Convert the polar equation to rectangular form [tex]r = 2 cos theta + 2 sin theta[/tex]


A. [tex](x-1)^2-(y-1)^2=2[/tex]

B. [tex](x+1)^2-(y+1)^2=2[/tex]

C. [tex](x-2)^2-(y-2)^2=1[/tex]

D. [tex](x+2)^2-(y+2)^2=1[/tex]

The expressions that are equivalent to 4√5 is

A) 2√20

C) [tex]3\sqrt5+\sqrt5[/tex]

D) [tex]4\times 5^{1/2}[/tex]

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is [tex]4\sqrt5[/tex].

Now simplifying the given option expressions then,

A) [tex]2\sqrt{20}[/tex] = [tex]2\sqrt{4\times5}[/tex]

= [tex]2\times2\sqrt{5}[/tex]

= [tex]4\sqrt5[/tex]

B) [tex]6^{1/2}-5^{1/2}[/tex]

[tex]= \sqrt6-\sqrt5[/tex]

C) [tex]3\sqrt5+\sqrt5[/tex]

= [tex]4\sqrt5[/tex]

D) [tex]4\times 5^{1/2}[/tex]

[tex]= 4\sqrt5[/tex]

E) [tex]2\sqrt{10}[/tex]

F) [tex]3\times5^{1/2}[/tex]

[tex]=3\sqrt5[/tex]

Hence  the expressions that are equivalent to 4√5 is

A) 2√20

C) [tex]3\sqrt5+\sqrt5[/tex]

D) [tex]4\times 5^{1/2}[/tex]

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Accοrding tο the ratiοs, there are 108 dandeliοns in the garden.

A ratiο is a cοmparisοn οf twο quantities οr values, οften expressed as a fractiοn. Ratiοs can be used tο express the relatiοnship between twο οr mοre quantities.

We can use the ratiο οf dandeliοns tο peοnies tο find the number οf dandeliοns when we knοw the number οf peοnies.

The ratiο οf dandeliοns tο peοnies is 12 tο 5, which means that fοr every 12 dandeliοns, there are 5 peοnies.

We knοw that there are 45 peοnies in the garden, sο we can set up a prοpοrtiοn tο find the number οf dandeliοns:

12/5 = x/45

Tο sοlve fοr x, we can crοss-multiply and simplify:

12*45 = 5x

540 = 5x

x = 108

Therefοre, there are 108 dandeliοns in the garden.

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The probability of tossing two dice and showing at least a 4 or the sum of dice is precisely 7 is 5/12 or approximately 0.417.

To find the probability of tossing two dice and showing at least a 4 or the sum of dice is precisely 7, we need to add the probabilities of these two events happening.

The probability of rolling at least a 4 on one die is 3/6, or 1/2 because there are three ways to roll a number greater than or equal to 4 (4, 5, or 6) out of six possible outcomes. The probability of rolling at least a 4 on both dice is the product of the probabilities of rolling at least a 4 on each die, which is (1/2) x (1/2) = 1/4.

The probability of rolling a sum of 7 on two dice is 6/36, or 1/6 because there are six possible ways to roll a sum of 7 (1+6, 2+5, 3+4, 4+3, 5+2, or 6+1) out of 36 possible outcomes.

To find the probability of rolling at least a 4 or a sum of 7, we need to subtract the probability of rolling both from the total probability of rolling either. The total probability of rolling at least a 4 or a sum of 7 is the sum of their probabilities minus the probability of rolling both, which is:

(1/2) + (1/6) - (1/4) = 5/12

Therefore, the probability of tossing two dice and showing at least a 4 or the sum of dice is precisely 7 is 5/12 or approximately 0.417.

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Let's call the price of the motorcycle "x".

We know that Lenny paid 12.5% in tax, which is the same as 0.125 as a decimal.

To find out how much tax Lenny paid, we can multiply the price of the motorcycle by 0.125:

0.125x = $1437.50

Now we can solve for x by dividing both sides by 0.125:

x = $11,500

Therefore, the price of the motorcycle, not including tax, was $11,500.

