Find an equation following defining the following function and state the domain of the function.

the answer is (C) $0 is incorrect, and (B) $5,000.00 and (D) $45.00 are also incorrect. The correct answer is (A) $450.00.

what is insurance ?

Insurance is a contract between an individual or an entity (the insured) and an insurance company (the insurer), in which the insurer agrees to compensate the insured for financial losses or damages that occur due to unexpected events, in exchange for the payment of premiums by the insured.

Based on the information provided, the employee with a family plan is on the "Individual+Spouse" premium plan, which has a monthly premium of $450.00. This means that regardless of whether or not the employee visits a doctor or hospital, they are required to pay this amount every month to maintain their insurance coverage.

Therefore, the answer is (C) $0 is incorrect, and (B) $5,000.00 and (D) $45.00 are also incorrect. The correct answer is (A) $450.00.

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Answer:

the best move is king because it did not have a king

A) Surface area of Can is 276.32 [tex]cm^2[/tex].

B)The reason is that the top of the can has to be open to be used as a pencil holder. Therefore, you do not have to include the area of the top which is  [tex]\pi r^2[/tex] .

What is surface area?

A three-dimensional object's surface area is the space it takes up when viewed from the outside.

Here the given radius = 4 cm and height h = 9 cm.

A) Now using cylinder surface area formula then,

=> Surface area SA = [tex]\pi r^2+2\pi rh[/tex] square unit.

=> SA = [tex]3.14\times4^2+2\times3.14\times4\times9[/tex]

=> SA = [tex]3.14\times16[/tex]+ 226.08

=> SA = 50.24+226.08

=> SA = 276.32 [tex]cm^2[/tex]

B) Here top of the paint is used to open a pencil holder. So we don't need bottom circle area. [tex]\pi r^2[/tex] is the formula for the area of a circle which means you can use it to calculate the area of the top of the can.

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The expression 3z^2 - 27 can be simplified by factoring out the greatest common factor (GCF), which is 3:

3z^2 - 27 = 3(z^2 - 9)

Now, we can simplify the expression further by recognizing that the term inside the parentheses is the difference of squares, which can be factored as:

z^2 - 9 = (z + 3)(z - 3)

Substituting this back into our original expression, we get:

3z^2 - 27 = 3(z^2 - 9) = 3(z + 3)(z - 3)

Therefore, the simplified form of the expression 3z^2 - 27 is 3(z + 3)(z - 3).

In online and blended learning environments, discussion-based assessments are often used as a way for students to engage in collaborative and reflective learning.

These assessments require students to participate in online discussions, often in small groups or with the whole class, to share ideas, ask questions, and build upon each other's thinking.

There are several ways that discussion-based assessments can be used in online and blended learning environments:

As a form of formative assessment:

Discussion-based assessments can be used as a way for teachers to check for student understanding and to provide feedback in real-time.

This can help teachers adjust their instruction to better meet the needs of their students.

As a way to encourage student engagement: Discussion-based assessments can help students feel more connected to their peers and to the learning community.

By providing opportunities for students to interact with each other, teachers can help students feel more invested in their learning.

As a way to promote critical thinking:

Discussion-based assessments can help students develop critical thinking skills by providing opportunities for them to analyze, evaluate, and synthesize information.

Through online discussions, students can learn how to articulate their own ideas and respond to the ideas of others.

As a way to promote collaborative learning:

Discussion-based assessments can help students develop collaborative learning skills by providing opportunities for them to work together to solve problems, share information, and build on each other's ideas.

To effectively use discussion-based assessments, teachers need to design questions and prompts that are thought-provoking and require students to engage in higher-order thinking.

Teachers also need to establish clear expectations for participation and provide guidelines for respectful and constructive discourse.

Finally, teachers should be actively engaged in the discussion and provide feedback and guidance to help students develop their thinking and communication skills.

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In a sample of 10,000 observations from a normal population, about 27 would be expected to lie beyond three standard deviations of the mean, therefore, the correct option is b.

For a normal distribution, about 99.7% of the data is expected to lie within three standard deviations of the mean. This is known as the empirical rule or the 68-95-99.7 rule.

Using this rule, we can estimate the number of observations beyond three standard deviations of the mean for a sample of 10,000. Since the distribution is normal, we know that the mean and standard deviation completely describe the distribution.

