In circle O, OP = 8 and the area of shaded sector = 8. Find the length of PRQ.
Express your answer as a fraction times .

Answer:

X = 34, Y=56

Step-by-step explanation:

BOA is an isosceles triangle.

Angle CBO = 90°

Angle DBO = 90 - 56 = 34

Angle ODB = 34° and ODB is x

Angle EBD is also 90°

Y = 180 - (90+34) = 56

The value of x is 34 degree and y is 56 degree.

Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.

We have, BOA is an isosceles triangle.

< CBO = 90°

So, < DBO = 90 - 56

<DBO = 34

and, <ODB = 34°

Now, let the angle ODB be x

As, from the figure < EBD is also 90°

So, <y = 180 - (90+34)  (Angle sum property)

<y = 56

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The distance DE is 338.25m

Similar triangles are triangles that have the same shape, but their sizes may vary. . The ratio of corresponding sides of Similar triangles are equal.

Therefore AB /DE = CB/CE

CE = 80+250

= 330

represent DE by x

82/x = 80/330

330× 82 = 80x

80x = 27060

x = 338.25

Therefore the distance DE is 338.25m

Using cosine rule to find the angle of D

c² = a²+b² +2abcos C

330² = 300²+ 338.25²+2× 300× 338.25cos D

108900 = 90000 + 114413.1 + 202950cosD

202950cos D = 108900-204413.1

202950cos D = -955131

cos D = -955131/202950

cosD = -0.471

D = cos^-1( 0.471)

D = 62° ( nearest degree)

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Answer:

Step-by-step explanation:

The fraction of vehicles on the road are trucks is 3/7

Let's assume there are a total of x vehicles on the road.

According to the first statement, 3/7 of those vehicles are trucks followed by a car. This means that (3/7)x trucks are on the road and are followed by a car.

According to the second statement, 3/9 of the vehicles are cars followed by a truck. This means that (3/9)x cars are on the road and are followed by a truck.

We know that the total number of vehicles on the road is x. So we can write

(3/7)x + (3/9)x = x

Simplifying this equation

(27/63)x + (21/63)x = x

(48/63)x = x

We can then solve for x

x = 63

So there are 63 vehicles on the road.

To find out what fraction of vehicles on the road are trucks, we need to determine what fraction of those 63 vehicles are trucks.

According to the first statement, 3/7 of the vehicles are trucks followed by a car.

So the fraction of vehicles that are trucks is 3/7

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Answer:

The length and width of the roof can be used to calculate the total square footage of the roof. For example, if the roof is 20 feet long and 10 feet wide, the total square footage would be 200 square feet.

Once the total square footage is known, the number of sheets of plywood needed can be calculated. Each sheet of plywood is 4 feet x 8 feet, or 32 square feet. Therefore, 200 square feet of roof would require (200/32 = 6.25) 6.25 sheets of plywood. In order to cover the entire roof, 7 sheets of plywood would need to be used.

Step-by-step explanation:

Kaleb and Gage are standing approximately 12.72 feet apart from each other based on their angles of elevation to a basketball hoop that is 10 feet high.

Let's assume that Kaleb and Gage are standing on the same line perpendicular to the basketball hoop. Let's also assume that the distance between Kaleb and the hoop is x, and the distance between Gage and the hoop is y.

Using trigonometry, we can set up two equations based on the angles of elevation:

tan(40) = 10/x

tan(30) = 10/y

Solving for x and y:

x = 10/tan(40) ≈ 12.72 feet

y = 10/tan(30) ≈ 17.32 feet

Therefore, Kaleb and Gage are standing approximately 12.72 feet apart.

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Answer:

x=15

Step-by-step explanation:

(2x+60)=6x

2x+60=6x

subtract 2x from both sides

60=4x

divide by 4

15=x

Answer:

To determine the cost of the shirt, we can set up an equation using algebra. Let x be the cost of the shirt in dollars. We know that Marissa spent a total of 45 on the hat and the shirt, and the hat cost 10. Therefore, we can write the equation:

x + 10 = 45

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 10 from both sides:

x = 35

Thus, the cost of the shirt is $35.

Step-by-step explanation:

the initial salary is $52,365

increment = $57,128

Raise = $57,128 - $52,365 = $4,763

%raise = $4,763/$52,365 × 100

= 9.1%

The nurse will advise the patient to take 1 ml of medication with each dose.

The physician orders medication at 400 mg po twice daily. The pharmacy supplies medication with a dosage strength of 2 grams per 5 ml.

