can you please explain this in detail, there is a similar question to this on my test, the other two options are 250° or 270°

Which is the standard equation for a circle centered at the origin with radius r be,

⇒   x² + y²  = r²

Hence option D is correct.

We have to find the standard equation of circle,

Given that,

Center of circle is at (0, 0)

And radius is r

Let a point (x, y) on the circle.

We know that,

The distance between the point (x, y) and origin is also known as radius of the circle,

Since we know that,

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Therefore distance between (0, 0) and (x, y),

⇒   √[ (x - 0)² + (y - 0)²] = r

Squaring both sides we get,

⇒   (x - 0)² + (y - 0)²  = r²

⇒   x² + y²  = r²

This  is the standard equation of circle.

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Ki traveled at an average speed of approximately 41.05 miles per hour without any stops.

To calculate the average speed at which Ki traveled from Memphis to Atlanta, we can use the formula:

Average Speed = Total Distance / Total Time

First, let's calculate the total time taken for the journey. Ki started from Memphis at 5:30 am and arrived in Atlanta at 3:00 pm, which is a total of 9.5 hours.

Next, we divide the total distance traveled, which is 391 miles, by the total time taken, which is 9.5 hours:

Average Speed = 391 miles / 9.5 hours

Calculating this, we find that Ki's average speed was approximately:

Average Speed ≈ 41.05 miles per hour

Therefore, Ki traveled at an average speed of approximately 41.05 miles per hour without any stops.

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Answer:

Step-by-step explanation:

9 is dependent 6 is independent

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:

6

Step-by-step explanation:

(3√3)^2/3 = (∛3)²  X ∛(√3)²  

= 3

27^2/3 = (∛27)²

= 3² = 9

9^-1/2 = 1/√9

= 1/3

so the answer is  3 + (9 X 1/3)

= 3 + 3

= 6

Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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Answer:

$81.18

Step-by-step explanation:

Sale Price = Original Price - (Original Price * Discount Percentage)

Given:

Original Price = $82

Discount Percentage = 10%

Let's calculate the sale price:

Sale Price = $82 - ($82 * 10%)

Sale Price = $82 - ($82 * 0.1)

To simplify the calculation, we can convert 10% to its decimal form by dividing by 100:

Sale Price = $82 - ($82 * 0.1)

Sale Price = $82 - ($82 * 0.01)

Sale Price = $82 - $0.82

Using a calculator, we can find the value:

Sale Price = $81.18

Therefore, the sale price after a 10% discount would be $81.18.

Answer: $73.80 is sale price

Step-by-step explanation:

Original: $82

10% of 82

=.1(82)

=8.2       >this is your discount

Subtract

82-8.2

$73.80 is sale price

During the Christmas holidays, there are 1,053 more passengers who are late for their planes each day compared to a normal day.

Calculating the difference between the quantity of late passengers on a typical day and the quantity of late passengers on holidays is necessary.

1,835 travellers were late over the Christmas break.

On an average day, there are 782 travelers who are late.

Difference = Number of late passengers during the Christmas holidays - Number of late passengers on a normal day

Difference = 1,835 - 782

Difference = 1,053

Therefore, during the Christmas holidays, there are 1,053 more passengers who are late for their planes each day compared to a normal day.

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Answer:

Step-by-step explanation:

During the Christmas holidays, there is an increase of 1,053 passengers who are late for their planes each day compared to the average daily number of 782 passengers who are late. This surge in late passengers during the holiday period contributes to delays in 14 planes.

The higher volume of travelers, combined with potential factors like weather conditions, congestion, and heightened travel demand, likely leads to a greater number of individuals encountering delays and difficulties reaching their departure gates on time.

Hope it helps! :)

The value of x is equal to 4 units.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since H is the midpoint of line segment GI, we can logically deduce the following relationship:

Line segment GI = Line segment GH + Line segment HI

Line segment GH = Line segment HI

By substituting the given line segments into the equation above, we have the following:

4x - 6 = 2x + 2

4x - 2x = 6 + 2

2x = 8

x = 8/2

x = 4 units.

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Answer:

View explanation

Step-by-step explanation:

The highlighted arc from D to O

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.

Their present ages are Option d. 14yrs, 38yrs​

Note that algebraic expressions are described as expressions that are made up of terms, variables, constants, factors and coefficients

From the information given, we have that;

Let son's age = x

Two years ago son's age= x-2.

His Father's age at that time = 3(x-2).

Present age of Father = 3x-6+2

collect like terms, we have that;

Present age of father =3x-4

Two years hence father's age=3x-4+2=3x-2.

Two years hence son's age = x+2.

Given that;

-5×(x+2)=2 ×(3x-2)

expand the bracket, we get;

5x + 10= 6x - 4

collect like terms

10+4=6x-5x

14=x

Son's age=  14 years.

Father's age: 38 years.

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Answer:

23

Step-by-step explanation:

An integer is a whole number that can be positive, negative, or zero, without any fractional or decimal parts.

