OWX is a sector of a circle with a radius of
32 cm.
OYZ is a sector of a circle with a radius of
21 cm.
The central angle of both sectors is 75°.
Work out the area of the shaded shape WXZY
Give your answer in cm² to 1 d.p.
try help please

Answer: B : 5cm, 12cm and 13cm

Step-by-step explanation:

it says the amount of centimeters on each side on the ruler. its the small numbers

Using the triangle proportionality theorem, the length of CD is calculated as: 12 cm.

The triangle proportionality theorem states that if a line is parallel to one side of a triangle, it divides the other two sides proportionally.

To calculate the length of the line, recall the triangle proportionality theorem which states that:

Given the following:

AB = 10 cm

AC = 15 cm

BE = 8 cm

CD = ?

Based on the triangle proportionality theorem, we have:

AC/AB = CD/BE

Substitute:

15/10 = CD/8

Cross multiply:

10CD = 120

CD = 120/10

CD = 12 cm

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The volume of the right square pyramid is 320 in³.

Volume is a measure of the amount of space that an object takes up. It is usually measured in cubic units, such as cubic centimeters, cubic meters, or cubic feet. Volume is an important concept in mathematics, physics, and engineering, as it can be used to calculate the size and mass of an object. It can also be used to calculate the amount of liquid or gas that can fit into a container.

The volume of a right square pyramid can be calculated using the formula V = (1/3)lhs.

Therefore, the volume of the right square pyramid with the given dimensions is:

V = (1/3) x 10 in x 6 in x 16 in

V = 320 in³

Therefore, the volume of the right square pyramid is 320 in³.

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The volume of the pyramid is 320in cubic units

volume is a measure of space occupied by an object,

the formula for the volume of a pyramid is equal to one third of the product of the height and the base area of the pyramid

The pyramid that has a square base is known as Square pyramid.

square pyramid has 4 faces and 1 square base.

The volume of the square pyramid is given by the formula

V=(1/3)*(base area of a square)*(height of the square pyramid)cubic units

V=(1/3)AH cubic units

The volume of the pyramid is V= (base length*base width*height)/3

V=(1/3)l*s*h

V=(1/3)10*16*6

V=320 in

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Answer:

The answer is 13.

Step-by-step explanation:

First, we must find the hypotenuse for right angle:

[tex]c^{2} = a^{2} + b^{2}\\ \\\\c^{2} = 12^{2} + 5^{2} \\c^{2} 144 + 25 \\c^{2} = 169 \\c^{2} =\sqrt{169}\\c^{2} = 13[/tex]

The size of the angle that the line DE makes with the plane ABCD is 50.8 degrees

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

The figure

To start with, we calculate the measure of length BE using the following tangent ratio

tan(60) = BE/60

So, we have

BE = 60√3

Next, we calculate DB using the Pythagoras theorem

DB = √(60² + 60²)

Evaluate

DB = 60√2

The measure of the required angle is then calculated as

tan(Angle) = 60√3/60√2

Evaluate

tan(Angle) = 1.2247

Take the arc tan

Angle = 50.8 degrees

Hence, the angle is 50.8 degrees

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The complete equation using the numbers from1 to 9 will be:

2:2 = 3×3:9 = 4×4 =16.

A contrast between two numbers in arithmetic, this is referred to as a proportion. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

In the question given:

By using the digits 1 to 9 at one time each, we have to form the equation to make the equality true.

Now,

All the numbers from 1 to 9 are = 1, 2 ,3, 4, 5, 6, 7, 8 and 9

Let the proportion be = 1

Hence, the equivalent ratios are:

1:1, 2:2. 3:3

Now, according to the question the required equation will be:

2:2 = 3×3:9 = 4×4 =16.

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Answer: The representations of these functions are alike in that they both describe the movement of the falling object. They are different in that one function measures the distance the object has traveled from its starting point, while the other measures its distance from the ground.

Step-by-step explanation:

The volume of the cone in terms of π is [tex]90.312\ inches^{3}[/tex].

A cone is a three-dimensional body with a flat base that is connected to a pointed top.

The formula for the volume of a cone is :

[tex]Volume,V = \frac{\pi r^{2}H }{3}[/tex]

It is given that height, H = 15 inches.

The formula for the circumference of the base is = [tex]2\pi r[/tex]

So, we can say that :

[tex]2\pi r=8.5\pi[/tex]

[tex]r=\frac{8.5}{2} =2.25[/tex] inches

Therefore, the volume of the cone is, V:

[tex]=\pi \times 4.25^{2} \times 15\\ =90.312\ \text{inches}^{3}[/tex]

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The result is the 95% confidence interval for µ.

