If 2a + 3b represents the perimeter of a rectangle and a - 2b represents its width, the
length is…

The correct statement is option B) Aircraft B is closer to the control tower.

In the coordinate plane, we use two numbers to locate a point. The first number represents the point's horizontal position, and the second number represents its vertical position.

To find the distance between two points in the coordinate plane, we use the distance formula, which is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and d is the distance between them.

Using the coordinates given in the problem, we can find the distance between the air traffic control tower and each aircraft. For Aircraft A, which is located at 4(39,52), the distance from the control tower is:

dA = √((39-0)² + (52-0)²) * 4

dA = √(39² + 52²) * 4

dA ≈ 332.12

For Aircraft B, which is located at B(25,60), the distance from the control tower is:

dB = √((25-0)² + (60-0)²)

dB = √(25² + 60²)

dB ≈ 64.80

As we can see, the distance from the control tower to Aircraft A is much greater than the distance to Aircraft B. Therefore, the correct answer is option B) Aircraft B is closer to the control tower.

Option C is not correct because the distances are not the same, and option D is not correct because there is no information in the problem to suggest that the triangle is equilateral.

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Complete Question:

16. MULTIPLE CHOICE An air traffic control tower is located at (0,0) on a coordinate plane. Aircraft 4 is located at 4(39,52) and aircraft B. is located at B(25,60). What statement is true about this situation?

A) Aircraft A is closer to the control tower.

B) Aircraft B is closer to the control tower.

c) Both aircraft are the same distance from the control tower.

D AOAB is an equilateral triangle.

Answer:

125,000

Step-by-step explanation:

\( {5}^{5} \)

is the answer.

In this case, The critical numbers are x = 1.

To find the critical numbers of g(y) = (y-2)/(y^2-2y+4), we first find the derivative g'(y) and then set it equal to zero or find where it's undefined.

g'(y) = (2y-2)/((y^2-2y+4)^2).

The critical numbers are y = 1. 2.

For f(x) = x^(-2)ln(x), you probably meant f(x) = x^(-2)ln(x).

In this case, find the derivative f'(x) and set it equal to zero or find where it's undefined.

f'(x) = -2x^(-3)ln(x) + x^(-2)(1/x).

The critical numbers are x = 1.

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Answer:

q = - 5 , q = \(\frac{7}{5}\)

Step-by-step explanation:

5q² + 18q = 35 ( subtract 35 from both sides )

5q² + 18q - 35 = 0 ← in standard form

consider the factors of the product of the coefficient of the q² term and the constant term which sum to give the coefficient of the q- term

product = 5 × - 35 = - 175 and sum = + 18

the factors are + 25 and - 7

use these factors to split the q- term

5q² + 25q - 7q - 35 = 0 ( factor the first/second and third/fourth terms )

5q(q + 5) - 7(q + 5) = 0 ← factor out (q + 5) from each term

(q + 5)(5q - 7) = 0 ← in factored form

equate each factor to zero and solve for q

q + 5 = 0 ( subtract 5 from both sides )

q = - 5

5q - 7 = 0 ( add 7 to both sides )

5q = 7 ( divide both sides by 5 )

q = \(\frac{7}{5}\)

solutions are q = - 5 , q = \(\frac{7}{5}\)

• so we know the final number is 6 so lets look at the rest of the question:

• Let unknown number = y

• so ( y-2 ), so twice the difference of a number 2 is 6 will be expressed as follows :

2(y-2) = 6

Answer: Look in the attachment:

Step-by-step explanation: If it was random sampling, it would all be done randomly, barley without doing anything, and NOT doing anything particular, the 4 that are circled (in the attachment) are the ones that I am talking about; they ARE NOT examples of random sampling. If you look at the attachment, you might understand a little more :P

Answer:

B cuz i said so

Step-by-step explanation:

Answer:

\(\angle F =\bold{88^\circ}\)

Step-by-step explanation:

Given a \(\triangle FGH\) with the following angles:

\(\text{m}\angle F = (6x-14)^{\circ}\)

\(\text{m}\angle G = (4x-8)^{\circ}\)

\(\text{m}\angle H = (x+15)^{\circ}\)

To find:

\(\text{m}\angle F\) = ?

