The compound shape below is formed from a semicircle and a rectangle.

Calculate the area of the compound shape.
Give your answer in cm² to 1 d.p.

Answer: Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:

10 × (2.5 + 1.2) = 37 cm.

Step-by-step explanation:

To represent the length of the bracelet, we need to determine the length of each repetition of the basic pattern and then multiply it by the number of times the pattern is repeated.

The length of each repetition of the basic pattern is the sum of the length of one blue bead and one green bead, which is:

B + 1.2 cm

Since the basic pattern is repeated 10 times, the total length of the bracelet is:

10 × (B + 1.2) cm

And we know that the total length of the bracelet is 37 cm, so we can set up an equation:

10 × (B + 1.2) = 37

Simplifying the equation, we can divide both sides by 10:

B + 1.2 = 3.7

Subtracting 1.2 from both sides, we get:

B = 2.5

Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:

10 × (2.5 + 1.2) = 37 cm.

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Since OX is perpendicular to PQ, and OY is perpendicular to RS, we know that OX and OY are both radii of the circle. Therefore, we can write:

OX = OY

This is because all radii of a circle are equal in length. Alternatively, we could also say that OX and OY are both the distance from the center O to the respective lines PQ and RS. Since PQ=RS, OX and OY are equal in length.

In a circle, the center is the point from which all points on the circumference are equidistant. This means that any line segment from the center to a point on the circle is a radius of the circle.

In this problem, we have two lines PQ and RS, both of which are tangent to the circle at points P and R respectively. We also have two lines OX and OY, each of which is perpendicular to one of the tangent lines.

Because the tangent lines are perpendicular to their respective radii (PQ is perpendicular to OX, and RS is perpendicular to OY), we can conclude that OX and OY are both radii of the circle, and therefore, they have the same length.

Note that both are still angles at 90 degrees.

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The approximate area that is watered by the sprinkler, we need to use the formula for the area of a circle, which is A = πr^2, where A is the area, π is a constant equal to approximately 3.14, and r is the radius of the circle.

In this case, we are given that the distance from the sprinkler to the outer edge of the circle is 2.5 m, which is the radius of the circle. Therefore, we can substitute this value into the formula and get:

A = [tex]3.14 x 2.5^2[/tex]

A =[tex]19.625 m^2[/tex]

So, the approximate area that is watered by the sprinkler is 19.625 square meters. This means that any plants, grass or other vegetation within this area will receive water from the sprinkler.

It is important to note that this is only an approximation since the shape of the watered area may not be a perfect circle and the sprinkler may not spray water evenly in all directions.

Additionally, the amount of water sprayed by the sprinkler and the time it takes to water the area will also affect the actual amount of water received by the plants.

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The woman performed 100 joules of work to push the cart of groceries over a distance of 10 meters.

To find the work performed by the woman, we will use the work-energy theorem which states that work (W) is equal to the change in energy. In this case, the woman applies a 10 Newton force and uses 100 joules of energy. The formula for work is:

W = F × d × cos(θ)

Where W is work, F is force, d is the distance over which the force is applied, and θ is the angle between the force and the direction of motion. Since the woman used 100 joules of energy, we can rewrite the equation as:

100 J = 10 N × d × cos(θ)

We don't have information about the angle θ, but if we assume that she applied the force horizontally, which is in the same direction as the motion, the angle θ would be 0 degrees, and the cosine of 0 is 1. Therefore, the equation becomes:

100 J = 10 N × d

To find the distance (d), we can now solve for d:

d = 100 J / 10 N

d = 10 meters

So, 100 joules of work was performed by the women to push the cart of groceries over a distance of 10 meters.

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By using Numerical integration method such as Simpson's rule or Monte Carlo simulation, we will get the area

To calculate the area of surface S, we first need to find the limits of integration. The paraboloid hyperbolic is located between the cylinders x + y = 1 and x = 2. This means that the limits of integration for x are 1 and 2, and for y they are -sqrt(4-[tex]x^2[/tex]) and sqrt(4-[tex]x^2[/tex]).

