if it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?

The value of P(A and B)  is 1/5.

What is Sample Space?

The set of all potential outcomes or results of an experiment or random trial is referred to as the sample space in probability theory. The sample points, or potential ordered outcomes, are listed as elements in the set notation used to represent a sample space.

Here, we have

Given

Sample Space = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 3, 4}

B={1, 3, 5, 7, 9}

We have to find P(A and B).

First, we will find A and B i.e A∩B

A∩B = {1,3}

Now, we will find P(A and B).

P(A and B) = n(A∩B)/n(S)

P(A and B) = 2/10

P(A and B)  = 1/5

Hence, the value of P(A and B)  is 1/5.

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The graph cannot be proportional because y stays the same

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

The graph

On the graph, we can see that:

As x increases, the values of y remains unchanged

For the graph to be proportional, it must be a straight line that passes through the origin

And the variables must change

Hence, the true statement is the graph cannot be proportional

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Answer:

Biotic factors of a marine ecosystem typically include algae, plankton, bacteria, seaweed, corals, fish, sharks, seals, whales, penguins and jellyfish.

Step-by-step explanation:

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From the equation, the value of m is 4

The given parameter is

0.m1+ 0.m2 + 0.m3 = 11/14

Simplify this to have

m1 / 99 + m2 / 99 + m3 / 99 = 11/14

Simplify the equation further

( m1 + m2 + m3 ) / 99 = 11/14

⇒( m1 + m2 + m3 ) = 126

By multiplication we have

( 10 * m + 1 ) + ( 10 * m + 2 ) + ( 10 * m + ) = 126

Simplify to get

30 * m + 6 = 126

30 * m = 120

m = 4

Therefore the value of m is 4

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Translated question:

Please help, given that 0.m1 +0.m2 +0.m3 = 14/11, Find the value of m

Circumference of the circle is 37.68 feet

A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).

R is specified as 6 feet, with a diameter of 12 feet (2 x 6).

Circumference: 12 feet times 3.14 inches, or 37.68 feet

If r is equal to 6 cm, the circumference is given by c = 2 (6) = 12 cm. If you'd rather have a number, the solution is 37.7 cm, rounded to the closest tenth.

D is the diameter, which is equal to 2 times r in the circumference formula ( r is the radius).

The distance between the center of the sphere and any plane passing through it is known as the circumference. 

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The height of the balloon is 21.33

According the the question the relation between height and surface area of balloon is

H=pA

where ,

H is height

p is proportionality constant

A is surface area

Surface area = 81

Height = 12

By Replacing the given values we get,

12=p x 81

p=12/81

Using it in given conditions,

H=(12/81)x144

H=21.33

So the height of the balloon in the given condition is 21.33

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Answer: 240

Step-by-step explanation: you take 10 times 12 and you get 140

Answer:

$240

Step-by-step explanation:

If ten friends went out and each was $24 it’s 10x24 which is equal to $240

Answer: 35%

Step-by-step explanation:

The distance Alex jumped and the distance Eric jumped compared with the state records indicates that the magnitude of Eric's score was closer to their grades state  record

The magnitude of a value is the value itself, indicating the distance of the number from zero.

Alex is an eight grader

Eric is a seventh grader

The distance Alex jumped = 39.75  feet

The distance Eric jumped = 37 feet 11 inches

The eight grade record = 42.25 feet

The seventh grade record = 39 feet 3 inches

Each athlete distance  jumped is compared with  the record for the grade at which they jumped

The deviation of the distance  jumped from the record scores are;

Alex's difference between distance jumped  and the record = 39.75 - 42.25 =  -2.5

The difference between the distance Eric jumped and the record =  37 feet + 11 inches - (39 feet + 3 inches)  =  -(1 feet + 4 inches)

-(1 feet + 4 inches) = -1.[tex]\overline 3[/tex] inches

The magnitude of the difference between the distance Eric jumped and the state record is smaller, therefore, Eric was closer to the state record

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Answer: I can confirm that Eric is closer!

Step-by-step explanation:

Answer:

Explanation: Its D.

Option (a) is correct option.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.

Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality. When two or more parameters are proportional to one another either directly or indirectly, their relationship is stated as a = kb or a = k/b, where k denotes the direction of the relationship between the two variables.The proportionality constant is thus k.

Constant of proportionality in given case is nothing but slope of given graph.

Slope is given by tangent of the angle made by line with positive x-axis.

p =slope of line

p = [tex]\frac{y-axis}{x-axis}[/tex]

p=[tex]\frac{140}{2}[/tex] = 70

So option (a) is correct.

