Write a paragraph, flowchart, or 2-column proof for the following conjecture:
Given: angle 1 = angle 4
Prove: angle 3 = angle 2

Answer:

\(a_{n}\) = 3 + 5(n - 1)

Step-by-step explanation:

there is a common difference between consecutive terms , that is

8 - 3 = 13 - 8 = 18 - 13 = 5

this indicates the sequence is arithmetic with explicit formula

\(a_{n}\) = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 3 and d = 5 , then

\(a_{n}\) = 3 + 5(n - 1) ← is the explicit formula

Answer:

You haven't provided expressions, so I can work out the problem for you. When we divide fractions, remember always "keep, switch, flip!" That's what we're gonna do here. We keep the 2/5, switch the sign to multiplication, and flip the 7/8 to 8/7. Therefore, we have 2/5*8/7. That gives us 16/35. Hope this helps!

Step-by-step explanation:

Answer: To convert 20% profit into a profit amount, you would multiply 20% by the revenue or cost of the item or service.

Let's say,

You have revenue of $1000

So,

20/100 * 1000 = $200

So the 20% profit on the revenue of $1000 is $200.

It's important to note that profit is the amount of money you make after you subtract your costs from your revenue. It's the amount you have left after all the expenses, taxes and other deductions are made.

Step-by-step explanation:

Anthony's "hiring process" or "recruitment period" was 30 days.

The blank can be filled with "hiring process" or "recruitment period" to indicate the duration between placing the advertisement for a new assistant on November 1 and hiring Marquis on December 1. This period represents the time it took Anthony to evaluate applicants, conduct interviews, and make the decision to hire Marquis.

The hiring process typically involves several steps, such as advertising the job opening, reviewing applications, conducting interviews, and finalizing the selection. The duration of this process can vary depending on various factors, including the number of applicants, the complexity of the position, and the efficiency of the hiring process.

In this case, the hiring process took 30 days, indicating the length of time it took for Anthony to complete the necessary steps and choose Marquis as the new assistant. This duration provides insight into the timeframe Anthony needed to assess candidates and make a hiring decision.

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Answer: 212,031,320,745

Step-by-step explanation: Hope this helps :)

Slope = -0.5

Y-intercept = 34

Equation:  y = -0.5x + 34

Answer = It will take 16 days for the water level to be 26 feet.

The question is an illustration of a linear function.

The given parameters are:

\(\mathbf{Level = 34ft}\)

\(\mathbf{Rate = -0.5ft/day}\)

The equation of the function is:

\(\mathbf{y = Level +Rate \times x}\)

Where:

y represents the water level

x represents the number of days

So, we have:

\(\mathbf{y = 34- 0.5 \times x}\)

\(\mathbf{y = 34- 0.5 x}\)

A linear equation is represented as;

\(\mathbf{y = mx + b}\)

So, by comparison:

\(\mathbf{Slope(m) = -0.5}\)

\(\mathbf{y-intercept (b) = 34}\)

When the water level is 26, it means y = 26.

So, we have:

\(\mathbf{y = 34- 0.5 x}\)

\(\mathbf{26 = 34 - 0.5x}\)

Collect like terms

\(\mathbf{26 - 34= - 0.5x}\)

\(\mathbf{-8= - 0.5x}\)

Divide both sides by -0.5

\(\mathbf{16= x}\)

Rewrite as:

\(\mathbf{x = 16}\)

Hence, the number of days to reach 26ft is 16

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Answer:

6meters wide

Step-by-step explanation:

10×3=30 area

10×y=60

60÷10=6

The unit cost for a pair of shoes at FootAction is $33.33.

The unit cost is a function of the total cost divided by the number of units.

The unit cost is the cost per one (pair).

The unit cost is also described as the unit rate, which gives a unit's cost.

Unit costs can be computed using a division operation.

The cost of 2 pairs of Nikes at FootLocker = $69.98

The cost of 3 pairs of shoes at FootAction = $99.99

1 pair of shoes at FootAction will cost = $33.33 ($99.99/3)

Thus, based on their unit costs, we can conclude that a pair of shoes costs $34.99 at FootLocker and $33.33 at FootAction.

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The Pythagorean theorem is a fundamental concept in geometry that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be expressed as:

a² + b² = c²

where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.

The converse of the Pythagorean theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

The Pythagorean theorem is a powerful tool in solving problems involving right triangles. It allows us to calculate unknown side lengths or determine whether a triangle is a right triangle based on the lengths of its sides. It has numerous applications in various fields, including engineering, architecture, physics, and navigation.

Understanding the Pythagorean theorem and its converse is essential for working with right triangles and applying geometric principles. It provides a foundation for further exploration of trigonometry and advanced geometric concepts.

