how to determine if we can apply the existence and uniquness theorem to guarantee that there is exactly one unique soltuion

the parameter and obtain the standard form of the rectangular equation would be: [tex]\frac{y-k}{r} = sin\theta.................(2)\\\\[/tex]

[tex]x=h+rcos\theta ,y=k+rsin\theta\\x-h=rcos\theta\\\frac{x-h}{r}=cos\theta...................(1)y=k+rsin\thetay-k=rsin\theta[/tex]

[tex]\frac{y-k}{r} = sin\theta.................(2)\\\\[/tex]

square and add both the equations

[tex]\frac{(x-h)^2}{(r^2)} + \frac{(y-k)^2}{(r^2)} = sin^2\s\theta + cos^2\s\theta\\\\\frac{(x-h)^{2}}{r^{2}}+\frac{(y-k)^{2}}{r^{2}}=1\\\\ the value of (sin^{2}\theta+cos^{2}\theta=1)\\\\(x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

The overall rectangular (or standard) form of the perplexing numbers is a + b I. We can change over complex numbers in rectangular form, by tracking down r = a 2 + b 2 and θ = tan − 1 ⁡.

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The walkway has a 656 square foot area.

Comparing a quantitative measurement with a recognized standard amount of some kind is the act of measurement. For instance, in the measurement 10 kg, kg is indeed the basic measure used to describe mass of a physical quantity, and 10 is the size of the physical quantity.

In order to determine the size of the walkway, we must first determine the size of the bigger rectangle that includes the yard and the walkway, from which we must then deduct the yard's area.

The dimensions of the bigger rectangle will be:

Length: 29ft + 2(4ft) = 37ft

Width: 45ft + 2(4ft) = 53ft

Hence, the larger rectangle's area is:

37ft x 53ft = 1961ft²

The yard's actual size is:

29ft x 45ft = 1305ft²

As a result, the distinction between the two sections is the size of the walkway:

1961ft² - 1305ft² = 656ft²

Hence, the walkway has a 656 square foot area.

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Answer:

Changes in light and dark.

Step-by-step explanation:

I also do K12 loll

Changes in light or dark is the environmental stimulus which is detected by flatworm's eyespots.

A sum total of all the living and non-living elements and their effects that influence human life.

Flatworm's eyespots detect changes in light or dark in the environment. They are not capable of detecting distinct shapes or a wide variety of colors.

The eyespots are simple sensory structures that are used to detect the presence or absence of light and dark, and to detect changes in light intensity.

They are primarily used to help the flatworm locate and respond to light, which can be important for activities such as finding food or avoiding predators.

Hence, changes in light or dark is the environmental stimulus which is detected by flatworm's eyespots.

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the speed of the bus in meters per second is 8.33 m/s. If a bus travels a distance of 1 kilometer in 2 minutes, we can use the formula for speed to calculate its speed in meters per second (m/s).

The formula for speed is:

Speed = Distance ÷ Time

Here, the distance is 1 kilometer, which is equal to 1000 meters (since 1 kilometer = 1000 meters), and the time is 2 minutes, which is equal to 120 seconds (since 1 minute = 60 seconds).

So, we can plug these values into the formula:

Speed = 1000 meters ÷ 120 seconds

Simplifying this expression, we get:

Speed = 8.33 meters per second (rounded to two decimal places)

Therefore, the speed of the bus in meters per second is 8.33 m/s.

To put this into context, it's important to understand that speed is the rate at which an object moves, while velocity is the rate at which it moves in a specific direction. So, in this case, we have only calculated the speed of the bus, not its velocity. However, knowing the speed of the bus can be useful for a variety of applications, such as determining how long it will take to travel a certain distance, or calculating the fuel efficiency of the vehicle

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Answer:

Please choose me please

Step-by-step explanation:

Answer:

The sample may be biased because the 50 people were selected at a local college baseball game, which could introduce selection bias. People attending a college baseball game may have different characteristics than the general population of the city, and therefore may not be representative of the population's opinions on the issue of building a new football stadium using tax funds. Additionally, the fact that they were selected at a baseball game may also introduce bias, as they may be more likely to be interested in sports and therefore more likely to support a tax-funded stadium. Overall, the sample may not be representative of the population's views, and therefore the conclusions drawn from the sample may not be generalizable to the entire population.

The equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1 (option D).

To derive the equation of a line, we need to use the point-slope formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Plugging in the given values, we have:

y - (-5) = -3(x - 2)

Simplifying this expression, we get:

y + 5 = -3x + 6

y = -3x + 1

Thus, the equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1.

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Complete Question:

Choose the equation below that represents the line passing through the point (2, - 5) with a slope of −3.