Calculation of area:
Using the formula for the surface area of a paraboloid hyperbolic, which is given by:
A = 2π ∫∫ (1 + (∂z/∂x[tex])^2[/tex] + (∂z/∂y[tex])^2[/tex][tex])^{(1/2)[/tex] dA
We can calculate the area of surface S. First, we need to find the partial derivatives of z with respect to x and y:
∂z/∂x = -2x/(2+[tex]y^2[/tex])
∂z/∂y = -2y/(2+[tex]x^2[/tex])
Substituting these values into the formula for surface area, we get:
A = 2π ∫[tex]1^2[/tex] ∫-sqrt(4-[tex]x^2[/tex])^sqrt(4-[tex]x^2[/tex]) (1 + (-2x/(2+y^2)[tex])^2[/tex]+ (-2y/(2+[tex]x^2)[/tex][tex])^2[/tex][tex])^{(1/2)[/tex]dydx
Using a numerical integration method such as Simpson's rule or Monte Carlo simulation, we can calculate this integral to get the area of surface S.

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Answer:

34.65 mi²

Step-by-step explanation:

Area of parallelogramam = b · h

b = 6.3 mi

h = 5.5 mi

Let's solve

6.3 · 5.5 = 34.65 mi²

So, the area of the shape is 34.65 mi²

Anallency will have $134.46 more money than Alejandro after one year of their respective deposits.

Alejandro and Anallency are depositing money in separate accounts with different interest rates. Alejandro is depositing $1,750 in an account that earns a simple interest rate of 6.5% per year, while Anallency is depositing $1,675 in an account that earns a compounded interest rate of 7.5% per year. After one year of their respective deposits, Anallency will have $134.46 more money than Alejandro.

The difference in interest earned between the two accounts is the reason for the difference in money earned by Alejandro and Anallency. Alejandro's account earns a simple interest rate, which means that he earns 6.5% of his initial deposit every year, regardless of how much interest he has already earned.

On the other hand, Anallency's account earns a compounded interest rate, which means that she earns interest on both her initial deposit and on any interest earned in previous years.

The formula for calculating simple interest is I = Prt, where I is the interest earned, P is the principal (or initial deposit), r is the interest rate, and t is the time in years. Using this formula, we can calculate that Alejandro will earn $113.75 in interest after one year.

The formula for calculating compounded interest is A = P(1 + r/n)^(nt), where A is the amount of money at the end of the time period, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Using this formula, we can calculate that Anallency will have $248.21 more in her account than Alejandro after one year.

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The mean is equal to the median, so the data is symmetrical.

Given that :

Colin surveyed 12 teachers at his school to determine how much each person budgets for lunch.

The data is :

10   5   8   10   12   6   8   10   15   6   12   18

Mean is the average of these numbers.

Mean = (10 + 5 + 8 + 10 + 12 + 6 + 8 + 10 + 15 + 6 + 12 + 18) / 12

         = 10

Now median is the element in the middle arranged in an order.

Arrange the data in ascending order.

5  6  6  8  8  10  10  10  12  12  15  18

The middle element is the average of the 6th and 7th elements.

Median = (10  10) / 2 = 10

So mean and the median is equal. So the data is symmetrical.

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Hunter assumed he would only get 64 problems correct on his test, but he actually got 78 correct, So his percent error is 18%.

To calculate Hunter's percent error, we'll use the given formula:

Percent error = ((Prediction - Actual) / Actual) x 100

Prediction = 64 (the number of problems Hunter assumed he would get correct)
Actual = 78 (the number of problems he actually got correct)

Now, plug in the values:

Percent error = ((64 - 78) / 78) x 100
Percent error = (-14 / 78) x 100
Percent error ≈ -17.95%

Since percent error is typically expressed as a positive value, we can round to the nearest percent and report it as:

Percent error ≈ 18%

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The coordinates of transforming image of the vertices of the triangle ABC are A' (1, -1) ,B' (3, 1) , and C' (1, 4).

In triangle ABC,

Coordinates of the vertices of triangle ABC are,

A(-1,1), B(1,3) and C(4,1)

The transformation T y=x reflects the points across the line y=x.

The image of each point, we simply swap the x and y coordinates of each point.

So, applying the transformation T y=x to the vertices of triangle ABC, we get,

A' = (-1, 1) → (1, -1)

B' = (1, 3) → (3, 1)

C' = (4, 1) → (1, 4)

This implies,

The image of triangle ABC under the transformation T y=x is triangle A'B'C', where,

A' is located at (1, -1)

B' is located at (3, 1)

C' is located at (1, 4)

Therefore, in triangle ABC labeling the coordinates of the vertices of A'B'C'  after transformation are as follows,

A' (1, -1)

B' (3, 1)

C' (1, 4)

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The above question is incomplete, the complete question is:

Triangle ABC has vertices A(-1,1), B(1,3) and C(4,1). The image of ABC after the transformation T y=x is A’ B’ C’. State and label the coordinates of A’ B’ C’.

