sophie is designing a new board game, and is trying to figure out all the possible outcomes. how many different possible outcomes are there if she rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, flips a coin, and rolls a fair die in the shape of a cube that has six sides labeled 1 to 6?

The volume of the solid of intersection is V = (2/3) × 2πr³ = V = (4/3)πr³.

To find the volume of the solid of intersection of the two right circular cylinders of radius r whose axes meet at right angles, we can use the formula:

V = (2/3)πr³

where r is the radius of the cylinders.

First, we need to find the height of the intersection. Since the axes of the cylinders meet at right angles, the height of the intersection will be equal to the diameter of each cylinder. So, the height of the intersection will be 2r.

Now, we can find the volume of the solid of intersection by multiplying the area of the base (which is a circle of radius r) by the height of the intersection (2r):

V = πr²(2r)

Simplifying this equation, we get:

V = 2πr³

So, the volume of the solid of intersection of the two right circular cylinders of radius r whose axes meet at right angles is 2/3 of the total volume of a cylinder with radius r and height 2r, which is 2πr³.

Therefore, the volume of the solid of intersection is:

V = (2/3) × 2πr³
V = (4/3)πr³

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Ladder diagrams are graphical representation techniques used to show how a particular control system operates, such as a mechanical process or a computer algorithm.

They are composed of two vertical lines that represent the power rails of the control circuit.

In this problem, the goal is to create a ladder diagram that will cause the output, alarm lamp ALRM 534, to be 0 N

when

(1) either the infeed conveyor CONV1541 is OFF or the outfeed conngo CONV1542 is OFF and

(2) the limit switch LS1535 is open and

(3) the proximity suid PS1536 is closed.

We'll do this issue for a SLC-500 plc.

Ladder diagram for SLC-500:

Firstly, since the alarm lamp is to be activated when the conditions are false, we will use a Normally Closed (NC) contact for each condition.

Next, draw the circuit for infeed conveyor CONV1541 OFF and the limit switch LS1535 is open.

Then, we'll add the other conditions, such as the outfeed conveyor CONV1542 OFF and the proximity switch PS1536 closed.

Finally, connect the alarm lamp ALRM1534 to the circuit to make it work when all of the specified conditions are met.

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Answer:

I would say the 3rd one, i think

Step-by-step explanation:

Answer:

(4,3)

Step-by-step explanation:

moving down 1 unit makes the point (-2,3)

moving 6 units to the right makes the point(4,3)

\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

Answer:

a is the answer because when x⁴ will go up it will be x-4

Answer:

2x+5=35.

2x+5-5=35-5

2x=30

2x/2=30/2

x=15

Answer:

63 is this right?

Step-by-step explanation:

10 x 9 = 90

so 7 x 9 = 63

Answer:

Step-by-step explanation:

is the explicit formula for the geometric sequence −8,−40,−200,−1000...

Solution:

The nth term of geometric sequence is given as:

Where,

n is the term location

is the first term of sequence

r is the common ratio between terms

Given sequence:

-8 , -40 , -200 , -1000 , ..

Thus, common ratio, r = 5

Substituting the values we get,

Thus the explicit formula is found

Learn more:

The explicit formula for the geometric sequence Negative one-ninth, one-third, negative 1, 3, negative 9, ellipsis is f (x) = negative one-ninth (negative 3) Superscript x minus 1. What is the common ratio and recursive formula for this sequence?

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Given the explicit formula for a geometric sequence find the first five terms and the 8th term an = 2.(1/4)^n,_1

Answer:

22 m

Step-by-step explanation:

The computation of the how much far does the boat travel is as follows:

sin 43 degrees = 15 ÷ d

d = 15 ÷sin 43 degrees

= 15 ÷ 0.6820

= 21.99

= 22 m

Hence, the how much far does the boat travel is 22 m

We simply applied the above formula so that the correct value could come

The same is to be considered

Answer:

26 - 11 = 15

Step-by-step explanation:

Answer:

Step-by-step explanation:

If Farmer Cora has a total of 128 onions and wants to place an equal number in each bags then, seeing since he has not decided on the amount of bags, he has the following options

128 onions in 1 Bag

64 onions in 2 Bag

32 onions in 4 Bag

16 onions in 8 Bag

8 onions in 16 Bag

4 onions in 32 Bag

2 onions in 64 Bag

1 onion in 128 Bag

Any of the above options will make each bag have an equal number of onions.

