probability of an event occurring given that another event has already occurred.

The probability that a student who passed the first test also passed the second is the probability of both events occurring (passing both tests) divided by the probability of the first event occurring (passing the first test).

We can use the information provided to calculate this probability:

Probability of passing both tests = 0.45 (45%)

Probability of passing the first test = 0.60 (60%)

Probability of passing both tests given that the student passed the first test = (Probability of passing both tests) / (Probability of passing the first test) = 0.45 / 0.60 = 0.75

So the probability that a student who passed the first test also passed the second is 0.75 or 75%.

It means, if we know that a student passed the first test, there's a 75% chance that the student also passed the second test.

Step-by-step explanation:

If Colah Company purchased $2,000,000 of Jackson, Inc., 6% bonds at par on July 1, 2021. The journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

Journal entry is used by companies to record their day to day business transaction.

July 1 2021

Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000

December 31 2021

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

December 31 2021

Debit Available-for-sale securities $300,000

Unrealized Gain - Other comprehensive income $300,000

($2,000,000 - $2,300,000)

June 30 2022

Debit Cash $60,000

Credit Interest income  $60,000

(6% ×$2,000,000 / 2)

The entry necessary upon sale of the Jackson bonds on July 1, 2022 is:

July 1 2022

Debit Available-for-sale securities  $2,300,000

Unrealized Gain-Other comprehensive income account $300,000

Credit Cash $1,800,000

Credit Realized Loss on the sale of Available-for-sale securities $200,000  

[$1,800,000 - $2,000,000= $200,000 (Realized Loss)]

2. Table to show the effect of the Jackson bonds on Colah’s net income,

                             2021                   2022                       Total

Net Income       $60 ,000        ($140,000)              ($80,000)

( 60,000 - $200,000= -$140,000)

OCI                       $300,000                                         $300,000

Comprehensive Income $360,000 ($140,000) $220,000

Therefore the  journal entries for the purchase of the Jackson bonds on July 1 is: Debit Available-for-sale securities $2,000,000

Credit Cash $2,000,000.

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The distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.

This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

So, we have the points:

(-2, 3) and (5, -3)

Distance formula: d=((x2 - x1)² + (y2 - y1)²)

Insert values and calculate as follows:

d=((5 - (-2))² + (-3 - 3)²)

d=((7)²+(-6)²)

d=√85
d=9.21

Therefore, the distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.

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Answer:

To find out how many paddle balls will be in each hopper, you can divide the total number of paddle balls by the number of hoppers.

paddle balls ÷ hoppers = paddle balls per hopper

2798 ÷ 40 = 69.95

So there will be approximately 69.95 paddle balls in each hopper. Since it's not possible to put 0.95 of a paddleball in a hopper, you can round it to the nearest whole number. This means each hopper will have 70 paddleballs.

Step-by-step explanation:

Answer: x =2

Step-by-step explanation: Since the two triangles have to shared sides then all sides must be equal so 9x-12=3x. -6x=-12 and x =2

Answer:

9x=12

so

x=12/9 = 4/3

and

The general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (-9x^2)e^(2x).

The given differential equation is y'' + 2y = −18x^2e^(2x)

To solve this equation by undetermined coefficients, we first find the characteristic equation of the homogeneous equation, which is r^2 + 2 = 0.

The solutions to this equation are r = i and r = -i. Therefore the general solution to the homogeneous equation is yh(x) = c1 cos(x) + c2 sin(x)

Now, we use the method of undetermined coefficients to guess the form of the particular solution. Since the non-homogeneous term is −18x^2e^(2x), we guess that the particular solution is of the form

yp = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x).

Substituting this into the differential equation, we get

y'' + 2y = (6Ax + 2B)e^(2x) + 2Cxe^(2x) = −18x^2e^(2x)

Equating the coefficients of the like terms, we get:

6A = 0, 2B = −18, and 2C = 0

Solving for A, B and C, we get A = 0, B = −9 and C = 0

Therefore, the general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x) = (-9x^2)e^(2x)

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Answer:

I beleive 4

Step-by-step explanation:

let me know if im wrong

Answer: 250

Step-by-step explanation:

249 is closer to 250 than 240

Answer:

Step-by-step explanation:

249 is rounded to closest to 250

Answer:

We can set up an equation using the information provided. Let x be the cost to clean a pair of pants.

The cost to clean 4 shirts is 4*2.95 = $11.80

The cost to clean 5 pants is 5x

The total cost is $11.80 + 5x = $29.05

So, we can represent the cost to clean a pair of pants as:

x = $29.05 - $11.80 / 5

This number sentence shows the cost to clean a pair of pants is x = $4.81

The amount of vanilla in one container of pudding is given as follows:

One teaspoon.

The amount of vanilla in one container of pudding is found applying the proportions in the context of the problem, via a rule of three.

The rule of three is defined as follows:

1/6 teaspoon - 2/12 containers.

x teaspoon - 1 container.

The first line can be simplified as follows:

1/6 teaspoon - 1/6 containers.

(as 2/12 = 1/6).

Hence there is one teaspoon of vanilla in one container of pudding.

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Answer:

The lateral surface of an object is all of the sides of the object, excluding its base and top (when they exist). The lateral surface area is the area of the lateral surface. This is to be distinguished from the total surface area, which is the lateral surface area together with the areas of the base and top.

The answer is 1.4

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.