How many milliliters does the nurse advise the patient to take with each dose?

The nurse should advise the patient to take 1 ml of medication with each dose.

To find the number of milliliters, the following formula will be used.

Dose × Volume/Strength

Given, Dose = 400 mg

Strength = 2 grams per 5 ml

Volume = ?

To convert 400 mg to grams, divide by 1000.

400 mg = 400/1000 = 0.4 g

Now, put the values in the formula,

0.4 g × Volume / 2 g/ 5 ml= 5/2 × 0.4/1= 5/2 × 0.4= 1 ml

Hence, the nurse will advise the patient to take 1 ml of medication with each dose.

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Answer:

Hello! Yes, when completing the square, you are essentially transforming a quadratic equation from standard form to vertex form. The vertex form of a quadratic equation is given by:

y = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola and 'a' is a constant that determines the shape and direction of the parabola.

To convert a quadratic equation from standard form (ax^2 + bx + c) to vertex form, we follow these steps:

1. Divide both sides of the equation by 'a' to make the coefficient of x^2 equal to 1.

2. Move the constant term (c/a) to the right-hand side of the equation.

3. Complete the square by adding and subtracting (b/2a)^2 on the left-hand side of the equation.

4. Factor the left-hand side of the equation as a perfect square trinomial.

5. Write the equation in vertex form by identifying the values of 'a', 'h', and 'k'.

Answer:

15 yards and 2 feet

Step-by-step explanation:

There are 3 feet in a yard

47/3= 15 and R 2

15 yard and 2 feet

Ans :-

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Solution:-

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[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

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hope it helps ∼

According to the question, Tyler's playlist has 36 songs. Noah's playlist has one-quarter as many songs as Tyler's playlist. then Noah's playlist has 9 songs.

     Let the number of songs on Noah's playlist be represented by x.

     To solve the question, we'll set up an equation, which is given as:

                      36 / 4 = x

      Simplifying the above equation we get:

                         9 = x

     Therefore, Noah's playlist has 9 songs.

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Applying the appropriate circle theorem, the values are:

1. x = 9; 2. Measure of arc DL = 66°; 3.x = 11; 4. x = 0; 5. x = 15

The central angle theorem is a circle theorem that states that the measure of the central angle is the same as the measure of the arc it intercepts.

1. 63 + 44 + 7x + 10 = 180

117 + 7x = 180

7x = 180 - 117

7x = 63

x = 9

2. Measure of arc DL = 2(33) [based on the inscribed angle theorem]

Measure of arc DL = 66°

3. 9x + 3 = 1/2(154 + 50) [based on the angle of intersecting chords theorem]

Solve for x:

9x + 3 = 102

9x = 102 - 3

9x = 99

x = 11

4. 35 = 1/2(171 + 2x - 101) [based on the secant-tangent theore]

Solve for x:

70 = 2x + 70

70 - 70 = 2x

2x = 0

x = 0

5. 8 * x = 12 * 10 [based on the intersecting chords theorem]

8x = 120

x = 15

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Using fractiοn it can be derived that Albertο can run 250.25 miles in 11 days.

In Mathematics, a fractiοn can be defined as the part οf the whοle thing. Fοr example, a cake is divided intο five equal pieces, then each piece is represented by 1/5. There are prοper fractiοns and imprοper fractiοns. The upper value οf a fractiοn is called numeratοr and the lοwer value οf the fractiοn is called denοminatοr.

This is a prοblem based οn fractiοn.

If Albertο runs 3 1/4=13/4 miles each day.[This was a mixed fractiοn. Here it is cοnverted tο imprοper fractiοn.]

Sο in 7 days Albertο can run (7×13)/4 miles

In 11 days he can run (7×13×11)/4 miles.

sο he can run in 11 days = 1001/4 miles.

It is a fractiοnal fοrm. We cοnvert it intο decimal number.

Hence Albertο can run in 11 days 250.25 miles.

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The initial amount is worth $ 1538.46

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any additional interest that may be added over time.

Simple interest is calculated as a percentage of the principal amount and is usually expressed as an annual rate.