Answer:

Your question is:

1437.5 is 12.5% of what number?

1437.5 = 0.125x

x = 1437.5/.125 = $11,500

Therefore, the answer is $11,500!

Step-by-step explanation:

Please brainliest if the helped you a lot! And tell me if I am wrong! I would be so sorry if it was wrong! :D

Step-by-step explanation:

Two rectangles  2   x  25 x 40

one rectangle      40 x 40

two triangles   (Area = 1/2 * base * height)

                                  2  x    1/2  * 40 * 15  

  Total = 4200 m^2

To find the inverse of the function y = x² + 4x + 4, we first replace y with x and x with y:

x = y² + 4y + 4

Next, we rearrange the equation to isolate y on one side of the equation:

x - 4 = y² + 4y

y² + 4y = x - 4

Now, we complete the square by adding (4/2)² = 4 to both sides of the equation:

y² + 4y + 4 = x

We can rewrite the left side of the equation as (y + 2)²:

(y + 2)² = x

Finally, we take the square root of both sides of the equation and solve for y:

y + 2 = ±√x

y = ±√x - 2

Since the original function is not one-to-one, we need to restrict the domain to obtain the inverse function. Specifically, we restrict the domain of the original function to x ≥ -2, since for values of x less than -2 there are two corresponding y-values. Therefore, the inverse function of y = x² + 4x + 4 for this restricted domain is:

y = ±√x - 2, x ≥ -2

Answer:

Let's call the number of nuts "n", the number of bolts "b", and the number of screws "s".

From the problem, we know:

s = 3n (Since there are 3 times as many screws as nuts)

b = n + 32 (Since there are 32 more bolts than nuts)

n + s + b = 782 (Since the total number of nuts, screws, and bolts is 782)

Now we can use substitution to solve for one of the variables in terms of the others. Let's solve for "n":

n + 3n + (n + 32) = 782

5n + 32 = 782

5n = 750

n = 150

Now we know there are 150 nuts. We can use this information to find the number of bolts:

b = n + 32

b = 150 + 32

b = 182

Finally, we can use the information we have about the screws to find their number:

s = 3n

s = 3(150)

s = 450

Therefore, there are 450 screws in the box.

answer 1646

let nuts be-782

screw=3X nuts

bolts = 32 X nuts

Screw=3x782=1646

hope this helps

Answer: 5/13

Step-by-step explanation: i did this IXL and got it right

The polynomial that represents the profit is P(x) = 6x^2z + 8x^2 + 18xz + 24x + 12z + 16.To find the polynomial that represents the profit P(x), we need to multiply the revenue polynomial R(x) by the cost polynomial C(z). We can set up the multiplication as:

P(x) = R(x) * C(z)

P(x) = (2x^2 + 6x + 4) * (3z + 4)

Using the distributive property, we can multiply each term of the first polynomial by each term of the second polynomial:

P(x) = (2x^2 * 3z) + (2x^2 * 4) + (6x * 3z) + (6x * 4) + (4 * 3z) + (4 * 4)

Simplifying each term, we get:

P(x) = 6x^2z + 8x^2 + 18xz + 24x + 12z + 16

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The hypothesis can be accepted or rejected based on the results of the experiment.

A good hypothesis from the given group of answer choices can be accepted or rejected. It is important for a hypothesis to be testable and falsifiable, which means that it should be possible to support or disprove it through experimentation or observation.

A control is necessary in experiments to compare the results and determine if the independent variable has an effect on the dependent variable.

Repeated experimentation is essential to ensure the validity and reliability of the results obtained.

Therefore, the correct answer is none of the above.
A hypothesis is an educated guess or a proposed explanation for an observation or a scientific problem.

In order to be considered a good hypothesis, it should have the following characteristics:
1. Testable and falsifiable: A good hypothesis should be possible to test through experimentation, observation, or other scientific methods. This means that it should be possible to gather evidence that either supports or disproves the hypothesis.
2. Clearly stated: A good hypothesis should be stated clearly and concisely, so that it is easy to understand what is being proposed and what the expected outcome is.
3. Based on existing knowledge: A good hypothesis should be based on existing knowledge and previous research. This means that it should be grounded in known facts, theories, or observations.
4. Specific: A good hypothesis should be specific in its predictions, making it easier to test and providing clearer results.
In conclusion, a good hypothesis can be accepted or rejected, should be testable and falsifiable, requires a control, and requires repeated experimentation to ensure the reliability and validity of the results.