The given expressions for three consecutive integers are:

Give that twice the first number is 20 more than the second:

[tex]2x = (x + 1) + 20[/tex]

Solve this equation for x:

[tex]\begin{aligned}2x &= (x + 1) + 20\\2x&=x+1+20\\2x&=x+21\\2x-x&=x+21-x\\x&=21\end{aligned}[/tex]

The expression for the largest integer is (x + 2).

Therefore, to find the largest number, substitute the found value of x into this expression:

[tex]\begin{aligned}\sf Largest\;number&=(x+2)\\&=21+2\\&=23\end{aligned}[/tex]

Therefore, the largest number is 23.

The cash cycle, also known as the operating cycle or cash conversion cycle, is a financial metric that measures the time it takes for a company to convert its investments in inventory and other resources into cash flow from sales. It provides insight into the efficiency of a company's working capital management.

The cash cycle can be calculated using the following formula:

Cash Cycle = Inventory Conversion Period + Receivables Conversion Period - Payables Conversion Period

1. Inventory Conversion Period (ICP):

ICP measures the average number of days it takes for the company to convert its raw materials into finished goods. It is calculated as:

ICP = (Average Inventory / Cost of Goods Sold) x Number of Days in a Year

Average Inventory = (Opening Inventory + Closing Inventory) / 2

Cost of Goods Sold = Total Sales - Closing Inventory

2. Receivables Conversion Period (RCP):

RCP measures the average number of days it takes for the company to collect payment from its customers. It is calculated as:

RCP = (Average Receivables / Total Sales) x Number of Days in a Year

Average Receivables = (Opening Receivables + Closing Receivables) / 2

Opening Receivables = Total Sales x Percentage of Sales on Credit

Closing Receivables = Total Sales x Percentage of Sales on Credit - Collections

3. Payables Conversion Period (PCP):

PCP measures the average number of days it takes for the company to pay its suppliers. It is calculated as:

PCP = (Average Payables / Total Purchases) x Number of Days in a Year

Average Payables = (Opening Payables + Closing Payables) / 2

Opening Payables = Total Purchases x Percentage of Purchases on Credit

Closing Payables = Total Purchases x Percentage of Purchases on Credit - Payments

Now, let's calculate the cash cycle using the provided information:

Given data:

Opening balances:

Raw material: ₹1,00,000

WIP: ₹45,000

Finished goods: ₹1,35,000

Debtors: ₹6,00,000

Creditors: ₹8,60,000

Closing balances:

Raw material: ₹2,00,000

WIP: ₹65,000

Finished goods: ₹1,25,000

Debtors: ₹5,45,000

Creditors: ₹9,75,000

Costs incurred during the year:

Manufacturing costs: ₹11,60,000

Excise duty: ₹18,80,000

Selling and distribution expenses: ₹6,20,000

Admin. overheads: ₹2,00,000

Total sales: ₹2,01,96,800

Total purchases: ₹1,46,00,000

Percentage of sales on credit: 40%

Percentage of purchases on credit: 70%

1. Calculate the Inventory Conversion Period (ICP):

Average Inventory = (Opening Inventory + Closing Inventory) / 2

Opening Inventory = Raw Material + WIP + Finished Goods

Closing Inventory = Raw Material + WIP + Finished Goods

Opening Inventory = ₹1,00,000 + ₹45,000 + ₹1,35,000 = ₹2,80,000

Closing Inventory = ₹2,00,000 + ₹65,000 + ₹1,25,000 = ₹3,90,000

Average Inventory = (₹2,80,000 + ₹3,90,000) / 2 = ₹3,35,000

Cost of Goods Sold = Total Sales - Closing Inventory

Cost of Goods Sold = ₹2,01,96,800 -

Hello!

[tex]3x^{2} + 7x-12x - 34 - 2x^{2} + 10\\\\3x^{2}- 2x^{2} + 7x-12x - 34 + 10\\\\x^{2} - 5x - 24\\\\x^{2} + 3x - 8x - 24\\\\(x^{2} + 3x) + (-8x - 24)\\\\x(x + 3) - 8(x + 3)\\\\\boxed{(x - 8)(x+3)}[/tex]

If Erin had 150m/ of buttermilk and recipe require 0.25 cups of buttermilk, she has more than the required amount, so she has sufficient buttermilk for the recipe.

1.2 To determine if Erin has enough buttermilk for the recipe, we need to convert the given quantities to a common unit.

150 ml of buttermilk is equivalent to 0.15 liters (since 1 liter = 1000 ml).

Now, let's convert 0.25 cups to liters. Since 1 cup is approximately 0.2366 liters, we have:

0.25 cups ≈ 0.25 * 0.2366 liters = 0.05915 liters.

Comparing the amount of buttermilk Erin has (0.15 liters) with the amount required by the recipe (0.05915 liters), we can see that Erin has enough buttermilk. She has more than the required amount, so she has sufficient buttermilk for the recipe.

1.3.1 To determine the total mass of the ingredients, we need to convert the given quantities to a common unit, kilograms.

0.8 kg of flour is already in kilograms.

650 g of sugar is equivalent to 0.65 kg (since 1 kg = 1000 g).