The formula to calculate simple interest is:

Simple Interest = Principal x Rate x Time/ 100

Here we have

You are going to receive $2,000 in 6 years from now

The annual simple interest rate is 5%

Let 'P' be the initial or principal amount

Using the formula, I = PTR/100

Simple interest will gain on 'P' at 5% for 6 years

=> I = P(6)(5)/100  

=> I = 0.3P

And total amount = P + 0.3P = 1.3P

It is given that after 6 years we get $ 2000

=> 1.3P = 2000

=> P = 1538.46

Therefore,

The initial amount is worth $ 1538.46

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Answer:

The combined taxable income of the couple is $61,900 + $59,400 = $121,300. This falls in the tax bracket for Married Filing Jointly between $67,900 and $137,050. Therefore, their tax rate will be 25%.

Step-by-step explanation:

The rate of tax couple has to pay is 25 percent.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

The combined taxable income of the couple is $61,900 + $59,400 = $121,300.

This falls in the tax bracket for Married Filing Jointly between $67,900 and $137,050.

Therefore, their tax rate will be 25%.

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By using the complement probability that none of the 6 people prefer brand A paint, the probability that at least 1 person in a sample of 6 prefers brand A paint is 0.9939 or approximately 99.39%.

To find the probability that at least 1 person in the sample of 6 prefers brand A paint, we need to find the probability of the complement event that none of the 6 people prefer brand A paint, and subtract it from 1.

The probability that one person prefers brand A paint is 0.53, and the probability that one person does not prefer brand A paint is 0.47. Since we are dealing with a binomial distribution, we can use the formula for the probability of k successes in n trials:

P(k successes) = n! / (k! * (n - k)!) * p^k * (1 - p)^(n - k)

Using this formula, we can calculate the probability of 0 people preferring brand A paint:

P(0 people prefer brand A) = 6! / (0! * 6!) * 0.53^0 * 0.47^6 = 0.0061

Therefore, the probability of at least 1 person preferring brand A paint is:

P(at least 1 person prefers brand A) = 1 - P(0 people prefer brand A) = 1 - 0.0061 = 0.9939

So, the probability that at least 1 person prefers brand A paint is 0.9939 or approximately 99.39%.

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The total amount allocated to the Department of Health is R145,026,540,000, calculated by multiplying the total expenditure by the percentage allocated to the department expressed as a decimal.

To calculate the total amount allocated to the Department of Health, we need to multiply the total expenditure by the percentage allocated to the department, which is 12.6%.

Then, we must divide the percentage by 100 to get the decimal equivalent:

12.6/100 = 0.126

Next, we can calculate the total amount allocated to the Department of Health by multiplying the total expenditure by the decimal equivalent of the percentage:

Total amount allocated to the Department of Health = 0.126 x R1 149 390bn

Simplifying this expression, we get:

Total amount allocated to the Department of Health = R145,026,540,000

Therefore, the total amount allocated to the Department of Health is R145,026,540,000.

The calculation involves multiplying the total expenditure by the decimal equivalent of the percentage allocated to the department, which gives the amount allocated to the Department of Health.

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Answer:

a normal distribution

∠ABO and ∠BCO equal to 35

Measure of arc AD = 180 - measure of arc CD = 180 - 125 = 55

m∠AOB = 55 ( measure of central angle is equal to intercepted arc)

∠OAB = 90 degrees (Tangent makes an angle of 90 degrees with the radius)

In triangle AOB ,

∠AB0 = 180 - (90 + 55) = 35 degrees(angle sum property of triangle)

In triangle BOC, ∠BOC = 125,

m∠, BCO = 35 degrees

Yes, all rational and irrational numbers have decimal expansions. Rational numbers can be expressed as terminating or repeating decimals, while irrational numbers have non-repeating, non-terminating decimal expansions.

In decimal form, rational numbers have a finite or repeating pattern of digits after the decimal point, while irrational numbers have an infinite, non-repeating pattern of digits after the decimal point. For example, the rational number 1/4 is expressed as 0.25, while the irrational number pi is expressed as 3.14159265358979323846... where the decimal goes on infinitely without repeating. In conclusion, every real number can be represented in decimal form, either as a terminating or repeating decimal, or as a non-repeating, non-terminating decimal.

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Answer: -125

Step-by-step explanation:

-5*-5=25

But, because its squared you have to multiply 25 * -5

A negative times a positive is a negative so,

25 * -5 = -125

Hope this helped!

Answer:

3a⁴bc-3a²4b²c²-3a²bc³

Step-by-step explanation:

remove brackets by multiplying by the numbers out the brackets.As they are no like terms that is where we end our answers

The points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16) and The slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.

(a) To find where the tangent line is horizontal, we need to find values of t where the derivative of y with respect to x (dy/dx) is equal to 0.