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Answer: 39

Step-by-step explanation:

x = (56/100) * y

where x is the amount we're trying to find and y is the total amount.

We're given that 56% of this value is $21.84, so we can substitute these values into the equation:

21.84 = (56/100) * y

To solve for y, we can divide both sides by 56/100:

y = 21.84 / (56/100)

Simplifying this expression, we get:

y = 39

Therefore, the number that represents 56% of this value is $21.84.

The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36 = 0.028

The likelihood that a specific occurrence will occur.

The proportion of the total number of possible outcomes to the number of outcomes in an exhaustive set of equally probable outcomes that result in a particular event.

Two six-sided dice are rolled there are 36 possibilities for outcomes which means 6 possibilities for the first dice and 6 for the second dice.

Therefore 36 is the total possibility outcome.

Count the number of outcomes for the one dice show 5 and the second dice show 6.

There is only one possibility two show the (5, 6) from the total s3 outcomes.

so the probability of rolling a 5 and a 6 i = 1/36 or about 0.028.

Therefore, the total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36.

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Using the hypothesis test, the p-value is greater than the significance level, we fail to reject the null hypothesis. There is not enough evidence to suggest that a headed mannequin is more effective in selling clothing.

To perform a hypothesis test to determine if a headed mannequin is more effective in selling clothing, we can use a two-sample proportion test.

Let p1 be the proportion of women who would purchase the dress when presented on a mannequin with a head, and p2 be the proportion of women who would purchase the dress when presented on a headless mannequin.

The null hypothesis is that there is no difference between the two proportions, i.e. p1 = p2, and the alternative hypothesis is that p1 > p2 since we want to test if the headed mannequin is more effective.

We can use a significance level of 0.05. Using the given data, we calculate the test statistic as:

z = (p1 - p2) / √(p × (1-p) × (1/n1 + 1/n2))

where p = (x1 + x2) / (n1 + n2), x1 = 18, x2 = 12, n1 = 50, and n2 = 45.

The calculated z-value is approximately 1.02.

Using a standard normal distribution table, we find the p-value to be approximately 0.155.

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The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4 is  (8/5, (16 + 8j)/5).

We can use the ratio formula for finding the coordinates of the point that divides the line segment AB in the ratio of 1:4:

Let the coordinates of the point dividing the line segment AB be (x, y). Then:

x = (41 + 14)/5 = 8/5

y = (44 + 42j)/5 = (16 + 8j)/5

Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8/5, (16 + 8j)/5).

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The x-intercept is (12, 0) and the y-intercept is (0, 12/7) or (0, 1 5/7) in mixed number form.

What are the intercepts?

Intercepts are the points where the graph intersects either the x-axis or the y-axis. The x-intercept is the point where the graph intersects the x-axis, which means the y-coordinate of the point is 0. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of the point is 0. To find the intercepts of a function, you can set one of the variables (x or y) to 0 and solve for the other variable. The resulting point will be the intercept.

To find the x-intercept, we set y to zero and solve for x:

x + 7(0) = 12

x = 12

So the x-intercept is (12, 0).

To find the y-intercept, we set x to zero and solve for y:

0 + 7y = 12

y = 12/7

So the y-intercept is (0, 12/7) or (0, 1 5/7) in mixed number form.

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So, the equation of the given curve is a circle centered at (-13, 13) with a radius of 3. Therefore, the correct option is:

[tex](x + 13) ^ 2 + (y - 13) ^ 2 = 9[/tex].

An equation is a mathematical statement that shows the equality between two expressions, typically separated by an equal's sign (=). Equations are used to represent a wide range of mathematical and scientific relationships, such as physical laws, chemical reactions, and statistical models. The expressions on either side of the equals sign can contain variables, constants, and mathematical operations, and solving the equation involves finding the value or values of the variables that make the equation true. Equations can take many forms, including linear equations, quadratic equations, trigonometric equations, and differential equations, among others.