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Answer:

-7  -4  0 1 7

Step-by-step explanation:

x=0

x²-49=0

x²=49

x=±7

x²+3x-4= ² + 4 − − 4= ( + 4 ) − 1 ( + 4 )=(x+4)(x-1)=0

x+4=0

x=-4

x=1

Its actually pretty simple, all you do is graph both inequalities and wherever both of the shaded areas overlap is where all of the solutions will be. Hope this helps

the set of all points on segment WZ, [W, Z], would include points that are twice as far apart as the points on segment XY, [X, Y].

The set of all points on segment XY can be represented as [X, Y], where X and Y are the endpoints of the segment.

The set of all points on segment WZ can be represented as [W, Z], where W and Z are the endpoints of the segment.

Given that the second segment, WZ, is twice as long as the first segment, XY, we can say that the length of segment WZ is twice the length of segment XY.

Mathematically, if the length of segment XY is d, then the length of segment WZ would be 2d.

In summary, the set of all points on segment XY, [X, Y], and the set of all points on segment WZ, [W, Z], consist of the endpoints of the segments and the points between them. The points on segment WZ are spaced twice as far apart as the points on segment XY due to the difference in their lengths.

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Answer:

____________

the answer is B

___________

explanation

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(x^2 - 2x) - 3xy + 6y

Factor out the greatest common factor (GCF) from each group.

x(x - 2) - 3y (x - 2)

Factor the polynomial by factoring out the greatest common factor, x - 2

(x - 2) (x - 3y)

Answer:

Step-by-step explanation:

your answer would be B.

add and subtract the second turn to the expression and Factor by grouping

a) If you draw one card at random, the probability it is a two or a four is 4/52 or 1/13.

b) If you draw one card at random, the probability it is a spade or a King is 16/52 or 4/13.

c) If you draw two cards at random, the probability of drawing two hearts, with replacement is

(13/52) × (13/52) = 169/2704 or 1/16.

d) If you draw two cards at random, the probability of drawing two Aces, without replacement is (4/52) × (3/51) = 12/2652 or 1/221.

Solution details:

a) If you draw one card at random, the probability it is a two or a four is 4/52 or 1/13.

There are four 2s and four 4s in the deck.

Therefore, the probability of drawing one of these cards is 4/52.

Simplifying it, 1/13.

b) If you draw one card at random, the probability it is a spade or a King is 16/52 or 4/13.

There are four Kings in the deck, and there are 13 spades in the deck, including the King of spades.

There are four Kings, including the King of spades.

Four plus 13 equals 16 total cards.

The probability of drawing one of these cards is 16/52.

Simplifying it, 4/13.

c) If you draw two cards at random, the probability of drawing two hearts, with replacement is

(13/52) × (13/52) = 169/2704 or 1/16.

There are 13 hearts in the deck, and we’re assuming that you’re drawing with replacement.

As a result, the probability of drawing two hearts is (13/52) × (13/52).

Simplifying it, 169/2704.  

d) If you draw two cards at random, the probability of drawing two Aces, without replacement is (4/52) × (3/51) = 12/2652 or 1/221.

Since the first ace has a probability of 4/52, or 1/13, the probability of the second ace is 3/51.

This is since one card has been removed from the deck, making it 51 instead of 52.

Multiplying the two probabilities gives us (4/52) × (3/51) or 12/2652. Simplifying it, 1/221.

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The probability that the sum of the numbers shown will be 6 when rolling two is equals to the 1/80. So, the correct answer is option (a).

The probability of a simple event happening is defined as the number of times the event can happen, divided by the number of possible event. The probability of occurrence of the event A is P(A) = n/N. We have a twenty sided die has each side showing numbers from 1-20. Let us consider an event A , A : the event of getting sum of 6 when two dice are rolled. Also, Assume that it is fair dice, we have all the outcomes to be equally likely. We have, to determine the probability of occurrence of the event A, P(A)= No. of favourable outcomes/total num of outcomes = n/N

Thus the favourable outcomes for event A, n = {(1,5),(5,1),(2,4),(4,2),(3,3)} = 5

On rolling a die, total possible outcomes

= 20 so, on rolling two dice, we have total number of outcomes as, N = 20× 20= 400.

Thus the probability of occuring of event A, P(A) = n/M = 5/400 = 1/80.

Hence, required probability is 1/80.

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Complete question:

On a 20-sided die, each side shows a number from 1-20. What is the probability that the sum of the numbers shown will be 6 when rolling two?

a. 1/80

b. 1/6

c. 395/400

d. 1/400

Answer: It is not possible to use only translations and dilations to map one circle to another unless the two circles are identical in size and shape.

A translation is a transformation that moves an object without changing its size, shape, or orientation. It involves moving every point on the object the same distance in the same direction. Since a circle is defined by all the points that are equidistant from its center, a translation will simply move the entire circle in the same direction, but will not change its size or shape.

