A small delivery company can deliver only in a small part of the city. Write an equation for the boundary where the company delivers. and find its radius.

The maximum fishery biomass that can be removed yearly while still sustaining the population is known as the Maximum Sustainable Yield (MSY).

The Maximum Sustainable Yield (MSY) represents the maximum amount of fishery biomass that can be harvested from a population each year while maintaining its long-term sustainability. It is a crucial concept in fisheries management, aiming to balance resource utilization with the need for population replenishment.

By setting harvest limits below the MSY level, fish stocks can regenerate, ensuring the continuation of the fishery in the future. MSY takes into account various factors such as population growth rates, reproductive potential, and ecosystem dynamics to determine a sustainable level of extraction.

Proper adherence to MSY principles helps prevent overfishing and promotes the conservation of aquatic resources.

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Answer:

3.8

Step-by-step explanation:19 divided by 5 equals 3.8

Step-by-step explanation:

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

x=35

Step-by-step explanation:

3x+15=2x+50 (opposite angles are equal)

3x=2x+35

x=35

Given:

An angle in radian measure is

Required:

Find the degree measure of the angle.

Explanation:

The radian measure is

To convert the radian measure multiply it by

Final Answer:

Option b is the correct answer.

The surface area painted blue will be 1,488 square cm.

The correct option is: (D)

Surface area is the amount of space covering the outside of a three-dimensional shape.

We have, The plan is to paint 40% of the total surface area.

The surface area is :

Surface Area = (17 + 17 + 18 + 30 + 18) x 24 + 8 x 30 + 2 x 30 x 18

Surface Area  = 100 x 24 + 8 x 30 + 60 x 18

Surface Area = 2400 + 240 + 1080

Surface Area = 3720 square cm

Blue paint will be applied to 40% of the overall surface area of the doorstop, including the bottom face then

= 0.40 x 3720

= 1488 square cm

Therefore, the surface area painted blue will be 1,488 square cm.

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Answer:

y=-2x+8

Step-by-step explanation:

We want an equation of the form y=mx + b, where m is the slope and b is the value of y when x=0.

The slope of a line through the two given points:

(4,0) and (0,8)

Rise = (8-0) = 8

Run = (0-4) = -4

Slope = 8/-4 = -2

The y-intercept is given by the point (0,8), which tells us that b=8.

The equation is y = -2x + 8

Answer:

Which is the equation of the line passing through (0, 8) and (4, 0)?

The one that you are on is correct

Step-by-step explanation:

You're welcome.

a) The number of ways to draw five face cards from a standard deck of 52 cards is C(16, 5), where C(n, k) is the number of combinations of n things taken k at a time. The probability of drawing five face cards is therefore:

C(16, 5) / C(52, 5) = 4165 / 2598960

b) A full house consists of three of one rank and two of another. There are 12 face cards in each rank, so there are C(12, 3) ways to choose the three of one rank, and C(12, 2) ways to choose the two of another rank. The total number of full house hands consisting of face cards is therefore:

C(12, 3) * C(12, 2) = 220

The probability of drawing a full house with all face cards is:

220 / C(52, 5) = 220 / 2598960

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Barry's loan at an interest rate of 9% cost him $30.00 less than Alex's loan at an interest rate of 21%.

The difference in the cost of Barry's loan at an interest rate of 9% and Alex's loan at an interest rate of 21% can be calculated by finding the difference between the interest paid on each loan.

First, we'll calculate the interest paid on Barry's loan:

Interest = Principal x Interest Rate x Time

Interest = $1000 x 9% x 3/12

Interest = $22.50

Next, we'll calculate the interest paid on Alex's loan:

Interest = Principal x Interest Rate x Time

Interest = $1000 x 21% x 3/12

Interest = $52.50

Finally, we'll find the difference between the two:

Difference = $52.50 - $22.50

Difference = $30.00

Therefore, Barry's loan at an interest rate of 9% cost him $30.00 less than Alex's loan at an interest rate of 21%.

Note: The question is incomplete. The complete question probably is: Barry and Alex both took out a loan for $1000 for 3 month loan term. How much less did Barry’s loan at an interest rate of 9% cost him than Alex’s loan at an interest rate of 21%.

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The transformation of the rectangles ABCD and ABCD is for the 90-degree clockwise rotation about the origin and a translation of 7 units down.

Here the transformed rectangle is  the result of two steps, including the steps of  rotation and  translation from the x-y axis, near the origin.

Here change is in such a way that,  the first rotation is a 90 clockwise rotation about the origin, where the vertex c is near to the origin,  again there is a translation of 7 units down, considering the rotated rectangle As A'B'C'D'. here the proper explanation of the process is shown in the image attached.

