ANSWER THE FOLLOWING QUESTIONS:

The area A of each of the section of the circle would be =78.5m²

To calculate the area of each section of the circle given, the formula for the area of circle is used which is given as follows;

Area of circle = πr²

Where;

π = 3.14

r = 10m

area = 3.14× 10×10

= 314m

But the circle is divided into 4 sections. Therefore, the area of a section = 314/4 = 78.5m²

Therefore, the area of each sector of the circle after being divided into four would be= 78.5m².

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1. The equation of the line in graph 1 in slope-intercept form is

y = (2/3)x + 2/3.

2. The equation of the line in graph 2 is

y = (1/3)x + 4/3.

a. To find the equation of the line passing through (3, 4) and (0, 2) (points obtained from the graph) in slope-intercept form, we need to first find the slope of the line.

slope = (y2 - y1) / (x2 - x1)

Substituting the given values, we get:

slope = (2 - 4) / (0 - 3) = -2 / (-3) = 2/3

The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is given by:

y - y1 = m(x - x1)

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

y = (2/3)x + 2/3

b. points obtained from the graph (-3, 1) and (-6, 0)

slope = (y2 - y1) / (x2 - x1)

slope = (0 - 1) / (-6 - (-3)) = -1 / (-3) = 1/3

y - y1 = m(x - x1)

y - 1 = (1/3)(x - (-3))

y = (1/3)x + 4/3

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a) The fraction of all the meal combinations which have at least one vegan option is 1/8.

b) There are 168 different three-course meal combinations available.

A fraction is a way of representing a part or a ratio of a whole, using a numerator and a denominator separated by a slash ("/") or a horizontal line. The numerator represents the number of parts being considered, and the denominator represents the total number of equal parts that make up the whole.

According to the given information:

a) To work out the fraction of all the meal combinations which have at least one vegan option, we need to count the total number of meal combinations with at least one vegan option, and then divide it by the total number of meal combinations.

The vegan options in the table are:

Mozzarella salad (V)

Cheese pizza (V)

Aubergine curry (V)

There are a total of 4 salads (including the vegan salads) and 6 mains (including the vegan mains). So the total number of meal combinations without any restriction is 4 x 6 = 24.

Now, we can calculate the total number of meal combinations without any vegan option, which is 24 - 3 = 21 (since 3 options are vegan).

So, the fraction of all the meal combinations which have at least one vegan option is (total meal combinations - meal combinations without any vegan option) divided by total meal combinations:

= (24 - 21) / 24

= 3 / 24

= 1 / 8

Therefore, the fraction of all the meal combinations which have at least one vegan option is 1/8.

b) If diners also choose one of 7 dessert options, we can simply multiply the total number of meal combinations (24) by the number of dessert options (7) to get the total number of three-course meal combinations available:

24 x 7 = 168

So, there are 168 different three-course meal combinations available.

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Work Shown:

[tex]\displaystyle \int \sin(x) dx = -\cos(x)+C\\\\\displaystyle \int f(x)dx = g(x)+C\\\\\displaystyle \int_{a}^{b} f(x)dx = g(b)-g(a)\\\\\displaystyle \int_{0}^{\pi} f(x)dx = g(\pi)-g(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)-(-\cos(0))\\\\[/tex]

[tex]\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)+\cos(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -(-1)+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 1+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 2\\\\[/tex]

The area is 2 square units. You can use WolframAlpha or GeoGebra to confirm.

So the measure of angle HLK is 45 degrees.

In geometry, an arc is a part of a curve that is typically a segment of a circle. It is defined by any two points on the curve, which are called its endpoints, and by all the points that lie along the curve between those two endpoints. An arc can be measured by its degree measure, which is the measure of the central angle that intercepts the arc, or by its length, which is the distance between its endpoints along the curve. In the context of a circle, an arc is also called a circular arc.

Here,

Since the measure of minor arc HK is 90°, we know that angle HJK is also 90°, since it is an inscribed angle that intercepts the same arc.