Assuming the sample is representative of the population, we can use the empirical rule to estimate the number of observations beyond three standard deviations of the mean. Since three standard deviations from the mean cover 99.7% of the data, the remaining 0.3% of the data would be expected to lie beyond three standard deviations.

Therefore, the correct answer is c. about 27, since 0.3% of 10,000 is approximately 27.

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Answer: To estimate the mean length of the insects Kylie found, we can use the formula:

mean = (sum of (length * frequency)) / (sum of frequency)

We can calculate the sum of (length * frequency) by multiplying each length by its corresponding frequency and adding up the products. We can also calculate the sum of frequency by adding up all the frequencies. Using the table given, we have:

sum of (length * frequency) = (5 * 5) + (8 * 15) + (7 * 25) = 5 + 120 + 175 = 300

sum of frequency = 5 + 8 + 7 = 20

Substituting these values into the formula, we get:

mean = 300 / 20

= 15

Therefore, an estimate of the mean length of the insects Kylie found is 15 millimetres.

Step-by-step explanation:

Answer:

|a+5|=a+5

Step-by-step explanation:

if a>-5 or a= -5 |a+5|=a+5

if a< -5 |a+5|= -a-5

(2, -6)

When a point (x,y) is rotated counterclockwise by 180° about the origin, the new point becomes (-x, -y) ie the new x coordinate becomes negative of the original x coordinate and the new y coordinate becomes the negative of the original y coordinate

So resulting point W' = (-(-2), -6) = (2, -6)

Answer:

(2, -6)

Step-by-step explanation:

When a point (x,y) is rotated counterclockwise by 180° about the origin, the new point becomes (-x, -y) ie the new x coordinate becomes negative of the original x coordinate and the new y coordinate becomes the negative of the original y coordinate

So resulting point W' = (-(-2), -6) = (2, -6)

Applying the Poisson probability distribution​ formula,  the values of μ​, ​x, and e are: μ​ ≈ 0.866, ​x = 4, and e ≈ 2.71828

To apply the Poisson distribution formula, we need to identify the values of μ​, ​x, and e:

μ​ is the mean or average number of hits per region. We can calculate μ​ as the total number of hits divided by the total number of regions:

μ​ = total number of hits / total number of regions = 505 / 583

μ ≈ 0.866

​x is the number of hits we want to find the probability for, which in this case is 4.

e is the mathematical constant e, which is approximately equal to 2.71828 and is used in the Poisson distribution formula to calculate the probability of x hits.

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A tie costs 12 euros and a shirt costs 25 euros.

Let's start by assigning variables to the unknown values. Let x be the price of a tie, and let y be the price of a shirt. We know that y = x + 13, since a shirt costs 13 euros more than a tie.

We also know that we bought three shirts and two ties, and paid a total of 99 euros. Using this information, we can set up an equation

3y + 2x = 99

Here we have to use to substitution method, substituting y = x + 13, we get

3(x + 13) + 2x = 99

Simplifying this equation, we get

5x + 39 = 99

Subtracting 39 from both sides, we get

5x = 60

Dividing both sides by 5, we get

x = 12 euros

Now that we know the price of a tie, we can use y = x + 13 to find the price of a shirt

y = x + 13

y = 12 + 13

y = 25 euros

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The explicit form of the geometric sequence is an = 27 * (-2/3)^(n-1)

In a geometric sequence, each term is obtained by multiplying the previous term by a fixed number called the common ratio, denoted by r.

So, if we know the first term and the common ratio, we can find any term in the sequence, including the nth term, using the formula:

an = a1 * r^(n-1)

where a1 is the first term and an is the nth term.

To find the common ratio, we can divide any term by the previous term:

r = -18/27 = -2/3

Now we can use the formula to find the nth term.

an = 27 * (-2/3)^(n-1)

Therefore, the explicit form of the geometric sequence is an = 27 * (-2/3)^(n-1)

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Answer:

$35.35

Step-by-step explanation:

First, let's add all these prices together:

$8.95 + $11.49 + $12.75 = $33.19

Then, let's find how much will the whole price increase with the taxes:

[tex] \frac{33.19 \times 6.5\%}{100\%} = 2.15735[/tex]

And finally, let's add this number and the old price together:

$33.19 + $2.15735 = $35.34735 ≈ $35.35

Shannon broke down 1536 into three numbers: 256, 72, and 56, and then added the products of these three numbers to get her final answer of 256.

what is products and addition ?

