Compute the length of the segment tangent from the origin to the circle that passes through the points $(3,4),$ $(6,8),$ and $(5,13).$

The horizon is about 1,027 miles away if a person is in the international space station about 240 miles above the surface of the earth.

As a general rule, the horizon is located 2.9 miles away from an observer on the Earth's surface, and it is because of the planet's curvature. If a person moves up in the sky, the horizon line will also move up because the person's line of sight is increasing in distance.

In other words, if a person moves to a higher altitude, they will be able to see farther. The calculation to determine the distance of the horizon is based on the following formula:
D = √[(2Rh) + h²]

D is the distance to the horizon

R is the radius of the earth

h is the height above sea level of the observer in meters.

The radius of the Earth is about 6,371 kilometers, and it can be converted to meters by multiplying it by 1,000. The altitude of the International Space Station (ISS) is approximately 408 kilometers above the Earth's surface or 240 miles.

Using this information, we can calculate the distance to the horizon.
D = √[(2 * 6,371,000) + (408,000)²]D = √[(12,742,000) + (166,464,000,000)]D = √[166,476,742,000]D ≈ 408,216 meters
≈ 1,338,381.8 feet ≈ 403.6 km ≈ 252 miles

Therefore, if a person is on the International Space Station about 240 miles above the Earth's surface, the horizon will be around 1,027 miles away.

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Answer:

Step-by-step explanation:

ok equation are like fraction but let me put it like this lets say x+y=7;x+2y=11 thats how you do eqution done.

The largest possible length of fencing is found as 30 feet.

Let the  width of the fencing be 'w'.

Let the  length of the fencing be 'L'.

Then,

L = 3w

The perimeter of the fencing be-

P = 2(l+w)

80 = 2(3w+w)

Put the value of L

80 = 2(4w)

80 = 8w

Simplifying.

80/8 = 8w/8

10 = w

Then, L = 3w = 3*10 = 30 feet.

Thus, the largest possible length of fencing is found as 30 feet.

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The complete question is-

Lance is building a rectangular fence for his chickens. He wants the length to be three times the width and he has 80 feet of fencing. What is the largest possible length? Write an equation and solve.

Answer:

hello! :) have a good day!

Exact Form:

x= 87/35

Decimal Form:

x= 2.48571428

Mixed Number Form:

x= 2 17/35

The change in height of the parasail = 1/100.

Height of defined as the measurement that is taken for an object which starts from its base to the topmost point. This is usually measured in meters.

From the question,

The height of the parasail above the water level= 3/100

The height of the parasail above the water level after 5 minutes= 1/50

The change in height of the parasail is determined by finding the difference between the two heights.

That is, = 3/100 - 1/50

= 0.03- 0.02 = 0.01

When changed to fraction is = 1/100

Therefore, the change in height after 5 minutes is = 1/100

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Answer:

y=mx+b

Step-by-step explanation:

subtract -3-(-1)=slope

put the slope where it says m and then add the x next to it

And for b its -3 or -1

Answer:

300 jumping jacks

Step-by-step explanation:

120 ÷ 2 = 60 jumping jacks per minute

60 × 5 = 300 jumping jacks

Sam can do 300 jumping jacks in 5 minutes.

Hope that helps.

Answer:

60

Step-by-step explanation:

120 / 2 = 60 (jumping jacks per minute)

60 * 5 = 300

Best of Luck!

A circle can be represented as an equation or on a graph

The equations of the circles are \(x^2 + y^2 = 36\) and \((x + 4)^2 + (y + 2)^2 = 16\)

The equation of a circle is represented as:

\((x - a)^2 + (y - b)^2 =r^2\)

Where:

Center = (a,b)

Radius = r

For circle A, we have the equation to be:

\((x - 0)^2 + (y - 0)^2 =6^2\)

\(x^2 + y^2 = 36\)

For circle B, we have the equation to be:

\((x + 4)^2 + (y + 2)^2 =4^2\)

\((x + 4)^2 + (y + 2)^2 = 16\)

Hence, the equations of the circles are \(x^2 + y^2 = 36\) and \((x + 4)^2 + (y + 2)^2 = 16\)

See attachment for the graphs

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Answer:

A. (green)
x2 + y2 = 36

B. (orange)
(x + 4)2 + (y + 2)2 = 16

Step-by-step explanation:

Have an AWESOME day
Love yaa
-NaomiTheGenius

The matrix representation of the linear transformation, which is the reflection in the line \(x_1 = x_2\) in \(R^2\), is given by \(\left[\begin{array}{ccc}-1&0\\0&-1\\\end{array}\right]\)

To find the matrix representation of the reflection in the line \(x_1 = x_2\), we need to determine how the transformation affects the standard basis vectors of \(R^2\), i.e., the vectors [1 0] and [0 1].

