Enter the number that belongs in the green box

Answer:  A   Polar is (6√2,  [tex]\frac{3\pi }{4}[/tex])

Step-by-step explanation:

Draw a line to point (see image).   You need to find the length of that line and then the angle.   Polar(length, angle)

Using pythagorean theorem

length²  = (6)² + (-6)²

length² = 36 +36

length =√72

length  = [tex]\sqrt{36 *2}[/tex]

length = 6√2

To find angle:

The triangle size is 6-6-6√2  Let's proportionally shrink so we can use unit circle numbers to figure angle.    Becomes: 1-1-√2

So when we do sin x =  opp/adj

sin x = [tex]\frac{1}{\sqrt{2} }[/tex]              >get rid of radical on bottom

sin x  = [tex]\frac{\sqrt{2} }{2}[/tex]             > when is sin = [tex]\frac{\sqrt{2} }{2}[/tex]     This happens at [tex]\frac{\pi }{4}[/tex]   but we are in the 2nd quadrant so the angle is [tex]\frac{3\pi }{4}[/tex]

Polar is (6√2,  [tex]\frac{3\pi }{4}[/tex])

The polar coordinates are (6([tex]\sqrt[]{2}[/tex], 3pi/4).

Rectangular coordinates are in the form of (x, y) and Polar coordinates are expressed in the form of (r, [tex]\theta[/tex]).  

x = r cos([tex]\theta[/tex]), y = r sin([tex]\theta[/tex]) and  x^2 +y^2 =r^2                                       ...(1)

So by using above formulas we can solve our question.

Here , x= -6 and y= 6

r^2 = (-6)^2 +(6)^2

       =72

=>r = 6([tex]\sqrt[]{2}[/tex])

Put the values of x and y in the mentioned formula in eq(1)

-6 =  6([tex]\sqrt[]{2}[/tex] )cos[tex]\theta[/tex]

 6 = 6([tex]\sqrt[]{2}[/tex] )sin([tex]\theta[/tex]),

=>-1/([tex]\sqrt[]{2}[/tex] = cos([tex]\theta[/tex]) , 1/[tex]\sqrt[]{2}[/tex]=  sin[tex]\theta[/tex]

Here cos is negative and sin is positive so it lies in 2nd quadrant

so here [tex]\theta[/tex] lies between [tex]\frac{\pi}{2} \leq\theta\leq\pi[/tex]

[tex]\theta[/tex]= π-π/4

 =3π/4

So,(r, [tex]\theta[/tex]) = ( 6√2, [tex]\frac{3\pi}{4}[/tex] )

The values of m and n are 15 and 19, respectively in the given data.

From the given values:

x: 1, 2, 7, 4, 9

y: 3, 5, 11, m, n

Looking at the x-values, we can observe that they are increasing by 1 each time.

Looking at the y-values, we can observe that they are increasing by 2 each time except for the last two values (m and n) which are unknown.

Based on this pattern, we can establish the following equation:

y = 2x + 1

Now, let's calculate the values of m and n using this equation:

For x = 7:

y = 2(7) + 1

y = 14 + 1

y = 15

Therefore, m = 15.

For x = 9:

y = 2(9) + 1

y = 18 + 1

y = 19

Therefore, n = 19.

Hence, the values of m and n are 15 and 19, respectively.

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Brynen will use 7.71 gallons of gas driving to and from work this week.

To calculate the gallons of gas Brynen will use driving to and from work this week, we need to consider the round trip distance and the car's fuel efficiency.

Given:

Brynen drives 27 miles each way to work.

His car gets 35 miles per gallon of gas.

To find the total distance Brynen will travel in a week, we need to calculate the round trip distance for each workday and multiply it by the number of workdays (five days).

Round trip distance = 27 miles (one-way distance) * 2 = 54 miles (round trip distance)

Total distance traveled in a week = 54 miles (round trip distance) * 5 days = 270 miles

Next, we can determine the total gallons of gas Brynen will use using his car's fuel efficiency.

Gallons of gas used = Total distance / Fuel efficiency

Gallons of gas used = 270 miles / 35 miles per gallon

Gallons of gas used ≈ 7.71 gallons (rounded to the nearest tenth)

Therefore, Brynen will use approximately 7.71 gallons of gas driving to and from work this week.

