Determine if the two triangles in the following diagram are congruent. If so, select the correct way they can be proven congruent.

SSS - Side, Side, Side

SAS - Side, Angles, Side

ASA - Angle, Side, Angle

AAS - Angle, Angle, Side

HL - Hypotenuse, Leg

Answer:

16

Step-by-step explanation:

because it is a square number. The other numbers, if you square root them you won't get a whole number.

The right answer is (B), which is $145,000, given that his building property insurance costs $652.50 annually.

In mathematics, interest usually refers to the sum of money that is charged or made over the course of a given period of time on a principal sum of money. In finance and economics, interest—which can be basic or compound—is frequently used to calculate borrowing costs and return on investment. The principal sum, the interest rate, and the duration for which the interest is being charged or earned are the three factors used to compute simple interest.

given

We are informed that Floyd's home is situated in a suburban area, where building property insurance costs $0.45 for every $100 of coverage.

Assume Floyd's home is worth x. Then, the yearly payment for his home's building property insurance is:

0.0045x = $652.50

After finding x, we obtain:

x = $652.50 ÷ 0.0045

x ≈ $145,000

Floyd's home is therefore currently worth about $145,000.

The correct response is (B ) $145,000 as  his building property insurance is $652.50 per year.

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Thus, the computer was initially worth $3340 as the PC will be worth $835 after six years.

In mathematics, the unitary approach entails determining the value of a single unit in a certain circumstance and using that value to resolve other issues that are connected to it. It is a quick and efficient method for handling issues involving direct proportion, indirect proportion, and other circumstances of a same nature. In disciplines including mathematics, science, business, and engineering, the unitary technique is widely employed.

given

Let V be the computer's starting value.

The computer's value drops to V/2 after four years.

The computer's value is decreased to V/2 1/2 = V/4 after six years.

We are informed that the PC will be worth $835 after six years. When we set this equal to V/4, we obtain:

V/4 = 835

Adding 4 to both sides results in:

V = 4 × 835 = $3340

Thus, the computer was initially worth $3340 as the PC will be worth $835 after six years.

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According to the World Air Quality Report 2020, the annual average PM2.5 concentration in Singapore was 14.8 μg/m³ (micrograms per cubic meter which can be expressed in scientific notation as 1.48 x 10^-5 g/m³.

The PM2.5 concentration refers to fine particulate matter that can pose health risks when inhaled, and sources of such pollution in urban areas can include traffic, industrial activities, and power generation.

Despite its relatively low PM2.5 concentration compared to many other cities in the world, Singapore continues to work on improving air quality and reducing pollution through measures such as promoting the use of public transportation, implementing emission standards for vehicles, and encouraging the adoption of clean energy technologies.

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The answer that refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time is prevalence.

Prevalence is the total number of cases of a disease or disorder in a population at a given point in time, and does not include cases that have been resolved or previously diagnosed cases. It is an important measure of the health of a population, as it allows researchers to identify patterns in the distribution of a disease or disorder and helps inform public health strategies.

Prevalence is calculated by dividing the total number of cases of a disease or disorder in a population at a given point in time, by the size of the population. For example, if a population of 100,000 people has 500 cases of a particular disease, the prevalence would be 0.005 or 0.5%.

Prevalence is an important metric in epidemiology and public health, and is often used in combination with incidence rates to measure the health of a population. Incidence rates measure the number of new cases of a disease or disorder that occur in a population over a certain time period, whereas prevalence is a snapshot of the total number of cases of a disease or disorder in a population at a given point in time.

Knowing the prevalence of a disease or disorder in a population helps public health practitioners understand the magnitude of a health issue, inform public health strategies, and identify risk factors and trends in the distribution of a disease or disorder.

