A convenience sample of forty people is taken from a population. Which of the following is a reason why you can not make a statistical inference on the population?

The sample size is not large enough.

The population isn’t given to be approximately normal.

The sample is not given to be normally distributed.

The wrong sampling method was used.

Answers

Answer 1

Answer:

The wrong sampling method was used.

Step-by-step explanation:

In convenience sampling, first few responses are considered and not all parameters are considered. This is the easiest method of sampling but least effective

Answer 2

(D) The wrong sample method was used.

Sample:

The term 'sample' can mean -

A sample is a statistical term for a portion of a population.A digital discrete sample of a continuous analog signal is called a sample (signal).A sample, a specimen, or a little amount of anything.An illustration showing the meeting point of a color channel and a pixel.Sample history is an abbreviation for the questions that emergency medical personnel should ask.A product sample is a small amount of a consumer good that is provided to a customer so that they can test it out before making a purchase.Statistics:The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. Populations can refer to a variety of groupings of individuals or things, such as "every individual living in a nation" or "each atom making up a crystal." Every facet of data, including the planning of data collecting in terms of the layout of surveys and experiments, is covered by statistics.

Therefore, the correct answer if the problem is (D) the wrong sample method was used.

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Related Questions

A rectangle as an area of 240 square ft the base is 15 what is the height of the rectangle

Answers

Answer:

16 ft

Step-by-step explanation:

Hi there,

The formula for the area of a rectangle is A = b*h.

So, let's start out by plugging in what we know.

240 = 15h

Now, solve for h by dividing both sides by 15

h = 16

So, the height of the rectangle is 16 ft

Hope this helps! Stay safe!

- Emily

Yasmin arrived home from play practice at 4:25 pm. The walk took 15 minutes. Practice began 20 minutes after the final bell and lasted for a half hour. When did school end

Answers

Answer:

Step-by-step explanation3:45

Answer:

3:20 p.m

Step-by-step explanation:

if angle 5 is 120 degrees, what is the measure of angle 6?

Answers

Final answer:

Without more context, the measure of angle 6 cannot be determined from the given information that angle 5 is 120 degrees.

Explanation:

To determine the measure of angle 6, we need additional information about the context in which angle 5 and angle 6 are related. Since the question does not provide sufficient details, such as whether the angles are supplementary, complementary, or part of a geometric figure like a triangle or polygon, it's not possible to provide the measure of angle 6 based solely on the given information that angle 5 is 120 degrees. In geometry, the relationships between angles often depend on the shapes they are part of or the lines intersecting with them. If angle 5 and angle 6 are supplementary angles (angles that add up to 180 degrees), for instance, we could subtract the measure of angle 5 from 180 degrees to get angle 6. However, without more details, we cannot accurately provide the measure of angle 6.

The sum of three numbers is 10. Two times the second number minus the first number is equal to 12. The first number minus the second number plus twice the third number equals 7. Find the numbers. Listed in order from smallest to largest, the numbers are

Answers

Answer:

The answer to your question is x = -2, y = 5 and z = 7

Step-by-step explanation:

Data

first number = x

second number = y

third number = z

Process

1.- Write equations to solve this problem

                 x + y + z = 10           Equation l

                 2y - x = 12                Equation ll

                  x - y + 2z = 7           Equation lll

2.- Solve equation ll for x

                x = 2y - 12

3.- Substitute the previous equation in equation l and lll

               (2y - 12) + y + z = 10                     (2y - 12) - y + 2z = 7

                2y - 12 + y + z = 10                       2y - 12 - y + 2z = 7

                3y + z = 10 + 12                             y + 2z = 19

                3y + z = 22

4.- Solve for y and z

                     -2(3y + z = 22)

                          y + 2z = 19

                    -6y - 2z = -44

                       y + 2z = 19

                   -5y   + 0 = -25

                      y = -25/-5

                      y = 5

-Find z

                       5 + 2z = 19

                             2z = 19 - 5

                             2z = 14

                               z = 14/2

                               z = 7

5.- Find x

                  x + 5 + 7 = 10

                  x = 10 - 5 - 7

                 x = -2

Listed in order from smallest to largest: -2, 5, 7.

Let's denote the three numbers as follows:

- First number: x

- Second number: y

- Third number: z

We have three equations based on the given information:

1. x + y + z = 10

2. 2y - x = 12

3. x - y + 2z = 7

We can solve this system of equations to find the values of x, y, and z.