It's important to note that this calculation assumes that Brynen's car maintains a consistent fuel efficiency of 35 miles per gallon throughout the entire week and that no additional driving outside of the work commute is considered. Factors such as traffic, variations in fuel efficiency, or additional trips would affect the actual gas consumption.

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To find the area of a sector, you can use the formula:

Area of Sector = (θ/360) * π * r^2

where θ is the central angle in degrees, r is the radius, and π is a mathematical constant approximately equal to 3.14159.

Let's calculate the areas for the given sectors:

r = 16 mi, θ = 150°

Area of Sector = (150/360) * π * (16 mi)^2

= (5/12) * π * 256 mi^2

≈ 334.930 mi^2

Therefore, the area of sector 16 is approximately 334.930 square miles.

Answer: Therefore, the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches is 0.884. Rounded to 3 decimal places, the answer is 0.884.

Step-by-step explanation:We can use the standard normal distribution to find the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches.

First, we need to standardize the values using the formula:

z = (x - mu) / sigma

where:

x = 52.2 and 60.6 (the values we want to find the probability between)

mu = 55.7 (the mean)

sigma = 2.6 (the standard deviation)

For x = 52.2:

z = (52.2 - 55.7) / 2.6 = -1.346

For x = 60.6:

z = (60.6 - 55.7) / 2.6 = 1.885

Next, we use a standard normal distribution table or calculator to find the area between these two z-scores:

P(-1.346 < z < 1.885) = 0.884

Therefore, the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches is 0.884. Rounded to 3 decimal places, the answer is 0.884.

Answer:

14

Step-by-step explanation:

Assuming you meant to find MN.

Given that MN is parallel to the bases of the given trapezoid, and is connected to the midpoints of both sides, we can infer that MN is the midsegment of the given trapezoid.

The length of a midsegment is given by half the sum of the bases.
Therefore, MN = (18 + 10)/2 = 28/2 = 14

Answer:

m = 5/4

Y-intercept: (0,0)

Step-by-step explanation:

The equation is in slope-intercept form y = mx + b

m = the slope

b = y-intercept

Our equation y = 5/4x

m = 5/4

Y-intercept is located at (0,0)

Answer:

the slope is 5/4 and the y-intercept is 0

Step-by-step explanation:

The slope is the number before x.

The y intercept is the constant term in the equation.

Info related to the question

The equation I just worked with was given in slope intercept form :

Where the slope is defined as m and the intercept is defined as b.

The conical base of the silo provides stability and structural integrity, enabling the company to offer reliable storage solutions for grains. It optimizes space utilization and supports easy handling and retrieval of stored grains.

The silo manufactured by the company features a conical base, as depicted in the drawing. The given dimensions are as follows: the height is 8.5 feet, the length measures 4 feet, and the width is 13 feet.

The height of 8.5 feet refers to the vertical distance from the base of the silo to the top of the conical base. It represents the overall height of the silo structure.

The length of 4 feet represents the measurement from one side of the conical base to the other. This dimension determines the diameter of the circular base of the silo.

The width of 13 feet signifies the measurement from the front to the back of the conical base. It determines the circumference of the circular base of the silo.

With these dimensions, the silo exhibits a conical shape, where the circular base gradually tapers towards the top. This design is well-suited for storing grains, as it allows for efficient distribution of pressure and facilitates the flow of grains during loading and unloading processes.

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The translated coordinates are:

A: A'(-6, -5)  ⇒ A''(-3,-7)

B:  D'(2,-5)  ⇒  D''(8, -7)

C: C (2, 0)   ⇒ C'(5, -2)

D: D(5,-5)    ⇒ D'(8, -7)

E; C'(-1,0)     ⇒ C''(2, -2)

F: A (-3,-5)   ⇒ A'(0, -7)

G: B'(-5, 0 ) ⇒  B''(-2, -2)

H: B (-2, 0)  ⇒  B'(1, -2)

Here,

We have to apply a translation of 2 units down and 3 units right to these coordinates.

Translation means moving the entire polygon in a particular direction by a certain distance.

To apply the translation,

Add the same amount of distance to the x-coordinate of each vertex for the rightward motion, and subtract the same amount of distance from the y-coordinate of each vertex for the downward motion.

In this case,

the translation is 2 units down and 3 units right.