By the inscribed angle theorem, the measure of angle HLK is half the measure of arc HK. Therefore,

measure of angle HLK = 1/2 * measure of arc HK

= 1/2 * 90°

= 45°

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Any value of x that is less than -4 is a solution to the inequality x < -4.

Any value of x that is less than -4 is a solution to the inequality x < -4.

Some examples of such values are:

x = -5

x = -10

x = -100

In fact, any value that is to the left of -4 on the number line is a solution to the inequality x < -4. On a number line, we represent this inequality by shading everything to the left of -4.

To understand this visually, imagine a number line with -4 as the reference point.

All the values to the left of -4 will be negative, and all the values to the right of -4 will be positive.

So, the inequality x < -4 means that x can be any value to the left of -4 on the number line.

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Answer:0.00000221

Step-by-step explanation:

Move the decimal place 6 times

Answer:

y = - 9x + 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )

m = [tex]\frac{-31-50}{5-(-4)}[/tex] = [tex]\frac{-81}{5+4}[/tex] = [tex]\frac{-81}{9}[/tex] = - 9 , then

y = - 9x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, - 31 )

- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )

14 = c

y = - 9x + 14 ← equation of line

Answer:

Set your calculator to degree mode.

[tex] \tan( \alpha ) = \frac{23}{35} [/tex]

[tex] \alpha = {tan}^{ - 1} \frac{23}{35} = 33.31[/tex]

The angle of elevation of the sun is about 33°.

The calculated value of the logarithmic expression log(a⁵b⁵/c⁸) is 69

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

log a = 9

log b = -8

log c = -6

The expression to calculate is given as

log(a⁵b⁵/c⁸)

When the expression is expanded using product and quotient rules, we have

log(a⁵b⁵/c⁸) = loga⁵ + logb⁵ - logc⁸

Apply the power rule of logarithm to rewrite as

log(a⁵b⁵/c⁸) = 5loga + 5logb - 8logc

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

log(a⁵b⁵/c⁸) = 5 * 9 + 5 * -8 - 8 * -8

Evaluate

log(a⁵b⁵/c⁸) = 69

Hence, the value of the logarithmic expression log(a⁵b⁵/c⁸) is 69

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The volume of solid B is about 7π cubic meters, which is approximately 21.99 cubic meters when rounded to the nearest thousandth.

The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since solids A and B are similar, they have the same shape, but different sizes.

Let V₁ be the volume of solid A, and V₂ be the volume of solid B. The scale factor k from solid A to solid B is 1/4, which means that the dimensions of solid B are 1/4 of the dimensions of solid A.

We can find the radius and height of solid B by multiplying the radius and height of solid A by 1/4. Therefore, we have:

V₂ = π(r/4)²(h/4) = (π/16)rh²

We are given that V₁ = 112π cubic meters, so we can solve for rh²:

112π = πr²h

rh² = 112

Substituting into the formula for V₂, we get:

V₂ = (π/16)rh² = (π/16)(112) = 7π

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In this experiment, we want to repeat the time measurements for each height a few times.
By repeating the measurements, we can reduce the statistical errors associated with random fluctuations in the measurement process. These fluctuations can be caused by factors such as variations in the environmental conditions or in the way the measurements are taken. By taking multiple measurements and calculating the average, we can reduce the impact of these random errors.
By reducing statistical errors, repeating the measurements can also help to reduce systematic errors, which are caused by consistent biases or inaccuracies in the measurement process. By taking multiple measurements and analyzing their differences, we can identify and correct for any systematic errors.
Hence, repeating the time measurements for each height a few times helps to increase the accuracy of the results by reducing both statistical and systematic errors.

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Answer:

9.9 inches

Step-by-step explanation:

Visualize the scenario for a second. If the ladder is leaning against the wall, we can assume that it is the hypothenuse of the triangle that is forming here. The angle of elevation in this scenario is the angle formed by the ladder and ground.