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Answer:

Point A(5, -1) is mapped to A'(1, 5)

The rule is:

This is 90° anticlockwise rotation

Point B(-4, 6) will map to:

Answer:

60 s

Step-by-step explanation:

Here is the complete question

Two students were racing home from school. Eric rides his skateboard and Robby rides his bicycle. Eric leaves 40 seconds before Robby. Eric traveled at a speed of 10 feet per second. Robby traveled at a speed of 30 feet per second. For how many seconds had Eric traveled when the both boys were the same distance from school?

Solution

Let Robby start his race at time t seconds. Eric starts his race at 40 seconds later implies his time is t' = t + 40.

Since Robby moves at a speed of 30 ft/s, the distance he travels in time, t seconds is d = 30t

Since Eric moves at a speed of 10 ft/s, the distance he travels in time, t' seconds is d' = 10t' = 10(t + 40).

When their distances are the same, d = d'. So,

30t = 10(t + 40)

expanding the bracket, we have,

30t = 10t + 400

collecting like terms, we have,

30t - 10t = 400

20t = 400

dividing both sides by 20, we have

t = 400/20

t = 20 s

Since the time Eric has travelled is t' = t + 40 = 20 + 40 = 60 s.

So, Eric has travelled 60 s when the boys have travelled the same distance from the school..

Answer:

x=1

Step-by-step explanation:

-16+x=-15

-16+x+16=-15+16   Add the terms to both sides of the equation.

After that you simplify.

These real-world applications help young learners see the practical applications of geometry and develop a deeper understanding of geometric concepts while making learning more engaging and meaningful.

Relevance: Connecting math to real-world applications helps students see the practical value and relevance of the concepts they are learning. It provides a meaningful context and motivation for learning.

Engagement: Real-world applications make math more interesting and engaging for students. It brings concepts to life and helps students see how math is used in everyday life.

Deep understanding: By applying math concepts to real-world situations, students develop a deeper understanding of the concepts and their connections. It promotes critical thinking, problem-solving skills, and the ability to apply mathematical knowledge in different contexts.

Transferability: Real-world applications help students see how math concepts can be transferred and applied to various situations. It promotes the ability to apply learned concepts to new and unfamiliar problems.

Some real-world applications of geometry that would be appropriate for young learners include:

Measurement: Young learners can apply geometric concepts to measure and compare the lengths, areas, and volumes of objects in their environment. For example, measuring the length of a room, comparing the sizes of different shapes, or estimating the volume of a container.

Navigation and Maps: Young learners can use geometry to understand maps, directions, and spatial relationships. They can learn about reading maps, understanding coordinates, and finding distances between locations.

Architecture and Construction: Exploring geometric shapes, angles, and symmetry can help young learners understand the principles of architecture and construction. They can design and build simple structures using different shapes and understand the importance of stability and balance.

Art and Design: Geometry plays a significant role in art and design. Young learners can explore symmetry, patterns, and shapes in various art forms. They can create tessellations, explore rotational symmetry, or design patterns using geometric shapes.

Everyday Objects: Geometry is present in everyday objects around us. Young learners can identify and classify shapes in their environment, such as identifying spheres, cubes, cylinders, and cones in objects like balls, boxes, cups, and ice cream cones.

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domain is {x | x, -6, -1, 0, 3}

To determine the domain of the given function, we need to identify all the valid input values (x-values) for which the function is defined. Looking at the given data, we have the following pairs of x and y values: (-6, -7), (-1, 1), (0, 9), and (3, -2).

The domain of the function is simply the set of all x-values from these pairs. Thus, the domain of the function is {-6, -1, 0, 3}, as these are the valid input values for which we have corresponding output values.

In summary, the domain of the given function is {-6, -1, 0, 3}.

Therefore, domain is {x | x, -6, -1, 0, 3}

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Answer:

The first answer 130c

Step-by-step explanation:

The total weight is 18.5 kilograms

Given:

The inequality is:

\(y>5x+3\)

To find:

The y-intercept, slope and type of line (solid or dotted).

Solution:

The slope intercept form of a line is:

\(y=mx+b\)            ...(i)

Where, m is the slope and b is the y-intercept.

We have,

\(y>5x+3\)

The relation equation is:

\(y=5x+3\)             ...(ii)

On comparing (i) and (ii), we get

\(m=5\)

\(b=3\)

It means the slope is 5 and the y-intercept is 3.

The sign of the inequality in the given inequality is ">". It means the boundary line is not included in the solution set. So, the boundary line is a dotted line.

Therefore, the slope is 5, the y-intercept is 3 and the line is a dotted line.

Answer:

Angle 1 - 148

Angle 2 - 32

Angle 3 - 73

Angle 4 - 148

Angle 5 - 105

Step-by-step explanation:

Angle 1 forms a line with angle 32 and equals 180, therefore Angel 1 = 180 - 32 = 148

Angle 2 has the same value as the opposing angle, 32

Angle 3 combined with 32 and 75 equals 180, therefore

Angle 3 = 180 - 32 - 75

Angle 3 = 73

Angle 4 is equal to angle 1

Angle 5 combined with 43 and Angle 2 (32) equals 180

Angle 5 = 180 - 43 - 32

Angle 5 = 105

The first derivative of the given function with respect to x is 0.9x^(-0.1)y^1.8 and the first derivative of the given function with respect to y is 1.8x^0.9y^0.8.