From equation 2, we can isolate x:

x = 2y - 12

Now substitute the value of x in equations 1 and 3:

1. (2y - 12) + y + z = 10

3y + z = 22

3. (2y - 12) - y + 2z = 7

y + 2z = 19

Now we have a system of two equations with two variables (y and z):

1. 3y + z = 22

2. y + 2z = 19

Let's solve for one of the variables in terms of the other. From equation 2, we can isolate y:

y = 19 - 2z

Now substitute this value of y into equation 1:

3(19 - 2z) + z = 22

57 - 6z + z = 22

-5z = -35

z = 7

Substitute the value of z back into the equation for y:

y = 19 - 2(7)

y = 5

Now that we have values for y and z, we can substitute them back into the equation for x:

x = 2y - 12

x = 2(5) - 12

x = 10 - 12

x = -2

So, the numbers are:

First number: -2

Second number: 5

Third number: 7

Listed in order from smallest to largest: -2, 5, 7.

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The sum of two negative numbers is always a negative number. Choose the correct answer below A. True B. False

Answers

Answer:

True

I hope this helps :)

Answer:

True

Step-by-step explanation:

True because there are only negative numbers in the calculation. Zero pairs are formed when a positive and a negative number are added

Elisondra is eating at a restraurant with three friends. They want to choose at random who will order first. If you
model the situation with the spinner, how many equal-sized sections should the spinner have?
what will be the equal sized sections ?

Answers

Answer:

4 i did the quizzzzzzzzzzzzzzzzzzzzzzzzz

Step-by-step explanation:

Please help, geometry

Answers

Step-by-step explanation:

As it is a quadrilateral so sum of all angles of quadrilateral is equal to 360°

14x - 11° + 8x + 7° + 5x + 18° + 10x + 13° = 360°

37x+ 27° = 360°

37x = 360° - 27°

37x = 333°

x = 333° / 37

Therefore x = 9°

Now

<B = 8 * 9° + 7° = 79°

Hope it will help you.

Answer: The answer is 79.0°

Step-by-step explanation:

A quadrilateral will always have 360° and four sides. Keep that in mind, that's a universal rule of geometry.

Here, the sum of all sides is equal to 360°. Therefore, we make an equation:

[tex](14x-11) + (8x+7) + (5x+18) + (10x + 13) = 360[/tex]

Simplify by adding and subtracting like terms.

[tex]37x +27=360[/tex]

Isolate x by first passing the 27 to the other side.

[tex]37x = 333[/tex]

Divide by 37 to isolate x.

[tex]x = 9[/tex]

To find m∠B, we plug in x to [tex](8x+7)[/tex]

which gives you: [tex](8*9+7) = 79[/tex]

The answer is 79.0°

Curious if it is correct? Let's double check.

Plug in the x=9 to all the x values and add them up. You should get 360, which makes the answer correct.

If tan B = 1.6732, what is the measure of B to the nearest tenth of a degree

Answers

Answer:

59.1 °

Step-by-step explanation:

-Given that Tan B=1.6732

-Angle B is equivalent to the tan inverse of the tan B value:

[tex]\angle B=Tan^{-1}B\\\\\angle B=Tan^{-1}(1.6732)\\\\=59.1350\approx59.1\textdegree[/tex]

Hence, angle B is 59.1 °

Final answer:

To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732.

The measure of angle B is approximately 59.7 degrees.

Explanation:

To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732. First, convert the tangent value to radians by using the formula tan(B) = opposite/adjacent. Then, take the arctan of B to find the measure in radians. Finally, convert the radians to degrees by multiplying by 180/pi.

Step-by-step:

Convert the tangent value to radians: tan(B) = opposite/adjacent => B = arctan(1.6732)Convert radians to degrees: B (in degrees) = B (in radians) * 180/pi

Plugging in the given value, B ≈ 59.7 degrees to the nearest tenth of a degree.

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You have been asked to determine where a water works should be built along a river between Chesterville and Denton to minimize the total cost of the project. The pipe to Chesterville costs $3000 per mile and the pipe to Denton costs $7000 per mile. Find the length of each pipe so that the total cost is a minimum. What is the cost?

