a) r = 29 cm, b) Angle AOC = 1.39 rad,


c) Shaded Region= 68 cm sq, d) Perimeter = 87.7 cm


a) r = 130 cm, b) Angle AOC = 12.9 rad,


c) Shaded Region= 675 cm sq, d) Perimeter = 867 cm


a) r = 30 cm, b) Angle AOC = 1.29 rad,


c) Shaded Region= 67.5 cm sq, d) Perimeter = 86.7 cm


ABC is the segment of a circle, centre O, radius

r. This segment is enclosed in a rectangle APQC.


Given that AC = 36 cm and AP = 6 cm,

Find

a) r

b) the angle AOC is radian

c) the area of the shaded region

Answer:

For the original triangle:

A is at (-3, 6), B is at (1, 2), C is at (-5, 1).

For the new triangle:

A' will be at (-3 - 3, -(6 + 2)) = (-6, -8)

B' will be at (1 - 3, -(2 + 2)) = (-2, -4)

C' will be at (-5 - 3, -(1 + 2)) = (-8, -3)

Step-by-step explanation:

[tex]volume = {x}^{3 \\} \\ so \: 1000000 = {x}^{3 \\} \\ x = \sqrt[3]{1000000} \\ x = 100[/tex]

Step-by-step explanation:

If you take the sides you already have, 2, 7, 4, and 3, and add them together, you get 16. Lets take the portion of the perimeter you already have, and lets say this figure is a rectangle.

Divide 16 by 2 to give two sides of the rectangle a portion of the perimeter.
Since the area of a rectangle is width times height, lets create a formula:

8x = 44, 44 being the area, and 8x being the width times the variable of the height.

You get 5.5. for the height of the rectangle.

Add 8+8 to 5.5+5.5
you get 27

The standard form of a quadratic function is:

`f(x) = ax^2 + bx + c`

If the zeros of the function are 3 and 1/2, then the factors of the function are:

`(x - 3)` and `(x - 1/2)`

To find the quadratic function using these factors, you can first multiply them together:

`(x - 3)(x - 1/2) = x^2 - 7/2x + 3/2`

Now we have:

`f(x) = x^2 - 7/2x + 3/2`

This is the quadratic function in standard form that has zeros of 3 and 1/2.

Let's assume that each van and each bus can carry "x" number of students.

Let's assume there are "x" students in each van and each bus. Therefore, the total number of students in High School A's senior class is 8x + 8x = 16x. We know that the total number of students in High School A's senior class is 240, so we can set up an equation:

16x = 240

Solving for x, we get:

x = 15

So, each van and each bus had 15 students in it for High School A's senior class.

Similarly, for High School B, the total number of students is 4x + 1x = 5x. We know that the total number of students in High School B's senior class is 54, so we can set up an equation:

5x = 54

Solving for x, we get:

x = 10.8

Since the number of students must be a whole number, we can round up to 11. Therefore, each van and each bus had 11 students in it for High School B's senior class.

Therefore, the total number of students in High School A's senior class is 1x + 6x = 7x. We know that the total number of students in High School A's senior class is 372, so we can set up an equation:

7x = 372

Solving for x, we get:

x = 53

Therefore, each van and each bus can carry 53 students for High School A's senior class.

Similarly, for High School B, the total number of students is 4x + 12x = 16x. We know that the total number of students in High School B's senior class is 780, so we can set up an equation:

16x = 780

Solving for x, we get:

x = 48.75

Since the number of students must be a whole number, we can round up to 49. Therefore, each van and each bus can carry 49 students for High School B's senior class.

Let's assume that the price of one senior citizen ticket is "s" and the price of one child ticket is "c". Therefore, we can set up two equations based on the given information:

[tex]3s + 9c = 75[/tex]

[tex]8s + 5c = 67[/tex]

We can solve these equations simultaneously to find the values of "s" and "c". One way to do this is to multiply the first equation by 8 and the second equation by 3, so that we can eliminate "c" and solve for "s":

[tex]24s + 72c = 600[/tex]

[tex]24s + 15c = 201[/tex]

Subtracting the second equation from the first, we get:

57c = 399

Solving for "c", we get:

c = 7

Substituting this value into one of the original equations, we can solve for "s":

[tex]3s + 9(7) = 75[/tex]

[tex]3s + 63 = 75[/tex]

[tex]3s = 12[/tex]

[tex]s = 4[/tex]

Therefore, one senior citizen ticket costs $4 and one child ticket costs $7.

Let's assume that the speed of the boat in still water is "b" and the speed of the current is "c".

