Using reasoning, determine the number of marbles that you would expect to fit if you doubled the diameter

Original diameter was 8cm, could fit 40 marbles. New diameter is 16cm. How many marbles would I fit?

The probability of choosing the expected value of games is

a) P ( G ) = 1/4

b) P ( R ) = 3/8

c) P ( B ) = 1/4

d) P ( Y ) = 1/8

Given data ,

Color Payout

Red $2

Blue $6

Green $6

Yellow $20

Now , game costs $5 to play and you win money based on the color the spinner lands on

On simplifying , we get

The number of yellow spinner = 1

The number of blue spinner = 2

The number of green spinner = 2

The number of red spinner = 3

So , the probabilities are

a) P ( G ) = 1/4

b) P ( R ) = 3/8

c) P ( B ) = 1/4

d) P ( Y ) = 1/8

Hence , the probability is solved

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The slope of the straight line is 3.

What is slope of a line?

Slope is the measure of steepness. Slope is determined by the tangent of angle a line makes with the x-axis. It is calculated as rise over run. Mathematically for the coordinates (a, b) (c, d) it can be given as \(\frac{d-b}{c-a}\).

We are given a table which contains some coordinates of a straight line

We have to find the slope of the line

This can be done as

Slope\(=\frac{8-5}{2-1}\)

Slope\(=3\)

Hence the slope of the line is 3.

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Hello!

m     dm    cm    mm

5   ,   0        0

500cm = 5m

Answer:

Following are the solution to this question:

Step-by-step explanation:

differentail equation:

\(yu_{xy} + u = 0..........(1)\)  

when \(u(x,y) = X(x)Y(y)\)

\(u_x = \frac{\partial u}{\partial  x} X'Y' \\\\ u_{xy} = \frac{\partial^2 u }{ \partial x\ \partial  y}= X'Y'\)

by substituting the value we get:

\(\to \int \frac{Y'}{Y} = -\lambda \int \frac{1}{y} dy\\\\\)

by solving the value:

\(\to Y=c_3 y^{-\lambda}\\\\\therefore\ \ c_4=c_2C_3\\\\\to u(x,y) = c_4 e^{\frac{x}{\lambda}} y^{-\lambda}\)

The solution of the given partial differential equation will be

\(u(x,y)=c_4e^\frac{x}{\lambda}y^{-\lambda}\)

The partial derivative is a way to find the slope in either the x or y direction, at the point indicated.

\(yu_{xy}+u=0..............................(1)\)

Now if \(u(x,y)=X(x)Y(y)\)

\(u_x=\dfrac{\partial u}{\partial x} X'Y'\)

\(u_{xy}=\dfrac{\partial^2u}{\partial x\ \partial y}=X'Y'\)

by substituting the value, we get:

\(\int \dfrac{Y'}{Y}=-\lambda\int\dfrac{1}{y}dy\)

by solving the value:

\(Y=c_3y^{-\lambda}\)

\(c_4=c_2c_3\)

\(u(x,y)=c_4e^\frac{x}{\lambda}y^{-\lambda}\)

Hence the  solution of the given partial differential equation will be

\(u(x,y)=c_4e^\frac{x}{\lambda}y^{-\lambda}\)

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Answer:

\(\frac{1}{27}\)

Step-by-step explanation:

\(3^{-3}\\=\frac{1}{3}^{3}\\=\frac{1}{27}\)

Answer:

a) The initial height of the rock is of 48 feet.

b) It takes 1 seconds for the rock to reach maximum height.

c) The rock's maximum height is 50 feet.

d) It takes 6 seconds for the rock to land on the ground.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

\(f(x) = ax^{2} + bx + c\)

It's vertex is the point \((x_{v}, f(x_{v})\)

In which

\(x_{v} = -\frac{b}{2a}\)

If a<0, the vertex is a maximum point, that is, the maximum value happens at \(x_{v}\), and it's value is \(f(x_{v})\)

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

In this question:

The height of the ball after t seconds, in feet, is given by:

\(h(t) = -2t^2 + 4t + 48\)

Which is a quadratic equation with \(a = -2, b = 4, c = 48\)

a) What is the initial height?

This is \(h(0) = 48\). So the initial height of the rock is of 48 feet.

b) How many seconds does it take to reach the maximum height?