Answer:

y=4/3x+17

Step-by-step explanation:

y-y1 = m(x-x1)

m is the slope

y-9 = 4/3(x-(-6))

y-9 = 4/3(x+6)

y-9 = 4/3x+8

y-9 = 4/3x+8

y=4/3x+17

The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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We are told that Jason has $325 and that he earns $105 per week. That means that if "w" is the number of weeks then the amount of money he has in total is what he has saved by the product of $105 by the number of weeks. That is, if A is the amount he has, then:

Now, we are asked how many weeks it takes to get to $900. This means that we set A = 900 and solve for "w".

To solve for "w" we first subtract 325 on both sides:

Now we divide both sides by 105

Solving the operations:

Therefore, it takes Jason 5.5 weeks to get to $900

The factors of the given expression are 2av² and (2av³-9).

The given expression is 4a²v⁵-18av².

The factors are the polynomials which are multiplied to produce the original polynomial.

2av²(2av³-9)

Therefore, the factors of the given expression are 2av² and (2av³-9).

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Answer:

Use the distributive property to multiply 3 by x−2.

y=(3x−6)(x+1)(x−4)

Use the distributive property to multiply 3x−6 by x+1 and combine like terms.  y=(3x  2  −3x−6)(x−4)

Use the distributive property to multiply 3x  2 −3x−6 by x−4 and combine like terms. y =3x  3 −15x  2  +6x+24

Step-by-step explanation:

I also up a link there of a graph. Please tell me if you can open it. Hope this helps! :P

Answer:

88 yards

Step-by-step explanation:

because the park is 11 inches wide in the drawling, and the scale of it is 1:8

so the actual width of the park is

\(11/1/8=11*8=88 yards\)

11 divided by 1/8

Given:

Radius of a circle = 2.1 units

Arc length = 21.2 units

To find:

The central angle in radians to the nearest 10th.

Solution:

We know that the intercepted arc length is

\(s=r\theta\)

Where, s is the arc length, r is the radius and \(\theta\) is the central angle in radians.

Putting the given values, we get

\(21.2=2.1\theta\)

\(\dfrac{21.2}{2.1}=\theta\)

\(10.095238=\theta\)

\(\theta\approx 10.1\)

Therefore, the angle in radians is 10.1.

Answer:

Any assistance you can provide would be greatly appreciated. Any help you can give would be greatly appreciated. But "assistance" is a more formal word than "help". "Provide" is also formal.

The flow rate of 5 MGD is equivalent to 7.73615 cfs

To convert million gallons per day (MGD) to cubic feet per second (cfs), we need to use the conversion factor between the two units. The conversion factor is 1 MGD = 1.54723 cfs.

Therefore, to convert MGD to cfs, we can multiply the given value of MGD by the conversion factor. For example, if we have a flow rate of 5 MGD, we can convert it to cfs as follows:

5 MGD x 1.54723 cfs/MGD = 7.73615 cfs

So, the flow rate of 5 MGD is equivalent to 7.73615 cfs. Similarly, we can convert any given flow rate in MGD to cfs by using the same conversion factor.

It is important to note that these units are commonly used in the context of water supply and distribution systems, where flow rates are a crucial factor in the design and operation of such systems. Therefore, knowing how to convert between different flow rate units is essential for engineers and technicians working in this field.

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The types of polygons are different based on the number of sides they have and the sum of their interior angles.

The characteristics of different polygons are defined by the number of sides they have and the measure of their angles. Some polygons include:

There are other polygons and they change based on the number of sides they have.

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Answer/Step-by-step explanation:

Given:

12 Miles per Hour = (12 Miles = 1 Hour)

(1 Hour = 60 Minutes)

What is the rate in miles per minute?

60 Minutes x 12 Miles = 720 Miles

How many miles will the cyclist travel in 15 minutes?

12 Miles ÷ 100 = 0.12

0.12 x 15 Minutes = 1.8 Miles

The range of the given function would be -

Range → {-2, 3, 5, 6}

An function in mathematics defines a relationship between one variable (the independent variable {x})  and another variable (the dependent variable {y}). Example → y = f{x} = ax + b.

Given is the graph of the function as shown in the image.

