Part A Find the y-intercept and slope of the line. ​

Each corresponding side of the two triangles is equal, we can conclude that △abc ≅ △dbc.

Required:

1. Show that angles ∠A and ∠D are equal.

2. Show that angles ∠B and ∠D are equal.

3. Show that sides AB and BD are equal.

Not Required:

1. Show that angles ∠C and ∠D are equal.

2. Show that sides AC and CD are equal.

To show that △abc ≅ △dbc,

we need to use the Side-Side-Side (SSS) Congruence Theorem. This theorem states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the two triangles are congruent.

Therefore, to show that △abc ≅ △dbc, we have to show that each corresponding side of the two triangles is equal. Additionally, we have to show that the angles opposite of the corresponding sides are equal. This can be done using the Angle-Angle-Side (AAS) Congruence Theorem. This theorem states that if two angles and the side between them in one triangle are equal to the same two angles and the side between them in another triangle, then the two triangles are congruent.

To show that △abc ≅ △dbc, we must show that angles ∠A and ∠D are equal, angles ∠B and ∠D are equal, and sides AB and BD are equal. The other steps (showing that angles ∠C and ∠D are equal and sides AC and CD are equal) are not required, since they are implied by the equal angles and sides already established.

Once all of these equalities have been established, we can conclude that △abc ≅ △dbc.

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The z-score is 0 and the probability that the sample mean will be greater than 59.8 is 0.5000

From the question, the given parameters about the distribution are

The z-score

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (59.8 - 59.8)/18.0

Evaluate

z = 0

The probability

The probability that the sample mean will be greater than 59.8 is then calculated as:

P(x > 59.8) = P(z > 0)

From the z table of probabilities, we have;

P(x > 59.8) = 0.5

Hence, the probability is 0.5000

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The values of the expressions are P 9, 3 = 504, C 9, 3 = 84, P 8, 8 = 40320 and C 9, 9 = 1

From the question, we have the following parameters that can be used in our computation:

(A) P9, 3. (B) C9, 3. (C) P8, 8. (D) C9, 9.

The above expressions are permutation and combination expressions

Using the above as a guide, we have

Expression (A) P9, 3

Apply the permutation formula

P n, r = n!/(n - r)!r!

So, we have

P 9, 3 = 9!/6!

Evaluate

P 9, 3 = 504

Expression (B) C 9, 3

Apply the combination formula

C n, r = n!/(n - r)!r!

So, we have

C 9, 3 = 9!/(6! * 3!)

Evaluate

C 9, 3 = 84

Expression (C) P8, 8

Apply the permutation formula

P n, r = n!/(n - r)!r!

So, we have

P 8, 8 = 8!/0!

Evaluate

P 8, 8 = 40320

Expression (D) C 9, 9

Apply the combination formula

C n, r = n!/(n - r)!r!

So, we have

C 9, 9 = 9!/(9! * 0!)

Evaluate

C 9, 9 = 1

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The area of the flag is 32 in²  

The right-angled triangle that has two equal sides is known as the Isosceles right triangle. In other words, if an Isosceles triangle has two equal sides then the triangle is said to be an Isosceles right triangle.  

The formula for the Area of an Isosceles right triangle is given by  

Where x is the equal sides of the triangle.

Here we have

The equal side of a right-angle triangled Flag is 8 inches

=> As we know Area right-angle triangle =  x²/2      

Area of the flag = 8²/2

= 64/2 = 32 inch²    

Therefore,

The area of the flag is 32 in²  

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Stem-and-leaf plots contain original data values where histograms do not. Therefore, option B is the correct answer.

The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.

The "stem" is used to group the scores and each "leaf" shows the individual scores within each group.

The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets. The disadvantage of a stem leaf diagram is not visual.

Therefore, option B is the correct answer.

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On solving the provided function, we can say that altitude of the given isosceles triangle is 6.63 unit.

A triangle with two sides that have the same length is said to be isosceles. Let's carry out a little exercise to better comprehend this. Fold the corners of a rectangular piece of paper in half.

An isosceles triangle has the following characteristics: two equal sides and two equal angles. The two equal sides are referred to as the legs of the triangle, and the angle between them as the vertex angle or apex angle.T he base and the apex angle are divided by the perpendicular from the apex angle. The isosceles triangle is divided into two congruent triangles by the perpendicular, which is sometimes referred to as its line of symmetry.

