This trapezoid-based right prism has a volume of 30\text{ cm}^330 cm 3 30, start text, space, c, m, end text, cubed.

Answer:

The rate of the increasing volume is 50000\(\pi \frac{mm^{3}}{s}\)  

Step-by-step explanation:

The rate of the increasing volume can be calculated as follows

The formula to calculate the volume V of a sphere is

\(V=\frac{4}{3} \pi r^{3}\)

Where r is the radius

It is given that the radius is increasing at 5 mm/s, then it follows that

\(\frac{dr}{dt} =5\frac{mm}{s}\)

Since volume V is a function of radius  r, and radius  r is the function of time t, then the chain rule formula to find derivatives is introduced here

\(\frac{dV}{dt}=\frac{dV}{dr}\cdot \frac{dr}{dt}\)

The first step is to find \(\frac{dV}{dr}\)

\(V=\frac{4}{3} \pi r^{3}\)

By the formula of  \(\frac{d}{dx} (x^{n})=nx^{n-1}\), then for \(V=\frac{4}{3} \pi r^{3}\)

\(\frac{dV}{dr}=3\cdot \frac{4}{3} \pi r^{3-1}\)

\(\frac{dV}{dr}=4 \pi r^{2}\)

The second step is to find \(\frac{dV}{dt}\)

\(\frac{dV}{dt}=\frac{dV}{dr}\cdot \frac{dr}{dt}\)

Substitute \(4 \pi r^{2}\)  for  \(\frac{dV}{dr}\) , \(5\frac{mm}{s}\)  for  \(\frac{dr}{dt}\)

\(\frac{dV}{dt}=4 \pi r^{2}\cdot 5 \frac{mm}{s}\)

For the given radius rate, the formula of the increasing volume is

\(\frac{dV}{dt}=4 \pi r^{2}\cdot 5 \frac{mm}{s}\)

Since the given diameter of the sphere is 100 mm, then the radius of the sphere is

radius = \(\frac{diameter}{2}\)

radius = \(\frac{100~\text{mm}}{2}\)

radius = 50 mm

The third step is to find the rate of increasing volume of the given sphere

Substitute 50 for r, then it follows that

\(\frac{dV}{dt}=4 \pi (50~\text{mm})^{2}\cdot 5 \frac{mm}{s}\)

\(\frac{dV}{dt}=4 \pi ~2500~\text{mm}^{2}\cdot 5 \frac{mm}{s}\)

\(\frac{dV}{dt}=50000 \pi \cdot \frac{mm^{3}}{s}\)

Hence the rate of increasing volume of the given sphere is \(50000 \pi \cdot \frac{mm^{3}}{s}\)

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The first equation, x_1 + 4x_2 - 2x_3 = 0, represents a plane in three-dimensional space. Its solution set consists of all points (x_1, x_2, x_3) that satisfy the equation. Since the equation equals zero, the solution set corresponds to all points lying on this plane.

The second equation, x_1 + 4x_2 - 2x_3 = -5, is similar to the first equation but with a constant term of -5 on the right-hand side. This shifts the entire plane downward by 5 units along the z-axis. Consequently, the solution set represents all points on the shifted plane.

To describe the solution set of the second equation, x = [x_1 x_2 x_3], in parametric vector form, we can express one variable in terms of the other variables. By rearranging the equation, we have x_1 = -5 - 4x_2 + 2x_3. Letting x_2 = t and x_3 = s, we can write the solution set as x = [-5 - 4t + 2s, t, s]. This parametric vector form allows us to express the solution set using two free variables, t and s, with x_1 being dependent on those variables.

The solution set of x_1 + 4x_2 - 2x_3 = 0 represents a plane in three-dimensional space, while the solution set of x_1 + 4x_2 - 2x_3 = -5 represents the same plane shifted downward by 5 units along the z-axis. The solution set of the second equation can be described in parametric vector form as x = [-5 - 4t + 2s, t, s], where t and s are free variables.