The product is the result of multiplying two or more numbers together. For example, the product of 2 and 3 is 6, denoted as 2 x 3 = 6.Addition is another arithmetic operation that involves combining two or more numbers to find a total or a sum.

In the given question,

To solve 1536 ÷ 6, Shannon broke down the number 1536 into three numbers that are divisible by 6.

Let's start by finding the factors of 6: 1, 2, 3, and 6.

We need to find three numbers whose sum is equal to 1536 and each of which is divisible by 6.

We can start with the largest factor of 6, which is 6 itself. We can divide 1536 by 6 to get 256.

Now we need to find two more numbers whose sum is 128 and are also divisible by 6.

One such pair of numbers is 72 and 56.

We can verify that the sum of these three numbers is indeed 1536:

256 + 72 + 56 = 384 + 56 = 440 + 256 = 696 + 840 = 1536.

So, Shannon broke down 1536 into three numbers: 256, 72, and 56, and then added the products of these three numbers to get her final answer of 256.

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The area of the shape is 331km²

The area of shape is the space enclosed within the perimeter or the boundary of a given shape. Area is measured in units².

The shape above can be divided into 4 shapes.

The area of the first triangle = 1/2 bh

= 1/2 × 14 × 21

= 7× 21

= 147km²

The area of the first rectangle = l× b

= 14 × 5

= 70km²

The area of the second triangle = 1/2 bh

= 1/2 × 10× 18

= 10× 9

= 90km²

area of the second rectangle = l × b

= 4 × 6

= 24 km²

area of the shape = 147+90+70+24 = 331km²

Therefore the area of the shape is 331km²

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As a result, Bank Padarn's AER is 2.0186%. This shows that Bank Padarn gives a greater interest rate when compared to the AER provided by Banc Teilo (1.9%).

A benchmark 30-year fixed mortgage's current average interest rate is 6.91% as of today, Tuesdays, March 21, 2023, a decrease of 3 basis points from seven days ago. If you're looking to refinance your mortgage, the current average 30-year fixed interest rate of 6.93%, which has been constant over the past week.

We must convert a nominal rate provided by Bank Padarn to the an AER in order to contrast the two rates.

AER is calculated as (1 + r/n)n - 1 where r is just the nominal rate of return & n is the annual frequency of interest payments.

r = 1.98% and n = 12 for Banc Padarn (since interest is paid monthly). The algorithm yields the following results when we enter these values: AER Equals (1 + 0.0198/12)12 - 1 ≈ 0.020186 = 2.0186%

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Number of students should be sampled to be within 0.5 drink of population mean with 95% probability is 617 students.

To determine the sample size required to estimate the population mean with a given level of precision, we can use the formula for the margin of error

Margin of error = Z × (standard deviation / sqrt(sample size))

where Z is the critical value of the standard normal distribution corresponding to the desired level of confidence. For a 95% confidence level, Z is 1.96.

We want the margin of error to be no more than 0.5 drinks, so we can set up the equation

0.5 = 1.96 × (6.3 / sqrt(sample size))

Solving for the sample size, we get

sqrt(sample size) = 1.96 × 6.3 / 0.5

sqrt(sample size) = 24.82

sample size = (24.82)^2

sample size = 617

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The expected recorded score of the given data of short quiz is,

Expected recorded score is 8.5.

And maximum of the two expected recorded score is 12.45.

Expected recorded score e(x + y),

e(x + y) = ΣΣ (x + y)  p(x, y)

Simplify this expression by rearranging the sum,

e(x + y) = ΣΣ x p(x, y) + ΣΣ y  p(x, y)

Using the table given,

ΣΣ x p(x, y)

= (0×0.02) + (5×0.04) + (10×0.01) + (0×0.06) + (5×0.13) + (15×0.15) + (0×0.02) + (5×0.20) + (10×0.16)

= 4.6

ΣΣ y p(x, y)

= (0×0.02) + (0×0.06) + (0×0.02) + (5×0.10) + (5×0.13) + (5×0.01) + (10×0.20) + (10×0.15) + (10×0.16)

= 3.9

Expected recorded score is,

e(x + y)

= 4.6 + 3.9

= 8.5

The maximum of the two scores is recorded,

Then the recorded score will be either x or y, whichever is larger.

