Find the values of x and y.
E
25
24
20
D
G

The measure of the arc length AB is 16π/15 centimeters.

Since,

An arc length is simply the distance between two points along a section of a curve.

We know that;

The arc length is expressed as:

s = 2πr × (θ/360°)

Where s is the arc length, r is the radius, θ is the angle and π is constant pi.

Given that:

Radius r = 3cm

Angle θ = 64 degree

Arc length s = ?

Now, Plug the values into the above formula

s = 2πr × (θ/360°)

s = 2 × π × 3cm × ( 64°/360°)

s = 16π/15 cm

Therefore, the arc length is 16π/15 cm.

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a. A translation on a coordinate plane involves moving every point on the plane a certain distance in a particular direction without distrupting their orientation. The shape and size of the figure do not change, only that the position shifts.

b. If the translation is moving 3 units to the right, it is affecting the x-coordinate. Basically, the x-coordinate of each point on the plane is increased by 3 units, while the y-coordinate remains the same.

c. If the translation is moving 8 units down, it is affecting the y-coordinate. Basically, the y-coordinate of each point on the plane is decreased by 8 units, while the x-coordinate remains the same.

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The relative frequency of "tails" when the companions coalesce their results is close to 0.524.

In order to ascertain the relative frequency of "tails" when the friends amalgamate their outcomes, one must accumulate the amount of tails, then divide that sum by the entirety of trials:

Relative frequency of "tails" = total number of tails / cumulative number of trials

= 129 / (117 + 129)

= 129 / 246

≈ 0.524

Consequently, the relative frequency of "tails" when the companions coalesce their results is close to 0.524.

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Thermal energy and heat transfer principles guide the design of efficient systems, minimizing heat loss and maximizing performance.

It is crucial to take into account a number of aspects that may impact the functionality and efficiency of systems and objects that include thermal energy and heat transmission. You would need to take into account things like the kind and quantity of heat source, the materials utilized, the insulation, and the processes employed for heat transfer, for instance.

Additionally, you would have to think about ways to increase heat transmission effectiveness and reduce heat loss. High thermal conductivity materials may be used, or the system may be designed to have more heat-transfer surface area.

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Answer:

Step-by-step explanation:

There are 560 cubes with edge lengths of 1/2 cm needed to fill the rectangular prism.

The volume of a rectangular prism is found by multiplying its length by its width by its height.

So, the volume of this rectangular prism is:

Volume = length x width x height

Volume = 7 cm x 4 cm x 2 1/2 cm

Volume = 70 cm³/2

Now, we need to find out how many cubes with edge lengths of 1/2 cm can fit into this volume.

The volume of each cube with an edge length of 1/2 cm is:

Volume of cube = edge length x edge length x edge length

Volume of cube = (1/2 cm)³

Volume of cube = 1/8 cm³

To find no. of cubes are needed, we need to divide the volume of the rectangular prism by the volume of each cube:

Number of cubes = (Volume of rectangular prism) / (Volume of each cube)

Number of cubes = (70 cm³/2) / (1/8 cm³)

Number of cubes = (70 cm³/2) x (8/1 cm³)

Number of cubes = 560 cubes

Therefore, 560 cubes with edge lengths of 1/2 cm are needed.

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Based on the percentage of blue paint to red paint, Bo's purple paint will be bluer.

The percentage refers to the quotient of one value (proportion of blue paints) compared to another (the sum of blue and red paints).

Percentages are ratios expressed over 100.

                           Blue     Red   Ratio (%) of Blue to Red

Bo's paints            3          4       3:4 = 43% (3/7 x 100)

Sum of ratios = 7

Latanya's paints   2          3       2:3 = 40% (2/5 x 100)

Sum of ratios = 5

Thus, based on the ratios or percentages of to red paints, Bo's purple paint will be bluer than Latanya's.

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When the transformation is preformed on a coordinate plane, the coordinates of the new point would be located in a different quadrant.

The coordinates of the new point on this figure are (-6, -2).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point A = (6, 2)  →  Coordinates of point A' = (-6, -2)

In conclusion, the transformation rule (x, y) → (-x, -y) is used for the rotation of a geometric figure about the origin in a clockwise or counterclockwise (anticlockwise) direction.

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The lines intercept at the point (3, 9), and:

A system of linear equations can have one solution, no solutions, and infinite solutions, these are the only options.

If we have an equation system, the solutions are the spots where the graphs of the equations intersect.

We know that the solution of the system of linear equations is (3, 9), which signifies that the linear equations intersect at that location.