Solution:

Here, we can simply use the angle sum property of a triangle to find the value of \(\text{m}\angle F\).

As per the angle sum property of a triangle, the sum of all the interior angles a triangle is equal to \(180^\circ\).

\(\angle F + \angle G + \angle H = 180^\circ\)

Putting all the given values in the above equation, we get:

\((6x-14)^{\circ} + (4x-8)^{\circ} + (x+15)^{\circ} = 180^\circ\\\Rightarrow 11x-7=180^\circ\\\Rightarrow 11x=180+7\\\Rightarrow 11x=187\\\Rightarrow x = \bold{17}\)

Putting the value of \(x\) in \(\angle F\)

\(\text{m}\angle F = (6x-14)^\circ\\\Rightarrow \text{m}\angle F = (6\times 17-14)^\circ\\\Rightarrow \text{m}\angle F = \bold{88^\circ}\)

Answer:

(a) To find the missing angle, we would do inverse tan.

\(angle =tan^{-1}\frac{opp}{adj}\)

\(angle = tan^{-1}\frac{17}{21}\)

angle= 39.0 degrees or 0.7 radians

(b) To find the missing angle, we would do inverse sin.

\(angle= sin^{-1}\frac{opp}{hyp}\)

\(angle= sin^{-1}\frac{12.7}{22.1}\)

angle= 35.1 degrees or 0.6 radians

Since we are looking for the value of f(7), we need to find the corresponding output value when the input is 7. From the given function, we see that input 7 corresponds to output 2. f(7) = 2.

To determine the value of f(7), we need to look at the given function f and substitute 7 for the independent variable.

The function f is defined by the ordered pairs (7,2), (9,7), (4,9), and (3,4). The first value in each ordered pair represents the input, while the second value represents the output.

In summary, when we substitute 7 for the independent variable in the given function f = (7,2), (9,7), (4,9), (3,4), we find that f(7) = 2.

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If Corey buys 27 inches of trim for a craft project, Corey bought 3/4 of a yard of trim for the craft project.

To determine what fraction of a yard Regina buys, we need to know how many inches are in a yard. There are 36 inches in a yard.

To convert 27 inches to yards, we need to divide by 36:

27 ÷ 36 = 0.75 yards

So Corey bought 0.75 yards of trim for the craft project.

To find the fraction of a yard, we need to express 0.75 as a fraction with a denominator of 1:

0.75 = 75/100 = 3/4

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Complete question is:

Corey buys 27 inches of trim for a craft project. What fraction of a yard does Regina buy?

Balance of trade is the difference that is between the value of a country's exports and the value of its imports.

Your information is incomplete. Therefore, an overview will be given. The balance of trade or net exports, is the difference between the monetary value of a nation's exports and imports over a period.

The balance of Trade formula = Country's Exports – Country's Imports.

For example, suppose the USA imported $1.8 trillion but exported $1.2 trillion to other countries, then the USA had a trade balance of -$600 billion.

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Answer:

The correct answer is A. $6,221,000,000

Step-by-step explanation:

just took the test

Answer:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love u this is irrelevent but idrc lol

Step-by-step explanation:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love u this is irrelevent but idrc lol

The series is absolutely convergent.

To determine if the series is absolutely convergent, conditionally convergent, or divergent, we first analyze the absolute value of the series. We consider the series Σ|sin(8n)/6n| from n=1 to infinity. Using the comparison test

since |sin(8n)| ≤ 1, the series is bounded by Σ|1/6n| which is a convergent p-series with p>1 (p=2 in this case).

Since the series Σ|sin(8n)/6n| converges, the original series Σsin(8n)/6n is absolutely convergent. Absolute convergence implies convergence,

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The series sin(8n)/(6n) is divergent (by comparison with the harmonic series), the original series is not convergent.

To determine the convergence of the given series, we need to analyze it using the given terms. The series is:

Σ(sin(8n) / 6n) from n = 1 to infinity.

First, let's check for absolute convergence by taking the absolute value of the series terms: Lim m as n approaches infinity of |(sin(8(n+1))/(6(n+1))) / (sin(8n)/(6n))|

= lim as n approaches infinity of |(sin(8(n+1))/(6(n+1))) * (6n/sin(8n))|

= lim as n approaches infinity of |sin(8(n+1))/sin(8n)|
Σ|sin(8n) / 6n| from n = 1 to infinity.