The Metropolis-Hasting (M-H) algorithm is a Markov Chain Monte Carlo (MCMC) method used to sample from a probability distribution. In this case, we want to sample from the posterior distribution of µ, given the recorded data and the prior distribution. The M-H algorithm works by proposing a new value for µ, calculating the acceptance probability, and then deciding whether to accept or reject the proposed value. Here are the steps to construct the M-H algorithm:

Start with an initial value for µ, denoted as µ0.
Propose a new value for µ, denoted as µp, from the proposal distribution q(µ| µo) : N(θ: mean = µp, std = 2).
Calculate the acceptance probability, denoted as α, using the likelihood function L(µ) and the prior distribution p(µ):
α = min{1, [L(µp)/L(µ0)]*[p(µp)/p(µ0)]*[q(µ0| µp)/q(µp| µ0)]}
Generate a random number u from the uniform distribution U(0,1).
If u ≤ α, accept the proposed value and set µ0 = µp. Otherwise, reject the proposed value and keep µ0 unchanged.
Repeat steps 2 to 5 for a specified number of MCMC draws (15000 in this case), and discard the first 1500 draws as the burn-in phase.
Calculate the 95% confidence interval for µ using the remaining 13500 draws.

The 95% confidence interval for µ can be calculated by finding the 2.5th and 97.5th percentiles of the posterior distribution of µ. This can be done by sorting the 13500 draws of µ in ascending order and finding the values that correspond to these percentiles. The result is the 95% confidence interval for µ.

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a) (TRUE)

If b is a linear combination of the columns of the matrix A, then the linear system Ax = b has a unique solution.

b) (FALSE)

If {u, v, w} is linearly independent, then {u+w, v + w} is linearly independent.

c) (FALSE)

If V = span{V1, V2, V3} and dim(V) = 2, then {V2, V3} is a basis of V.

a) If b is a linear combination of the columns of matrix A, then the linear system Ax = b has a unique solution. This is (always) true because if b is a linear combination of the columns of matrix A, then it can be written as Ax.

Therefore, if A is invertible, then x = A^(-1)b is a unique solution to Ax = b.

b) If {u, v, w} is linearly independent, then {u+w, v+w} is linearly independent. This is (possibly) false because {u+w, v+w} is linearly dependent if u = -v = w.

Therefore, {u+w, v+w} is not linearly independent.

c) If V = span{V1, V2, V3} and dim(V) = 2, then {V2, V3} is a basis of V.

This is (possibly) false because {V2, V3} is a basis for V if and only if V2 and V3 are linearly independent and span(V).

However, dim(V) = 2 implies that V is a 2-dimensional subspace of R^3, so {V1, V2, V3} cannot be linearly independent.

Therefore, {V2, V3} is not necessarily a basis for V.

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We can use LCM to find a common denominator for these fractions. The LCM of 70, 2, and 5 is 70 x 2 x 5 = 700. The result of the expression is approximately 29.3885.

To solve this problem using LCM, we first need to convert all the mixed numbers to improper fractions:

Three and three seventieths = (3 x 70 + 3) / 70 = 213 / 70

Six and a half = (6 x 2 + 1) / 2 = 13 / 2

Nine and three fifths = (9 x 5 + 3) / 5 = 48 / 5

Now we can use LCM to find a common denominator for these fractions. The LCM of 70, 2, and 5 is 70 x 2 x 5 = 700.

We can then convert each fraction to an equivalent fraction with denominator 700:

213/70 = 3.042857... ≈ 3.043

13/2 = 455/70 = 6.5

48/5 = 192/20 = 96/10 = 480/50

Now we can substitute these equivalent fractions into the original expression and simplify:

3.043 × 6.5 + 480/50 = 19.7885... + 9.6 = 29.3885.

LCM stands for the "Least Common Multiple" and is a mathematical concept used to find the smallest multiple that two or more numbers have in common. In other words, it is the smallest positive integer that is divisible by all the given numbers.

To find the LCM of two or more numbers, we can start by finding their prime factorization. Then, we can take the highest power of each prime factor that appears in any of the factorizations and multiply them together to get the LCM. Taking the highest power of each prime factor (2^3 x 3^1), we get 24, which is the smallest multiple that both 6 and 8 have in common.

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Answer:

Step-by-step explanation:

Pages Alana writes = m+4

to fill in the blanks add 4 to 5, 7, and 9 because of the 4 extra pages Alana writes.