Answer:

To find the area of a triangle given its vertices, we can use the formula:

Area = 1/2 * |(x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))|

where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the three vertices.

Using this formula, we can calculate the area of the triangle with vertices at (5,0), (-3,1), and (2,6) as follows:

Area = 1/2 * |(5*(1-6) + (-3)(6-0) + 2(0-1))|

= 1/2 * |-25 - 18 - 2|

= 1/2 * |-45|

= 22.5

Therefore, the area of the triangle is 22.5 units squared. So the answer is option C: 22.5 units squared.

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The charge for the companies is the same at 500 minutes

From the question, we have the following parameters that can be used in our computation:

This means that

A(x) = 50 + 0.05x

B(x) = 0.15x

When the charge for the companies are the same, we have

0.15x = 50 + 0.05x

So, we have

0.1x = 50

Divide

x = 500

Hence, the number of minutes is 500

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If there were four girls and four boys to choose from, the new sample size is one that will be a total of 16 possible combinations.

When making selections for the student council's representatives, the sample size belongs to the whole of the feasible options.

To know the sample size, we must reason every conceivable permutation involving a single female and a single male.

So, if there were four girls and four boys to choose from, the new sample size would be:

There are:

4 choices for girls

4 choices for boys.

So, for each girl's choice, there would be 4 corresponding choices for boys.

Hence it will be:

4 x  4 = 16

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Answer:

102 cm³

Step-by-step explanation:

density = m/v

1 g = 0.001 kg

Volume of real statue = v = m/d = 1632 kg / 0.002 kg/cm³ = 816,000 cm³

scale factor for height:  200 cm : 10 cm  =  20 : 1

scale factor for volume:  20³ : 1³  = 8,000 : 1

Volume of model = 816,000 cm³ / 8,000 = 102 cm³

Therefore , the solution of the given problem of circle comes out to be since the numbers 1, 2, and 3 cannot be dispersed evenly around the circle with the necessary amount of gaps.

Each element of the aeroplanes creates a circle when viewed from this new angle and at a distance. (center). Its structure is composed of surfaces and undulating regions that contrast with one another. Additionally, it rotates equally within the centre in all directions. Every ultimate extent of a circular or restricted double sphere is the same as the sphere's "center."

Here,

One potential twin circle that we can create is as follows:

=> 1 2 1 3 2 5 4 5 4 3

Here, the first twin pair 1 is divided into three pairs, with the second twin pair 2 being divided into two pairs, the third twin pair being divided into three pairs, and so on. This satisfies the criteria of the puzzle, and we can verify that every twin pair appears precisely twice.

When the numbers are reversed, a second potential twin circle results:

=> 3 4 5 4 5 2 3 1 2 1

As a result, there is no such twin circle since the numbers 1, 2, and 3 cannot be dispersed evenly around the circle with the necessary amount of gaps.

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The probability of selecting two country songs followed by an R&B song is 0.0202.

The probability of selecting two country songs followed by an R&B song is determined below as follows:

The total number of songs in the playlist = 40

The probability of the first song being country = 15/40.

The probability of the second song also being country = 14/39

The probability of the third song being R&B =s 10/38

Therefore, the probability of selecting two country songs followed by an R&B song is:

Probability(country, country, R&B) = (15/40) x (14/39) x (10/38)

Probability(country, country, R&B)  = 0.0202

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The piecewise function that represents the situation is therefore:

Costs                                           Possible hours

13                                                     0 < x ≤ 1

20                                                 1 < x ≤ 3

50                                                   3 < x ≤ 10

We see that up to one hour, the cost to Marshall would be $ 13 so the possible hours at that price is 0 < x ≤ 1 .

Likewise from one hour, the price goes up to $ 20 which means that possible hours become  1 < x ≤ 3 because the price will increase at 3 hours again.

From 3 hours, the price becomes $ 50 and there are a maximum of 10 hours so the hours become 3 < x ≤ 10 .