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In the identity verification process, at least four pieces of identifying information are needed for individuals to be able to confirm their identities. The following are the correct minimum pieces of identifying information for individuals required in the identity verification process:

Full nameA valid photo ID, such as a driver's license, passport, or national ID number Date of birth Address According to the anti-money laundering laws and regulations, these four identifying pieces of information are necessary to confirm an individual's identity. The goal of identity verification is to ensure that a customer is who they claim to be and to avoid fraudulent activity. Identity verification has become an important part of any institution's compliance efforts as a result of increased regulatory scrutiny. It is critical that businesses and organizations are aware of their regulatory obligations when it comes to verifying customer identities, and that they implement effective identity verification methods to mitigate the risk of fraud and ensure regulatory compliance .

Therefore, when verifying the identity of a customer, the above information should be obtained in a secure and confidential manner, with the customer's consent. These documents must be checked for signs of forgery or tampering, and the customer must be given the opportunity to provide additional documentation if necessary.

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Answer:

There are 11 cows and 8 ducks

Step-by-step explanation:

x will represent number of cows and (19-x) will represent ducks

[tex]4x+2(19-x)=60[/tex]

multiply 2 with (19-x)

[tex]4x+38-2x=60[/tex]

add your x's

[tex]2x+38=60[/tex]

subtract 38 on both sides

[tex]2x=22[/tex]

then divided 2 on both sides

[tex]x=11[/tex] cows

now to find ducks subtract

[tex]19-11[/tex]

your answer will be 8

So there are 11 cows and 8 ducks

to double check do this

[tex]11*4 + 8*16\\=44+16\\=60[/tex]

Answer:

The second one, (x+1)(3x+2)

The answer is (x+1)(3x+2)

hope it helps

Answer:

Compound angle identities are trigonometric identities that relate the trigonometric functions of the sum or difference of two angles to the trigonometric functions of the individual angles.

The main compound angle identities are:

1. sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)

2. cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)

3. tan(A ± B) = (tan(A) ± tan(B)) / (1 ∓ tan(A)tan(B))

where A and B are any two angles.

These identities can be used to simplify trigonometric expressions, solve trigonometric equations, and prove other trigonometric identities.

For example, we can use the compound angle identity for sin(A + B) to find sin(π/4 + π/6):

sin(π/4 + π/6) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6)

sin(π/4 + π/6) = (√2/2)(√3/2) + (√2/2)(1/2)

sin(π/4 + π/6) = (√6 + √2) / 4

Compound angle identities are an important part of trigonometry and are used in various fields such as physics, engineering, and mathematics.

We know that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the sum. In particular, the sum cannot be uniformly distributed on the numbers from 2 to 12.

Explanation:

When we roll a fair die (i.e. an unbiased die), the probabilities of getting any one of the six possible numbers {1, 2, 3, 4, 5, 6} are equal to 1/6 each. But, when we use a biased die, the probabilities of getting any of the six possible numbers will no longer be equal. Some numbers will be more likely to occur, while others will be less likely to occur

For example:

if one of the dice has a weight in such a way that it always rolls a 6, then the probability of getting a sum of 2 will be zero, the probability of getting a sum of 7 will be 1/6, and the probability of getting a sum of 12 will be zero.However, if the dice are biased in some other way, we can still get non-zero probabilities for the sums of 2, 7, and 12. But, the probability of getting those three sums will not be the same. For instance, if one die is biased to always roll a 1, and the other die is biased to always roll a 6, then the probabilities of getting each of the sums 2, 7, and 12 are as follows:

P(2) = P(1, 1) = (1/6)² = 1/36

P(7) = P(1, 6) + P(6, 1) + P(2, 5) + P(5, 2) + P(3, 4) + P(4, 3) = 6(1/6)(1/6) = 1/6P(1

2) = P(6, 6) = (1/6)² = 1/36

So, the probability of getting a sum of 7 is six times as likely as getting a sum of 2 or 12. Therefore, the sum cannot be uniformly distributed on the numbers from 2 to 12.

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The multiplicative rate οf change  οf the given expοnential functiοn is 1/5.(1st οptiοn).