When the transformation reflects the vector [1 0] in the line \(x_1 = x_2\), it maps it to the vector [-1 0].

Similarly, when it reflects the vector [0 1], it maps it to the vector [0 -1].

The matrix representation of the transformation is obtained by arranging the images of the standard basis vectors as columns of a matrix.

In this case, we have [-1 0] as the first column and [0 -1] as the second column.

Thus, the matrix representation of the reflection in the line x1 = x2 in \(R^2\) is given by the 2x2 matrix:

\(\left[\begin{array}{ccc}-1&0\\0&-1\\\end{array}\right]\)

This matrix can be used to apply the transformation to any vector in \(R^2\) by matrix multiplication.

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( 0 , -1 , 5) point lies on xyz plane .

The xy-plane is the plane that houses the x- and y-axes, while the yz-plane and the xz-plane house the y- and z-axes, respectively. Space is divided into eight sections known as octants by these three coordinate planes. The positive axes determine the first octant, which is in the front.

To be expressed, everything needs a perspective and a point of view. The three spatial dimensions are represented by the X, Y, and Z coordinates. These stand for length, width, and depth. We employ the same X, Y, and Z denotations when referring to machines, but we assign them different values or meanings. Even more intriguingly, there are no clear laws defining the meaning, which makes it difficult to converse on these levels.

this given point lies on xyz plane bcz the point itself shows coordinates which is only possible in xyz plane .

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Step-by-step explanation:

The marked price of an article is 25% above the SP and the CP is 20% below the selling price. What is the rate of discount and the profit percentage?

Let C, M & S denote cost-price, marked-price & sell-price respectively of the article.

Hence from above data we get following relations,

M = (1 + 25/100)*S = 1.25*S ….. (1a)

C = (1 - 20/100)*S = 0.80*S ….. (1b)

From (1a) we get,

S = (100/125)*M = (4/5)*M

or S = (1 - 1/5)*M = (1 - 20/100)*M ….. (2a)

From (1b) we get,

S = (100/80)*C = (5/4)*M

or S = (1 + 1/4)*C = (1 + 25/100)*C ….. (2b)

Therefore

It is evident from (2a) that

the discount percentage = 20% [Ans]

It is evident from (2b) that

the profit percentage = 25% [Ans]

Answer: 171.19

V=lwh

w=3.65

l=14

h=7-3.65

=3.35

V=171.185 ≈171.19

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Firstly, create an equation or formula

- because they are congurent, IN = AT, so:

2x+10 = 26 (minus 10 from both sides)

2x = 16 (divide both sides by 2)

x = 8

Sub into the formula:

2 x 8 + 10 = 26

26 = 26

Answer:

mean = 8

Step-by-step explanation:

assuming you mean ∑ x = 40

then

mean = ∑ x ÷ n = 40 ÷ 5 = 8

Answer:

A. -30+4√21/55

Step-by-step explanation:

edge

The exact value of sin(v + w) for the given values of sin (v) and cos (w) is 0.37.

The sine of an angle is the ratio of the height to the hypotenuse of the given triangle.

The cosine of the angle is the ratio of the base to the hypotenuse of the triangle.

Given, sin (v) = - 3/5, cos (w) = 10/11

Therefore, cos (v) = √[1 - (- 3/5)²] = √[1 - 9/25] =  √(16/25) = - 4/5 (As, 'v' is an angle in Quadrant III)

sin (w) = √[1 - (10/11)²] = √[1 - 100/121] =  √(21/100) = - (√21)/10 (As, 'w' is an angle in Quadrant IV)

Now, sin(v + w)

= sin (v) cos (w) + cos (v)sin (w)

= (- 3/5)(10/11) + (- 4/5)(- √21)/10

= -6/11 + (2√21)/10

= - 0.55 + 0.92

= 0.37

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Polynomials are closed under the operation of addition, subtraction, and multiplication only. Here's why:

1. Addition: (Closed)

Reason: Say we have two polynomials: (x⁴ + 2x³ - 4) and (3x³ - 2x² + 6x). If we add these two polynomials, (x⁴ + 2x³ - 4) + (3x³ - 2x² + 6x), it will result to x⁴ + 5x³ - 2x² + 6x - 4 which is also a polynomial.