A dilation is a transformation that changes the size of an object, but not its shape or orientation. It involves multiplying the distance of every point on the object from a fixed center point by a scale factor. While a dilation can change the size of a circle, it will also change the distance between points on the circle, and thus change its shape.

Therefore, if the two circles are not identical in size and shape, it would be necessary to use other transformations, such as rotations or reflections, to map one circle to the other.

Step-by-step explanation:

The specific range depends on the material properties and the energy levels involved.

The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.

Acoustic Mode:

The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.

The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.

The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.

Optic Mode:

The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.

The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.

The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.

It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.

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Answer:

2x = 256

Step-by-step explanation:

Your problem → 82.5 + 8(0.25x) = 338.5

82.5+8(0.25x)=338.5

⇒-256+80.25x=0

⇒2x-256=0

⇒2x=256

⇒x=256/2

⇒x=128

Answer:

(4, -4) = (x, y) = A

Step-by-step explanation:

 5x + 2y = 12

- (5x - 2y = 28)

4y = -16

y = -4

5x + 2(-4) = 12

5x - 8 = 12

5x = 20

x = 4

Answer:

your answer is point g and h

The purpose of accounts receivable confirmations is to obtain third-party verification of the account's balance and to determine how frequently misstatements take place.

Here,

Only a small portion of the entire population is often subject to accounts receivable confirmation. The confirmation's goals are to gain external confirmation of the account's balance and to get a sense of how frequently misstatements in the accounts occur.

The majority of errors revealed by discrepancies on the confirmation replies won't be significant; however, discrepancies must be examined individually and collectively to establish their impact on the total balance of accounts receivable.

Even while the discrepancies between individuals may not be significant, they could point to a significant issue with the internal controls over accounts receivable when applied to the entire population.

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Mean absolute percentage error is used in situations where you need to compare forecasting methods for different time periods.

The most used metric for gauging forecast accuracy is mean absolute percent error. It belongs to the category of scale-independent percentage errors, which may be used to compare series on various scales.

MAPE = mean (| eᵢ |/yᵢ )*100

where eᵢ is the error term and yᵢ is the actual data at the time i.

The drawback of MAPE is that it loses definition if the actual figure for any observation in the data has a value of 0.

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The probability that there are 3 or fewer occurrences is 0.2650. So, the correct option is (B) 0.2650.

To calculate this probability we need to use the Poisson distribution formula. Poisson distribution is a statistical technique that is used to describe the probability distribution of a random variable that is related to the number of events that occur in a particular interval of time or space.The formula for Poisson distribution is:P(X = x) = e-λ * λx / x!Where λ is the average number of events in the interval.x is the actual number of events that occur in the interval.e is Euler's number, approximately equal to 2.71828.x! is the factorial of x, which is the product of all positive integers up to and including x.

Now, we can calculate the probability that there are 3 or fewer occurrences using the Poisson distribution formula.P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)P(X = x) = e-λ * λx / x!Where λ is the average number of events in the interval.x is the actual number of events that occur in the interval.e is Euler's number, approximately equal to 2.71828.x! is the factorial of x, which is the product of all positive integers up to and including x.Given,λ = 5∴ P(X = 0) = e-5 * 50 / 0! = 0.0067∴ P(X = 1) = e-5 * 51 / 1! = 0.0337∴ P(X = 2) = e-5 * 52 / 2! = 0.0843∴ P(X = 3) = e-5 * 53 / 3! = 0.1405Putting the values in the above formula,P(X ≤ 3) = 0.0067 + 0.0337 + 0.0843 + 0.1405 = 0.2650.

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Answer:

4^3 and 8^2

Step-by-step explanation:

Answer:

12

2

Step-by-step explanation:

4 × 4 × 4 × 8 x 8

Solution:

2 2 2 3 3 2+2+2+3+3

2 x 2 x 2 x 2 x 2 = 2

12

2

2 raised to the 12 power

Answer:

36 - 18 longest side = 18

Step-by-step explanation: This would mean both sides are 18.

Each step of the proof are:

The given parameter is:

Lines a and b are parallel.

This is represented as; a || b

Corresponding angles are equal.

∠1 and ∠5 are corresponding angles.

So, we have: ∠1 ≅ ∠5

Also, they are congruent.

So, we have ∠1 ≅ ∠5

Vertical angles are equal.

∠5 and ∠7 are vertical  angles.

So, we have: ∠5 ≅ ∠7

Also, they are congruent.

So, we have ∠5 ≅ ∠7

According to the transitive property;

If ∠1 ≅ ∠5 and ∠5 ≅ ∠7, then ∠1 ≅ ∠7

Hence, it has been proved that ∠1 ≅ ∠7

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Answer:

Properties of Dilation

Dilations in Animation

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