That will give you: 9, 11, and 13 as your answers

The distance between the points (-9, 4) and (3, 12) is approximately 14.42 units.

what exactly is distance?

Distance is the amount of space between two objects or locations. It is a measure of how far apart two things are from each other, typically expressed in units such as meters, kilometers, miles, feet, or yards. Distance can be measured in a straight line, known as the "Euclidean distance," or it can be measured along a path or route, known as the "distance traveled." Distance is a fundamental concept in many areas of science and mathematics, including physics, geography, and geometry

The formula for calculating the distance between two points is d = ((x2 - x1)2 + (y2 - y1)2).

Let's use this formula to find the distance between the two points (-9, 4) and (3, 12):

d = √((3 - (-9))² + (12 - 4)²)

= √(12² + 8²)

= √(144 + 64)

= √208

≈ 14.42

So the distance between the points (-9, 4) and (3, 12) is approximately 14.42 units.

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Answer:

Bears: 12

Tigers: 5

Step-by-step explanation:

9:15

the common factor of 9 and 15 is 3. so we divide both sides by 3.

3:5

12:20

a) The expression can be factored as (5xy+8z)(5xy-8z).

b) The expression can be factored as (2x+3y)(2x-3y).

The expressions that can be factored as a difference of squares are:

- 25x^(2)y^(2)-64z^(2)
- 4x^(2)-9y^(2)

A difference of squares is an expression in the form a^2 - b^2, which can be factored as (a+b)(a-b). In the first expression, 25x^(2)y^(2) can be rewritten as (5xy)^2 and 64z^(2) can be rewritten as (8z)^2. Therefore, the expression can be factored as (5xy+8z)(5xy-8z).

In the second expression, 4x^(2) can be rewritten as (2x)^2 and 9y^(2) can be rewritten as (3y)^2. Therefore, the expression can be factored as (2x+3y)(2x-3y).

The other two expressions, 16x^(2)+25y^(2) and x^(3)-125, cannot be factored as a difference of squares because they do not have the form a^2 - b^2.

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Answer:

To express the value 0.0000547 in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point.

0.0000547 = 5.47 × 10^(-5)

The exponent -5 indicates that we moved the decimal point 5 places to the right.

The solutions for the absolute value equation are x = 0 and x = -4.

To solve the absolute value equation |(5x + 10)/(2)| = 5, we need to remove the absolute value bars and create two separate equations, one positive and one negative. Then we can solve for x in each equation.

First, let's remove the absolute value bars and create two separate equations:

(5x + 10)/2 = 5 and (5x + 10)/2 = -5

Now we can solve for x in each equation:

(5x + 10)/2 = 5

5x + 10 = 10

5x = 0

x = 0

And:

(5x + 10)/2 = -5

5x + 10 = -10

5x = -20

x = -4

So the solutions to the equation |(5x + 10)/(2)| = 5 are x = 0 and x = -4.

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Answer:

42 minutes are not spent on instructions

Step-by-step explanation:

First, we must find out how many minutes is in [tex]\frac{7}{8}[/tex] hour

[tex]60*\frac{7}{8}=\frac{60*7}{8} =\frac{420}{8} =52.5[/tex]

In [tex]\frac{7}{8}[/tex] hour, there is about 52 [tex]\frac{1}{2}[/tex] minutes

Then we must add up the fractions that are NOT the instructions

[tex]\frac{1}{2} +\frac{3}{10} =\frac{5}{10} +\frac{3}{10} =\frac{8}{10} =\frac{4}{5}[/tex]

[tex]\frac{4}{5}[/tex] of the total time (52 [tex]\frac{1}{2}[/tex] minutes) is not spent on instructions

Then we must multiply the fraction of time spent on other things ([tex]\frac{4}{5}[/tex]) by total time (52 [tex]\frac{1}{2}[/tex] minutes) in order to find out how many minutes weren't spent on instructions.

[tex]\frac{4}{5}*52 \frac{1}{2} =\frac{4}{5}* \frac{105}{2}=\frac{420}{10} =42[/tex]

42 minutes are not spent on instructions

The natural logarithm function is ln(p) = ln(100) - 0.35t

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

The table of values

The function can be represented as

p = ae^kt

Using the points on the table, we have

ae^(k * 0) = 100

So, we have

a = 100

This gives

p = 100e^kt

Using another point, we have

70.5y = 100e^(k * 1)

70.5y = 100e^k

So, we have

e^k = 0.705

Take the natural logarithm of both sides

k = ln(0.705)

k = -0.35

The function becomes

p = 100e^(-0.35t)

Take the natural logarithm of both sides

ln(p) = ln(100) - 0.35t

Hence, the function is ln(p) = ln(100) - 0.35t

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We will see that the measure of angle z is 70°

First we can get the angle in the right vertex in the triangle in the right side.