A.) y = −3x − 13

B.) y = −3x + 11

C.) y = −3x + 13

D.) y = −3x + 1

Answer:

The answer is y = -3x + 1

Answer:

The slope of the line passing through the points (1, -1) and (4, 8) is 3.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the following formula:

[tex]slope = (y2 - y1) / (x2 - x1)[/tex]

Here, the given points are (1, -1) and (4, 8). So,

[tex]slope = (8 - (-1)) / (4 - 1) = 9 / 3 = 3[/tex]

Therefore, the slope of the line passing through the points (1, -1) and (4, 8) is 3.

Using equations, we can find that he purchased 6 footballs.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example.

Here in the question,

Let the number of footballs purchased be f.

Let the number of basketballs purchased be b.

Cost of each football = $60.

Cost of each basketball = $30.

Total amount spent = $450

Now,

60f + 30b = 450

Given,

2b = f

⇒ b = f/2

Putting the value of b in the equation,

60f + 30(/2f) = 450

⇒ 60f + 15f = 450

⇒ 75f = 450

⇒ f = 6

Therefore, he purchased 6 footballs.

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Answer: The probability is approximately 15.74%.

Step-by-step explanation: The probability that a worker selected at random makes between $450 and $550 can be found by standardizing the distribution of weekly wages using the formula:

z = (x - μ) / σ

where x is the weekly wage, μ is the mean weekly wage, and σ is the standard deviation of weekly wages.

Then we can use a standard normal distribution table or calculator to find the probability that a worker selected at random makes between $450 and $550.

Using this formula, we get:

z1 = (450 - 400) / 50 = 1

z2 = (550 - 400) / 50 = 3

The probability that a worker selected at random makes between $450 and $550 is equal to the probability that a standard normal random variable Z is between 1 and 3. This can be found using a standard normal distribution table or calculator.

Using a standard normal distribution table, we find that P(1 < Z < 3) = 0.1574.

Therefore, the probability that a worker selected at random makes between $450 and $550 is approximately 15.74%.

Hope this helps, and have a great day!

x 2 + y 2 = 20

This is the form of a circle. Use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.

r = 2 √ 5

h = 0

k = 0

The center of the circle is found at ( h , k )

. Center: ( 0 , 0 )

These values represent the important values for graphing and analyzing a circle.

Center: ( 0 , 0 )

Radius: 2 √ 5

Therefore, the table showing the original points and their corresponding dilated points is:

Original Point     Dilated Point

(0,1)                  (0,1/2)

(4, -3)                (2, -3/2)

(-6,1)                 (-3,1/2)

I believe you might have meant "dilated point", which is a term commonly used in geometry. A dilated point is a point that has been enlarged or reduced in size with respect to a fixed center of dilation.

To dilate a point, you need to multiply its coordinates by a scale factor, which is a constant value greater than zero. If the scale factor is greater than one, the point will be enlarged, and if it is less than one, the point will be reduced in size. The fixed center of dilation is the point about which the dilated point is enlarged or reduced.

given by the question.

To apply the dilation rule of (1/2x, 1/2y) to a given point (x,y), we need to multiply the x-coordinate and y-coordinate of the original point by 1/2.

Using this rule, we can find the dilated points for the given set of points as follows:

For the point (0,1), we have:

1/2x = 1/2 * 0 = 0

1/2y = 1/2 * 1 = 1/2

So, the dilated point is (0, 1/2).

For the point (4, -3), we have:

1/2x = 1/2 * 4 = 2

1/2y = 1/2 * (-3) = -3/2

So, the dilated point is (2, -3/2).

For the point (-6,1), we have:

1/2x = 1/2 * (-6) = -3

1/2y = 1/2 * 1 = 1/2

So, the dilated point is (-3,1).

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The probability that the mean of a random sample of 52 pregnancies is less than or equal to 222 days is approximately 0.0005 (rounded to four decimal places).

Let's discuss it further below.

To solve the problem, we use the z-score formula, which is as follows:

z=(X−μ)/σX = sample mean = 222 days

μ = population mean = 226 days

σ = standard deviation of the population = 15 days

n = sample size = 52

To find the probability, we need to convert the sample mean to a z-score, which is calculated as follows:

z=(X−μ)/σ=(222−226)/(15/√52)=−4/2.096=−1.91

Now we need to find the probability that a random sample of 52 pregnancies has a mean gestation period of 222 days or less, which is equivalent to finding the probability that a z-score is less than or equal to −1.91.

Using a z-table or calculator, we find that the probability of a z-score being less than or equal to −1.91 is approximately 0.0005 (rounded to four decimal places).