Therefore, we can set up two equations based on the given information:

[tex]336 = (b + c) * 12[/tex]

[tex]336 = (b - c) * 14[/tex]

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As per the combination method, Cameron can wear a different outfit for 6 days.

If we want to find the number of different combinations of shirts that Cameron can wear with a pair of shorts, we need to calculate the value of 3C1 (which means choosing 1 shirt out of 3). Using the formula above, we get:

³C₁ = 3! / (1! x (3-1)!) = 3

So there are 3 possible combinations of shirts that Cameron can wear with a pair of shorts.

Since Cameron has 2 pairs of shorts, he can wear each combination twice (once with each pair of shorts). Therefore, the total number of different outfits he can wear is:

3 (number of shirt combinations) x 2 (number of pairs of shorts) = 6

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Answer:

area = 127[tex]units^{2}[/tex]

perimeter = 46 units

Step-by-step explanation:

count them

Marissa will need 4 cups of olive oil for a recipe. If olive oil costs two dollars per cup, she will need 4 x 2 = 8 dollars to buy the olive oil.

To make a recipe, Marissa needs 4 cups of olive oil. At a cost of $2 per cup, she would need to spend a total of 4 x $2 = $8 to buy the necessary amount of olive oil. This is a straightforward multiplication problem where the quantity of olive oil required is multiplied by the cost per cup. By using the multiplication operator, we can find the total cost needed to purchase the olive oil. Therefore, the total cost of the olive oil is directly proportional to the quantity of olive oil needed, with the cost per unit remaining constant at $2 per cup.

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Using Pythagorean theorem, the perimeter of the plot of land is 1783/16 feet.

What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental mathematical concept that outlines the relationship between a right triangle's three sides. It states that the square of the hypotenuse's (triangle's longest side) length equals the sum of the squares of the other two sides (the legs).

The Pythagorean theorem can be expressed numerically as follows:

a² + b² = c²

Let x= length of the shorter leg. Then, using the given ratio, the length of the hypotenuse can be expressed as 16x/65.

By the Pythagorean theorem, we have:

x² + 189² = (16x/65)²

Simplifying this equation, we get:

4225x² + 189² * 65² = 16² * x²

Solving for x, we get:

x = 315/4

Therefore, the perimeter is

189 + 315/4 + √(189² + (16/65)² * 315²/16)

Simplifying this expression, we get:

189 + 315/4 + 243/4 = 207/4 + √(2134441/256)

207/4 + 1463/16 = 1783/16

Therefore, the perimeter of the plot of land will be  1783/16 feet.

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When they are 111 miles apart, the current time is 4:10 p.m.

If the time taken for two trains to be apart by 111 miles by "t" time.

Then at that time, t, the train which is at 82 mph, should have traveled a distance of 82T miles.

d1 = 82t

At the same time, t, the train which is at 66 mph, should have traveled a distance of 66T miles.

d2= 66t

The total distance traveled by both trains is d1 + d2 = D

D = 82t + 66t

D = 148t

From the given data, D = 111

Hence, 148t = 111

Solving the equation, the time t

t = 111÷148

t = 0.75

Converting it into minutes,

t = 0.75*60

t = 45 mins.

The current time ( T ) = the time at which both the trains left ( t1 ) + 45 mins.

T = t1+t

T = 3:25 + 45 min.

T =4:10 pm

Therefore, the current time is 4:10 p.m

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The complete question is-

At 3:25 p.m., two trains left Kalamazoo, Michigan. one train traveled westward at a constant rate of 82 miles per hour, while the other traveled eastward at a constant rate of 66 miles per hour. if they are now 111 miles apart, what time is it now? show your work on how you solved this situation.

Answer:

i don't know i haven't done integers in a long time

Step-by-step explanation:

The height of the office building is 187.5 feet.

It is typically measured horizontally along the X-axis. Height is defined as the distance between the bottom and top of an object. In Geometry, it is sometimes referred to as altitude.

Let's call the office building's height h. We can use a proportion to find h:

height of office building / length of shadow cast by office building = height of tree / length of shadow cast by tree

h / 15 = 5 / (2/5)

The right side of the equation can be simplified as follows:

5/(2/5) = 5 * 5/2 = 12.5

When we plug this into the proportion and solve for h, we get:

h / 15 = 5 / (2/5)

h / 15 = 12.5 \sh = 15 * 12.5 \sh = 187.5

As a result, the office building's height is 187.5 feet.

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Answer:

275

Step-by-step explanation:

You have a 1 in 2 chance

550/2

275 times

The enthalpy change of each step in the cycle must be added together to obtain the enthalpy of formation of the desired compound.