We have:

dy/dx = (dy/dt)/(dx/dt) = (5t^4 - 5)/(12t^2 - 3)

Setting dy/dx = 0, we get:

5t^4 - 5 = 0

t^4 = 1

t = ±1 or t = ±i

Substituting t = 1 into the parametric equations gives us the point (1,-4). Substituting t = -1 gives us the point (-1,4). Substituting t = i or t = -i gives us points on the imaginary axis, which are not part of the real plane.

Therefore, the points where the tangent line is horizontal are (1,-4) and (-1,4).

To find where the tangent line is vertical, we need to find values of t where dx/dt is equal to 0.

We have:

dx/dt = 12t^2 - 3

Setting dx/dt = 0, we get:

t^2 = 1/4

t = ±1/2

Substituting t = 1/2 into the parametric equations gives us the point (13/16, -5/16). Substituting t = -1/2 gives us the point (-13/16, 5/16).

Therefore, the points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16).

(b) To determine the intervals where the slope of the tangent line is positive or negative, we need to examine the sign of the derivative dy/dx.

From part (a), we know that dy/dx is equal to:

dy/dx = (5t^4 - 5)/(12t^2 - 3)

The denominator is always positive, so the sign of dy/dx is determined by the numerator.

For t < -1, we have 5t^4 - 5 > 0, so dy/dx > 0.

For -1 < t < 1, we have 5t^4 - 5 < 0, so dy/dx < 0.

For t > 1, we have 5t^4 - 5 > 0, so dy/dx > 0.

Therefore, the slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.

(c) To determine the intervals where the curve is concave upward or downward, we need to examine the sign of the second derivative d^2y/dx^2.

We have:

d^2y/dx^2 = ((d^2y/dt^2)(dx/dt) - (dy/dt)(d^2x/dt^2)) / (dx/dt)^3

Calculating the second derivatives, we get:

d^2y/dt^2 = 20t^3

d^2x/dt^2 = 24t

Substituting these into the expression for d^2y/dx^2, we get:

d^2y/dx^2 = (20t^3)(12t^2 - 3) - (5t^4 - 5)(24t) / (12t^2 - 3)^3

Simplifying this expression, we get:

d^2

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The expression has basic mathematical operators. is The measurement of the two angles ∠J and ∠K is 76° and 65° respectively.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given to us

∠J = (7x + 13)°,

∠K = (83 - 2x)°,

the sum of the two angles is 141°.

As it is given that the sum of the two angles is 141°, therefore, the expression for the sum of the two angles can be written as,

∠J + ∠K = 141°

(7x + 13)° + (83 - 2x)° = 141°

7x + 13 +83 - 2x = 141

5x = 141 - 83 - 13

5x = 45

x = 9

Now, we got the value of x, substitute the value of x in given measurements, therefore,

∠J = (7x + 13)°

∠J = 7(9) + 13

∠J = 63 + 13

∠J = 76°

∠K = (83 - 2x)°

∠K = (83 - 2(9))°

∠K = (83 - 18)°

∠K = 65°

Hence, the measurement of the two angles ∠J and ∠K is 76° and 65° respectively.

there are 200 green balloons,  there are 120 red balloons ,  there are 10 apples and 5 bananas in the bowl, for a total of 15 fruits.  To solve this problem, we need to use the given ratio and the total number of balloons to find the number of green balloons.

Let's assume the number of green balloons is x. Then, the number of red balloons is 3/5 of x, or (3/5)x.

The total number of balloons is 320, so we can write an equation based on the given information:

x + (3/5)x = 320

To solve for x, we can simplify the equation:

(8/5)x = 320

x = 200

Therefore, there are 200 green balloons.

To check our answer, we can use the ratio given in the problem:

(3/5)x = (3/5) * 200 = 120

So there are 120 red balloons.

Let's assume the number of bananas is x. According to the given ratio, the number of apples is twice that of bananas, or 2x.

The total number of fruits in the bowl is 15, so we can write an equation based on the given information:

x + 2x = 15

To solve for x, we can simplify the equation:

3x = 15

x = 5

Therefore, there are 5 bananas in the bowl.

To find the number of apples, we can use the ratio given in the problem:

2x = 2 * 5 = 10

So there are 10 apples in the bowl.

To check our answer, we can verify that the ratio of apples to bananas is 2:1:

10/5 = 2

Therefore, there are 10 apples and 5 bananas in the bowl, for a total of 15 fruits.

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