The given function is f(x, y) = x^0.9y^1.8. The question is to find the first derivative of the given function with respect to x and y respectively.

Here are the solutions; The first derivative of the given function with respect to x is given by ∂f(x, y)/∂x:∂f(x, y)/∂x = 0.9x^(-0.1)y^1.8

On the other hand, the first derivative of the given function with respect to y is given by ∂f(x, y)/∂y:∂f(x, y)/∂y = 1.8x^0.9y^(1.8 - 1)∂f(x, y)/∂y = 1.8x^0.9y^0.8

Therefore, the first derivative of the given function with respect to x is 0.9x^(-0.1)y^1.8 and the first derivative of the given function with respect to y is 1.8x^0.9y^0.8.

The above steps use the concept of partial derivatives of a function with respect to a variable that can be applied in such types of questions.

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The given function is

\(f(x,y) = x⁰.⁹ y¹.⁸\)

Now, let's find the first derivative of the function with respect to x and y.

First derivative of the function with respect to x:

We have to use the chain rule here.

According to the chain rule,

the derivative of the outer function is multiplied by the derivative of the inner function.

The inner function is \(y¹.⁸,\)

whose derivative with respect to x is 0.

Therefore, we only have to differentiate the outer function with respect to x.

\(f(x,y) = x⁰.⁹ y¹.⁸∂f/∂x = ∂/∂x (x⁰.⁹ y¹.⁸)∂f/∂x = 0.⁹x^(-0.1) y¹.⁸∂f/∂x = 0.⁹y¹.⁸/x^0.1\)

First derivative of the function with respect to y:

We have to use the chain rule here.

According to the chain rule, the derivative of the outer function is multiplied by the derivative of the inner function.

The inner function is \(x⁰.⁹,\)

whose derivative with respect to y is 0.

Therefore, we only have to differentiate the outer function with respect to y.

\(f(x,y) = x⁰.⁹ y¹.⁸∂f/∂y = ∂/∂y (x⁰.⁹ y¹.⁸)∂f/∂y = 1.⁸ x⁰.⁹ y^(0.8)∂f/∂y = 1.⁸x^0.9 y^0.8\)

Hence, the first derivative of the given function with respect to x is

\(0.⁹y¹.⁸/x^0.1\)

and with respect to y is \(1.⁸x^0.9 y^0.8.\)

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The inequality expression given has a solution of 1 < x < 5.

Inequality are expressions not separated by an equal sign. Given the inequality expression below;

|x − 3| + 8 > 6

The expression can be divided into x − 3 + 8 > 6 and -(x - 3) + 8 > 6

For the inequality x − 3 + 8 > 6

x - 3 > 6 - 8

x - 3 > -2

x > 1

For the inequality -(x - 3) + 8 > 6

-(x - 3) > 6 - 8

-(x - 3) > - 2

x - 3 < 2

x < 5

Hence the solution to the given inequality is 1 < x <5

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The number of cubic centimeters of paint that will fit in the cylindrical container is:

66.36 cm³

The volume of a cylinder can be determined by multiplying the area of the base by the height. It may be expressed using the formula:

V = πr²h

where π (pi) is approximately equal to 3.14, r is the radius, and h is the height.

You should also note that the radius of the cylinder is one-half of the diameter.

V = πr²h

Since the cylindrical container of paint has a diameter of 3 cm, its radius would be 1.5 cm. Furthermore, its height is around 7 cm. As a result, by substituting the given values into the formula, we may get the following result:

V = πr²hV = π(1.5)²(7)

V = 66.36 cm³

Therefore, the cylindrical container of paint can hold approximately 66.36 cubic centimeters of paint.

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Answer:

A) 15x+9x

B) you have to graph

C)yes, all she wants to do is make 90 bucks she can totally do more if she wants

D) you can choose

Step-by-step explanation:

15*12 & 9*12

Answer:

Answer:

m∠1 = 180° - 46° = 134° ⇒  Consecutive interior angles are supplementary

m∠2 = 46                      ⇒  Alternate interior angles are congruent

Step-by-step explanation:

The translated points are A'(7, 9), B'(8, 8), and C'(4, 12) when they have been translated 6 units to the right and 10 units up.

A coordinate plane is a plane in which a set of two number lines are represented, horizontal line is called x-axis and vertical line is called y-axis.

The given points are,

A(1, -1), B (2, -2) and C(-2, 2).

When the points are translated 6 units to the right and 10 units up implies that,

There will be increase of 6 units in x coordinate and increase of 10 units in y coordinate

The point coverts as

A'(7, 9), B'(8, 8), and C'(4, 12)

The translated points are A'(7, 9), B'(8, 8), and C'(4, 12).

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