An expοnential functiοn is a Mathematical functiοn which is  οf the fοrm

f (x) = aˣ, where “x” is  variable here and a real number and “a” is a cοnstant which is called the base οf the functiοn where a shοuld be greater than zerο.

The expοnential functiοn is given here in tabular fοrm.

Here frοm the table οf expοnential functiοn we get when x= 2 then

y= 2/5

again when x= 3 then y= 2/25

sο (2/5)×(1/5) = 2/25

again fοr x= 4 , y= 2/125

(2/25)×(1/5) = 2/125

sο every time the expοnential functiοn is multiplied by 1/5 and we get the next result.

Hence, The multiplicative rate οf change  οf the given expοnential functiοn is 1/5.

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Answer:

14 = 2 x 7

28 = 2² x 7

56 = 2³ x 7

Answer: 5% Of Tape

there is going to be 5% of tape for the coaster

Answer: 90

Step-by-step explanation: I've done this before, this was the correct answer

Answer:90

Step-by-step explanation:

r=2 s=3 t=5

2x3 squared is 2x(3x3)=18

18x5=90

The line of reflection for the given angle is  corresponding vertices.

1. Identify the original angle and its reflected angle in the diagram.
2. Find the midpoint between the corresponding vertices of the original and reflected angles.
3. Draw a line through the midpoint that is perpendicular to the line connecting the corresponding vertices.

In general, to reflect an angle across a line, you would draw a perpendicular line from the vertex of the angle to the line of reflection, and then extend the sides of the angle to intersect the line of reflection at the same angle. The line of reflection would be the perpendicular bisector of the segment connecting the vertex of the original angle to the corresponding vertex of the reflected angle.

This line is the line of reflection, and the angles are reflected across it. The justification for this method is that the line of reflection is equidistant from the corresponding points of the original and reflected angles

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Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

__________________

hope it helps ⸙

If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.

Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.

The formula to calculate the future value of an annuity due is:

[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]

Where,

FV = Future Value

PMT = Payment (amount) each period

r = Interest Rate per period

n = Number of periods

To find the future value of an annuity due for 20 years:

[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]

To find the future value of an annuity due for 40 years:

[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]

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The exponential function [tex]P(t) = P0 \times 1.04^t[/tex] represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.

What is an exponential function?

The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The context that represents exponential growth is "A town's population grows at a rate of 4% every year."

Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.

As the population grows, the growth rate also increases, resulting in an exponential increase over time.

Let P(t) be the population of the town after t years, where t is a positive integer.

The exponential function that models the population growth is -

[tex]P(t) = P0 \times (1 + r)^t[/tex]

where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.

In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.

Therefore, the exponential function for the town's population growth is -

[tex]P(t) = P0 \times (1 + 0.04)^t[/tex]

Simplifying the expression, we get -

[tex]P(t) = P0 \times 1.04^t[/tex]

This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.

In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).

Therefore, the exponential growth is displayed by town's population growing 4% every year.

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you estimate that your UA climbed to an altitude greater than 400 feet above ground level (AGL), you must submit a written report of the deviation to the Federal Aviation Administration (FAA).

If you are operating a small unmanned aircraft (UA) and have had a near mid-air collision (NMAC) with a manned airplane, and you estimate that your UA climbed to an altitude greater than 400 feet above ground level (AGL), you must submit a written report of the deviation to the Federal Aviation Administration (FAA).

According to the FAA regulations, any UAS operator involved in an NMAC with a manned aircraft must submit a report to the FAA within ten days of the incident. This report must include the date, time, and location of the incident, as well as a detailed description of the events leading up to the NMAC.

You can submit the report online via the FAA's Aviation Safety Reporting System (ASRS) website. The ASRS is a voluntary reporting system that allows pilots and UAS operators to report incidents without fear of enforcement action, provided that the incident was not a result of reckless or intentional behavior.

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Choir B has a higher percentage of students who like musicals.

what is percentage ?