Probability distribution of the maximum score,

P(max(x, y) = 0)

= P(x=0, y=0)

= 0.02

P(max(x, y) = 5)

= P(x=5, y=0) + P(x=0, y=5) + P(x=5, y=5)

= 0.06 + 0.04 + 0.13

= 0.23

P(max(x ,y) = 10)

= P(x=10, y=0) + P(x=0, y=10) + P(x=10, y=5) + P(x=5, y=10) + P(x=10, y=10)

= 0.01 + 0.15 + 0.20 + 0.10 + 0.16

= 0.62

P(max(x, y) = 15)

= P(x=15, y=0) + P(x=0, y=15) + P(x=15, y=5) + P(x=5, y=15) + P(x=15, y=10) + P(x=10, y=15) + P(x=15, y=15)

= 0.01 + 0.10 + 0.10 + 0.10 + 0.01 + 0.01 + 0.01

= 0.34

Expected recorded score can be calculated as the weighted sum of the possible maximum scores,

E(max(x, y)) = Σ max(x, y) × P(max(x, y))

Substituting the probabilities, we get,

E(max(x ,y))

= 0×0.02 + 5×0.23 + 10×0.62 + 15×0.34

= 0+ 1.15 + 6.2 + 5.1

= 12.45

Expected recorded score is 12.45 (upto two decimal places).

Therefore, expected recorded score is 8.5 and maximum of the expected recorded score is 12.45.

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The above question is incomplete, the complete question is:

An instructor has given a short quiz consisting of two parts. for a randomly selected student, let x = the number of points earned on the first part and y = the number of points earned on the second part. suppose that the joint pmf of x and y is given in the accompanying table.

                                                 y

     p(x, y)                     0               5                  10                               15

    0                           0.02          0.06              0.02                          0.10

x   5                           0.04           0.13              0.20                          0.10

   10                           0.01            0.15              0.16                          0.01

(a) if the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score e(x + y)? (enter your answer to one decimal place.)

(b) if the maximum of the two scores is recorded, what is the expected recorded score? (enter your answer to two decimal places.)

Answer:  k = 67 4/5

Step-by-step explanation:

101 3/5 =k+33 4/5

first isolate your variable by subtracting 33 4/5 from both sides

101 3/5 - 33 4/5 = k

now subtract

to subtract 4/5 from 3/5, you have to borrow 5/5 or 1 whole from 101 and add it to 3/5.  5/5 + 3/5 = 8/5.  101 - 1 = 100.

so now you have

100 8/5 - 33 4/5 = k

100 - 33 = 67

8/5 - 4/5 = 4/5

your answer is 67 4/5

Check your work.

67 4/5 + 33 4/5 = 100 8/5 simplified to 101 3/5, our starting number.

solution is true so problem solved!

The model that fits the data is a linear model and the equation is y = -72.5x + 2102.6

See attachment

Based on the graph, the model would you choose to fit this data is a linear regression, and the equation is

y = -72.5x + 2102.6

This is because the points appears to be linear

We have

x = 3

So, we have

y = -72.5 * 3 + 2102.6

y = 1885.1

So, the amount is 1885.1

Here, we have

y = 0

So, we have

-72.5x + 2102.6 = 0

This gives

x = 29

Hence, the time is 29 minutes

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Answer:

I can see the pattern. There will be 30 toothpicks to make 10 squares accordingto your pattern. The pattern with an expression is +3.

Step-by-step explanation:

If you list the 4,7,10 and see the pattern between these numbers. You are adding 3 to the 4 to the 7 and 7 to the 10. Then, follow the pattern until you get 10 squares.

Answer:

-2299

Step-by-step explanation:

12(-72) = -864

(-3 - 32) = -35

41(-35) = -1435

-864 + -1435 = -2299

A city has a population of 28,000 people. Suppose that each year the population grows by 4.5%. What will the population be in 13 years?

Answer: Approximately 496,21 people

This is an exponential growth question, specifically population growth. We will use the following equation to help us solve this situation:

[tex]P(t) = a(1+r)^t[/tex]

[tex]P(t) = \text{total population} \ (??)[/tex]

[tex]\text{a = initial population = 28,000}[/tex]

[tex]\text{r = growth factor (the percent as a decimal) = 0.045}[/tex]

[tex]1 + r = 1 + 0.045 = 1.045[/tex]

[tex]\text{t = time in years = 13}[/tex]

So, we can substitute all our information and solve:

[tex]P(13) = 28,000(1.045)^{13} = 496,21.49[/tex]

Rounding to the nearest whole person, 496,21 people in 13 years.