[tex]12 ^2=10^2 +(a/2)^2\\ 144 -100 = a^2\\ 44 = a^2\\ a^2 =44 ; a =\sqrt{44} =6.63\\[/tex]

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Set is the collection of objects with defined property and represented in curly brackets {} . Example: A = { 2, 4, 6 }.

Set is defined as:

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Answer:

Step-by-step explanation:

it's a rectangular box  with dimensions, 17.7 x 6.8 x 6.7 = 806.412

806.4 [tex]ft^{3}[/tex]   to the nearest 10th  

Devon's monthly payment will be about 416.6

To make for the life of the loan.

What is interest ?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. The three types of interest include simple (regular) interest, accrued interest, and compounding interest.

Have given,

He considered to take lone about 75,000 for a 15 year period,

In 1 year he will be paid [tex]\frac{75,000}{15}[/tex] = 5000

Then in 1 month he will be paid [tex]\frac{5000}{12}[/tex] = 416.6

Devon's monthly payment will be about 416.6

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The required perimeter of the given figure will be 60.84 m.

We have been given the figure which is made up of a rectangle and half a circle.

We have to determine the perimeter of the given figure.

As per the given figure, the required solution would be as:

The required perimeter = 2 × (rectangle's length) + rectangle's width + circumference of half a circle

The required perimeter = 2 × 15 + 12 + π × 6

The required perimeter = 30 + 12 + 3.14 × 6

The required perimeter = 30 + 12 + 18.84

Apply the addition operation, and we get

The required perimeter = 60.84 m

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Answer:

5040 ways

Step-by-step explanation:

We need to place 3 particular books so that they are always together.

let 3 books are one books

we have 5 books

these can be arranged in ⁵P5 = 5! = 12O

total books = 3 × 2 = 6

Required no. of books are 120×6 = 720.

Answer:

372 miles

Step-by-step explanation:

You need to multiply 62 and 6

Answer:

The car will travel 434 miles in 7 hours.

Step-by-step explanation:

To get the answer you simply need to multiply 62, which is the speed of the car, by 7 hours, how long it will travel.

Therefore, the answer is 434 miles.

The roots of the given equation are real and distinct because the value of b2-4ac is greater than 0

where a, b, and c are the coefficients in the standard form of the quadratic equation ax²+bx+c=0

Given quadratic equation is 2x²-6x+3=0  on comparing with the standard form of the quadratic equation ax²+bx+c=0

We have a=2, b=(-6) ,c=3

Hence b²-4ac,

Here b²-4ac is also known as discriminant.

=(-6)²-(4×2×3)

=36-24

=12≥0

12 (Twelve) is obviously greater than zero (0)

here value of b²-4ac>0

Hence the nature of the roots of the given equation is real and distinct.

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Question

What is the nature of roots of 2x²- 6x+ 3= 0?

When dividing 456.3 by 100, how should the decimal point be moved is:

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point. 12.5 is a decimal number, for instance.

In mathematics, the decimal system—also known as the Hindu-Arabic number system or the Arabic number system—is a positional numeral system that uses 10 as its base and calls for the use of 10 different numbers, including 0, 1, 2, 3, 4, 5, 6, 7, and 8. To indicate decimal fractions, a dot (decimal point) is also necessary.

We use decimals on a daily basis when dealing with things like money, weight, and length. Decimal numbers are used when higher accuracy is required than full numbers can provide.

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Answer:

Step-by-step explanation:

Paul's Pizzeria: y = 15x

Leo's Pizzeria: y = 12x

Therefore, Paul's Pizzeria takes in more money per pizza <3

The correct statements of the given statements are -

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is the distance of the elevator from the ground in floors.

Therefore, the correct statements of the given statements are -

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Step-by-step explanation:

The committee should sell adult tickets for $10 and child tickets for $5 to raise $1,440 from ticket sales.