Percentage is a way of expressing a proportion or a fraction out of 100. It is a widely used concept in mathematics, finance, statistics, and other fields. For example, if 20 out of 100 students in a class like pizza, we can say that the percentage of students who like pizza is 20%. To calculate the percentage, we usually multiply the given fraction by 100. For instance, if 3 out of 5 students like math, we can calculate the percentage of students who like math as follows:

(3/5) x 100 = 60%

Thus, 60% of the students in the class like math.

To determine which choir has a higher percentage of students who like musicals, we need to calculate the percentage of students in each choir who like musicals.

For choir A, 39 out of 52 students like musicals:

39/52 = 0.75 or 75%

For choir B, 35 out of 44 students like musicals:

35/44 = 0.795 or 79.5%

Therefore, choir B has a higher percentage of students who like musicals.

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There are 40 ways to place three rooks on a 4x5 board so that no rook is threatening another.

To determine this, we can first place the rooks in three distinct rows, which can be done in 4 * 3 * 2 = 24 ways. Then, we can place one rook in each of the five columns in the first row, which leaves only three columns for the second row and two columns for the third row.

Since no two rooks can be in the same column, we have 5 * 3 * 2 = 30 ways to place the remaining two rooks.

Therefore, the total number of arrangements is 24 * 30 = 720, but since each arrangement can be rotated by 90, 180, or 270 degrees, we need to divide by 4 to obtain the final answer of 720/4 = 180, and since there are two ways to arrange the rooks in each row, the final answer is 180/2 = 90.

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Answer:

radius=PC

diameter=AB

chord=AC

central angle=angleAPC

tangent=AD

Jason is correct when he says that a graph of the relationship includes the point (63, 140).

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The relationship is defined according to the equation presented as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one, which is also the constant ratio of the relationship.

From the table given at the end of the answer, when x = 54, y = 120, hence the constant is given as follows:

k = 120/54

k = 2.2222.

Hence the equation is:

y = 2.2222x.

When x = 63, the output of the function is given as follows:

y = 2.2222 x 63

y = 140.

Hence Jason is correct when he says that a graph of the relationship includes the point (63, 140), as when x = 63, the output of the function is of y = 140.

The table is given by the image presented at the end of the answer.

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The solution of the given inequality is x ∈ (-1,5). The graph has been plotted and attached below.

What is an inequality?

In mathematics, an inequality is a relationship that unfairly compares two numbers or other mathematical expressions. Size comparisons between two numbers on the number line are most usually made.

We are given an inequality as -4 < 4x < 20.

Now, on splitting the inequality, we get two inequalities which are:

-4 < 4x and 4x < 20.

On solving -4 < 4x, we get

⇒ -4 < 4x

⇒ -1 < x

Similarly, on solving 4x < 20, we get

⇒  4x < 20

⇒  x < 5

So, we get -1 < x < 5 which means x ∈ (-1,5).

The graph of the inequality has been plotted and attached below.

The red part represents -1 < x and the blue part represents x < 5.

Hence, the solution of the given inequality is x ∈ (-1,5).

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Answer:

Mark ate 3.3 times the square inches of pizza than Joannie ate.

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr (where r is the radius). If the circumference of a small pizza is 12π inches, then its radius is:

[tex]\implies \sf Radius_{small\;pizza}=\dfrac{circumference}{2\pi}=\dfrac{12\pi}{2\pi}=6\;inches[/tex]

The formula for the area of a circle is A = πr² (where r is the radius).

Therefore, the area of a small pizza is:

[tex]\implies \sf Area_{small\;pizza}=\pi \cdot 6^2=36\pi \; in^2[/tex]

If the small pizzas are cut into 6 congruent pieces, the area of one slice of small pizza is:

[tex]\begin{aligned}\implies \sf Area_{small\;slice}&=\sf \dfrac{Area_{small\;pizza}}{6}\\\\&=\dfrac{36 \pi}{6}\\\\&=6 \pi \; \sf in^2\end{aligned}[/tex]

Therefore, the area of one slice of small pizza is 6π square inches.