When adding polynomials, the variables and the exponents don't change. This guarantees that the sum of these variables with exponents will always be a polynomial.

2. Subtraction: (Closed)

Reason: Say we have two polynomials: (x⁴ + 2x³ - 4) and (3x³ - 2x² + 6x). If we subtract these two polynomials, (x⁴ + 2x³ - 4) - (3x³ - 2x² + 6x), it will result to x⁴ - x³ + 2x² - 6x - 4 which is also a polynomial.

When subtracting polynomials, the variables, and the exponents don't change. This guarantees that the difference of these variables with exponents will always be a polynomial.

3. Multiplication: (Closed)

Reason: Say we have two polynomials (x + 2) and (x - 4). If we multiply these two polynomials, (x + 2)(x - 4), it will result in x² - 2x - 8, which is also a polynomial.

When multiplying polynomials, the variables do not change but the exponents will be added to each other. In this case, we can guarantee that the new exponents will be positive whole numbers still and this guarantees that the answer will be a polynomial.

4. Division: (Not closed)

Reason: When dividing polynomials, exponents are being subtracted from each other, therefore, we might have a result of a negative exponent. Negative exponents are not allowed in a polynomial. Example, say we have two polynomials (x²) and (x⁴), if we divide (x²) by (x⁴), the resulting value would be:

The resulting value is x to the power of negative 2, and is not a polynomial.

The approximate distance around half of the circle is 44/7 meters. The total amount of fencing Helen needs is 212/7 meters (approx 30.29 meters).

The given figure shows the rectangular section of the garden with a semicircle. We need to find out the perimeter around the three sides of the rectangular section of the garden, the approximate distance around half of the circle and the total amount of fencing Helen needs.

The perimeter of the rectangular garden: We know that the perimeter of the rectangle = 2(Length + Width)Given, Length = 8 meters width = 4 meters.

Substitute these values in the formula:

Perimeter of rectangle = 2(8 + 4)Perimeter of rectangle = 24 meters Therefore, the perimeter around the three sides of the rectangular section of the garden is 24 meters.

Approximate distance around half of the circle:

We know that the circumference of the semicircle = 1/2(2πr)

Given, radius = 4 metersπ = 22/7

Substitute these values in the formula: Circumference of semicircle = 1/2(2×22/7×4)

Circumference of semicircle = 44/7 meters

Therefore, the approximate distance around half of the circle is 44/7 meters.

The total amount of fencing Helen needs:

The total amount of fencing Helen needs = Perimeter of a rectangle + Circumference of a semicircle.

Total amount of fencing Helen needs = 24 + 44/7Total amount of fencing Helen needs = 168/7 + 44/7

The total amount of fencing Helen needs = is 212/7 meters

Therefore, the total amount of fencing Helen needs is 212/7 meters (approx 30.29 meters).

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ANSWER. My answer might be wrong also.

Answer:

The answer is below

Step-by-step explanation:

We need the images corresponding to the question, I have researched and found them, I will leave them attached in the question:

Now, in the case under monopoly, the profit maximization amount will be 51.

The monopolist is a price maker. Therefore, he will determine the amount of production that will maximize revenue. Furthermore, the monopolist is the one who faces a downward sloping demand curve because he can sell more if the price falls.

Now, the profit-maximizing price and output is where the marginal revenue equals the marginal cost, then it is extended to the market demand curve to determine what market price corresponds to that quantity.

Under perfect competition, the profit maximization amount is 75. In the long run, a competitive firm is in equilibrium when MR = MC = AC. It will produce that output where LMC = LAC.

We find that the proportion of her laps that fall between 127 and 130 seconds is about 0.139. Any lap time under 135.25 seconds would be considered one of the fastest 2% of her laps. The middle 70% of her laps are between 119 and 131 seconds.

To answer your questions, we first need to have some context on what we're dealing with. You mentioned "her laps," so I assume we're talking about a person who is running or swimming laps. We also need to know the distribution of her lap times (i.e., are they normally distributed, skewed, etc.) in order to answer these questions accurately. For now, let's assume that her lap times are normally distributed.
To find the proportion of her laps that are completed between 127 and 130 seconds, we need to calculate the area under the normal distribution curve between those two values. We can do this using a calculator or a statistical software program, but we need to know the mean and standard deviation of her lap times first.