Next, recall each trig function and determine which best belongs. We have the hypothenuse and we need the side opposite the angle. Therefore, we use sine. (probably using a calculator for trig questions)

Therefore, we can now set up our equation and solve. (x is the height of the wall)

sin 56 = [tex]\frac{x}{12}[/tex]         Initial equation

12 sin 56 = x     Multiply each side by 12 so that we get x by itself.

x ≈ 9.9               Punch 12 sin 56 into a calculator and your done!

Therefore, the answer is about 9.9 inches. (If you got something different, make sure that your calculator is in degrees and not radians! Some calculators abbreviate it as DEG and RAD respectively.)

Answer: The angle of depression from Jesenia to the duck is 25.17°. The solution has been obtained by using trigonometry.

What is trigonometry?

Right-angled triangles, their sides, angles, and connections are the main topics of the mathematical field of trigonometry.

We are given that that Jesenia is standing on a pedestrian bridge that is 9.5 feet above the lake and the duck is 4.5 feet away from jesenias position on the bridge.

This means that perpendicular is 9.5 and base is 4.5.

We know that tan θ is value of opposite side to adjacent side.

So, we get

⇒ Tan θ =

⇒ Tan θ = 0.47

⇒ θ = 25.17°

Hence, the angle of depression from Jesenia to the duck is 25.17°.

Step-by-step explanation:

Welcome!

Based on the information we can infer that the area of the figure is 464 ² units.

To calculate the area of this figure we must assume that it is a complete square and find its area as shown below:

Now we must find the area of the non-grid regions and subtract them from the area we found previously:

576 - 112 = 464 units ²

According to the above, the area of the figure is 464 units ²

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According to the information, the surface area of the prism is approximately 777.868 square inches, and its volume is approximately 3156.846 cubic inches.

Since the hexagonal bases are regular, we know that all the six triangles are congruent to each other.

Let's call the side length of the hexagon s. Then, the apothem of each triangular face is given as 9 inches, and the base of each triangular face is given as 10 inches. Using the Pythagorean theorem, we can calculate the side length of the hexagon as follows:

s^2 = (10/2)^2 + 9^2

s^2 = 25 + 81

s^2 = 106

s ≈ 10.2956 inches

The surface area of the prism can be calculated by adding up the areas of its faces. The hexagonal base has an area of:

A_base = (3√3/2) * s^2 ≈ 450.978 square inches

The area of each triangular face is:

A_tri = (1/2) * base * height = (1/2) * 10 * 9 = 45 square inches

So the total surface area of the prism is:

A_total = 2A_base + 6A_tri

A_total = 2(450.978) + 6(45)

A_total ≈ 777.868 square inches

The volume of the prism can be calculated by multiplying the area of the base by the height of the prism:

V = A_base * height

V = 450.978 * 7

V ≈ 3156.846 cubic inches

Therefore, the surface area of the prism is approximately 777.868 square inches, and its volume is approximately 3156.846 cubic inches.

Note: This question is incomplete. Here is the complete information:

Calculate the surface area and volume of this prism.

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Answer:

B

Step-by-step explanation:

the equation y=3/2x-3 has a slope of 3/2 and a y intercept of -3

So, first find the graph(s) that have the y intercept of -3.  The only options would be B and C.

Next, from the y-intercept of -3, go UP 3, and to the RIGHT 2 to find your next point.  This eliminates option C for the slope.  The slope of option C is 2/3, not 3/2.

So, option B is correct.  Hope this helps ;)

Answer:

B

Step-by-step explanation:

y = mx + b

y = mx (slope) + b (y-intercept)

The y-intercept of y = 3/2x - 3 is -3, so the graph needs to have a point at (0, -3). The slope is 3/2, if you go up 3 times and to the right twice from the point (0, -3), it will point (2, 0).

Answer:

the event would be independent.

Step-by-step explanation:

because the penny and dime are two seperate variables

the area of given figure made from two part Parallelogram and Triangle is 288sq cm

A parallelogram is a four-sided shape with opposite sides that are parallel and equal in length. The opposite angles of a parallelogram are also equal in measure. Parallelograms can have various orientations, but their opposite sides will always be parallel.