Let x be the price of adult tickets in dollars and y be the price of child tickets in dollars. We can set up the following system of equations to represent the given information:

x + y = 300 (the total number of tickets sold)

180x + 120y = 1440 (the total amount of money raised)

x = 2y (the price of adult tickets is twice the price of child tickets)

Substituting the third equation into the first equation, we get:

2y + y = 300

3y = 300

y = 100

Substituting this value for y into the third equation, we get:

x = 2*100

x = 200

Substituting these values for x and y into the second equation, we get:

180200 + 120100 = 1440

This equation is true, so the solution x = $200 and y = $100 is valid. Therefore, the committee should sell adult tickets for $10 and child tickets for $5 to raise $1,440 from ticket sales.

Part A: The common difference is 4.

Part B: The 4th term is 17 and the 5th term is 21  of this sequence.

What do you mean by arithmetic sequence?

The difference between each term in an arithmetic sequence is a constant. To put it another way, we just add the same value repeatedly, indefinitely.

According to the given question,

We have the given information:

The arithmetic sequence:

5, 9, 13,...

Now, we need to find the common difference and we will find it in this way,

The common difference is the difference between two consecutive terms in a sequence. To find it, we just need to do simple subtraction.

d = t2 - t1

= 9-5 = 4

So, the common difference is 4.

Then, we need to find the 4th and 5th terms of this sequence,

t4 = t3 + d

= 13+4

= 17

t5 = t4 + d

=17 + 4

=21

Therefore, the 4th term is 17 and the 5th term is 21.

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The common difference of this arithmetic sequence is 4 and 4th, 5th term of this arithmetic sequence is 17 and 21.

Each phrase in an arithmetic sequence increases by adding or subtracting a specific constant, k. Each word in a geometric sequence is raised by either multiplying by or dividing by a certain constant, k.

Part A:

The constant difference between consecutive terms of an arithmetic sequence is called the common difference and its is denoted by d.

Therefore, the common difference (d) is equal to 9 - 5 = 4.

The 4th and 5th terms of this sequence are

Part B:

Using Arithmetic progression formula,

aₙ = a + (n- 1)d

where

n = nth term

a (first term = 5

d = common difference = 4

4th term of the sequence

a₄ = a + (n- 1)d

a₄ = 5 + (4 - 1)4

a₄ = 17

5th term of the sequence

a₅ = a + (n- 1)d

a₅ = 5 + (5 - 1)4

a₅ = 21

Hence the 4th and 5th term of this arithmetic sequence is 17 and 21.

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The formula for a prism is as follow,

The surface area of a prism = (2×Base Area) +Lateral Surface Area

The volume of a prism =Base Area× Height

A prism is a solid whose perimeter is defined by a number of congruent parallel plane polygons, two of which are known as the ends, and two of which are known as the side faces.

The polyhedron known as a prism has two parallel polygonal bases. A prism is a transparent optical device with flat, polished surfaces that refract light. The two polygonal bases are connected by their lateral faces. Longitudinally, the faces are primarily rectangular. It could even be a parallelogram occasionally.

The surface area of a prism is made up of the combined areas of the lateral faces and the two polygonal bases.

The total area that a prism takes up in three dimensions is known as its volume.

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Answer:

-1

Step-by-step explanation:

I got -1 by getting two points from the graph where the line touches. The two points I got were (0,-3) and (1, -4). When it asks you to find the domain it's asking you to find for the slope. The domain and the slope are the same thing. To find slope you use the slope formula which is y2-y1 over x2-x1. Once you set up your equation you should get -4-(-3) over 1-0. When you solve it you should get -1/1 and -1 divided by 1 is -1. So then the slope is -1....
(hope you were able to understand it... I might've not chosen the right points but hopefully I did...I'm sorry if you get it wrong)

The nature of the roots of the quadratic equation 4x² - 5x + 3 is complex.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

4x² - 5x + 3

This is in the form of ax² + bx + c

a = 4

b = -5

c = 3

Now,

D = b² - 4ac

If D < 0 there will be complex roots.

Now,

D = (-5)² - 4 x 4 x 3 = 25 - 48 = -23

D < 0

This means,

The roots are complex.

Thus,

The equation has complex roots.

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A multiplicity example in mathematics is when a function has multiple solutions to a given equation.

For example, when solving the equation x2 + 4x + 3 = 0, there are two solutions, x = -3 and x = -1. This means that the equation has a multiplicity of two. This can be seen in the graph of the equation, which has two points of intersection on the x-axis.