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Answer:

  see attached

Step-by-step explanation:

You want a normal curve labeled with the mean and the values for three standard deviations above and below the mean. The mean is 94, and the standard deviation is 3.

It can work well to label the middle box with the mean (94). Each box to the right is 3 more than the one to its left. This is true across the whole diagram.

The labeled diagram is attached.

<95141404393>

To find out how much the Guilderian trader must pay for the same 50 flop barrel of pickles, we need to calculate the cost per gulp and then multiply it by the number of gulps in the barrel.

Given that the Guilderian trader initially exchanged 25 gulps for the 50 flop barrel of pickles, we can determine the cost per gulp by dividing the total cost (50 flops) by the number of gulps (25).  Cost per gulp = 50 flops / 25 gulps = 2 flops/gulp . Since the gulp depreciates to 0.5 flops per gulp, the Guilderian trader must pay 0.5 flops per gulp for the same barrel of pickles.

Therefore, the Guilderian trader must pay 0.5 flops/gulp * 25 gulps = 12.5 flops for the 50 flop barrel of pickles. For the Florish trader, we need to calculate the cost per flop and then multiply it by the number of flops in the crate.

Given that the Florish trader initially exchanged 40 flops for the 20 gulp crate of apples, we can determine the cost per flop by dividing the total cost (40 flops) by the number of flops (20).

Cost per flop = 40 flops / 20 flops

= 2 flops/flop .

Therefore, the Florish trader must pay 2 flops per flop for the same crate of apples.

The Guilderian trader must pay 12.5 flops for the same 50 flop barrel of pickles, and the Florish trader must pay 2 flops for the same 20 gulp crate of apples.

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Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.

The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.

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Therefore, based on the information provided, the perpendicular distance from the x-axis to the center of Shape B, or the distance from the origin along the y-axis to the center of Shape B, is 1.5 units.

To determine the perpendicular distance from the x-axis to the center of Shape B or the distance from the origin along the y-axis to the center of Shape B, we need to consider the properties of Shape B.

In this context, when we say "center," we are referring to the midpoint or the central point of Shape B along the y-axis.

The given answer of 1.5 units suggests that the center of Shape B lies 1.5 units above the x-axis or below the origin along the y-axis.

The distance is measured perpendicular to the x-axis or parallel to the y-axis, as we are interested in the vertical distance from the x-axis to the center of Shape B.

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x= 4  is a number and five is at least half the difference of six and the same number.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.

Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.

Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

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Answer:

a) y=4x-3

b) y=-1/2x+4

c) y=-3x+8

d) y=5/3x-1

Step-by-step explanation:

y1-y2/x1-x2

Plug in the numbers and solve.

Answer:

option. c. 720°

.....................

Answer:

720degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

20

Answer:

256 codes

Step-by-step explanation:

Answer:

80 degrees because if you look at 1 its 62 plus 18

Answer:

3 batches

Step-by-step explanation:

First simplify 1/2 into 3/6

which into 1/6 makes three which means Mark can make 3 batches of cookies.

(If Mark had a full pound he could make 6 batches of cookies)*

Have a good day. :)

Hope this helps!

(brainliest would be appreciated)

Answer:

3 batches

Step-by-step explanation:

From the graph of miles driven and pricing, it can be observed that for 200 miles option A price is $100 and option B price is $70.

So option A cost more than option B.

Determine the difference between $100 and $70 to obtain how much option A cost more than option B.

So option A cost $30 more than option B.

From the graph, it can be observed that lines of option A and option B intersect each other at (50,40). So option A and option B cost same for 50 miles.

Answer:

w > 2

Steps:

w +2  > 4

w + 2 - 2 > 4 - 2

w > 2

The prediction interval is then calculated as follows as: ±0.0196.

The prediction interval for the length of life of a horse can be calculated using the following formula:

Prediction interval = ±1.96 * standard error

here the standard error is the standard deviation of the sampling distribution of the estimate.

The standard error can be estimated using the formula:

Standard error = √[(1/n) * sum((estimate - y\()^2\)]

here n is the sample size, estimate is the sample mean, and y is the true population mean.