The enthalpy of formation of a compound that cannot be synthesized directly from the constituent elements can be calculated using the Hess's Law. Hess's Law states that the enthalpy change of a reaction is independent of the route taken from reactants to products. This law allows for the enthalpy of formation of a compound to be determined by summing the enthalpy changes of a series of known reactions, referred to as a ‘thermochemical cycle’, which lead to the compound of interest. To use this law, the enthalpy of formation of the intermediate species formed during the reaction must be known.

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Using area of the rectangle, we can find that the new flower garden will be 13m in length (greater dimension).

The formula for calculating a rectangle's area can be used to determine how much space the rectangle takes up within its perimeter. Multiplying the length by the width yields the area of a rectangle (breadth).

As a result, the following formula can be used to determine the area of a rectangle whose length and breadth are "l" and "w," respectively. The rectangle's area is L × W. A rectangle's area is therefore equal to length * width.

Now here the dimensions of the rectangle are, l = 13m and b, = 9m.

Area of the rectangle is 13 × 9 = 117m².

Now the area of the rectangle is increased to 221m².

So, when we increase the length from 13 m to 17m and the breadth from 9m to 13m, we get area = 17 × 13 = 221m².

Therefore, length of the new garden will be 17m long.

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The expression "p(8 or less than 7)" suggests that we are looking for the probability of an event that satisfies one of two conditions: either the outcome is 8 or the outcome is less than 7. However, we need to know the specific probability distribution or situation in which this function p is being used to calculate a meaningful answer.

For example, if p represents the probability of rolling a certain number on a fair six-sided die, then p(8 or less than 7) would be 0, because 8 is not a possible outcome and all outcomes less than 7 are equally likely. However, if p represents the probability of a certain event occurring in a particular situation, then we would need more information about the nature of the event to calculate the probability.

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The total distance covered by Edwin in duration of 3 hours and 30 minutes at a speed of 70km per hour  is equal to 245 kilometers.

Use the formula,

distance = speed x time

To find the distance Edwin covers in 3 hours and 30 minutes.

First, convert 3 hours and 30 minutes to hours.

1 hour is equal to 60 minutes, so,

This implies,

3 hours and 30 minutes

= 3 + 30/60

= 3.5 hours

Now apply the formula we have,

distance = speed x time

⇒ distance = 70 km/h x 3.5 h

⇒ distance = 245 kilometers

Therefore, distance covered by Edwin will be 245 kilometers in 3 hours and 30 minutes, if he drives at a speed of 70 km/h.

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The z-score for a raw score of 12 in a distribution with a mean of 6 and a standard deviation of 3 is 2.

The z-score is a measure of how many standard deviations a raw score is above or below the mean of a distribution. It is calculated by subtracting the mean from the raw score and then dividing the result by the standard deviation.

In this case, we have a mean of 6 and a standard deviation of 3. To find the z-score for a raw score of 12, we can use the formula:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation.

Substituting the values we have, we get:

z = (12 - 6) / 3 = 2

Therefore, the z-score for a raw score of 12 in this distribution is 2. This means that the raw score of 12 is 2 standard deviations above the mean of 6. The z-score can be used to compare scores from different distributions, and to calculate probabilities and percentiles.

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Larger the value of r² (R²) imply that the observations are more closely grouped about the least squares line (regression line) option C.

The dependent variables on the y-axis and the independent variables on the x-axis are shown as a linear connection by a regression line. By examining the data pattern the variables' effects have created, the correlation is established.

As the (R2) is large therefore, the model is a good fit or bounded close to  regression line least squares line (regression line).

In a regression graph, the regression line that is closest to the data points is shown. By changing the value of x in the regression equation, this statistical tool helps study how a dependant variable y behaves when the independent variable x changes.

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Complete question:

Larger values of r2 (R2) imply that the observations are more closely grouped about the

Group of answer choices:

Answer:

the whole is always 180 so take away the x and y and add up the remaining problems and whatever is left after that is your answer.

Step-by-step explanation:

To calculate the number of different special pizzas possible with any 6 toppings out of 16, we can use the combination formula:C(16,6) = 16! / (6! * (16-6)!) = (161514131211) / (654321) = 8008

there are 8,008 different special pizzas possible with any 6 toppings out of 16.

To calculate the number of different special pizzas possible with any 6 toppings out of 16, we need to use the combination formula, which is given by:

C(n, k) = n! / (k! * (n - k)!)

where n is the total number of items to choose from, and k is the number of items we want to choose.