We know that the right angle and the 40° one are vertical angles, then the right angle also measures 40°

Also remember that the sum of the interior angles of any triangle is 180°, then:

105° + 40° +x = 180°

x = 180° - 40° - 105° = 35°

Then the right angle of the second triangle (the one that is below the line) also measures 35°

The bottom angle measures:

y + 85 = 180

y = 180 - 85 = 95

And if the last angle is k:

k + 95 + 35 = |80

k = 180 - 35 - 95 = 50

Then the right angle of the last triangle is also 50°, then we can write:

z + 60 + 50 = 180

z = 180 - 50 - 60 = 70°

That is the measure.

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23) The equation for the hyperbola is (y-2)^2/9 - (x-1)^2/16 = 1.

24) The equation for the circle is (x+1)² + (y-3)² = 17.

23. The equation for a hyperbola with center (h,k) and vertices (h,k+a) and (h,k-a) is:

(y-k)²/a²- (x-h)²/b² = 1

In this case, the center is (1,2), so h = 1 and k = 2. The vertices are (1,5) and (1,-1), so a = 3. To find b, we can use the fact that c^2 = a^2 + b^2, where c is the distance from the center to the foci. The foci are (1,7) and (1,-3), so c = 5. Therefore:

5² = 3² + b²

b² = 25 - 9

b² = 16

b = 4

So the equation for the hyperbola is:

(y-2)^2/3^2 - (x-1)^2/4^2 = 1

(y-2)^2/9 - (x-1)^2/16 = 1

24. The equation for a circle with center (h,k) and radius r is:

(x-h)² + (y-k)² = r²

In this case, the center is (-1,3), so h = -1 and k = 3. To find the radius, we can use the distance formula with the center and the point (3,2):

r = sqrt((3-(-1))² + (2-3)²

r = sqrt(4² + (-1)²)

r = sqrt(16 + 1)

r = sqrt(17)

So the equation for the circle is:

(x-(-1))² + (y-3)² = (sqrt(17))²

(x+1)² + (y-3)² = 17

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The distance between the hunter and the bird is 5.39

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below.

distance = √( (x₂ - x₁)² + (y₂ - y₁)²)

The hunter is at (0, 0) and shoots at (2, 5), so we can plug those values ​​into the formula for the distance:

distance = √( (2 - 9)² + (5 - 0)²)

distance = √( (2 )² + (5 )²)

distance = √( 4 + 25) = 5.39

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The numbers for which the rational expression is undefined are x=0 and x=-4.

To find the numbers for which the rational expression (7x^(4)+8)/(5x^(2)+20x) is undefined, we need to find the values of x that make the denominator equal to zero. This is because division by zero is undefined.

So, we need to solve the equation 5x^(2)+20x=0 for x.

We can factor out a common factor of 5x from the equation:

5x(x+4)=0

Now, we can use the zero product property to set each factor equal to zero and solve for x:

5x=0 or x+4=0

x=0 or x=-4

So, the numbers for which the rational expression is undefined are x=0 and x=-4.

In summary, the rational expression (7x^(4)+8)/(5x^(2)+20x) is undefined for x=0 and x=-4.

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Given that A = |b с| . |a d| and det(A) = -11, the following computations can be made:
(b) det(4A) det(A) = 4^2 * (-11) * (-11) = 1936
(c) det(2A - 1) = 2^2 * (-11) - 1 = -43
(d) det((24)^-1) = (1/24) ^2 = 1/576
(e) d a 9 det b h с e

The determinant of a matrix is defined as the sum of the products of the elements of the matrix multiplied by the corresponding cofactor. The cofactor is a signed minor of the matrix, which is obtained by deleting the row and column of the element for which the cofactor is being computed.
In the case of the matrix A = |b с| . |a d|, the determinant can be computed as follows:
|b с| . |a d| = (b*d) - (a*c)
Therefore, det(A) = (b*d) - (a*c) = -11.
To compute det(4A) det(A), first, find det(4A), which is equal to:
|4b 4c| . |4a 4d| = 4^2 * (b*d - a*c)
Thus, det(4A) = 16(b*d - a*c) = 16(-11) = -176.
Then, det(4A) det(A) = (-176) * (-11) = 1936.