Here is an organized list representing the sample space of drawing one letter tile and one number tile: {(A, 1), (A, 2), (A, 3), (B, 1), (B, 2), (B, 3), (C, 1), (C, 2), (C, 3)}

What is a sample space?

In probability theory, sample space refers to the set of all possible outcomes of a random experiment.

For example, if we toss a coin, the sample space would consist of two possible outcomes, heads or tails. Similarly, if we roll a die, the sample space would consist of six possible outcomes, the numbers 1 through 6.

The sample space is an important concept because it allows us to define the probabilities of events. In order to calculate the probability of an event, we divide the number of outcomes that are favorable to the event by the total number of possible outcomes in the sample space.

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Arithmetic operations helps us to determine the value of x for quotient of 20 divide 5 is subtracted from the difference of 16 and 6 is equals to the 6.

In arithmetic, a quotient can be defined as the result of the division of a number by any divisor. It is the number of times the divisor is contained in the dividend a quantity produced by the division of two numbers. The quotient can be determined by dividing the dividend with the divisor. Formula, Quotient = Dividend ÷ Divisor. We have to determine value of x which equals to quotient of 20 divide 5 is subtracted from the difference of 16 and 6. First we have to determine quotient 20 divides 5. Using quotient formula, quotient= 20 ÷ 5 = 4. So, Quotient is 4. Now, the difference of 16 and 6 that is equals to 16 minus 6 = 16 - 6 = 10. Thus, x = 16 - 6 - ( 20÷ 5)

=> x = 10 - 4

=> x = 6

Hence, required value of x is 6.

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Complete question :

The quotient of 20 divide 5 is subtracted from the difference of 16 and 6 equals to x. what is x?

Answer:

x=6

Step-by-step explanation:

20 ÷ 5 = 4. So, Quotient is 4. Now, the difference of 16 and 6 that is equals to 16 minus 6 = 16 - 6 = 10. Thus, x = 16 - 6 - ( 20÷ 5)

=> x = 10 - 4

=> x = 6

Hence, required value of x is 6.

Answer:

1<4(3)+2

1<12+2

1<14

so therefore we say the answer is 1 is lesser than 14

Using the law of sine, the missing side of the triangle is approximately 4.01 units.

The law of sines states that for any triangle ABC with sides a, b, and c opposite to angles A, B, and C respectively

a / sin(A) = b/sin(B) = c / sin(C)

Using this law, we can find the missing side b as follows:

b/sin(B) = c/sin(C)

Since angle B and angle C are complementary, we can find angle C as:

C = 180 - A - B = 180 - 58 - 48 = 74 degrees

Now we have

b/sin(48) = 5/sin(74)

Solving for b, we get

b = (5 x sin(48))/sin(74) ≈ 4.01 units

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The given question is incomplete, the complete question is;

use the law of sines to find the missing side of the triangle

Answer:

Step-by-step explanation:

the answer willbe 80

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(i)

y = 3x - 4

with slope m = 3 and y- intercept c = - 4

(ii)

y = - 3x + 7

with slope m = - 3 and y- intercept c = 7

Answer:

here we can see clearly,

Answer:

a)  The intercepts of the graph are (-75, 0), (75, 0), (0, -75) and (0, 75).

b)  The radius is 75 miles.

c)  The area of the region is 17,671 square miles (to the nearest square mile).

Step-by-step explanation:

The x-intercepts are the points at which the graph crosses the x-axis, so when y = 0. Therefore, to find the x-intercepts, substitute y = 0 into the given equation.

[tex]\implies x^2+y^2=5625[/tex]

[tex]\implies x^2+(0)^2&=5625[/tex]

[tex]\implies x^2&=5625[/tex]

[tex]\implies x&=\sqrt{5625}[/tex]

[tex]\implies x&=\pm75[/tex]

The y-intercepts are the points at which the graph crosses the y-axis, so when x = 0. Therefore, to find the y-intercepts, substitute x = 0 into the given equation.

[tex]\implies x^2+y^2=5625[/tex]

[tex]\implies (0)^2+y^2&=5625[/tex]

[tex]\implies y^2&=5625[/tex]

[tex]\implies y&=\sqrt{5625}[/tex]

[tex]\implies y&=\pm75[/tex]

Therefore, the intercepts of the graph are:

[tex]\hrulefill[/tex]

The general equation of a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h, k) is the center and r is the radius of the circle.