In this case, n = 16 (the total number of toppings available), and k = 6 (the number of toppings we want to choose).

Plugging these values into the formula, we get:

C(16, 6) = 16! / (6! * (16 - 6)!)

= (16 * 15 * 14 * 13 * 12 * 11) / (6 * 5 * 4 * 3 * 2 * 1)

= 8008

Therefore, there are 8,008 different special pizzas possible with any 6 toppings out of 16.

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In this simplex tableau, x₄, x₅, and z are the basic variables, while x₁, x₂, x₃, x₆, x₇, and x₈ are the nonbasic variables. The values of all the variables associated with this basic feasible solution are x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, and z = 620.

In this tableau, the basic variables are x₄, x₅, and z, while the nonbasic variables are x₁, x₂, x₃, x₆, x₇, and x₈.

The basic variable associated with row 1 is x₄, the basic variable associated with row 2 is x₅, and the basic variable associated with row 3 is z.

The values of all the variables associated with this basic feasible solution are:

x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, z = 620.

Note that these values correspond to the entries in the tableau in the "BV" column.

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The missing tableau is in the image attached below

There are 720 ways the first three positions of the order of finish can occur assuming no ties in a race with 10 horses.

To calculate the number of ways the first three positions can occur, we use the permutation formula:

nPr = n! / (n - r)!

where n is the total number of objects and r is the number of objects we are choosing.

In this case, we have 10 horses and we want to choose the first three positions, so we get:

10P3 = 10! / (10 - 3)! = 10! / 7! = (10 x 9 x 8) / (3 x 2 x 1) = 720

Therefore, there are 720 ways the first three positions of the order of finish can occur assuming no ties.

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Answer:

We can use the compound interest formula to find the total amount of interest Claire will get at the end of four years:

A = P(1 + r/n)^(nt)

Where:

A = the total amount of money in the account at the end of the four years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have:

P = £200000

r = 0.016 (1.6% expressed as a decimal)

n = 1 (compounded annually)

t = 4

So, the formula becomes:

A = £200000(1 + 0.016/1)^(1*4)

= £200000(1.016)^4

= £219,463.18

To find the total amount of interest Claire will get, we need to subtract the principal amount from the total amount of money in the account at the end of four years:

Total interest = £219,463.18 - £200,000

= £19,463.18

Therefore, Claire will get £19,463.18 in total interest at the end of four years.

We may conclude after answering the presented question that rectangle Therefore, the expression for the width of the porch is x + 2 feet.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

area of a rectangle

Area = length x width

To do this, we can factor the expression for the area, which gives us:

x² + 9x + 14 = (x + 2)(x + 7)

Area = length x width

(x + 2)(x + 7) = (x + 7) x width

x + 2 = width

Therefore, the expression for the width of the porch is x + 2 feet.

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Latrell would need to pay 105 to replace the felt on his pool table.

Latrell has a pool table that is 3 feet wide and 7 feet long.

The pool table's felt needs to be replaced, and the cost of the felt per square foot is $5.00.

Let's find out how much it would cost Latrell to replace the pool table's felt.

What is the surface area of the pool table.

To determine the surface area of the pool table,

we need to multiply the length by the width, as shown below:

Surface area = length × width

Surface area = 7 ft × 3 ft

Surface area = 21 square feet

Now that we know the surface area of the pool table, we can determine the cost of the felt.

Latrell will need 21 square feet of felt, and it costs $5.00 per square foot.

We can use the following formula to determine the total cost of the felt:

Total cost of felt = cost per square foot × surface area.

Total cost of felt = $5.00 × 21 square feet.

Total cost of felt = $105

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Answer: 27.50

Step-by-step explanation: 2.50 X 7 =17.50 + 10 = 27.50

The value of the investment at the end of 10 years would be $3,905.76 if the interest rate is 5% per year and compounds annually.

The value of an investment after a certain number of years depends on several factors, including the initial amount invested, the interest rate, and the compounding frequency.

Assuming a fixed interest rate and compounding frequency, we can use the formula for compound interest to calculate the value of the investment after 10 years.

For example, if the interest rate is 5% per year and the investment compounds annually, the formula would be:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the number of years

Plugging in the given values, we get:

A = 2400(1 + 0.05/1)^(1*10)

A = 2400(1.05)^10

A = 2400(1.6289)

A = $3,905.76

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Answer:

Step-by-step explanation:

4x - 5y = -17

-4x - 24y = -244

-29y = -261

y = 9

x + 54 = 61

x = 7

(9,7) Option B