To determine which option is correct, we can try to convert the given equation to the standard form of the equation of a circle, which is:

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

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

We can complete the square for the given equation by adding and subtracting appropriate constants:

[tex]x^2 + 26x + y^2 - 26y + 329 = 0[/tex]

[tex](x^2 + 26x + 169) + (y^2 - 26y + 169) = -329 + 2(169)[/tex]

[tex](x + 13)^2 + (y - 13)^2 = 9[/tex]

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The logarithmic function y = log(4x-a) is positive for all values of x which are greater than a/4.

A function of this type is a logarithmic function. which can be interpreted as "y equals the log, base b, of x" or "y equals the log of x, base b."

Finding the domain of x that makes the argument (4x-a) of the logarithm positive will help us identify the values of x for which the logarithm in the equation y = log(4x-a) is positive.

Remember that a positive number's logarithm is positive and a negative number's logarithm is indeterminate. (in the real number system).

We must therefore identify the x values that meet the inequality:

4x - a > 0

4x > a

x >a/4

After finding x, we obtain:

x > a/4

The equation y = log(4x-a) therefore has the following domain of x for which the logarithm is positive:

In other words, for all values of x larger than a/4, the expression y = log(4x-a) is defined and positive.

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Yes, Briony has enough material. She needs 18m of material, which is less than the 19m she has.

To find length of material, we need to calculate the length of each

curtain piece using the given length of material.

To convert a mixed number to an improper fraction, multiply the

denominator (the bottom number) by the whole number, and add the

numerator (the top number).

Now, to convert 2 1/4m into an improper fraction, we multiply the

denominator (4) by the whole number (2), then add the numerator (1).

This gives us (2 × 4) + 1 = 9.

Hence, 2 1/4m can be written as 9/4m.

Since Briony needs 8 pieces of curtain material 2 1/4m in length, she will need a total of:

8 × 2 1/4m = 8 × 9/4m = 18 1/4m.

Briony requires 18 1/4m of curtain material. Since she has 19 m length of

material, she has enough to create 8 pieces of curtain material of 2 1/4m

in length.

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Answer:

Step-by-step explanation:

You want the value of x and the length of side WA in rhombus WART with sides marked 7x-22 and 3x+10.

The sides of a rhombus are congruent, so ...

  7x -22 = 3x +10

  4x = 32 . . . . . . . . add 22-3x

  x = 8

  3x+10 = 3·8 +10 = 34

The value of x is 8, and side WA is 34 units.

By algebra properties, the values of x for each equation are listed below:

Case A: x = 0

Case B: x = 0

Case C: x = 1.584 or x = 1

Case D: x = 1.262 or x = - 0.631

Case E: x = 0.569

Case F: x = 2 or x = 1.322

In this problem we find six cases of equations containing exponential expressions where the value of x must be found. This can be done by means of algebra properties:

Case A

2²ˣ - 2 ˣ⁺¹ + 1 = 0

(2ˣ)² - 2 · 2ˣ + 1 = 0

u² - 2 · u + 1 = 0

(u - 1)² = 0

u = 1

2ˣ = 1

x · ㏒₂ 2 = ㏒₂ 1

x = ㏒₂ 1

x = 0

Case B

3²ˣ - 3ˣ = 0

(3ˣ)² - 3ˣ = 0

3ˣ · (3ˣ - 1) = 0

3ˣ - 1 = 0

3ˣ = 1

x = 0

Case C

2²ˣ - 5 · 2ˣ + 6 = 0

(2ˣ)² - 5 · 2ˣ + 6 = 0

u² - 5 · u + 6 = 0

(u - 3) · (u - 2) = 0

u = 3 or u = 2

2ˣ = 3 or 2ˣ = 2

x = ㏒₂ 3 or x = 1

x = 1.584 or x = 1

Case D

2 · (3²ˣ) - 9 · 3ˣ + 4 = 0

2 · u² - 9 · u + 4 = 0

2 · [u² - (9 / 2) · u + 2] = 0

2 · (u - 4) · (u - 1 / 2) = 0

u = 4 or u = 1 / 2

3ˣ = 4 or 3ˣ = 1 / 2

x = ㏒₃ 4 or x = ㏒₃ (1 / 2)