Answers

Answer:

Length of pipe to Chesterville is 8.376 miles and

Length of pipe to Denton is 5.46 miles

Step-by-step explanation:

Here we have

The distance of Chesterville from the river is 3 miles, while the distance of Denton from the river is 5 miles

The bank of the river is 10 miles long

Therefore, we have

If x is the distance from the point directly opposite to Chesterville to the location of the water works, the equation is;

Cost to Chesterville = [tex]3000\times \sqrt{x^2 + 3^2}[/tex]

Cost to Denton = [tex]7000\times \sqrt{(10-x)^2 + 5^2}[/tex]

Total cost is then;

[tex]7000\times \sqrt{(10-x)^2 + 5^2} + 3000\times \sqrt{x^2 + 3^2}[/tex]

We differentiate the above equation and equate it to zero to get the minimum cost as

[tex]\frac{\mathrm{d} (7000\times \sqrt{(10-x)^2 + 5^2} + 3000\times \sqrt{x^2 + 3^2})}{\mathrm{d} x}[/tex] = 0

[tex]7000\frac{2x-20}{2\sqrt{x^2-20x+125} } +3000\frac{2x}{2\sqrt{x^2+9} } = 0[/tex]

[tex]3500\frac{2x-20}{\sqrt{x^2-20x+125} } = -1500\frac{2x}{\sqrt{x^2+9} }[/tex]

[tex]3500\frac{\sqrt{x^2+9}}{\sqrt{x^2-20x+125} } = -1500\frac{2x}{2x-20 }[/tex]

[tex]x^4-20x^3+10.54x^2-22.05x+110.25 =0[/tex]

Solving the quartic equation we get

x = 7.82 miles

Therefore the length of is given as

Length of pipe to Chesterville  [tex]\sqrt{7.82^{2} +3^2 } = 8.376 \, miles[/tex]

Length of pipe to Denton = [tex]\sqrt{(10-7.82)^2 + 5^2} = 5.46 \, miles[/tex].

A student solved 3/x-4 =x/7 in six steps as shown.Which statement is an accurate interpretation of the students work

Answers

Answer:

A student solved 3/x−4=x/7 in six steps, as shown:

Step 1:  3=x(x−4)/7  

Step 2: 21=x(x−4)

Step 3: 21=x^2−4(x)

Step 4: 0=x^2−4(x)−21

Step 5: 0=(x−7)(x+3)

Step 6: x=−3, x=7

Which statement is an accurate interpretation of the student's work?

A.The student solved the equation correctly.

B.The student made an error in step 2.

C.The student made an error in step 5.

D.Only x=7 is a solution to the original equation.

Option A is the right choice.

Step-by-step explanation:

Given:

An equation and its step-wise work.

We have to check whether the steps are correct or not.

The equation is:

⇒ [tex]\frac{3}{x-4} = \frac{x}{7}[/tex]

Solution:

⇒ [tex]21=x(x-4)[/tex]              ...cross multiplying terms.

⇒ [tex]21=x^2-4x[/tex]    

⇒ [tex]x^2-4x-21=0[/tex]

⇒ [tex]x^2-7x+3x-21=0[/tex] ...using middle term splitting

⇒ [tex]x(x-7)+3(x-7)=0[/tex]

⇒ [tex](x+3)(x-7)[/tex]

⇒ [tex]x=-3\ and\ x=7[/tex]

The student have solved the question correctly.

Write your own word problem that involves 1 1/3 -2/3 . Solve the problem, and explain what your solution means in terms of the problem that you wrote.

Answers

Answer:

If there are eleven apples to be shared between 3 boys and two bananas to be shared between 3 girls, find the difference between them.

Step-by-step explanation:

So there are 11 apples to be shared between 3 boys, which is represented mathematically as 11/3

And 2 bananas to be shared between 3 girls, which can be represented mathematically as 2/3, find the difference.

The difference between them would be 11/3 - 2/3

Solving this problem, they both have the same denominator, so we subtract the numerators directly.

11/3 - 2/3 = 9/3

Which is equals to 3.

So the difference between both of them is 3.