Therefore, the answer is 0.0005.

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The sales price of the two shirt with 30%off on original price and 7% sales tax is equal to $22.47.

Original price of one shirt = $15

Number of shirts bought = 2

Sale discount = 30% off on original price

Sale price of one shirt = Original price - 30% of the original price

Substitute the value we get,

⇒Sale price of one shirt = 15 - (0.30)(15)

⇒Sale price of one shirt = $10.50

The cost of two shirts is equal to,

2 x $10.50 = $21.00

Sales tax = 7% of the total cost.

Substitute the value we have,

⇒Sales tax = 0.07 x $21.00

                   = $1.47

Total cost of two shirts = Cost of two shirts + Sales tax

⇒ Total cost of two shirts = $21.00 + $1.47

⇒ Total cost of two shirts = $22.47

Therefore, the total cost of two shirts at the sale price including the 7% sales tax is $22.47.

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The number of feet of fabric will the individual need to make 11 blankets is 79.2 feet

To find out how many feet of fabric the individual will need to make 11 blankets, we can use the unitary method.

We know that the individual used 7.2 feet of fabric to make one blanket. So, to find out how much fabric is needed to make 11 blankets, we can set up a proportion

7.2 feet of fabric is needed for 1 blanket

x feet of fabric is needed for 11 blankets

We can solve for x by cross-multiplying and then dividing

7.2 × 11 = x

x = 79.2 feet

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Therefore, since a movement is set to start at T minus 80, the move will be completed at T plus 10 seconds.

The amount of rotations a shape can undergo around its center before returning to its initial position is referred to as the order of rotation in mathematics and geometry. It is also referred to as a shape's circular symmetry. A circle, for instance, has an order of rotation of infinite because it can be rotated indefinitely around its center without changing how it appears. A cube has an order of rotation of four because it will remain the same in shape whether it is rotated 90, 180, 270, or 360 degrees around its center.

given

At T minus 80 seconds, or 80 seconds prior to liftoff, the move is slated to start.

We must multiply the duration of the maneuver by the beginning time to determine the time at which it will be finished.

The move is estimated to take 1 and a half minutes. Since there are 60 seconds in a minute, we can change this to seconds by multiplying it by 60:

1 and a half minutes is equal to 1.5 minutes, 1.5 minutes multiplied by 60 seconds is equal to 90 seconds.

The move lasts 90 seconds as a result.

We multiply the duration of the move (90 seconds) by the start time (T minus 80 seconds) to determine the time at which the maneuver will be finished:

The move will be finished in T minus 80 seconds plus 90 seconds.

By adding the integers, we can make this simpler:

When the move is finished, the time will be T minus 80 seconds + 90 seconds + T plus 10 seconds.

Therefore, since a movement is set to start at T minus 80, the move will be completed at T plus 10 seconds.

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The 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.

First, let's convert the number (1 .fi.)3000 into its decimal representation. This is done by dividing 3000 by 10 raised to the power of the number of digits following the decimal point, which in this case is 3. We get the answer 1000, or 1.000.
Now, we can look at the 100th digit to the right of the decimal point. This will be the 0th digit from the right of the decimal point, which is 0. Therefore, the 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.

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If the cycle time is 2 minutes per customer, 30 customers can be served per hour.

The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.

The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:

Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.

Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.

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The average rate of change of f(x) from x = -3 to x = 6 is 7.

What is meant by average?

The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.

To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.

For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:

[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]

The value of the function at [tex]x = 6[/tex] is:

[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]

The difference in the function values is:

[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]

The difference in the input values is:

6 - (-3) = 9

Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:

average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]

So, the average rate of change of f(x) from x = -3 to x = 6 is 7.

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The given equation of the circle is:

[tex] \rm \: x^2 + y^2 = 20[/tex]

We can write this equation in standard form by completing the square:

[tex] \rm x^2 + y^2 = 20[/tex]

[tex] \rm x^2 + y^2 - 20 = 0[/tex]

[tex] \rm (x^2 - 2x + 1) + (y^2 - 20) = 1[/tex]

[tex] \rm (x - 1)^2 + y^2 = 21[/tex]

Therefore, the center of the circle is (1, 0) and the radius is the square root of 21.

Answer:

Step-by-step explanation:

it is either Graph A or B pick one of them

Answer:

Graph D is correct

Step-by-step explanation:

if you choose a point, let's say 0,0 and plug in the values for x and y, you'll get

[tex]0 \leqslant - 2[/tex]

Since this equation isn't true, 0,0 can't be filled.

to choose between graphs c and d, you look at the line and because c is dotted, it means it isn't solution. because your sign is less than or equal to, the line has to be solid.

therefore, graph d is the correct answer

Answer:

Let the maximum number of operations the computer can perform per second be x.