For det(2A - 1), first, find 2A - 1, which is equal to:
|2b 2c| . |2a 2d| - |1 0| . |0 1|
= 2|b с| . |a d| - |1 0| . |0 1|
= 2A - |1 0| . |0 1|
= 2A - I
where I is the identity matrix.
Therefore, det(2A - 1) = det(2A - I) = det(2A) det(I^-1)
Since det(I) = 1, det(I^-1) = 1/det(I) = 1/1 = 1.
Therefore, det(2A - 1) = 2^2 * (-11) * 1 - 1 = -43.
Finally, to compute det((24)^-1), it is necessary to find the inverse of the matrix 24.
|a b| . |c d| = 24I
=> |a b|^-1 . |c d| = (1/24)I
=> (1/24) . |d -b| . |-c a| = (1/24)I
Therefore, |d -b| . |-c a| = I
Since the determinant of the identity matrix is 1, it follows that:
1 = det(I) = det(|d -b| . |-c a|) = (a*d) - (b*c)
Hence, det((24)^-1) = (1/24)^2 = 1/576.

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Answer: $170

Step-by-step explanation:

6x + 18(6) = 1128.

6x + 108 = 1128

6x = 1020

x = 170

The price of one ticket is 170

Answer:

To determine the location of point H, we need to first find the length of the three sides of the fenced area using the given points E, F, and G.

The length of EF is:

sqrt[(3-1)^2 + (5-5)^2] = 2 units

The length of FG is:

sqrt[(6-3)^2 + (1-5)^2] = sqrt(25) = 5 units

The length of EG is:

sqrt[(6-1)^2 + (1-5)^2] = sqrt(20) = 2sqrt(5) units

The total length of the three sides is:

2 + 5 + 2sqrt(5) = 7 + 2sqrt(5) units

Since Landon has 16 units of fencing, he needs to find a point H such that the length of the fourth side of the fenced area (EH) is:

16 - (7 + 2sqrt(5)) = 9 - 2sqrt(5) units

Let's assume that point H has coordinates (x, y). Then, we can use the distance formula to find the length of EH:

sqrt[(x-1)^2 + (y-5)^2] = 9 - 2sqrt(5)

Squaring both sides and simplifying, we get:

(x-1)^2 + (y-5)^2 = 81 - 36sqrt(5) + 20

(x-1)^2 + (y-5)^2 = 101 - 36sqrt(5)

Now, we can plug in the coordinates of each of the answer choices and see which one satisfies this equation:

For (0, 1):

(0-1)^2 + (1-5)^2 = 16, which is not equal to 101 - 36sqrt(5)

For (0, -2):

(0-1)^2 + (-2-5)^2 = 65, which is not equal to 101 - 36sqrt(5)

For (1, 1):

(1-1)^2 + (1-5)^2 = 16, which is not equal to 101 - 36sqrt(5)

For (1, -2):

(1-1)^2 + (-2-5)^2 = 65, which is equal to 101 - 36sqrt(5)

Therefore, the answer is (1, -2), and Landon can place point H at coordinates (1, -2) to fence in the dog park without having to buy more fencing.

Answer:

12:44

12:16

12:08

12:32

12:28

Correct answer:

12:16

Step-by-step explanation:

Explanation:

The path traveled by the tip of the minute hand over the course of one hour is a circle of radius r=6. The circumference of that circle is

C=2πr=2π⋅6=12π.

The tip has traveled 10 inches since noon, so the fraction of the circle traveled is 1012π,

and the number of minutes that have expired since noon is 1012π⋅60≈16.

Therefore, to the nearest minute, the time is 12:16.

The car traveled for 6 hours at 70 mph and 4 hours at 80 mph.

To find out how many hours the car traveled at each speed, we can use a system of equations. Let x be the number of hours the car traveled at 70 mph and y be the number of hours the car traveled at 80 mph. We can set up the following equations:

Distance equation: 740 = 70x + 80y
Time equation: 10 = x + y

We can rearrange the time equation to solve for one of the variables in terms of the other:

y = 10 - x

Now we can substitute this into the distance equation:

740 = 70x + 80(10 - x)
740 = 70x + 800 - 80x
10x = 60
x = 6

So the car traveled for 6 hours at 70 mph. We can use this to find the number of hours the car traveled at 80 mph:

y = 10 - x = 10 - 6 = 4

So the car traveled for 4 hours at 80 mph.

Therefore, the car traveled for 6 hours at 70 mph and 4 hours at 80 mph.

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Answer:

5.66666666667

Step-by-step explanation:

5.66666666667  Because you do 22-5 divided by 3 I believe.