Can  we have more than one solutions?

Yes, you can have

These are the 3 options.

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The numbers arranged from greatest to least based on their absolute value is; |-34|, |-25|, |0.5|, |0.35|

The absolute value of a number is the expression or value of the distance of the number from 0 on the number line.

The numbers are; |-25|, |0.5|, |-34|, |0.35|

The absolute value of a number is positive, which indicates;

|-25| = 25

|0.5| = 0.5

|-34| = 34

|0.35| = 0.35

The above numbers arranged from greatest to least is therefore;

34 > 25 > 0.5 > 0.35

The numbers arranged from greatest to least based on their absolute value is therefore;

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Answer:

The sample space describing all possible outcomes is:

{H1, H2, H3, H4, T1, T2, T3, T4}

The outcomes for the event that the coin toss is heads are:

{H1, H2, H3, H4}

Step-by-step explanation:

If it pertains to using the format H1 to mean that the coin toss is heads and the number chosen is 1.

The volume of the given composite figure is: 1,283.33 ft³

The given composite figure is made up of a cone and a cylinder.

The formula for the volume of a cone is:

V = ¹/₃πr²h

Where:

r is radius

h is height

The formula for volume of a cylinder is:

V = πr²h

Where:

r is radius

h is height

Thus:

Total volume of composite figure is:

V =  (¹/₃* (22/7) * 7² * 7) + ((22/7) * 7² * 6)

V = 359.33 + 924

V = 1,283.33 ft³

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Answer:

15456

Step-by-step explanation:

My work is attached to this answer

The expected number of education majors in the sample is 20.

Since 80 out of 200 freshmen are education majors, the probability of randomly selecting an education major from the population is:

P(edu major) = 80/200 = 0.4

To find the expected number of education majors in a sample of 50 freshmen, we can use the formula for the expected value of a discrete random variable:

E(X) = n x p

Substituting the given values, we get:

E(X) = 50 x 0.4 = 20

Therefore, the expected number of education majors in a sample of 50 freshmen is 20.

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Answer: The difference in temperatures was 19°F.

Step-by-step explanation:

Answer:

19F

Step-by-step explanation:

The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.

The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.

The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.

Therefore, the probability of the friend being between 10 and 30 minutes late is:

P(10 < x < 30) = (height of rectangle) x (width of rectangle)

= (1/30) x 20

= 2/3

≈ 0.6667

So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

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Step-by-step explanation:

dependingon h o w m a n y bedrooms that are added to the

apartment, an additional $150will be added to $850.

The possible shapes of the fencing are a parallelogram and a rectangle.

Given that, a worker fences in a construction site using four pieces of fencing that have lengths of 20, yards 16, yards, 20 yards, and 16 yards.

We need to tell possible four-sided shapes that the worker can enclose with the fencing.

So, we can see that, the pair of sides are equal,

Which is condition in a parallelogram and a rectangle.

Hence, the possible shapes of the fencing are a parallelogram and a rectangle.

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Answer:

The slope is [tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

the slope is the number before the x.

Helping in the name of Jesus.

0≤x≤6 best describes the domain of the function.

The domain of a function describes the set of all possible input values.

In this case, the input variable is x, which represents the time in hours.

Since the horse runs for 6 hours, it is not possible for x to be greater than 6.

Additionally, x cannot be negative or zero, since time cannot be negative or zero.

Therefore, the domain of the function is 0 ≤ x ≤ 6.

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The missing measures in the triangle are given as follows:

m < F = 111.4º, m < D = 28.6º, f = 35.1.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Considering the triangle in this problem, the relation is given as follows:

sin(D)/18 = sin(40º)/24.2.

Hence the measure of angle D is obtained as follows:

sin(D) = 18 x sine of 40 degrees/24.2

sin(D) = 0.4781

m < D = arcsin(0.4781)

m < D = 28.6º.

The sum of the internal angle measures of a triangle is of 180º, hence the measure of angle F is obtained as follows:

m < F + 40 + 28.6 = 180

m < F = 180 - (40 + 28.6)

m < F = 111.4º

Then the length f is obtained as follows:

sin(111.4º)/f = sin(40º)/24.2

f = 24.2 x sine of 111.4 degrees/sine of 40 degrees

f = 35.1.

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Answer:

19.8 units

Step-by-step explanation:

From the diagram attached, to find the length of side AB, we need to use Pythagoras theorem on the right triangles. We can see that AB is the base of the two right triangle.