Large samples of women and men are​ obtained, and the hemoglobin level is measured in each subject. here is the​ 95% confidence interval for the difference between the two population​ means, where the measures from women correspond to population 1 and the measures from men correspond to population​ 2: negative 1.76 g divided by dl less than mu 1 minus mu 2 less than minus 1.62 g divided by dl−1.76 g/dl<μ1−μ2<−1.62 g/dl. complete parts​ (a) through​ (c) below.



a. what does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men? because the confidence interval includes nothing​, it appears that there is a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men. ​(type an integer or a decimal. do not​

Answers

Answer:

1.  The mean hemoglobin level in men is not equal to the mean hemoglobin level in women and

2. There is more hemoglobin in the average man than in the woman

Step-by-step explanation:

The confidence interval is from

-1.76 g/dl < μ₁ - μ₂ < -1.62 g/dl

Here we note that the range in the confidence interval for the difference between the two means lie in the negative part of the number line which is indicative of that μ₁ - μ₂ ≠ 0  or μ₁ ≠ μ₂

That is the statistic of the confidence interval implies that the mean hemoglobin level in men is not equal to the mean hemoglobin level in women and

That there is more hemoglobin in the average man than in the woman.

Fine the volume of the sphere. Leave the answer in terms of pi.

Answers

Given:

The area of the given sphere = 36π in²

To find the volume of the given sphere.

We need to find the radius first.

Formula

The area of a sphere [tex]A = 4\pi r^{2}[/tex]The volume of the sphere [tex]V = \frac{4}{3} \pi r^{3}[/tex]

where, r be the radius of the sphere.

Now,

According to the problem,

[tex]4\pi r^{2} = 36\pi[/tex]

or,[tex]4r^{2} = 36\\[/tex] [ Eliminating π from both the side]

or, [tex]r^{2} = \frac{36}{4}[/tex]

or, [tex]r = \sqrt{9}[/tex]

or, [tex]r = 3[/tex]

So,

The radius of the sphere is 3 inches

Therefore,

The volume of the sphere is

[tex]V = \frac{4}{3} \pi (3)^{3}[/tex]

or, [tex]V = 36\pi[/tex]

Hence,

The volume of the sphere is 36π cube inches.

80% is best represented by which the following fractions
A. 8/100
B.4/5
C.3/4
D.8/10

Answers

Answer:

B. 4/5

Step-by-step explanation:

8/10 simplified is 4/5 so the other person is still correct.

But if there's a fraction that could be simplified, then the simplified answer would be the best answer you're looking for.

What is the product of -9x (5-2x)

Answers

Answer:

Step-by-step explanation:

It s 55555555

Answer:

18x^2-45x

Step-by-step explanation:

-9x (5-2x)

=-9x X 5-(-9x) X 2x

=-9 X 5x+9 X 2xx

=18x^2-45x

I hope this helps!

Explain why a polar curve is not always bounded.

Answers

Answer: There are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time. A polar curve is required to have an unbounded function (right side of r = f(Θ)) to be an unbounded polar. An example of an unbounded curve would be r = Θ for 0 ≤ Θ.

Answer:

There are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time. A polar curve is required to have an unbounded function (right side of r = f(Θ)) to be an unbounded polar.

Step-by-step explanation:

its correct on EDGE2022

The three sides of a triangular lot are represented by x , 2 x , and 3 x + 2. Find each side if the perimeter of the triangular lot is 362 feet. The lengths of the sides of the triangle are :

Answers

Answer:

60 ft, 120 ft, 182 ft

Step-by-step explanation:

Hi there,

To find the perimiter of a polygon, you need to add of all of the sides.

So, let's do that:

x + 2x + 3x+2

Since we are given the perimeter, we make what we just did above, equal to the perimeter

x + 2x + 3x +2 = 362

Combine lke terms...

6x + 2 = 362

Subtract 2 from both sides to start to isolate the variable...

6x = 360

Divide both sides by 6 to isolate x...

x = 60

But we're not done yet...

The length of the first side is 60 ft, the length of the second side is 2*60 which is 120 ft, and the length of the third side is 3*60 + 2 which is 182 ft.

Let's check...

Does 60 + 120 + 182 = 362?

362 = 362

Our answers are right

Hope this helps! Stay safe!

- Emily

A cylinder has a radius of 30.8 centimeters and height of 20.5 centimeters. Which measurement is closest to the lateral surface area of the cylinder in square centimeters

Answers

Final answer:

To find the lateral surface area of a cylinder with a radius of 30.8 cm and a height of 20.5 cm, use the formula 2πrh. The calculation gives a result of approximately 3981.86 square centimeters.