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So basically you have to drag an angle to the box, example drag DFA to the box, then add what angle it is equal to. You have to calculate the angle and drag it opposite to the DFA. For DFA, it will be 58.

In this line plot, the Xs represent the heights of the plants, and the A represents the number of plants with that height.

The line plot that correctly shows Joel's data is:

Plant Heights

Х

Х

X

X

A

0

Height (feet)

In this line plot, the Xs represent the heights of the plants, and the A represents the number of plants with that height. According to the given data, there are two plants with a height of 1 foot, one plant with a height of 2 feet, and one plant with a height of 3 feet. Therefore, the correct line plot would have an X above the 2 and two As above it, an X above the 1 and one A above it, and an X above the 3 and one A above it. The other line plot shown does not correctly represent Joel's data.

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For -10 as the value of k the equation k – 3(k + 5) – 0. 5 = 3(0. 25k + 4) is true.

Given equation is k – 3(k + 5) – 0. 5 = 3(0. 25k + 4)

To solve the equation, firstly we have to solve or open the brackets using the distributive property that is a(x + y) = ax +ay

Thus the equation becomes, k - 3k - 15 - 0.5 = 0.75k + 12

Then we have to take all the terms with k on one side and other on the other or segregate the like terms, the equation now is

k - 3k - 0.75k = 12 + 15 + 0.5

Simplify the equation by adding or subtracting the like terms.

-2.75k = 27.5

Then we divide the coefficient of k by the other side and get our answer

k = 27.5 ÷ (-2.75)

k = -10

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The speed of the faster car is 90 kph and the speed of the slower car is 45 kph.

We are given that two cars are starting together and they travel in the same direction. Let one car be car A and the other car B. Speed of car B is twice the speed of car A. Let r be the rate of speed of car A and 2r be the rate of speed of car B.

We know that these two cars are 225 km apart. We will use the formula distance = speed * time. Let the distance car A travels after 5 hours be 5r. So, the distance traveled by car B after 5 hours will be 5(2r) = 10r.

Since car B is faster, it will have traveled farther after 5 hours. Therefore,

Distance traveled by car B - distance traveled by car A = 225

10r - 5r = 225

5r = 225

r = 45 kph

and

2r = 90 kph

Therefore, car A is traveling at 45 kph and car B is traveling at 90 kph.

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The top of the ladder is moving down the wall at a rate of 32/3 feet per second when the bottom of the ladder is 8 feet from the wall.

Let's denote the distance between the bottom of the ladder and the wall as x, and the distance between the top of the ladder and the ground as y. Since the ladder is leaning against the wall, we have a right triangle formed by the ladder, the wall, and the ground.

We know that the ladder has a length of 10 feet, so by the Pythagorean theorem, we have:

x^2 + y^2 = 10^2

Differentiating both sides with respect to time t, we get:

2x(dx/dt) + 2y(dy/dt) = 0

We want to find the rate of change of y (the speed at which the top of the ladder is moving down the wall), when x = 8 ft and dx/dt = 8 ft/s. We can substitute these values into the equation above and solve for dy/dt:

2(8)(8) + 2y(dy/dt) = 0

Simplifying this equation, we get:

dy/dt = -64/y

Now we need to find the value of y when x = 8 ft. We can use the Pythagorean theorem again:

x^2 + y^2 = 10^2

8^2 + y^2 = 100

y^2 = 100 - 64

y = sqrt(36) = 6 ft

Substituting this value of y into our equation for dy/dt, we get:

dy/dt = -64/6 = -32/3 ft/s

Therefore, the top of the ladder is moving down the wall at a rate of 32/3 feet per second when the bottom of the ladder is 8 feet from the wall.

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The option that best describes this data set is option B: categorical and univariate.

Categorical data refers to data namely divided into distinct classifications or groups. In this case, the water usage dossier is divided into five categories established the sources of water habit in the household: toilet, washer, shower, dishwasher, and tap.

Therefore, the water usage basic document file is considered categorical as well as univariate, as it is divided into distinct classifications based on start of water usage and includes singular variable, that is water usage per day.

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Answer:

option B: categorial and univariate

Step-by-step explanation:

i took the test :)

hope this helps xx

The paper airplane will not hit the ground within the given time frame.