A triangle, on the other hand, is a three-sided shape with three angles and three vertices. The sum of the angles in a triangle is always 180 degrees. Triangles can come in various shapes and sizes, such as equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), and scalene (all sides and angles are different).

given that

1st part:

Base=6cm

height=8cm

Area=1×Base×Height/2

Area=(1×6×8)cm²/2

Area=24cm²

it have two part so, Area=2×24=48sq cm

2nd part:

if we assume Parallelogram

Area=Base×Height

Area=15cm×8cm

Area=120 sq unit

it have two part so,2×120sq cm

240sq unit

total area of given figure is 48 sq cm+240sq cm=288 sq unit.

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The z-score of a car that is 6 years old is  -0.625.

To find the z-score of a car that is 6 years old, we can use the formula:

z = (x - μ) / σ

where x is the value we are interested in (in this case, 6 years old), μ is the mean of the distribution (8 years), and σ is the standard deviation (3.2 years).

Plugging in the values, we get:

z = (6 - 8) / 3.2 = -0.625

Therefore, the z-score of a car that is 6 years old is -0.625. This indicates that the car is 0.625 standard deviations below the mean age of cars driven by employees at the company. Since the distribution is normal, we can use this z-score to find the probability of finding a car with an age of 6 years or less, using a z-table or a calculator.

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4,396 flowers are needed to surrond the circular garden.

We know that the circumference of a circle of radius R is:

C = 2*3.14*R

Here the radius is 175ft, then the circumference is:

C = 2*3.14*175ft = 1,099ft

And we know that:

1ft = 12in

Then the circumference in inches is:

1,009*12 in = 13,188 in

If each flower is separated by 3 inches, the number needed is:

13,188 in/3in = 4,396 flowers.

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An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.

From the given information, we have the following equations:

[tex]x = 2(y+z) - 40[/tex] (the largest angle is 40 degrees less than twice the sum of the other two angles)

[tex]x = 2z + 10[/tex] (the largest angle is twice the smallest angle plus 10 degrees)

[tex]x + y + z = 180[/tex] (the sum of the angles of a triangle is 180 degrees)

To simplify the system of equations, we can use the second equation to substitute for x in the first equation:

[tex]2z + 10 = 2(y+z) - 40[/tex]

Simplifying this equation, we get:

[tex]y = z + 25[/tex]

Now we can substitute x and y in terms of z into the third equation:

[tex]x + (z+25) + z = 180[/tex]

Simplifying this equation, we get:

[tex]x + 2z = 155[/tex]

Finally, we can substitute x in terms of z from the first equation into this last equation:

[tex]2(y+z) - 40 + 2z = 155[/tex]

Simplifying this equation, we get:

[tex]y + 3z = 97[/tex]

Therefore, the equations that represent this system are:

[tex]x = 2(y+z) - 40\\y = z + 25\\x + 2z = 155\\y + 3z = 97[/tex]

So the correct answers are:

[tex]a.) x=2y+10\\d.) x=2z+y-40\\e.) 2(y+z)-40[/tex]

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The equations that represent this system are:

a.) x=2y+10

d.) x=2z+y-40

e.) 2(y+z)-40

What is angles ?

An angle is a polyhedron made up of two rays with a shared terminal, often known as sides or legs (called the vertex). Angles are used to express how much rotation or inclination there is between second line or planes and are commonly described in degrees or radians.