x = 1.262 or x = - 0.631

Case E

6 · (5²ˣ) - 11 · 5ˣ - 10 = 0

6 · u² - 11 · u - 10 = 0

6 · [u² - (11 / 6) · u - 5 / 3] = 0

6 · (u - 2.5) · (u + 0.667)

u = 2.5 or u = - 0.667

x = 0.569

Case F

2²ˣ⁺¹ - 13 · 2ˣ + 20 = 0

2 · (2ˣ)² - 13 · 2ˣ + 20 = 0

2 · u² - 13 · u + 20 = 0

2 · [u² - (13 / 2) · u + 10] = 0

2 · (u - 4) · (u - 5 / 2) = 0

u = 4 or u = 5 / 2

2ˣ = 4 or 2ˣ = 5 / 2

x = 2 or x = 1.322

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With a price of $1.25, 7,500 goods would be sold and a profit of $3,635 would be made. This price would maximize profit.

Profit in economics is the difference between an economic entity's revenue from outputs and all of its input costs.

It is equivalent to total income less total expenses, which includes both direct and indirect expenses.

Establishing sales methods and capturing your clients' interest requires first analyzing how profitable your goods and services are.

So, since you need to sell a certain number of items to maximize your profit, setting the price at $ 1.50 will enable you to sell 5000 items, and lowering the price by $10 will enable you to sell an additional 1000 items.

Assuming your fixed costs total $ 2000 and the cost of production per item is $ 0.50, you must determine the price to set per item, the number of items sold, and the maximum profit.

(5000 x 1.50) - (5000 x 0.50) - 2000 = 3000

(6000 x 1.40) - (6000 x 0.50) - 2000 = 3400

(7000 x 1.30) - (7000 x 0.50) - 2000 = 3600

(8000 x 1.20) - (8000 x 0.50) - 2000 = 3600

(7500 x 1.25) - (7500 x 0.50) - 2000 = 3625

Therefore, with a price of $1.25, 7,500 goods would be sold and a profit of $3,635 would be made. This price would maximize profit.

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Correct question:
You want to sell a certain number n of items in order to maximize your profit. Market research tells you that if you set the price at $1.50, you will be able to sell 5000 items, and for every 10 cents you lower the price below $1.50 you will be able to sell another 1000 items. Suppose that your fixed costs (“start-up costs”) total $2000, and the per item cost of production (“marginal cost”) is $0.50.

Solve the above engineering problem using calculus.

Hints: Find the price to set per item and the number of items sold in order to maximize profit, and also determine the maximum profit you can get.

To achieve M3, you must present your work using coherent, logical development of principles/concepts in determining the maximum profit and use technical language accurately.

To achieve D1, you must evaluate the validity of your answer using the given data.

The components of force F1 are F1x = 0N (along the x-axis) and F1y = -10N (along the y-axis).

To determine the components of the two forces acting upon an object with F1 = 10N at a 270° angle with the positive x-axis,

follow these steps:
Step 1: Convert the angle to a standard position
Since the angle is given in degrees and with respect to the positive x-axis, it is already in the standard position.

Step 2: Find the x and y components of F1
To find the components of F1, we'll use trigonometry.

At 270°, the force is pointing straight down along the negative y-axis.

So, the x-component (F1x) is 0, and the y-component (F1y) is -10N.
F1x = F1 * cos(270°) = 10N * 0 = 0N
F1y = F1 * sin(270°) = 10N * (-1) = -10N.

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The number of tiles used in the deck is 525. This can be answered by the concept of arithmetic sequence.