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There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

4x + 4 ≤ 9x + 84x + 4 ≤ 9x + 8

84x ≤ 4

x ≤ 1/21

x ≤ 0.05

Thus,

The value of x is less than or equal to 0.05.

x ≤ 0.05

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

4x + 4 ≤ 9x + 84x + 4 ≤ 9x + 8

Adding the like terms.

4x + 4 ≤ 93x + 4 ≤ 9x + 8

Subtracting 4 on all sides.

4x  ≤ 93x ≤ 9x + 4

Subtracting 4x on all sides.

0 ≤ 93x - 4x ≤ 5x + 4

We can write it as,

89x ≤ 5x + 4

89x - 5x ≤ 4

84x ≤ 4

x ≤ 4/84

x ≤ 1/21

x ≤ 0.05

Thus,

The value of x is less than or equal to 0.05.

x ≤ 0.05

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one leg of a right triangle is 6 inches longer than the other leg, and the hypotenuse is 30 inches. Thus,

The lengths of the legs of the triangle are 18 inches,24 inches and  30 inches.

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Given that,

one leg of a right triangle is 6 inches longer than the other leg.

hypotenuse is 30 inches.

Let assume, the other leg be x

It is given that, one leg of a right triangle is 6 inches longer than the other leg. So, One leg = x + 6

Since it is a right angled triangle,

h² = p² + b²

Where, h = hypotenuse

p = perpendicular

B = Base

So, (30)² = (x+6)² + x²

or, x = -24, 18

As, the length of side cannot be negative so x becomes 18.

Thus, x + 6 = 18 + 6 = 24 inches

Hypotenuse = 30 inches

Hence, the lengths of the legs of the triangle are 18 inches, 24 inches and  30 inches.

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Answer:

Center: (0,0)

Radius: 3

Graph:

Please find attachment to view the graph.

Step-by-step explanation:

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Using the parameters associated with the parabola and the formula for the equation using the focus and the focal diameter, The required equation is

[tex]x = \frac{-1}{62} (y+5)^{2}+ \frac{9}{2}[/tex] .

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

All points in a plane that are equally spaced out from a given point and a given line make up a parabola. The line is known as the directrix, and the point is known as the parabola's focus. The parabola's axis of symmetry is the subject of attention.

focus = (-11,5)

focal diameter =20

Required equation of parabola,

[tex]x = \frac{-1}{62} (y+5)^{2}+ \frac{9}{2}[/tex]

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Answer:

ANS:- 2439

Step-by-step explanation:

2439/3 = 813

2439/9 = 271

Answer:

She bought 3 large frames and 8 small frames.

Step-by-step explanation:

X= Large frames = $19

Y= Small frames  = $ 9

Total Frames Cost = $129

Total Frames = 11

Then, costs formula:

1) 19X + 9Y = 129

2) X + Y = 11

So here you have a equation system and we will solve it by substituion method:

2) Y = 11-X

replace Y in 1)

1) 19X + 9(11-X) = 129

19X +99 -9X = 129

10X = 129-99

10X = 30

X = 30/10

X = 3

Then

Y = 11-3

Y = 8

The option that best describe the transformation is

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object.

Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

the transformation is the problem is reflection which is equivalent to 180 degree rotation hence we say it is a certain angle rotation of point about the circle's center.

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Answer:

Use Pyramid Formua to get upper height.

And add with 5m lower height.

Answer:

[tex]3(a^2+2a)[/tex]

Step-by-step explanation:

[tex]\sqrt{3a}(\sqrt{12a}+a\sqrt{3a}) \\ \\ =\sqrt{36a^2}+a\sqrt{9a^2} \\ \\ =6a+a(3a) \\ \\ =3a^2+6a \\ \\ =3(a^2+2a)[/tex]

Answer:

write the equation in slope intercept form. Write the numbers in the equation as simplified proper fraction improper fraction or integer

The equation of the parallel line t is y = -4x  - 9.

The equation of line s is given as

y = -4x - 5/3

Also, from the question, the point on line t is given as Point = (-3, 3)

The equation of a line can be represented as

y = m x + c-------(1)

Where m represents the slope

c is the constant value

By comparing the equations, we have the following

m = -4

This means that the slope of y = -4x - 5/3 is -4

The slopes of parallel lines are equal

This means that the slope of the line t is -4

The equation of the parallel line is then calculated as:

y = m(x - x₁) +y₁

Where m = -4

(x₁, y₁) = (-3, 3)

Now, we should substitute the known values in the above equation(1)

y = -4(x + 3) + 3

By Evaluating we get

y = -4x - 12 + 3

y = -4x  - 9

Hence, the parallel line has an equation of y = -4x  - 9.

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The answer to this Question based on speed is 1m/s

What is speed?