From the given information, we have the following equations:

=> x=2(y+z)-40 (the largest angle is 40 degrees less than twice the sum of the other two angles)

=> x=2z+10 (the largest angle is twice the smallest angle plus 10 degrees)

=> x+y+z=180  (the sum of the angles of a triangle is 180 degrees)

To simplify the system of equations, we can use the second equation to substitute for x in the first equation:

=> 2z+10=2(y+z)-40

Simplifying this equation, we get:

y=z+45

Now we can substitute x and y in terms of z into the third equation:

x+z+25+z=180

Simplifying this equation, we get:

=> x+2z=155

Finally, we can substitute x in terms of z from the first equation into this last equation:

2(y+z)-40+2z=155

Simplifying this equation, we get:

y+3z=97

Therefore, the equations that represent this system are:

a.) x=2y+10

d.) x=2z+y-40

e.) 2(y+z)-40

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The water property that explains why the air temperature significantly changed but the water temperature stayed relatively the same is the property of specific heat.

Water's high specific heat capacity allows it to absorb and retain heat energy without much change in temperature, explaining why its temperature did not shift despite significant changes in the air temperature. Air has low specific heat capacity, while water has high.

Therefore, This caused the stream water temperature to remain stable despite environmental changes. Air temps change quickly due to its lower heat capacity.

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The number of hours it will take to complete the resurfacing project is:

51 hours

We are told that the department of  transportation is resurfacing 12. 75 miles of roadways in Collin County.

Now, we are also given that:

Number of miles completed each hour = 1/4 mile in section = 0.25 mile per hour

Thus, the number of hours it will take to complete the resurfacing project is:

That would be 12.75 divided by 0.25 hours

= 12.75/0.25

= 51 hours

Thus, we conclude that is the total time it will take to complete the project

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Answer:7

Step-by-step explanation: you divide 49 by 7 which gives you 7

Answer:

7

Step-by-step explanation:

1/7 of 49 would be equal to divided 49 by 7 to find 1 seventh of 49

49/7 = 7

so 1/7 of Chesters 49 CDS is equal to 7 CDS that Tony has.

hope this helps :)

The equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.

What is meant by equation?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign and can include variables, constants, and mathematical operations. Equations are used to represent relationships between quantities and to solve problems in mathematics and science.

What is meant by slope?

Slope refers to the measure of the steepness of a line. It is calculated by dividing the change in the y-coordinate (vertical distance) by the change in the x-coordinate (horizontal distance) between two points on the line.

According to the given information

The point-slope form of the equation of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

In this case, the line passes through the point (16, -14) and has a slope of 1. Plugging these values into the point-slope form, we get:

y - (-14) = 1(x - 16) y + 14 = x - 16 y = x - 30

So, the equation of the line that passes through the point (16, -14) with slope 1 is y = x - 30.

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The circumferences and areas of the circles are listed below:

Case 2: s = 54.689 cm

Case 3: 16257.980 ft²

Case 4: 26.999 mm

In this problem we need to determine the circumference and the area of the circle, whose equations are introduced below:

Circumference

s = 2π · R

Area

A = π · R²

Where:

Case 2 (A = 238 cm²)

R = √[(238 cm²) / π]

R = 8.704 cm

s = 2π · (8.704 cm)

s = 54.689 cm

Case 3 (s = 452 ft)

R = (452 ft) / 2π

R = 71.938 ft

A = π · (71.938 ft)²

A = 16257.980 ft²

Case 4 (A = 58 mm²)

R = √[(58 mm²) / π]

R = 4.297 mm

s = 2π · (4.297 mm)

s = 26.999 mm

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Answer:

Starting at the origin (0, 0), go right 3 units, then down 7 units. You will end at (3, -7).

The length of ZW is 45 inches.

A parallelogram is a member of quadrilateral which has a pair of opposite sides to be equal, and a pair of slant opposite sides.

In the given information, we have;

WX = YZ (a pair of opposite side of a parallelogram are equal)

2x + 15 = 4x - 21

collect like terms,

21 + 15 = 4x - 2x

36 = 2x

x = 36/2

x = 18

So that;

WX = 2x + 15

      = 2(18) + 15

WX = 36 + 15

      = 51

XY = x + 27

     = 18 + 27

     = 45

Therefore,

ZW = XY  (a pair of opposite sides are equal)

ZW = 45

The length of ZW is 45 inches.

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