At a certain school, 72% of the students play one or more sports. the percentage of students who play one or more sports and who graduate is 67%. find the probability that a student graduates given that the student plays one or more sports.

That point slope equation given does not pass through those points, the point slope equation y + 7 = -0.4(x - 10) does, though. The standard form of that would be 

2x + 5y = -15

You can get that by distributing the -0.4 out

y + 7 = -0.4x + 4

You can then add 0.4x to both sides, and subtract 7 from both sides to get

0.4x + y = -3

Now some teachers may accept this, but in correct standard form the coefficient of x is a whole number, so you have to multiply both sides by 5 to get rid of the decimal, and you get

110/154 = x/126

154x/13860

x = 13860 /154 = 90

 90 milligrams of medicine A

Answer:

As per list given

Step-by-step explanation:

Given are some measurements and we have to convert them into suitable units.

i) 10,000 grams = 10 kilograms

1/500,000 liters equal = 2 microliters

1 nanosecond = 1 billionth of a second

1 hectometer = 100 meters

1 milliampere = 0.001 ampere

1 megaton = 1,000,000 tons

It seems like the problem is asking for us to derive an expression for the force F⃗ stated in terms of the unit vectors i^ and j^.

The solution for this is:

U(x,y) = α (x^-2 + y^-2) 

F = - dU(x,y) 

F = - (dU/dx + dU/dy) 

F = - (-2αx^-3 - 2αy^-3) 

F = 2α (x^-3 + y^-3)

F = 2α (1/x^3 i + 1/y^3 j) 

A conservative force is related to the potential-energy function. In this particular context, the force exerted on an object in an xy-plane is calculated using the negative gradient of the potential energy function u(x,y) given.

The question presents a potential-energy function for an object moving in the xy-plane, with the function u(x,y)=α(1/x2+1/y2) where α is a positive constant. This case refers to the action of a conservative force.

A conservative force is characterized by the fact that the work done by the force is only dependent on the start and end points of the motion. In turn, this gives the freedom to define a potential energy for any conservative force. In the context of this potential-energy function, the conservative force acting on the object can be calculated from the negative gradient of the potential energy.

To express it quantitatively, given a potential energy function U(x), the force F acting on the object at a position x is given by F=-dU/dx. If we extend this to two dimensions in the xy-plane, the force F = - ∇U, where ∇ is the gradient operator.

Applying these concepts to your given potential energy function u(x,y)=α(1/x2+1/y2), the force acting on the object in the x and y directions can be calculated by differentiating this function with respect to x and y respectively, applying the opposite sign.

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The boat average velocity for the one hour trip is 54° north of east.

What is Average velocity?

Average velocity is defined as the change in position divided by the time interval in which the displacement occurs.

Given that;

A small boat travel 32 km north and then travels 45 km east.

Now,

Average velocity is calculated as;

By figure,

Average velocity = cotθ = 32/45

θ = cot⁻¹ (32/45)

θ = 54°

Thus, The boat average velocity for the one hour trip is 54° north of east.

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equation : total = 15x

let x = number of days

1 year = 365 days

x = 365

total = 15(365) = 5475 minutes

Step 1

Find the slope of the dotted line A

Let

[tex]A(-3,1)\\B(0,2)[/tex]

Find the slope m

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

substitute in the formula

[tex]m=\frac{(2-1)}{(0+3)}[/tex]

[tex]m=\frac{(1)}{(3)}[/tex]

[tex]mA=\frac{1}{3}[/tex]

Step 2

Find the equation of the line A

we know that

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]mA=\frac{1}{3}[/tex]

[tex]B(0,2)[/tex]

substitute

[tex]y-2=\frac{1}{3}(x-0)[/tex]

[tex]y=\frac{1}{3}x+2[/tex]

Step 3

Find the equation of the inequality A

we know that

the solution is below the dotted line A

so

the inequality A is    

[tex]y<\frac{1}{3}x+2[/tex]

Step 4

Find the slope of the solid line B

Let

[tex]B(0,2)\\C(1,0)[/tex]

Find the slope m

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

substitute in the formula

[tex]m=\frac{(0-2)}{(1-0)}[/tex]

[tex]m=\frac{(-2)}{(1)}[/tex]

[tex]mB=-2[/tex]

Step 5

Find the equation of the line B

we know that

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]mB=-2[/tex]

[tex]B(0,2)[/tex]

substitute

[tex]y-2=-2(x-0)[/tex]

[tex]y=-2x+2[/tex]

Step 6

Find the equation of the inequality B

we know that

the solution is below the solid line B

so

the inequality B is    

[tex]y\leq -2x+2[/tex]

therefore

The system of linear inequalities is

[tex]y<\frac{1}{3}x+2[/tex]

[tex]y\leq -2x+2[/tex]

using a graphing tool

the solution is the shaded area

see the attached figure

Tools of geometry consist of fundamental techniques and concepts in mathematics involving measurements, calculations, vectors, and moments of inertia among others. Active learning strategies like collaborative activities and problem-solving are effective in understanding these concepts.

The subject of your lesson, 'tools of geometry', refers to the fundamental concepts and techniques used in

Geometry

, which is a branch of mathematics concerned with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids. Some of these

tools

in geometry include the ability to measure and calculate length, mass, volume, density, temperature, and time, and to perform calculations and conversions in various unit systems. In geometry, you'll also find the concept of Moments of Inertia useful, this concept revolves around calculating the moment of inertia for uniformly shaped, rigid bodies and using the parallel axis theorem to find the moment of inertia about any particular axis. Geometry also involves vector analysis, where magnitudes have both direction and quantity, represented often in bold or with an arrow above them. A key aspect of learning geometry effectively is active participation through discussions, collaborative group activities, and hands-on problem-solving.

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Graphing a parabola starts by identifying the vertex from the equation of the parabola, determining whether the parabola opens upwards or downwards, plotting the vertex and other points and then joining these points with a smooth curve.

Graphing a parabola involves understanding the equation of the parabola which takes the form y = ax² + bx + c, where 'a', 'b', and 'c' are constants. To find the graph of the parabola from this equation, follow these steps:

Remember, parabolas are a type of conic sections, formed through the intersection of a plane with a cone.

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The concept of percentages indicates that if Ramon answered 80% of the questions correctly in a test, it means he correctly answered a higher proportion of questions than the statement '30% of the students answered 16 or more questions correctly' would imply. Therefore, this statement does not represent the part of a test that Ramon answered correctly.

This question concerns the concept of percentages in mathematics. The information provided indicates that Ramon correctly answered 80% of the questions on his math test. This implies that if the test had 100 questions, Ramon correctly answered 80 questions. Now let's consider the statement in the choices: '30% of the students answered 16 or more questions correctly.' This is in stark contrast to Ramon's result and therefore does not represent the part of the test questions that Ramon answered correctly. The 30% statement is considering the entire class's performance, not Ramon's individual accomplishment. Hence, the aforementioned statement is the one that doesn't represent the part of the questions Ramon answered correctly.

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