According to the problem, the computer is running at 65% of the maximum, so it is performing 0.65x operations per second. We also know that it is performing 30 operations per second. So we can write the equation:

0.65x = 30

Solving for x, we get:

x = 30/0.65

x ≈ 46.1538

Rounding to the nearest whole number, we get:

x ≈ 46

Therefore, the maximum number of operations the computer can perform per second is 46, which is option 2.

Given how many coins are provided in the bag determines the chances for example of its a single nickel and a single quarter it'd be q50/n50 though if there's two nickels and one quarter there would be a n75/q25 chance.

There are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe

WHAT IS COMBINATION ?

Combination refers to a mathematical concept used to count the number of ways in which a specific number of objects can be selected from a larger set, without considering their order. In other words, it is a way to calculate the number of possible combinations that can be formed from a given set of objects, where the order in which the objects are chosen does not matter. Combinations are denoted by the symbol "nCr" or "C(n,r)" and can be calculated using the formula: nCr = n!/r!(n-r)!, where n represents the total number of objects, and r represents the number of objects being chosen.

To solve this problem, we can use the combination formula. The number of ways to select k items from a set of n items is given by:

C(n, k) = n! / (k! * (n - k)!)

where n! means n factorial (i.e. n multiplied by all the positive integers less than n).

In this case, we want to select 10 employees for the dayshift and 4 employees for the night shift, out of a total of 14 employees. So the number of ways to make this assignment is:

C(14, 10) * C(4, 4) = (14! / (10! * 4!)) * (4! / (4! * 0!))

Simplifying this expression, we get:

C(14, 10) * C(4, 4) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) * 1

C(14, 10) * C(4, 4) = 1001 * 1

C(14, 10) * C(4, 4) = 1001

So there are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe

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The length of the LN in the given rectangle is 33.

What is the intersection spot called?

The point of intersection is the location where two lines meet one another. If two straight lines are not parallel, they will eventually meet at some point. The meeting place of two straight lines is known as the point of intersection. The intersection location can be determined by simultaneously solving the equations for two straight lines that are passing.

In a rectangle, diagonals intersect at the right angle. The interesting point divides the lines into equal halves.

By solving the two equations, we can get the value of x.

LN = 4x-7

MO = 2x+13

Now, by equating two diagonal equations:

  4x-7 = 2x+13

⇒4x-2x = 13+7

⇒2x = 20

⇒ x = 10

The required is LN = 4x-7

                               = 4(10) - 7

                               = 40-7

                     ∴ LN  = 33

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If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.

This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.

The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.

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The complete question is:

Complete the interpretation for the p-value:

If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .

Answer:

To find the probability of the next customer ordering peanut butter cup, we need to determine the total number of ice cream cones and the number of cones that are peanut butter cup.

The total number of cones is:

4 + 5 + 2 + 3 + 2 = 16

The number of cones that are peanut butter cup is 2.

Therefore, the probability of the next customer ordering peanut butter cup is:

2/16 = 0.125

So, the probability of the next customer ordering peanut butter cup is 0.125 or 12.5%.

The sample proportion would be 0.5.we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.

To determine what sample proportion would yield a p-value of 0.05, we must first understand the formula for calculating a p-value. The formula for a p-value is p-value = 1 - [tex](1 - proportion)^n[/tex], where n is the sample size. By manipulating this equation, we can solve for the proportion when the p-value is equal to 0.05. We can isolate the proportion by taking the inverse of both sides of the equation, which yields: proportion = 1 - [tex](1 - 0.05)^(1/n)[/tex]. Since the sample size is 90, we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.

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There are 24 different ways that the participant can sort the four ice cream samples.

Since the participant is given 4 different ice cream samples, there are 4 ways in which they can place their first preference. Once they have chosen their favorite ice cream sample, there are 3 remaining options for their second preference. Similarly, there are 2 options for their third preference, and only one option for their least favorite ice cream sample. Here we have to use the principle of counting

Therefore, the number of ways the participant can sort the ice cream samples based on preference is

4 x 3 x 2 x 1 = 24

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The two cars are 10 miles apart, measured in a straight line.

We can use the Pythagorean theorem to find the distance between the two cars. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's imagine that the cars have traveled for some time, forming a right triangle where the distance between them is the hypotenuse. The northbound car has traveled 6 miles, which corresponds to the length of one of the legs of the triangle. The eastbound car has traveled 8 miles, which corresponds to the length of the other leg of the triangle. Therefore, the distance between the two cars is

distance = √(6² + 8²) = √(36 + 64) = √100 = 10 miles

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