So the new coordinates will be:

A: A'(-6, -5) ⇒ A'( -6+ 3, -5-2)

              = A''(-3,-7)

B:  D'(2,-5)  ⇒ D'(5+3, -5 -2 )

                  = D''(8, -7)

Similarly apply for each coordinates we get,

C: C (2, 0)   ⇒ C'(5, -2)

D: D(5,-5)    ⇒ D'(8, -7)

E; C'(-1,0)     ⇒ C''(2, -2)

F: A (-3,-5)   ⇒ A'(0, -7)

G: B'(-5, 0 ) ⇒  B''(-2, -2)

H: B (-2, 0)  ⇒  B'(1, -2)

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Answer:

Step-by-step explanation:

The median time is less than 25 minutes

The angles supplementary to ∠EOF are ∠FOB and ∠COE.

Supplementary angles are those angles that sum up to 180 degrees. In

other words, two angles are called supplementary when their measures

add up to 180 degrees.

Therefore, let's find the angles that are supplementary angles to ∠EOF.

Therefore, let's use the angle relationships in the line intersection to find

the angles that are supplementary to ∠EOF.

Hence, the angles supplementary to  ∠EOF are ∠FOB and ∠COE

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Phi (Φ) can be determined for Cable 2 from:

[tex]tan^-1 (Fy/Fx).[/tex]

In trigonometry, [tex]tan^-1 (Fy/Fx)[/tex] represents the inverse tangent function, also known as arctan or atan.

This function is used to find the angle whose tangent is equal to the ratio of the y-component (Fy) to the x-component (Fx) of a vector.

By calculating the ratio Fy/Fx and applying the inverse tangent function, we can determine the angle phi (Φ) for Cable 2.

The value obtained from [tex]tan^-1 (Fy/Fx)[/tex] will represent the angle in radians.

It's important to note that the resulting angle phi (Φ) will provide information about the direction or inclination of Cable 2 based on the given vector components Fy and Fx.

In summary, to determine the angle phi (Φ) for Cable 2, we use the inverse tangent function, represented as[tex]tan^-1 (Fy/Fx),[/tex] which calculates the angle whose tangent is equal to the ratio of the y-component to the x-component of the vector.

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Answer:

Step-by-step explanation:

To find the arithmetic means in the given sequence, we need to determine the missing numbers between 175 and 235.

Let's calculate the differences between consecutive terms:

1st difference: 235 - 175 = 60

2nd difference: (Next number) - (Previous number) = (Next number) - 235

Since the differences are constant, we can add the same value to each term to find the missing numbers.

Let's calculate the missing numbers using the 1st difference:

175 + 60 = 235

175 + 60 + 60 = 295

175 + 60 + 60 + 60 = 355

Now we have the complete sequence: 175, 235, 295, 355.

To find the arithmetic means, we take the average of consecutive terms:

1st arithmetic mean: (175 + 235) / 2 = 205

2nd arithmetic mean: (235 + 295) / 2 = 265

3rd arithmetic mean: (295 + 355) / 2 = 325

Among the given choices, the correct answer is:

c. 220, 205, 190

This answer represents the correct sequence of arithmetic means between 175 and 235.

The coordinates of point M are (1, 2).

The gradient of CB is 5.

The equation of line AD in the form y = mx + c is: y = (-1/5)x + 37/5.

To solve the given problem, we can follow these steps:

1. Calculate the coordinates of point M:

Since the diagonals of a rhombus bisect each other, the midpoint of the diagonal AC will give us the coordinates of point M.

Midpoint formula:

x-coordinate of M = (x-coordinate of A + x-coordinate of C) / 2

                 = (-3 + 5) / 2

                 = 2 / 2

                 = 1

y-coordinate of M = (y-coordinate of A + y-coordinate of C) / 2

                 = (8 - 4) / 2

                 = 4 / 2

                 = 2

Therefore, the coordinates of point M are (1, 2).

2. The gradient (slope) of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the formula:

Gradient (m) = (-4 - 1) / (5 - 6)

            = -5 / -1

            = 5

Therefore, the gradient of CB is 5.