To find the equation for h( t), we need to find the rate of change or the  pitch of the function. We can do this by chancing  the difference in height and time for any two points on the line. Let's choose the first two points,( 0,200) and( 1,208).  

pitch = ( change in height)/( change in time)  

pitch = ( 208- 200)/( 1- 0) =  8  

So, the equation for h( t) can be written in  pitch- intercept form as   h( t) =  8t b  

To find the value of b, we can use any of the given points.

Let's use( 0,200)   200 =  8( 0) b  b =  200  

So, the equation for h( t) is   h( t) =  8t 200  

To find how long it'll take the aeroplane to hit the ground, we need to find when h( t) =  0,

since that would mean the height is 0  bases or the ground  position.   0 =  8t 200   working for t,

we get   t = -25

Since time cannot be negative the paper airplane will not hit the ground within the given time frame.

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a) To find y for the given x and Δx values, first calculate x + Δx:
x + Δx = 3 + 0.03 = 3.03

Now, use the function y = f(x) = 9x to find the y values:
y = 9(3) = 27 (for x = 3)
y = 9(3.03) = 27.27 (for x = 3.03)

b) To find dy, we first need to find the derivative of the function (f'(x)). The function is y = f(x) = 9x, and its derivative (using differentiation) is:
f'(x) = 9

c) To find dy for the given x and Δx values, we can now use the formula dy = f'(x)dx:
dy = f'(x)dx = 9(0.03) = 0.27

So, for the given x and Δx values, a) y is 27 and 27.27, b) dy is equal to 9, and c) dy for the given x and Δx values is 0.27.

The  expected value and standard error for the number of winning plays is $3.1 and $ 2.21.

The population mean's likelihood to differ from a sample mean is indicated by the standard error of a mean, and simply standard error.

It reveals how much what the sample mean will change if a study were to be repeated with fresh samples drawn from a single population.

Chance of winning $3 = 2/10

chance of losing $2 = 3/10

chance of losing $1 = 5/10

Average of tickets. = - $2.50

SD of tickets = $1.80.

The box model for net gain has 2 tickets labeled $3, 3 tickets labeled $2, 5 tickets labeled

a) Expected value for the net gain.

The Expected value for net = ∑ x.p(x)

Here

can take value $1, $2 and $3

Here p(x) us the probability of winning respectively.

So, Now, Expected gain is,

(2 x 3 x 2/10) + (3 x -2 x 7/10) + (5 x -1 x 5/10)

= 12/10 - 18/10 - 25/10

= -31/10 = -$3.1.

b) Standard error of the net gain,

S.D = [tex]\sqrt{E(x^2) - [E(x)]^2}[/tex]

Now E(x²) = (2 x 3² x 2/10) + (3 x -2² x 7/10) + (5 x -1² x 5/10)

= 36/10 + 84/10 + 25/10 = 145/10

= $ 14.5

SD = [tex]\sqrt{14.5 - 3.1}\\[/tex]

SD = $ 2.21

c) Chance that the net gain is $15

P(X=15) = (z = 15-(-2.50)/1.80

= P(z=9.72) = 0.99.

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Using the sine function and the given information, we can find that length of  y is approximately 203.3 feet.

We know that exterior angle of a triangle is equal to the sum of its opposite interior angles. So, we can find angle BAC as follows

BAC + ABC = 180 degrees

As sum of interior angles of a triangle

BAC + 90 = 180

BAC = 90 degrees

Now, we can use the sine ratio to find y

sin(31) = y/400

y = 400 * sin(31)

y ≈ 203.3 ft

Therefore, y is approximately 203.3 ft when rounded to the nearest tenth.

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--The given question is incomplete, the complete question is given

" Find y. Round to the nearest tenth:

In triangle ABC, 31° is the outer angle at A which is in between a line extended from A parallel to BC.

X  is CA

у is AB

400 ft is BC

Angle B is right angle

y = [ ? ]ft Enter"--

Answer:

2√6 + 9

Step-by-step explanation:

√24 + √81

= √4√6 + 9

= 2√6 + 9

The calculated value of sin of the angle is 1/96

From the question, we have the following parameters that can be used in our computation:

cos(θ) = 1/3

tan(θ) = 1/32

The value of sin of the angle is calculated as

sin(θ) = cos(θ) * tan(θ)

substitute the known values in the above equation, so, we have the following representation

sin(θ) = 1/3 * 1/32

Evaluate the products

so, we have the following representation

sin(θ) = 1/96

Hence, the value of sin of the angle is 1/96

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