Range represents the set of values along the {y} - axis. So, we can write the range as -

Range → {-2, 3, 5, 6}

Therefore, the range of the given function would be -

Range → {-2, 3, 5, 6}.

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Yes, the spokesman's claim that 70% of all U.S. adults drink cereal milk is true.

This can be tested using a hypothesis test, where the null hypothesis is that the proportion of people who drink cereal milk is equal to 70%, and the alternative hypothesis is that the proportion of people who drink cereal milk is not equal to 70%.

We then calculate the test statistic, which is the z-score of the sample proportion, ^. If the z-score is greater than the critical value (1.96 for a 95% confidence level), then we reject the null hypothesis and conclude that the proportion of people who drink cereal milk is not equal to 70%.

In this case, since the sample proportion is close to 70%, the z-score is very small, and the null hypothesis is accepted. Therefore, the spokesman's claim is true.

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Step-by-step explanation:

I am not sure what the actual details of the problem are, and what

4x + 6

7x + 15 are.

are the number of dashes ("-") an indicator ?

then the whole distance JL = 138 = 4+6 = 10 distance units.

1 distance unit is then 138/10 = 13.8

JK is then 4 distance units = 4×13.8 = 55.2

KL is the other 6 distance units = 6×13.8 = 82.8

or did the dashes not mean anything ?

and the 2 expressions stood for the 2 segment lengths ?

then it was just

JK = 4x + 6

KL = 7x + 15

and

JK + KL = JL

4x + 6 + 7x + 15 = 138

11x + 21 = 138

11x = 117

x = 117/11 = 10.63636363...

JK = 4x + 6 = 4×117/11 + 6 = 48.54545454... ≈ 48.55

Those numbers are x=55 and y= 15.

---------

1) Gathering the data

x-y=40

4y=x+5

2) Rewriting the system, and then solving it

x-y=40 ⇒x=40+y

4y=x+5

Applying substitution in the 2nd equation

4y=(40+y)+5

4y =40+y+5 Subtracting y from both sides

4y-y= 40+y-y +5

3y=40+5

3y= 45 Dividing by 3

y=15

Replacing in the first equation

x-15=40 Adding 15 to both sides

x-15+15=40+15

x=55

3) Those numbers are x=55 and y= 15.

Using the divergence theorem we can compute that the outward flux of the vector field is 16π .

The outward flux of F over the solid cylinder and z = 0 is

∫∫F·ds  = ∫∫∫ DivF dv

F = 2xy² i   +  2x²y j + 2xy k

Div F  =  D/dx (2xy²)  +   D/dy (2x²y )

Div F  =  2y²  +  2x²

In cylindrical coordinates   dV = rdrdθdz and as z = 0 the region is a surface ds = r·dr·dθ

Using the parametric form of the surface equation

x = rcosθ        y =  r sinθ      and z = z

Div F  = 2r² sin²θ  + 2r²cos²θ

∫∫∫ DivF dv  =  ∫∫ [2r²sin²θ  + 2r²cos²θ] × rdrdθ

∫∫ 2r² [sin²θ  + cos²θ] × rdrdθdz   ⇒  ∫∫ 2r³ drdθ

Integration limits

0 < r < 2          0 < θ < 2π

2∫₀² r³ ∫dθ

(2/4) × (2)⁴ × 2π

The divergence theorem, commonly known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.

In more detail, the divergence theorem states that the surface integral of a vector field across a closed surface, sometimes referred to as the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.

Therefore the flux is 16π .

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The missing factor in the second equation is 1, and the completed equation is: -24y + (-5) = -4(6y + 5/4)

We know that the GCF of -24y and -20 is 4. To find the missing factor in each equation, we can divide both terms by the GCF of 4.

For the first equation, we have:

-24y = 4 * (-6y)

Dividing both sides by 4, we get:

-6y = -24/4

Simplifying, we get:

-6y = -6

Therefore, the missing factor in the first equation is -1, and the completed equation is:

-24y + 20 = -4(6y - 5)

For the second equation, we have:

-20 = 4 * (-5)

Dividing both sides by 4, we get:

-5 = -20/4

Simplifying, we get:

-5 = -5/1

Therefore, the missing factor in the second equation is 1, and the completed equation is:

-24y + (-5) = -4(6y + 5/4)

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