[tex]\hrulefill[/tex]

The diameter of a circle is twice its radius.

If the diameter of a large pizza is 16 inches then its radius is:

[tex]\implies \sf Radius_{large\;pizza}=\dfrac{diameter}{2}=\dfrac{16}{2}=8\;inches[/tex]

The formula for the area of a circle is A = πr² (where r is the radius).

Therefore, the area of a large pizza is:

[tex]\implies \sf Area_{large\;pizza}=\pi \cdot 8^2=64 \pi \; in^2[/tex]

If the large pizzas are cut into 8 congruent pieces, the area of one slice of large pizza is:

[tex]\begin{aligned}\implies \sf Area_{large\;slice}&=\sf \dfrac{Area_{large\;pizza}}{8}\\\\&=\dfrac{64 \pi}{8}\\\\&=8 \pi \; \sf in^2\end{aligned}[/tex]

Therefore, the area of one slice of large pizza is 8π square inches.

[tex]\hrulefill[/tex]

If Joannie eats 2 slices of small pizza, the square inches of pizza she ate is:

[tex]\implies \sf Joannie=2 \times 6 \pi = 12 \pi\;in^2[/tex]

If Mark eats 5 slices of large pizza, the square inches of pizza he ate is:

[tex]\implies \sf Mark =5 \times 8 \pi = 40\pi\;in^2[/tex]

To calculate how many times greater are the square inches of pizza that Mark ate than the square inches of pizza that Joannie ate, divide the area Mark ate by the area Joannie ate:

[tex]\implies \sf \dfrac{40 \pi}{12 \pi} = \dfrac{10}{3}=3.3\;(nearest\;tenth)[/tex]

Therefore, Mark ate 3.3 times the square inches of pizza than Joannie ate.

Answer:

Step-by-step explanation:

Supplementary Angles and Adjacent Angles

Answer: It would be both supplementary and adjacent angles

Step-by-step explanation: both of the angles add up to 180 degrees

In linear equation, 0.75x + 2y ≤ 16 , 2x + 4y ≤  40 are the solution represent .

What is the most effective way to explain linear equations?

An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.

if the small pair is x, the large pair is y.

45 minutes = 0.75 hour

120 minutes = 2 hour

 so, 0.75x + 2y ≤ 16

   2x + 4y ≤  40

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The expressions 10x-7 and 7-10x represent the statement "seven less than ten times a number".

The verbal expression "seven less than ten times a number" can be written mathematically in different ways, depending on the intended meaning. One possible expression is:

10x - 7

In this expression, "10x" represents ten times a number, and "-7" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting 7 from the product of 10 and the number x.

Another possible expression is 7 - 10x

In this expression, "10x" represents ten times a number, and "7 - 10x" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting the product of 10 and the number x from 7.

If the focus is on finding the result of subtracting 7 from ten times a number, the first expression is more appropriate. If the focus is on finding the result of subtracting the product of 10 and a number from 7, the second expression is more appropriate.

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The mass of a 2018 Olympic gold medal in hectograms is 58.6 hg.

First, we need to know the mass of the Olympic gold medal in grams. According to the question, the mass of an Olympic gold medal is 586 grams.

To convert grams to hectograms, we need to divide the mass in grams by 100. This is because there are 100 grams in 1 hectogram.

To do the division, we can use a calculator. Dividing 586 by 100 gives us 5.86.

The answer we get is in hectograms, so we can write it as 5.86 hg. This means that the mass of a 2018 Olympic gold medal is 5.86 hectograms.

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If 300 people were sampled instead of 200, and the confidence level remained the same, it would produce a more accurate result.

Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students. In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

This is because a larger sample size allows for a better representation of the population, providing a more accurate result. Additionally, with a larger sample size, the confidence interval of the sample would be narrower, indicating a higher level of confidence in the accuracy of the result.

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