Speed can be defined as the rate at which an object moves from one point to another. It is usually measured in units of distance per unit of time, such as kilometers per hour (km/h) or miles per hour (mph). Speed is a scalar quantity, meaning it has magnitude but no direction. Speed can also be thought of as the rate of change of position. When an object is in motion, its speed is constantly changing due to the force of gravity, air resistance, and other external factors. The speed of an object can be affected by its weight, shape, and size. An object's speed can also be affected by other factors such as the friction of the surface it is moving on and the wind or air resistance. Speed is an important concept in physics, engineering, and many other fields.

we are given that velocity as a function of time along a single direction

we write v(t) = -2t+5

hence speed = mod(velocity)

speed at t = 2 sec = mod (velocity at t = 2 sec)

speed = mod(-2(2)+5)

speed = mod(-4+5)

speed = 1 m/s

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The required value of n for two similar pentagons is 15/4.

The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.

The given two pentagons have similar shape because one has been scaled to get the other.

It implies that the ratio of the corresponding sides for them will be equal. It can be written as follows,

5/n = 3(¹/₃)/2(¹/₂)

=> 5/n = (10/3)/(5/2)

=> 5/n = 20/15

=> n = 15/20 × 5

=> n = 15/4

Hence, the value of n for the given pentagon is 15/4.

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Answer:

8.0

Step-by-step explanation:

There are 1000 milliliters in one liter, so a two-liter bottle contains 1000 * 2 = 2000 milliliters of milk. Since one cup contains approximately 250 milliliters, a two-liter bottle contains 2000 / 250 = 8 cups of milk. Rounding this value to the nearest tenth, we find that there are approximately 8.0 one-cup servings of milk in a two-liter bottle.

As it passes through the point (2,6), it will convert to the function f(x) = (x + 2) -3 at (0,3).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. A "vertical line test" can be used when examining a graph to determine whether a relation is a function. The relation is not a function if any point on the graph may be used to build a vertical line that crosses the relation twice.

Here,

g(x) = f(x + 2) – 3

This represents a shift of two units to the left and three units down:

x moves from two to two units left (-2) to become 0  

y moves from six to three units down (-3) to become 3.

At (0,3), It will translate to the function f(x) = ( x + 2) -3 as it goes through the point (2,6).

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A. The system of inequality is plotted and the graph is attached

B. (1, 3) is not a solution because it does not satisfy the two equations

C. the three points that are solutions are

Substituting the given point into the two system of equation if it satisfies the equation then it is a solution

For (1, 3)

3x + y ≥  - 1

3 * 1 + 3 ≥ - 1

6 ≥ - 1 correct

2y - 4 > 3x

2 * 3 - 4 > 3 * 1

2 > 3 - wrong hence not a solution

For  (-1, 3)

3x + y ≥  - 1

3 * -1 + 3 ≥ - 1

0 > -1 correct

2y - 4 > 3x

2 * 3 - 4 > 3 * -1

2 > -3 correct this is a solution

(-1, 4) and (1, 4) other solutions are deduced form the attached graph where two the two shaded points intersect

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Reflection of point 1 over X axis is (-4, -2)

Reflection of point 2 over Y axis is (2, 3)

Reflection of point 3 over x = 1 is (2, 1)

Reflection of point 4 over y = x is  (2, -1)

What is Reflection of a point?

A reflection point occurs when a figure is constructed around a single point known as the point of reflection or center of the figure. For every point in the figure, another point is found directly opposite to it on the other side.

According to the given question:

1. Reflection of point 1 over X axis (x, -y) ⇔ (x, y)

 ∴ Reflection of (-4, 2) over X axis is (-4, -2)

2. Reflection of point 2 over Y axis (x, y) ⇔ (-x, y)

 ∴ Reflection of (-2, 3) over Y axis is (2, 3)

3. Reflection of point 3 over x = 1

 ∴ Reflection of (-2, 1) over x = 1 axis is (2, 1)

4. Reflection of point 4 over y = x is  (x, y) ⇔ (y, x)

 ∴ Reflection of (-1, 2) over X axis is (2, -1)

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By using simultaneous linear equation, it can be calculated that-

Number of children are 118 and number of adults are 363

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here, a simultaneous linear equation needs to be solved

Let the number of children be x and number of adults be y

481 people used the public swimming pool.

x + y = 481 ..... (1)

The daily prices are $1.75 for children and $2.00 for adults.
Total price = $(1.75x + 2y)

By the problem,

1.75x + 2y = 932.50

7x  + 8y = 3730 .... (2)

Multiplying (1) by 7

7x + 7y = 3367.... (3)

Subtracting (3) from (2)

y = 363

Putting the value of y in (1)

x  + 363  = 481

x = 481 - 363

x = 118

Number of children are 118 and number of adults are 363

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