By comparing the given equation with the general equation:

Take the positive square root of r² to find the radius of the circle (since length cannot be negative):

[tex]\implies r=\sqrt{5625}[/tex]

[tex]\implies r=75[/tex]

Therefore, the radius of the circle is 75 miles.

[tex]\hrulefill[/tex]

The formula for the area of a circle is:

[tex]A=\pi r^2[/tex]

where r is the radius.

To find the area of the region in which the broadcast from the station can be picked up, find the area of the circle with the radius from part b, r = 75:

[tex]\implies A= \pi \cdot 75^2[/tex]

[tex]\implies A=5625 \pi[/tex]

[tex]\implies A=17671.4586...[/tex]

Therefore, the area of the region is 17,671 square miles (to the nearest square mile).

Answer:

Step-by-step explanation:

To find:-

Answer:-

The given equation of the circle is ,

[tex]:\sf\implies x^2 + y^2 = 5625 \\[/tex]

[tex]\rule{200}2[/tex]

G R A P H : -

[tex]\setlength{\unitlength}{7mm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\vector(1,0){6}}\put(0,0){\vector(-1,0){6}}\put(0,0){\vector(0,1){6}}\put(0,0){\vector(0,-1){6}}\put(.2,2.5){$\sf (0,75)$}\put(.2, - 2.7){$\sf (0,-75)$}\put(2.5,0.2){$\sf (75,0)$}\put( - 4.2,.2){$\sf ( - 75,0)$}\put(4,4){$\bigstar \: \: \sf Centre = (0,0) $}\put(4,3){$\bigstar \: \: \sf Radius = 75\ miles $}\put(4,-4){$\boxed{\bf \textcopyright \: \: Tony Stark }$}\end{picture}[/tex]

[tex]\rule{200}2[/tex]

Answer a :-

The intercepts are the points at which the circle cuts the x-axis and y-axis . At x intercept , the value of y coordinate becomes 0 and at y intercept the x coordinate becomes 0 .

So for finding x intercept , plug in y = 0 , in the given equation of circle, as ;

[tex]:\sf\implies x^2 + (0)^2 = 5625 \\[/tex]

[tex]:\sf\implies x^2 = 5625 \\[/tex]

[tex]:\sf\implies x =\sqrt{5625} \\[/tex]

[tex]:\sf\implies x =\pm 75 \\[/tex]

[tex]:\sf\implies \red{ x = +75 , -75} \\[/tex]

Hence the circle cuts the x-axis at (75,0) and (-75,0).

To find out y intercept plug in x = 0 in the given equation of the circle as ,

[tex]:\sf\implies (0)^2 + y^2 = 5625 \\[/tex]

[tex]:\sf\implies y^2 = 5625 \\[/tex]

[tex]:\sf\implies y=\sqrt{5626}\\[/tex]

[tex]:\sf\implies y = \pm 75 \\[/tex]

[tex]:\sf\implies \red{ y = +75,-75} \\[/tex]

Hence the circle cuts the y-axis at (0,75) and (0,-75).

[tex]\rule{200}2[/tex]

Answer b :-

Next we are interested in finding out the radius of the circle, for that we need to compare the given equation of circle to the standard equation of circle .

Standard equation of circle :-

[tex]:\sf\implies \red{ (x-h)^2 + (y-k)^2 = r^2}[/tex]

where ,

We can rewrite the given equation of circle as ,

[tex]:\sf\implies (x-0)^2 + (y-0)^2 = 5625 \\[/tex]

[tex]:\sf\implies (x-0)^2+(y-0)^2 = 75^2\\[/tex]

On comparing to the standard form, we have;

[tex]:\sf\implies \red{ radius = 75\ miles } \\[/tex]

Hence the radius of the circle is 75miles .

[tex]\rule{200}2[/tex]

Answer c :-

To find out the area we can use the formula of area of circle , which is ;

[tex]:\sf\implies \red{Area=\pi(radius)^2} \\[/tex]

We already got the radius to be 75 miles in the previous part of the question. Plugging in that value would give us the area , as ;

[tex]:\sf\implies Area =\pi (75\ miles )^2 \\[/tex]

[tex]:\sf\implies Area = \dfrac{22}{7}\times 5625\ miles^2\\[/tex]

[tex]:\sf\implies \red{ Area = 17678.57 \ miles^2 } \\[/tex]

Hence the area of the circle is 17678.57 miles² .