3. To find the equation of line AD, we need to calculate the gradient (m) of AD and the y-intercept (c).

Gradient of CB = 5

Gradient of AD = -1/5 (negative reciprocal of 5)

To find the y-intercept (c), we can substitute the coordinates of point A (-3, 8) into the equation y = mx + c and solve for c:

8 = (-1/5)(-3) + c

8 = 3/5 + c

c = 8 - 3/5

c = 40/5 - 3/5

c = 37/5

Therefore, the equation of line AD in the form y = mx + c is:

y = (-1/5)x + 37/5.

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Answer:

0.5ml/hr

Step-by-step explanation:

Given:

Infusion rate: 0.002 units/min

To convert the infusion rate from units/min to ml/hr, we need to know the flow rate conversion factor specific to the medication and solution being administered.

In this case, we have the information that the patient is receiving 10 units of oxytocin (Pictocin) in 250 ml of D5W solution.

To calculate the ml/hr rate, we can use the following formula:

ml/hr = (Infusion rate in units/min * Volume in ml) / Time in min

ml/hr = (0.002 units/min * 250 ml) / 1 min

ml/hr = 0.5 ml/min

Therefore, the infusion rate of 0.002 units/min is equivalent to 0.5 ml/hr.

Answer:

C.

Step-by-step explanation:

A chord has two endpoints on the circle. A diameter is a special chord bc it also goes through the center.

RT is the diameter and the rest of answer A are radii (plural of radius)

answer B is a chord, the diameter, but thats not the only chord.

answer D are chords but they forgot RT.



So, C. is the best answer.

The required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.

Given that number of water bottles purchased is 75 and cost price (C,P) of the 75 water bottles is $443.25. The increase %  on the purchase price is profit % = 25%.

To calculate the selling price when cost price and profit % is given by following steps:

Step 1 - Calculate the 25% of the cost price which gives profit.

Step 2 - Calculate SP, Selling price = Cost price + profit.

That implies, Profit = 25% of C.P.

Profit = 25/100 × 443.25.

Therefore, Profit = $110.81.

That implies, Selling price(S.P) = Cost price + profit.

S.P = 443.25 + 110.81.

Thus, S.P = $554.06.

Hence, the required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.

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The circumference of a circle = pi x diameter

Circumference = 3.14 x 32 = 100.48 meters (rounded to two decimal places)

The farmer needs to build a fence around the edge of the field, which has a circumference of 100.48 meters. So the total length of fence needed is 100.48 meters.

Each meter of fence cost £15.95, therefore the cost of building the entire fence can be calculated as:

Total Cost = Length of fence x Cost per meter of fence Total Cost = 100.48 x £15.95 Total Cost = £1601.08

Therefore, it would cost the farmer a total of £1601.08 to build a fence around the edge of the circular field.

Answer:

$1603.47

Step-by-step explanation:

The statement, yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

To determine if being a student and preferring logo A are independent events, we need to compare the probabilities of these events occurring.

The probability of being a student, denoted as P(student), is given as 0.8. This means that out of the total population (125), 80% are students.

The probability of a student preferring logo A, denoted as P(student | logo A), is given as 0.8.

This means that out of the students (100), 80% prefer logo A.

If the events of being a student and preferring logo A are independent, then the probability of a student preferring logo A (P(student | logo A)) should be the same as the probability of being a student (P(student)).

However, in the given options, both options A and D state that P(student | logo A) = 0.8, which is the same as P(student).

This suggests that being a student and preferring logo A are independent events.

Hence, Yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

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Answer: The pair of equations required this the given question is x+y=100 and 3x+6y=396

Step-by-step explanation:

If x denotes the number of burritos and y denotes the number of salads sold. then,

1. x+y =100 (as there are a total of 100 meals sold)

2. 3x+6y=396(as the cost of each burrito is $3 and cost of each salad is $6, the total cost of the meal is $396)

Hence, The pair of equations required this the given question is x+y=100 and 3x+6y=396

Answer:

10.33 square units

Step-by-step explanation:

Area of the sector:

     ∠JKL = Ф= 74°

      JK = r = 4

[tex]\boxed{\text{\bf Area of sector = $ \dfrac{\theta}{360}\pi r^2$}}[/tex]

  Ф is the central angle of the sector.

  r is the radius

[tex]\sf Area \ of \ the \ sector = \dfrac{74}{360}*3.14*4*4[/tex]

                            = 10.33 square units

The height of the cylinder is 25.