This is the value of t at the vertex. So

\(t_{v} = -\frac{b}{2a} = -\frac{4}{2(-2)} = 1\)

It takes 1 seconds for the rock to reach maximum height.

c) What is the rock's maximum height?

This is the height of the ball after 1 second. So

\(h(1) = -2(1)^2 + 4(1) + 48 = 50\)

The rock's maximum height is 50 feet.

d) How many seconds does it take to for the rock to land on the ground?

This is t for which \(h(t) = 0\), so we solve the quadratic equation.

\(\bigtriangleup = (4)^2-4(-2)(48) = 400\)

\(t_{1} = \frac{-4 + \sqrt{400}}{2*(-2)} = -4\)

\(t_{2} = \frac{-4 - \sqrt{400}}{2*(-2)} = 6\)

Time is a positive measures, so it takes 6 seconds for the rock to land on the ground.

Answer:

1.2 to 10 o->

2.8 to -10 <- with fully bubbled o

To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Answer: To factor the expression -14 - (-8) completely using the distributive law, we need to simplify it first.

Remember that when we subtract a negative number, it is equivalent to adding the positive number. Therefore, -(-8) is the same as +8.

So the expression becomes:

-14 + 8

To factor it further using the distributive law, we can rewrite the addition as multiplication by distributing the -14 to both terms:

(-14) + (8) = -14 * 1 + (-14) * 8

This can be simplified as:

-14 + 8 = -14 * 1 + (-14) * 8 = -14 + (-112)

Finally, we can add the two negative numbers to get the result:

-14 + (-112) = -126

Therefore, the expression -14 - (-8) factors completely as -126.

In the given graphs, the first and third graphs are connected graphs.

A connected graph is a collection of vertices, or points, and edges, or lines, such that there is a path between every pair of vertices.

This means that it is not possible to find any isolated vertices or disjoint subsets of vertices, and every vertex is connected to at least one other vertex.

The edges of a connected graph represent the relationships or connections between the vertices.

Here we have 3 graphs

In the first graph, every vertex is connected to other vertices and we can go from one node to another node

Hence, The first graph is a connected graph

In the second graph, there are two graphs that are not connected to other. Hence, The Second graph is not a connected graph

In the third graph, every node is connected

Hence, The third graph is a connected graph.  

Therefore,

In the given graphs, the first and third graphs are connected graphs.

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Answer:

Jackson is incorrect.

Step-by-step explanation:

He should compare the values in equal place values to compare all the decimals, not just those of the same length. For example, 0.0561 < 0.05625 < 0.0564.

Answer:

C

Step-by-step explanation:

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

15x-8=0

x=8/15

Step-by-step explanation:

Answer:

D. 2x^2 - 2x + 2

Step-by-step explanation:

(3x2 – 2x + 5) – (x2 + 3) add or subtract like terms

3x^2 - x^2 - 2x - 3 + 5 = 2x^2 - 2x + 2

Answer:

2x^2 - 2x + 2

Step-by-step explanation:

Ape-x

Answer:

Tooth Paste

Step-by-step explanation:

Best guess

Answer:

The molecules of the substances must be touching

FOR EXAMPLE, a metal spoon placed in a hot coffee mug shows the flow of heat from coffee to the spoon. and now we can conclude that a condition that must exist in order for conduction to occur between two substances is that the objects must be touching each other.

Answer:

The molecules of the substances must be touching.

A

Step-by-step explanation:

Answer:

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time =

Time =

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

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Step-by-step explanation:

Step-by-step explanation:

1) given

2) 2 non - common sides in 1 ray

3) supplemental

5) opposite angles are congruent

Reasons:

(1) Given

(2) their 2 non-common sides in 1 ray

(3) definition of supplemental angles

(4) Substitution

(5) Opposite angles are congruent (equal)

(6) Substitution

(7) Definition of supplementary angles

Answer:

24 because you have to subtract

Square abοve wοuld have the same area as square F is b)square C.

The regiοn that an οbject's shape defines as its area. The area οf a figure οr any οther twο-dimensiοnal geοmetric shape in a plane is hοw much space it οccupies.

Here the square A is cοntains 4- 1 unit squares.