Since |sin(8n)| is bounded between 0 and 1, we have:

Σ|sin(8n) / 6n| ≤ Σ(1 / 6n) from n = 1 to infinity.

Now, the series Σ(1 / 6n) is a geometric series with a common ratio of 1/6, which is less than 1. Therefore, this geometric series is convergent. By the comparison test, since the original series has terms that are less than or equal to the terms in a convergent series, the original series must be convergent.

In summary, the given series Σ(sin(8n) / 6n) from n = 1 to infinity is convergent.

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======================================================

Explanation:

This sequence is arithmetic

The first term is a = -9

The common difference is d = 6 since we're adding 6 to each term to get the next one (eg: -3+6 = 3 or 3+6 = 9 or 9+6 = 15)

Plug those values into the arithmetic nth term formula below

an = a + d*(n-1)

an = -9 + 6*(n-1)

an = -9 + 6n-6

an = 6n - 15

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

As a check, let's plug in something like n = 1

an = 6n - 15

a1 = 6*1 - 15

a1 = 6 - 15

a1 = -9

We see that the 1st term is -9, which matches the sequence given

Now let's plug in n = 2

an = 6n - 15

a2 = 6*2 - 15

a2 = 12 - 15

a2 = -3

The 2nd term is -3. This also matches.

I'll let you check the other values of n to confirm the answer.

By representing 48 icons for Monday, Tuesday, and Wednesday, we will have completed the pictogram according to the given information.

To complete the pictogram, we need to represent the number of wheels sold on Monday, Tuesday, and Wednesday. The total number of wheels sold on these three days is 48.

We can represent this by drawing 48 icons or symbols on the pictogram.

Additionally, we know that 18 wheels were sold on Thursday and 22 wheels were sold on Friday. We do not need to represent these numbers on the pictogram, as they are not part of the question.

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To complete the pictogram:
- Draw x circles for Monday
- Draw 48 minus x circles for Tuesday
- Draw 48 minus x minus (48 minus x) circles for Wednesday
- Draw 18 circles for Thursday
- Draw 22 circles for Friday.

The incomplete pictogram shows information about the number of wheels sold by a shop on Monday, Tuesday, and Wednesday. The total number of wheels sold on these three days is 48. On Thursday, 18 wheels were sold, and on Friday, 22 wheels were sold.

To complete the pictogram, we need to represent the number of wheels sold on each day. Since the total for Monday, Tuesday, and Wednesday is 48, we need to divide this total into the three days. Let's say x represents the number of wheels sold on Monday. Then, the number of wheels sold on Tuesday would be 48 minus x. Similarly, the number of wheels sold on Wednesday would be 48 minus x minus the number of wheels sold on Tuesday.

Now, let's consider Thursday and Friday. We can represent the number of wheels sold on Thursday as 18 and the number of wheels sold on Friday as 22.

To complete the pictogram, we can use symbols or shapes to represent the number of wheels sold on each day. For example, we can use a circle to represent each wheel sold. We can draw x circles for Monday, 48 minus x circles for Tuesday, and 48 minus x minus (48 minus x) circles for Wednesday. Then, we can draw 18 circles for Thursday and 22 circles for Friday.

(Note: The exact shape and symbol used for the pictogram may vary, as long as it represents the correct number of wheels sold on each day.)

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The parameter is the percentage of coworkers who use the company's healthcare.

In statistics, the parameter is a numeric measurement that defines the characteristics of the population. It is generally denoted with Greek letters. In the provided scenario,

Ralph wants to estimate the percentage of coworkers that use the company's healthcare. He asks a randomly selected group of 200 coworkers whether or not they use the company's healthcare. Here, the parameter is the percentage of coworkers who use the company's healthcare.

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The equation of the line that passes through the point (-6,3) and has a slope of -4/3 is y=(-4/3)x-5.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is constant.