For the first right triangle with hypotenuse of 13 and height of 12, let x be the base, therefore using hypotenuse:

13² = 12² + x²

169 = 144 + x²

x² = 169 - 144

x² = 25

x = √25 = 5

For the second right triangle with hypotenuse of 15 and height of 12, let y be the base, therefore using hypotenuse:

15² = 12² + y²

225 = 144 + y²

y² = 225 - 144

y² = 81

y = √81 = 9

The length of AB = x + y = 9 + 5 = 14 unit

Since for a square all the sides are equal, therefore the length of each side of the square ABCD is 14 units.

In triangle ADC, the hypotenuse = AC, AD = DC = 14 unit. Using Pythagoras:

AC² = AD² + DC²

AC² = 14² + 14²

AC² = 196 + 196 = 392

AC = √392 = 19.8

The length of its diagonal is about 19.8 units

The graph of the population equation is on the image at the end.

Here we know that the function p(h) models the population of bacteria as the function of h, the number of hours.

And we can write this as the exponential function:

p(h) = 150*(3)^h

The graph of this will be an exponential that starts at 150 and triples for each increase in the horizontal variable, then the graph of this will be like the one you can see at the end of the answer.

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The radius of circle M is equal to 3.99 cm.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

12.36 = 89(3.142/360) × r²

12.36 = 0.7768r²

Radius, r = √15.9114

Radius, r = 3.99 cm.

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The probability that a person will wait for more than 9 minutes is approximately 0.0912 or 9.12%. This means that out of 100 people, about 9 of them will wait for more than 9 minutes in the line.

We know that,

To solve this problem, we need to use the normal distribution and standardize the variable of interest. We know that the mean waiting time is 5 minutes and the standard deviation is 3 minutes, so we can write: Z = (X - μ) / σ

where X is the waiting time, μ is the mean waiting time (5 minutes), σ is the standard deviation (3 minutes), and Z is the standardized variable.

To find the probability that a person will wait for more than 9 minutes, we need to find the area under the normal curve to the right of 9. We can do this by standardizing 9 using the formula above: Z = (9 - 5) / 3 = 1.33 .

We can use a standard normal table or a calculator to find the probability that Z is greater than 1.33. Using a calculator, we find that this probability is approximately 0.0912.

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The  line integral of F around the perimeter of the rectangle with corners (3,0),(3,2),(-3,2),(-3,0) traversed in that order is -333.06456

The F can be rewritten as

F(x,y)  = [6(x+y) , 6sin(y)

The path C on which we are going to evaluate the integral is

The set that could not represent the side of a right triangle are {27, 36, 46}.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be found using Pythagoras's theorem.

Therefore, using Pythagoras's theorem,

c² = a² + b²

where

Therefore, the hypotenuse is the longest side of the right angle triangle.

27² + 36² ≠ 46²

729 + 1296 ≠ 2116

2025 ≠ 2116

Hence, the sides that can't form a right triangle is {27, 36, 46}

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The length of the arc of a circle of radius 12 is 37.68.

The arc of a circle is defined as the part or segment of the circumference of a circle.

To calculate the arc of the circle, we the formula below.

Formula:

Where:

From the question,

Given:

Note: 360° = 2π radian

Substitute these values into equation 1

Hence, the length of the arc is 37.68.

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The missing terms in the geometric progression given are:

x = 10      y = 20

The nth term of a Geometric progression is expressed by the formula:

an = ar^(n - 1)

Where we have:

an = nth term

a = first term of the geometric progression

n = number of terms

r = common ratio

We are given the geometric progression 5, x, y, and 40, where:

a1 = 5

a4 = 40

Therefore, we have:

40 = 5 * r^(4 - 1)

40 = 5 * r³

40/5 = r³

8 = r³

r = ∛8

r = 2

Since we know a and r, find the 2nd and 3rd which are represented by x and y respectively, by applying an = ar^(n - 1):

a2 = 5 * 2^(2 - 1)

a2 = 5 * 2^1

a2 = 10

x = 10

a3 = 5 * 2^(3 - 1)

a3 = 5 * 2²

a3 = 20

y = 20

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If he business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written, checkbook balance after checks and deposit are processed is $6613.25.

To find the checkbook balance, we need to add up the initial balance, subtract the amounts of the written checks, and add the deposit made by the store manager.

Starting with the initial balance of $7349.44, we subtract the amount of the first check for $1349.67, leaving a balance of $6000.77. Then we subtract the second check for $344.12, leaving a balance of $5656.65.

Finally, we add the deposit made by the store manager for $956.60, which gives us a final balance of $6613.25.

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