The multiplicity is a measure of how many solutions a given equation has. It can be determined by using the discriminant, which is the difference between the square of the coefficient of the highest degree term, and four times the product of the coefficients of the lower degree terms, and the constant. In the example above, the discriminant is 16 - 12, which is 4. The multiplicity of the equation is determined by the sign of the discriminant: if it is positive, the equation has two solutions; if it is zero, the equation has one solution; and if it is negative, the equation has no solutions.

The multiplicity of an equation can also be used to determine the nature of the graph of the equation. If the equation has a multiplicity of two, the graph is a parabola, which is a curved line that has two points of intersection on the x-axis. If the equation has a multiplicity of one, the graph is a line, which has only one point of intersection on the x-axis. If the equation has a multiplicity of zero, the graph is a circle, which has no points of intersection on the x-axis.

The concept of multiplicity is important in mathematics, as it can be used to determine the number of solutions an equation may have, as well as the nature of the graph of the equation. Knowing the multiplicity of an equation can help to simplify the process of solving the equation.

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Random variable contains the random outcome of an event in probability, The mean and standard deviation are calculated in terms of expected values E(x) in case of random variable.

The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

for a random variable, we use expected value for mean and standard deviation.

mean = E(X)

Standard deviation = [tex]\sqrt {variance} =\sqrt {E(X^{2})-(E(X)^{2})}[/tex]

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The median price of the houses sold will be equal to $171000 and yes, the mean price is greater than the median price of the houses.

Mean in mathematics is a quantity that falls somewhere between the extremes of a set. There are different types of meanings, and how they are calculated relies on the connection that is known about or is believed to control the other members.

a.

The median of given prices will be,

Let's arrange the given prices in ascending order,

161000, $165000, $168000, $171000, $174000, $178000, $240000

Then, the middle term is the median,

So, median = $171000

b.

Number of terms = 7

The mean of the given prices will be,

(171000 + 165000 + 178000 + 161000 + 174000 + 168000 +240000)/7

= 1257000/7

Mean = 179571.4286

Comparing mean and median, the mean price is greater than the median.

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Answer:

Step-by-step explanation:

It will take 180 Hours to fill the pool if both hoses are used.

In our question, one data is missing. You require the pool's volume or some information that enables you to calculate it. The same statement given by you is part of a problem where you know a series of data that shows the time required to fill the pool at different flow rates:

flow rate           time

60 gal/h            300 h => 60 gal/h * 300 h = 18,000 gal

45 gal/h            400 h => 45 gal/h * 400 h = 18,000 gal

36 gal/h            500 h => 36 gal/h * 500 h = 18,000 gal

30 gal/h            600 h => 30 gal/h * 600 h = 18,000 gal

So for this pool to calculate (several times) that the volume is 18,000 gal.

You now possess two hoses, one of which has a flow rate of 40 gals per hour and the other of which has a flow rate of 60 gals per hour.

The total flow rate is the sum of the two flow rates"

total flow rate = 40 gal/h + 60 gal/h = 100 gal/h

And you just must divide the volume of the pool (18,000 gals) by the total flow rate (100 gal/h) to get the time to fill the pool:

time = volume / flow rate = 18,000 gal / 100 gal/h = 180 hours.

So, finally, our answer to fill the pool will be about 180 hours.

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flow rate           time

60 gal/h            300 h => 60 gal/h * 300 h = 18,000 gal

45 gal/h            400 h => 45 gal/h * 400 h = 18,000 gal

36 gal/h            500 h => 36 gal/h * 500 h = 18,000 gal

30 gal/h            600 h => 30 gal/h * 600 h = 18,000 gal

So for this pool to calculate (several times) that the volume is 18,000 gal.

You now possess two hoses, one of which has a flow rate of 40 gals per hour and the other of which has a flow rate of 60 gals per hour.

The total flow rate is the sum of the two flow rates"

total flow rate = 40 gal/h + 60 gal/h = 100 gal/h

And you just must divide the volume of the pool (18,000 gals) by the total flow rate (100 gal/h) to get the time to fill the pool:

time = volume / flow rate = 18,000 gal / 100 gal/h = 180 hours.

Here we can say that - A series of integers can be generated over time using the range() method.

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value the minimum. The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

given,

20, 25, 30, 45, 55, 90, 110,115,120

so range will be 120 - 20 = 100

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