Option C is the correct answer.

We have,

To find the height of the right cylinder, we need to use the given information of the diagonal length and the total surface area.

The diagonal length of a right cylinder can be found using the formula:

diagonal = √(height² + radius²)

Given that the diagonal length is 37, we can set up the equation:

37 = √(height² + radius²)

We also know that the total surface area of a right cylinder is given by:

surface area = 2πrh + 2πr²

Given that the total surface area is 492π, we can set up the equation:

492π = 2πrh + 2πr²

Simplifying the surface area equation, we have:

246 = rh + r²

Now we have a system of equations:

37 = √(height² + radius²)

246 = rh + r²

Since we only need to find the height of the cylinder, we can focus on the first equation:

37 = √(height² + radius²)

Squaring both sides of the equation, we get:

37² = height² + radius²

1369 = height² + radius²

Substituting the second equation (246 = rh + r²) into the equation above, we have:

1369 = height² + (246 - rh)

Simplifying further, we get:

1369 = height² + 246 - rh

Now, let's analyze the answer options:

a. 35

b. 42

c. 25

d. 17

e. 32

We need to substitute each value into the equation and check if it satisfies the equation.

After checking each option, we find that the height that satisfies the equation is:

c. 25

Therefore,

The height of the cylinder is 25.

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The step in which the subtraction property of equality was applied to solve the equation is given as follows:

D. The subtraction property of equality was not applied to solve this equation.

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality, and hence it is used to isolate a variable that is adding on a side of the expression.

For this problem, to remove the term -7, we add 7 to both sides of the expression, hence the addition property of equality was applied.

In the other step, the multiplication property was applied, hence option D is the correct option for this problem.

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The function implies that a city with a population of 53.3 thousand people produces 5 tons of fast fashion waste during the autumn/winter season.

The city of Dunwoody, Georgia has a population of 53,300, which is equal to 53.3 thousand people. So, we can express this in terms of f as follows:

W = f(53.3) = 5

This means that the function f(x) gives the amount of fast fashion waste produced by a city with a population of x thousand people. In this case, f(53.3) = 5, which means that a city with a population of 53.3 thousand people produces 5 tons of fast fashion waste during the autumn/winter season.

This is a significant amount of waste, and it is important to be aware of the environmental impact of fast fashion. Fast fashion is a term used to describe the rapid production of cheap, trendy clothing.

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Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

Answer:

w<13

Step-by-step explanation:

Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.

Answer:

w < 1`3

Step-by-step explanation:

Isolate the variable w on one side of the inequality sign.

w+7<20

w<20 - 7

w<13.

Answer:

(a) To find the probability that a household views television between 3 and 11 hours a day, we need to calculate the z-scores for 3 and 11 hours using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. The z-score for 3 hours is (3 - 8.35) / 2.5 = -2.14 and the z-score for 11 hours is (11 - 8.35) / 2.5 = 1.06. Using a standard normal distribution table, we find that the probability of a z-score being between -2.14 and 1.06 is approximately 0.8209.

(b) To find how many hours of television viewing a household must have in order to be in the top 3% of all television viewing households, we need to find the z-score that corresponds to the top 3% of the standard normal distribution. Using a standard normal distribution table, we find that this z-score is approximately 1.88. Using the formula x = μ + zσ, we can calculate that a household must view television for approximately 8.35 + (1.88 * 2.5) = 12.75 hours to be in the top 3% of all television viewing households.

(c) To find the probability that a household views television more than 5 hours a day, we need to calculate the z-score for 5 hours using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. The z-score for 5 hours is (5 - 8.35) / 2.5 = -1.34. Using a standard normal distribution table, we find that the probability of a z-score being greater than -1.34 is approximately 0.9099.

Answer:

Step-by-step explanation:

The mean daily viewing time of television is 8.35 hours and the standard deviation is 2.5 hours. We can use a normal probability distribution to answer the following questions about daily television viewing per household:

(a) The probability that a household views television between 3 and 11 hours a day is 0.9772 (rounded to four decimal places).

(b) To be in the top 3% of all television viewing households, a household must have 15.68 hours of television viewing per day (rounded to two decimal places).

The probability that a household views television more than 5 hours a day is 0.8944 (rounded to four decimal places).

I hope this helps! Let me know if you have any other questions.