Given here:

2.6-1.2=1.4

Hence, The answer is 1.4

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To the nearest percentage point, Lupita's retirement funds increased by 44% from June to July.

A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. Consequently, the percentage refers to a portion per hundred.

Given that Lupita had $115 in her bank account at the beginning of June

The amount Lupita had set aside climbed to $165 in July.

We are expected to calculate the percentage growth in money.

% increase

[tex]= {(165 - 115) / 115 } × 100 = 43.48%. ≈ 44%[/tex]

To the nearest percentage point, Lupita's retirement funds increased by 44% from June to July.

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Answer:

D) y = 5/3x - 7

A) 5/3

Step-by-step explanation:

5x - 3y = 21   Subtract 5x from both sides

5x - 5x - 3y = -5x + 21

-3y = -5x + 21  Divide all the way through by -3

[tex]\frac{-3y}{-3}[/tex] = [tex]\frac{-5}{-3}[/tex] x + [tex]\frac{21}{-3}[/tex]

y = [tex]\frac{5}{3}[/tex] x = 7

The slope is the number before the x 5/3

$0.14 is the selling price of each egg.

percentage, a relative value indicating hundredth parts of any quantity.

Given that shopkeeper buys 1800 eggs  $1.20 per dozen.

1 dozen = 12 eggs

So 1.20 ÷ 12 = $0.1 cost of one egg

Total cost (C) 1800×0.1 = $180

1800×0.95 = 1710 eggs to be sold

Profit % = 100×(SP - C)/C

33 = 100×(SP - 180/180

SP = $239.4

239.4 ÷ 1710 = $0.14 is the selling price of each egg.

Hence, $0.14 is the selling price of each egg.

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The rocket reaches a maximum height of 1045.6 feet.

The height of the rocket under free fall is described by a parabola and parabolas are explained by second order polynomials, whose form are:

y = a · x² + b · x + c

Where:

The maximum height can be found by means of discriminant of the quadratic formula associated with following variant:

a · x² + b · x + (c - y) = 0

Discriminant

b² - 4 · a · (c - y) = 0

b² = 4 · a · (c - y)

b² / (4 · a) = c - y

y = c - b² / (4 · a)

If we know that a = - 16, b = 246 and c = 100, then the maximum height reached by the rocket is:

y = 100 - 246² / [4 · (- 16)]

y = 1045.563 ft

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The linear system could the graph represent is, x + y = 2 & 2x + 2y = 8

So, Option D is correct.

The equation of a straight line is a relationship between x and y coordinates, The equation of a straight line for given two points  is y-y₁ = y₂-y₁/x₂-x₁(x-x₁)

Given that,

The graph of  linear system

first line intersects the  x & y   axes at (2,0) & (0,2) respectively

Similarly, second line intersects the  x & y   axes at (4,0) & (0,4) respectively

By using two point form of the line we can write equation for both the lines,

x + y = 2  _____ (1)

x + y = 4  _____ (2)

by multiplying 2 in equation  (2)

2x + 2y  = 8

Hence, The linear system is  x + y = 2 & 2x + 2y = 8

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One solution of the following system is:

A. (–6, 0)

The above mathematical expression requires that we use the substitution formula to obtain the correct value.

2y - 2x = 12     ... 1

x² + y² = 36     ... 2

For equation 1

2y = 12 + 2x

          2

y = 6 + x           ... 3

Now we substitute equation 3 in equation 2

x² + (6 + x)² = 36

= x² + 36 + 12x + x² = 36

2x² + 12x = 36 -36

2x² + 12x = 0

2x (x + 6) = 0

x = 0, -6

When we substitute x for 0 in the third equation, we will have

y = 6 + 0 = 6

If we substitute x to be -6 in the third equation, we will arrive at

y = 0.

Therefore, the two solutions that can be obtained are (0,6) and (-6,0) as seen in the first option.

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The binomial probability that exactly 4 out of 8 customers will use the Self-Checkout is 0.008.

Binomial probability is the probability based on the binomial distribution.

The binomial distribution is used in statistics to summarize the likelihood that a value will take one of two independent values (for example, success or failure) under a given set of parameters or assumptions.

The binomial distribution formula is:

Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ

P = binomial probability

x = number of times for a specific outcome within n trials

{ⁿ \ ₓ} = number of combinations

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trials

Random sample, n = 8

Specific outcome within n trials = 4

pˣ = 0.5⁴

= 0.0625

qⁿ = (1 - 0.5)⁸ ⁻ ⁴

= 0.5⁴

= 0.0625

Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ

= 8/4 x 0.0625 x 0.0625

= 2 x 0.0625 x 0.0625

= 0.0078125

= 0.008

Thus, the probability of precisely 4 customers using the Self-Checkout is 0.008.

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the bisectors of two supplementary angles are perpendicular to each other is proved along with the given diagram.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

from the given diagram we get,

∠BOP=x  &   ∠AOP=180-x

and, ∠NOP=x/2   &   ∠MOP=(90-x/2)

Now,

∠MON=∠MOP+∠NOP

          =90-x/2 + x/2

          =90

Hence, it is proved that  the bisectors of two supplementary angles are perpendicular to each other.

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Answer:

f(11) = 87

Step-by-step explanation:

substitute n = 11 into f(n) , that is

f(11) = 7 + 8(11 - 1) = 7 + 8(10) = 7 + 80 = 87

Answer:

=4-347-12-8-7+27

=-343

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Answer: (4-347-12)-(8+7-27)= -343