Let x be the number of tiles in each row in the arithmetic sequence. Then, the sum of the number of tiles in all 16 rows can be expressed as the sum of an arithmetic series:

S = (n/2)(a + l),

where n is the number of terms, a is the first term, and l is the last term. In this case, n = 16, a = 15, l = 30, and x is the common difference, which can be found by using the formula:

x = (l - a) / (n - 1)

Substituting the values given, we get x = 1.25. Therefore,

S = (16/2)(15 + 30) = 525.

Therefore, the total number of tiles used in the deck is 525.

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The value of A is 9/10.

What is binomial?

Binοmial refers tο a type οf prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, where each trial has οnly twο pοssible οutcοmes (success οr failure) and the prοbability οf success is cοnstant acrοss all trials.

The given expressiοn is the sum οf the first several terms οf a harmοnic series. Tο evaluate it, we can use the fοrmula fοr the sum οf the first n terms οf a harmοnic series:

1 + 1/2 + 1/3 + ... + 1/n = ln(n) + γ,

where ln(n) is the natural lοgarithm οf n and γ is the Euler-Mascherοni cοnstant (apprοximately 0.5772).

Using this fοrmula, we can write the expressiοn as:

A = 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/45

= (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ... + (1/9 - 1/10)

= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10

= 1 - 1/10

= 9/10

Therefore, the value of A is 9/10.

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Complete Question:

Find The value of A

A=1\3+1\6+1\10+1\15+...+1\45

The value of the expression 9 + (20 x one-fourth) – 6 ÷ 2  is 11.

What is PEMDAS?

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is a mnemonic or acronym used to remember the order of operations when simplifying mathematical expressions.

Using PEMDAS (Order of Operations), we perform the operations in the following order:

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Applying this to the given expression:

9 + (20 x one-fourth) – 6 ÷ 2

= 9 + (20 x 0.25) - 3 [simplify division first: 6 ÷ 2 = 3]

= 9 + 5 - 3 [simplify multiplication: 20 x 0.25 = 5]

= 11 [simplify addition and subtraction from left to right]

Therefore, the value of the expression is 11.

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Answer: x=9

Step-by-step explanation:

2x-3=6+x

Add similar variables.

2x-3=6+x

   +3     +3

2x=9+x

-x     -x

x=9

Hope this helped!

Answer:

x=9

Step-by-step explanation:

primero, tomas y restas x de ambos lados.

2x-3=6+x

-x. - x

eso te deja con x-3=6. luego sumas 3 a ambos lados

x-3=6

+3. +3

eso te deja con x=9

The length of side WX is 2.61 units

Trigonometric ratios are mathematical relationships that describe the proportions between the sides of a right triangle. There are three main trigonometric ratios: sine, cosine, and tangent.

Cosine (cos) is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse of the right triangle. It is expressed as cosθ = adjacent/hypotenuse.

Here we have

The triangle XYW is right-angled

Where Hypotenues WY = 4

The measure of angle W = 49°

From triangonometric ratios  

Cos θ = Adjacent/Hypotenuse.

Cos 49° = WX/4

0.6561 = WX/4      [ Since Cos 49° = 0.6561 ]

=> WX = 4(0.6561)

=> WX =  2.6244

=> WX = 2.61  
     

Therefore,

The length of side WX is 2.61 units

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The passengers selected for the in-flight survey in this scenario can be best referred to as a stratified random sample.

In stratified random sampling, the population is divided into smaller, non-overlapping groups, called strata, which share similar characteristics. In this case, the strata are the 40 flights selected by Northwest Airlines. From each of these strata, a random sample of passengers is chosen, which in this case, is a group of ten passengers from each flight.

This method ensures that each flight's passengers are represented in the survey, allowing for better generalizability of the results. By selecting passengers randomly within each stratum, the survey helps minimize selection bias and ensures that the sample reflects the diversity of the overall population of passengers. The stratified random sampling approach is especially useful when studying a large and diverse population, as it provides a more accurate representation of the population's characteristics compared to simple random sampling.

In summary, the passengers participating in the in-flight survey are best referred to as a stratified random sample because they are chosen from 40 randomly selected flights, with ten passengers randomly selected within each flight. This sampling approach ensures better representation of the overall population and helps minimize selection bias in the survey results.

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