Let's say the mean is 125 seconds and the standard deviation is 5 seconds. Using a standard normal distribution table or calculator, we find that the proportion of her laps that fall between 127 and 130 seconds is about 0.139.
To find the fastest 2% of laps, we need to look at the upper tail of the distribution. Again, we need to know the mean and standard deviation of her lap times to do this accurately. Let's say the mean is still 125 seconds and the standard deviation is 5 seconds. Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 98th percentile (i.e., the fastest 2% of laps) is about 2.05. We can then use the formula z = (x - mu) / sigma to find that x = z * sigma + mu, where x is the lap time we're looking for. Plugging in the numbers, we get x = 2.05 * 5 + 125 = 135.25 seconds.

Therefore, any lap time under 135.25 seconds would be considered one of the fastest 2% of her laps.
Finally, to find the middle 70% of her laps, we need to look at the area under the normal distribution curve between two values, just like in part However, we need to find the values that correspond to the 15th and 85th percentiles, since those are the cutoffs for the middle 70%. Using the same mean and standard deviation as before, we can use a standard normal distribution table or calculator to find that the z-scores corresponding to the 15th and 85th percentiles are -1.04 and 1.04, respectively.

We can find that the lap times corresponding to those z-scores are 119 seconds and 131 seconds, respectively. Therefore, the middle 70% of her laps are between 119 and 131 seconds.

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Answer:

1. ?

2. d

3. g

4. f

5. k

6. ?

7. j

8. l

9. h

10. b

11. ?

12.?

The first quartile of the given data set would be 15 which is The middle of the numbers from the beginning up.

When data points are organized in ascending order, the first quartile, or lower quartile, (Q1), is the value at which 25% of them are located.

The given data set is:

11,12,15,16,17,19,22,24,29,33,38

Since the number of elements in the data set is 11. As a result, the data are divided into two equal parts by the sixth term. The median of the data is 19.

The middle of the numbers from the beginning up to and including the first middle value: 11,12,15,16,17.

The middle value is 15.

Therefore, the first quartile of this data set would be 15.

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Answer:

-56 or "p minus 56"  (negative)

Step-by-step explanation:

If you lose points, your points will decrease because it's taking away your points. So, you lost 56 points.  

Answer:

I think A is the answer

hope this helps

have a good day :)

Step-by-step explanation:

Note that the proof that cot a= 1- cot b cot c is given as follows;

A math proof is a logical argument that uses mathematical reasoning and evidence to support a mathematical statement or theorem.

From the given information, we know that:

A + B + C = 180 ... (1)

sin A = sin B sin C ... (2)

We need to prove that:

cot A = 1 - cot B cot C

We can start by using the identity:

cot x = 1/tan x

So, we can rewrite the above equation as:

1/tan A = 1 - (1/tan B) (1/tan C)

Multiplying both sides by tan A, we get:

1 = tan A - (tan B)(tan C)/(tan A)

Using the identity:

tan (x+y) = (tan x + tan y)/(1 - tan x tan y)

We can write:

tan (A + B + C) = tan 180

Since tan 180 is undefined, we know that:

tan (A + B + C) = tan 0

So, we get:

tan A + tan B + tan C - tan A tan B tan C = 0

Since A + B + C = 180, we can rewrite the above equation using (1) and (2) as:

sin A/cos A + sin B/cos B + sin C/cos C - sin B sin C/sin A = 0

Multiplying both sides by cos A cos B cos C, we get:

sin B cos C cos A + sin C cos A cos B + sin A cos B cos C - sin B sin C cos A = 0

Rearranging, we get:

sin A cos B cos C = sin B cos A cos C + sin C cos A cos B - sin B sin C cos A

Dividing both sides by sin A cos B cos C, we get:

1 = cot A - cot B cot C + cot A cot B cot C

Simplifying, we get:

cot A = 1 - cot B cot C

Hence, the proof is complete.

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-3^3 = -27

Step-by-step explanation:

Thats because -3^3 is (-3×3×3) not (-3×-3×-3) which we are multiplying a the constant not the the powers

Jamie is right because when you cube a number, you multiply it by itself three times. And we know that when 3 negative numbers are multiplied are product will be negative.

The probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

Given that Edward works as a waiter, where his monthly tip income is normally distributed with a mean of $2,000 and a standard deviation of $350.

The z score formula is given by;`z = (x - μ) / σ`

Where; x is the raw scoreμ the mean of the populationσ is the standard deviation of the population.

The probability that Edward’s monthly tip income exceeds $2,350 is to be found.`z = (x - μ) / σ``z = (2350 - 2000) / 350``z = 1`

The value of z is 1.

To find the area in the right tail, use the standard normal distribution table.

The table value for z = 1.0 is 0.8413.

Therefore, the probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

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