Explanation:

The question asks for the closest measurement to the lateral surface area of a cylinder with a radius of 30.8 centimeters and a height of 20.5 centimeters. To find the lateral surface area of the cylinder, we use the formula: Lateral Surface Area = 2πrh, where 'r' is the radius, and 'h' is the height of the cylinder. Substituting the given values,

we get Lateral Surface Area = 2 × 3.14 × 30.8 cm × 20.5 cm.

Calculating this, we find:

Lateral Surface Area = 3981.864 square centimeters. Therefore, the closest measurement to the lateral surface area of the cylinder is 3981.86 square centimeters.

A bag contains 10 marbles of the same size that are red, yellow, and orange. The probability of picking a red marble is 10%. The probability of picking a yellow marble is 60%. Determine the probability of picking an orange marble from the bag and then classify the probability of picking an orange marble as likely or not likely to occur.

Answers

Answer:

30% not likely

Step-by-step explanation:

We have 10 marbles

The probability must equal 100%

10% red

60% yellow

----------------

70 %

That leaves 30% for orange

Orange is 30%

This is less than 50% so it is not likely to occur

Answer:

30%

not likely

Step-by-step explanation:

P(orange) = 100 - 10 - 60

= 30%

Less likely or not likely

What is the vertex form of the equation

y= -x^2+10x-30

Answers

Answer:

The answer to your question is Vertex = (5 , -5)

Step-by-step explanation:

Data

Equation                y = - x² + 10x - 30

Process

1.- Add 30 units in both sides

                             y + 30 = -x² + 10x - 30 + 30

2.- Simplify

                             y + 30 = -x² + 10x

3.- Factor -1 in the right side

                             y + 30 = -(x² - 10x      )

4.- Complete the perfect square trinomial

                             y + 30 - 5²= -(x² - 10x + 5²)

5.- Simplify

                             y + 30 - 25 = -(x² - 10x + 25)

                             y + 5 = -(x - 5

6.- Find the vertex

                            Vertex = (5 , -5)

least common multiple of 4, 8 and 2

Answers

Answer:

2

Step-by-step explanation:

your welcome

Answer:

2:2,4,6,8,10,12,14,16

4:4,8,12,16

8:8,16

the LCM is 16

Mr.Hawkins gets two bonus payments every year this year his bonus payment was 1/4of his salary his second payment was 1/8 of his salary what is the fraction for his combined bonus payments?

Answers

Answer:

  3/8

Step-by-step explanation:

1/4 + 1/8 = 2/8 + 1/8 = 3/8

After you give the fractions a common denominator, you can add their numerators to find the numerator of the result.

Mr. Hawkins's combined bonus payments are 3/8 of his salary.

Sara joins a fruit of the month club. The entry cost is $25 and then she pays $18 per month. If she participates for 8 months, how much will she pay in all?

Answers

Answer:

$169

Step-by-step explanation:

Sara must pay the entry fee, and then a fee of 18$/month. if she is a member for 8 months the total paid must be

[tex]25 + 18*8 = 169[/tex]

Answer:

$169

Step-by-step explanation:

25+18m=$

m represents the months she participates for

25+18(8)=$

25+144=$

169=$

She pays $169 to be in a fruit club. Wow.


You borrow $10,000 to buy a carThe simple interest rate is 3%. You pay the loan oft after 6 years. What is the total amount you paid for the loan?

Answers

Answer:

Step-by-step explanation:

Amount loaned = $10,000

Interest rate = 3%

Duration = 6 years

10,000 / 100 x 3/1 × 6

= 300 × 6

= 1800 + 10,000

Total Amount to pay

= $11,800

Grace earns $5 each times she walks her neighbor's dog. She walks the dog 5 times in one week. Then she spends $7 on a book and $9 on a building set. Write an equation to represent how much money Grace has left, m.

Answers

Answer:

$5 (5) - ($7+$9)=m

$25 - $16 =m

Step-by-step explanation:

$5 (5) - (7+9)=m

$25 - 16 =m

The equation to represent how much money Grace has left is:

m = $25 - $7 - $9

m = $25 − $16

m = $9

How do we represent the event in the form of an equation?

Grace earns $5 for each dog walk.