Given the slope of the line is -4/3, also, the line passes through the point (-6,3). Therefore, when the values are substituted in the general equation of a line to get the value of the constant, we will get,

y = mx + c

3 = (-4/3)(-6)+c

3 = 8 + c

c = -5

Thus, the equation can be written as y=(-4/3)x-5.

Hence, the equation of the line that passes through the point (-6,3) and has a slope of -4/3 is y=(-4/3)x-5.

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Answer:

Step-by-step explanation:

it does'nt matter because we don't know for sure

Answer:

24,024 different ways

Step-by-step explanation:

There are 9 boys and 13 girls competing for the medals. The number of ways to choose 3 boys out of 9 is C(9,3) = 84. The number of ways to choose 3 girls out of 13 is C(13,3) = 286. The total number of ways to choose 6 medals is the product of these two numbers: 84 * 286 = 24024.

According to the given statement the option B and C are correct:

b) unpaired t-test

c) one-sample t-test

We will apply an unpaired test in this situation because both populations are independent and unrelated to one another, making it impossible to pair the data from the two populations.

Consider the statement, "The mean from population A is bigger than the mean from population B," for example. This suggests that we'll utilize a single-tailed, unpaired test. Therefore, option d and b may be the best pairing.

To ascertain whether an unknown population mean differs from a given value, the one-sample t-test is a statistical hypothesis test.

The t-value is calculated using your sample data from the two groups and the 2-sample t-test. The procedure is quite comparable to the 1-sample t-test, and the signal-to-noise ratio can still be compared. The 2-sample t-test necessitates independent groups for every sample, unlike the paired t-test.

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The complete question you are looking for is:

In order to test if the mean from Population A is greater than the mean from Population B what kind of t-test would you use? (can be any combination of answers)

a) two-tailed t-test

b) unpaired t-test

c) one-sample t-test

d) one-tailed t-test

e) paired t-test

Answer:

1564

Step-by-step explanation:

1564

6/9384

-6

_____

33

-30

____

38

- 36

______

24

-24

__________

0

Answer:

1564

Step-by-step explanation:

attached........

Answer:

The Area of the square base is 114 In .2

The Area of each triangle face is 66 in .2

Gabriel will need 408 in .2 of paint

Answer:

Step-by-step explanation:

The area of the square base is 144 in.2.

The area of each triangular face is 66 in2.

Gabriel will need 408 in2. of paint.

\(f(x) = \frac{1}{9}x + 2 \\ \)

\(y = \frac{1}{9}x + 2 \\ \)

Subtract the sides of the equation minus 2

\(y - 2 = \frac{1}{9}x \\ \)

Multiply the sides of the equation by 9

\(9(y - 2) = x\)

\(9y - 18 = x\)

So ;

\( {f}^{ - 1}(x) = 9x - 18 \)

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

The surface area of the cone is 450π in². Therefore, the answer is option B.

The surface area of a cone can be represented as follows:

surface area of a cone = πr(r + l)

where

Therefore,

r = 9 inches

l = 41 inches

Hence,

surface area of a cone = π × 9(9 + 41)

surface area of a cone = 9π(50)

Therefore,

surface area of a cone = 450π inches²

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The equation given is siny = xsin(a + y). To prove that dxdy = sinasin2(a + y), we must first take the derivative of both sides of the equation.

Taking the derivative of the left side of the equation yields:

d/dy[siny] = d/dy[xsin(a + y)]

We can simplify the right side by using the chain rule, which states that if f is a function of g, then df/dx = df/dg * dg/dx. Applying this rule to the right side of the equation yields:

d/dy[siny] = d/dy[xsin(a + y)] = x * d/dy[sin(a + y)]

To evaluate the derivative of the right side of the equation, we must use the trigonometric identity that states
sin(A + B) = sinAcosB + cosAsinB. Applying this identity to the right side of the equation yields:

d/dy[siny] = x * [cos(a + y) d/dy[a + y] + sin(a + y) d/dy[a + y]]

Since a and y are both constants, their derivatives are both 0, leaving us with:

d/dy[siny] = x * sin(a + y) * d/dy[a + y]

Now that we have taken the derivative of both sides of the equation, we can now set them equal to each other, yielding:

d/dy[siny] = x * sin(a + y) * d/dy[a + y] = sinasin2(a + y)

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