900,000 mg of butter is equivalent to 900 g (since 1 g = 1000 mg), which is 0.9 kg.

Adding up the masses of the ingredients:

0.8 kg (flour) + 0.65 kg (sugar) + 0.9 kg (butter) = 2.35 kg.

Therefore, the total mass of the ingredients is 2.35 kilograms.

1.3.2 If sugar comes in 150 g bags at a cost of R5.95 per 150 g, we can calculate the total cost of the sugar needed for the recipe.

The recipe requires 650 g of sugar. Since each bag contains 150 g of sugar, we divide the required amount by 150 g:

650 g / 150 g = 4.3333 bags.

Since we cannot purchase a fraction of a bag, we need to round up to the nearest whole number. So, we'll need to buy 5 bags of sugar.

The total cost of the sugar is calculated by multiplying the number of bags by the cost per bag:

5 bags * 5.95 per bag = 29.75.

Therefore, the total cost of the sugar needed for the recipe is 29.75.

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The angle measures of the numbered angles from <1- 8 would be listed below as follows:

<1=147°

<2= 33°

<3= 147°

<4=33°

<5=33°

<6=147°

<7=33°

<8=147°

When two parallel lines a crossed by a transverse line then the following occurs:

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Answer:

288in³

Step-by-step explanation:

volume for one = 12 X 6 X 2 = 144.

for two books, it is 2 X 144 = 288in³

The solution to the system of equations is x = 2 and y = -1.

To solve the system of equations:

2x - 5y = 9 ...(1)

3x + 4y = 2 ...(2)

Multiplying equation (1) by 4 and equation (2) by 5, we can eliminate the variable 'y':

8x - 20y = 36 ...(3)

15x + 20y = 10 ...(4)

Adding equation (3) and equation (4), the 'y' terms cancel out:

(8x - 20y) + (15x + 20y) = 36 + 10

23x = 46

Dividing both sides of the equation by 23, we find:

x = 2

Plugging the value of 'x'

2(2) - 5y = 9

4 - 5y = 9

Subtracting 4 from both sides of the equation:

-5y = 9 - 4

-5y = 5

y = -1

Therefore, the solution to the system of equations is x = 2 and y = -1.

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For the expression  [tex]x^2^/^4x^3^/^6[/tex] the value of exponent of x is 1.

8ab²√5a is the simplified form of the expression 4√20a³b⁴ .

The given expression is [tex]x^2^/^4x^3^/^6[/tex]

x is the variable in the expression.

We know that when bases are same in the product then the powers will be added.

[tex]x^1^/^2^+^1^/^2[/tex]

When 1/2 and 1/2 are added we get 1.

So the value of r is 1.

Now 4√20a³b⁴ is the expression.

4√4×5a².a.b².b²

4.2.ab²√5a

8ab²√5a is the simplified form of the expression.

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Answer:

$27.01

Step-by-step explanation:

100% + 19.3% = 119.3%.

$32.22 = 119.3%

divide both sides by 119.3:

(32220/1193) = 1

multiply by 100 to get 100% ie the bill before the tip:

$27.01 = 100%

$27.01 is bill to nearest cent

x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Hello!

Solutions = -3 and 1.5

Option B has the highest overall cost by $64.50.

To determine the option that would result in the highest overall cost for the employee

we need to compare the costs of both options based on the estimated prescription drug expenses.

Option A:

Monthly premium: $94

Prescription coverage: 80%

Option B:

Monthly premium: $42

Prescription coverage: 75% for the first $500, 85% for costs over $500

Let's calculate the costs for each option:

Option A:

Total prescription drug cost: $1,250

Employee's share (20%): 20% × $1,250 = $250

Monthly premium: $94

Total cost for Option A: $250 + $94 = $344

Option B:

Total prescription drug cost: $1,250

Employee's share for the first $500 (25%): 25% × $500 = $125

Employee's share for costs over $500 (15%): 15% × ($1,250 - $500) = $112.50

Monthly premium: $42

Total cost for Option B: $125 + $112.50 + $42 = $279.50

Comparing the total costs for each option, we see that Option B has a lower overall cost for the employee.

Hence, Option B has the highest overall cost by $64.50.

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The statement "an n-ary relation R is a set of n-tuples" refers to a mathematical concept in which an n-ary relation R is defined as a collection or set of n-tuples.

In this context, an n-ary relation refers to a relationship or connection between n elements or entities. It represents a logical association between these elements based on certain criteria or conditions.

An n-tuple, on the other hand, is an ordered sequence or collection of n elements, where the order and position of each element in the sequence are important.

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Answer:

When you cut the sample size in half while making a statistical inference about the mean of a normally distributed population, the effect on the margin of error depends on the relationship between the sample size and the margin of error. Generally, the margin of error is inversely proportional to the square root of the sample size.

So, if you reduce the sample size by half, it means you are taking a smaller sample, which will result in a larger margin of error. In other words, the margin of error is multiplied by a factor greater than 1.

Among the given options, the correct answer is:

D. The margin of error is multiplied by 2.

This option correctly reflects the relationship between reducing the sample size by half and the resulting increase in the margin of error.