She walks the dog 5 times in one week, so she earns 5 walks * $5/per walk = $25.

She spends $7 on a book and $9 on a building set, so she spends a total of $7 + $9 = $16.

To find out how much money Grace has left, m, we subtract her total spending from her earnings.

So, the equation to represent how much money Grace has left is:

m = $25 − $16

m = $9

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What is the initial value of the function represented by this graph? (5 points) Question 7 options: 1) 1 2) 5 3) 6 4)

Answers

Answer:

Initial value is at t = 0

Y-intercept is the initial value

Which ordered pair is a solution of the equation?
y - 4= 7(x – 6)
Choose 1 answer:
A. Only 5,4
B. Only 6,5
C both 5,4 and 6,5
D. Neither

Answers

It will be D. Neither, because when you plug in 5 for x and 4 for y, the left side will equal 0, while the right side equals 7(5-6) = 7(-1) = -7, which does not equal 0 on the left side. If you use 6 for x and 5 for y, the left side will be 1 (5-4) and the right side will equal 0, 7(6-6) = 7(0) = 0, which does not equal to 1

What does vertex in graphs mean?

Answers

Vertex typically means a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices. (Pronounced: "ver - tiss- ease"). A square for example has four vertices.

Solve the following quadratic equations using completing the square x2 – 8x – 34 = 0

Answers

Answer:

x=4± 5sqrt(2)

Step-by-step explanation:

x^2 – 8x – 34 = 0

To complete the square Add 34 to each side

x^2 -8x -34+34=0+ 34

Take the coefficient of x, and divide by 2

-8/2 =-4

Then square it and add it to each side

(-4)^2 =16

x^2 – 8x +16 = 34+16

x^2 – 8x +16 = 50

We replace the left side with (x + the coefficient of x/2)^2

(x -4)^2=50

Take the square root of each side

sqrt((x -4)^2)=±sqrt(50)

x-4 = ±sqrt(25*2)

x-4 = ±sqrt(25)*sqrt(2)

x-4 = ±5sqrt(2)

Add 4 to each side

x=4± 5sqrt(2)

Answer:

4 + 5sqrt(2), 4 - 5sqrt(2)

Step-by-step explanation:

x² - 8x - 34 = 0

x = [-(-8) +/- sqrt((-8)² - 4(1)(-34))]/2

x = (8 +/- sqrt200)/2

x = 4 +/- 5sqrt(2)

A radio antenna is kept perpendicular to the ground by three wires of equal length. The wires touch the ground at three points on a circle whose center is at the base of the antenna. If the wires touch the ground at (9,-19),(-21,-19), and(14,16), what are the coordinates of the base of the antenna?

Answers

Answer:

The coordinates of the base of the antenna is (-6. 1)

Step-by-step explanation:

Here  we are required to find the center of a circle given points on the circumference

The equation of  a circle is

(x - h)² + (y - k)² = r²

Where:

x and y are points on the circumference

h and k are coordinates of the center of the circle and

r = The radius of the circle

Since we have the values for the points on the circumference, we are left with three unknowns, which we can find with three equations as follows;

By plugging in the values for x and y at the respective points we get,

At (9, -19) → (9 - h)² + (-19 - k)² = r²...............(1)

At (-21, -19) → (-21 - h)² + (-19 - k)² = r².....,...(2)

At (14, 16 ) → (14 - h)² + (16 - k)² = r² ............(3)

Solving, we get  from (1)  (-19 - k)² = r² - (9 - h)²

Plugging in the value of (-19 - k)² in equation (2) we get

(-21 - h)² + r² - (9 - h)² = r²

So that (-21 - h)²  - (9 - h)² = r² -  r² = 0

and   (-21 - h)²  - (9 - h)² = 0 gives

60·h +360 = 0 or h = -6

Plugging in the value of h = -6 in equation (3) we get

(14 - (-6))² + (16 - k)² = r²

20² + (16 - k)² = r² .................(4)

similarly from equation (1) we get

(9 - (-6))² + (-19 - k)² = r²

15² + (-19 - k)² = r²  ................(5)

Subtracting equation (5) from (4) gives

20² - 15² +  (16 - k)² - (-19 - k)² = 0

Which gives

-70·k + 70 = 0

or k = 1

Therefore the coordinates of the base of the antenna = (-6. 1).

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