Then length οf the square = 2 units,

If Square A is dilated by scale factοr 1/2 then,

Length οf square  F = \(2\times \frac{1}{2}\) = 1unit.

Area οf square F = 1*1 = 1 square unit.

Then in the given squares , square C οnly has 1 unit side length.

Hence the cοrrect οptiοn is b) Square C.

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Answer:

Value of x =  15.1 unit (Approx.)

Step-by-step explanation:

Given:

For angle 54°

Base of triangle = 11 unit

Perpendicular of triangle = x unit

Find:

Value of x

Computation:

Using trigonometry function;

Tanθ = Perpendicular / Base

Tan 54 = Perpendicular of triangle / Base of triangle

Tan 54 = x / 11

1.376 = x / 11

Value of x = 1.376 × 11

Value of x = 15.136

Value of x =  15.1 unit (Approx.)

The cosine of the angle  θ  is √5/5  whose terminal side passes through the given point

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: The terminal side goes through the point  (√5/5,2√5/5)

Thus we have cosθ =√5/5 and sin θ =-2√5/5

now tan θ =sinθ /cosθ

        tanθ    =-2√5/5 / √5/5

              θ = 63.434

Hence, cosθ =√5/5

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Answer:

2 just 2

Step-by-step explanation:

It is in the ones place

Answer:

Step-by-step explanation:

22 + t < 40

t < 18

Answer: b

Step-by-step explanation:

Answer:

-2 11/12 is the answer for me

Answer:

I believe it is D I'm a senior in pre-cal but I also dont have paper so I did it in my head rq

Answer:

Option B

\(\red{ \boxed{ \bold{ {f}^{ - 1} (x) = \sqrt[3]{ - x - 9} }}}\)

Step-by-step explanation:

\(f(x) = - {x}^{3} - 9 \\ plug \: f(x) = y \\ \implies \: y = - {x}^{3} - 9 \\ interchange \: x \: and \: y \\ \\ x = - {y}^{3} - 9 \\ \\ x + 9 = - {y}^{3} \\ \\ - x - 9 = {y}^{3} \\ \\ \sqrt[3]{ - x - 9} = y \\ \\ \sqrt[3]{ - x - 9} = {f}^{ - 1} (x) \\ \\ \red{ \boxed{ \bold{ {f}^{ - 1} (x) = \sqrt[3]{ - x - 9} }}}\)

a) Luego de calculado y analizado el campo eléctrico en torno a la carga puntual, la intensidad del campo eléctrico es igual a \(3.673\times 10^{13}\,\frac{N}{C}\).

b) Conocida la carga y la fuerza eléctrica asociada a la carga puntual, concluimos que la intensidad del campo eléctrico es igual a \(103.061\,\frac{N}{C}\).

a) Puesto que no se conoce la configuración geométrica de la fuente, se asume que es una carga puntual. En este caso, tenemos que el campo eléctrico (\(E\)), en newtons por coulomb, es definido por la siguiente expresión:

\(E = \frac{k\cdot q}{r^{2}}\) (1)

Donde:

Si sabemos que \(Q = 5\times 10^{4}\,C\), \(r = 3.5\,m\) y \(k = 9\times 10^{9}\,\frac{N\cdot m^{2}}{C^{2}}\), entonces la intensidad del campo eléctrico es:

\(E = \frac{\left(9 \times 10^{9}\,\frac{N\cdot m^{2}}{C^{2}} \right)\cdot (5\times 10^{4}\,C)}{(3.5\,m)^{2}}\)

\(E = 3.673\times 10^{13}\,\frac{N}{C}\)

La intensidad del campo eléctrico es igual a \(3.673\times 10^{13}\,\frac{N}{C}\).

b) Supongamos que existe una carga puntual, tenemos la siguiente expresión por la definición de campo eléctrico:

\(E = \frac{F}{q}\) (2)

Donde \(F\) es la fuerza eléctrica, en newtons.

Si sabemos que \(F = 10.1\,N\) and \(q = 98\times 10^{-3}\,C\), entonces el campo eléctrico es:

\(E = \frac{10.1\,N}{98\times 10^{-3}\,C}\)

\(E = 103.061\,\frac{N}{C}\)

La intensidad del campo eléctrico es igual a \(103.061\,\frac{N}{C}\).

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