In this case, the sample size is n = 2, the estimate is x = 2, and y = 18.89.01087.

Substituting these values into the formula, we get:

Standard error = √[(1/2) * (2 - 18.89.01087\()^2\)]

= √[(1/2) * (2 - 18.89.01087)]]  ]]\()^2\)]

= √[0.5 * (2 - 18.89.01087)\()^2\)]

= √[0.5 * 0.02087\()^2\)]

= √0.5 * 0.001156

= 0.001156

The standard error is approximately 0.001156.

The prediction interval is then calculated as follows:

Prediction interval = ±1.96 * standard error

= ±1.96 * 0.001156

= ±0.0196

Rounding to the nearest hundredth, the prediction interval is approximately 0.02.  

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Answer:

Step-by-step explanation:

The Answer is 203 Fahrenheit.

(95 x 9/5) + 32 = 203

The correct statement is that the value of n that make the relationship a function are any value except 1, 3, or 2

A function is a relationship that maps the elements of a set A to the elements of a set B, such that each element of A is mapped to exactly one element of the set B.

The ordered pair of known values are a function as the elements of the input variable are all different and the element of the output variable are also different, which indicates a 1 to 1 relationship.

The known elements of the set A in the question are; 2, 6, and 4

The elements of the set A are known as the domain of the function.

The known element of the set B are 8, 0, and 2

The fourth ordered pair (2·n, n), has a value similar to the pair (4, 2)

To prevent the presence of the elements 2,. 6, and 4, being assigned to other elements apart from 8, 0, and 2, the value of 2·n can be any value except 2, 6, 4

Therefore;

n can be any value except 2/2 = 1, 6/2 = 3, or 4/2 = 2

The correct statement is therefore;

n can be any value except 1, 3, or 2

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Answer:

x = 15

Step-by-step explanation:

Angle = exterior

x + 118= 133

x = 133-118

x = 15

Hence, x = 15

[RevyBreeze]

The situation can be visualized as follows:

```

             |

             |

             |

            /|

           / |

          /  |

         /   |

        /θ   |  180 ft

       /     |

      /      |

     /       |

    /        |

   /________|

      100 ft

```

We can see that we have a right triangle with one leg of length 100 ft (the shadow) and another leg of length 180 ft (the height of the building). We want to find the angle opposite the 100 ft leg, which we'll call θ.

Using the tangent function, we have:

tan(θ) = opposite/adjacent = 180/100 = 1.8

To find θ, we take the inverse tangent (or arctan) of both sides:

θ = arctan(1.8) ≈ 63.43 degrees

So the measure of the angle between the end of the shadow and the vertical side of the building is approximately 63.43 degrees.

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The equation of the line in the form of ax + by = c is 5x - 2y = -2.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation contains an equal sign "=" that separates the two expressions.

In mathematics, a line is a straight path that extends infinitely in both directions. It is a fundamental concept in geometry and is used to model many real-world situations in mathematics, science, engineering, and other fields.

To write the equation of a line in the form of ax + by = c, we need to rearrange the equation so that all the terms are on one side of the equation, and the coefficients of x and y are integers.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We can use the point-slope form of the equation to find the equation of the line that passes through the point (-4,-9) with a slope of 5/2:

y - y1 = m(x - x1), where (x1, y1) = (-4, -9)

y - (-9) = (5/2)(x - (-4))

y + 9 = (5/2)(x + 4)

Multiplying both sides by 2, we get:

2y + 18 = 5x + 20

Rearranging terms, we can write the equation in the form of ax + by = c:

5x - 2y = -2

Therefore, the equation of the line in the form of ax + by = c is 5x - 2y = -2.

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Answer: 7693cm

Step-by-step explanation:

The volume of a cone is given as:

= 1/3πr²h

where π = 3.14

radius = 3.5cm

height = 12

Volume = 1/3πr²h

= 1/3 × 3.14 × 3.5² × 12

= 153.86cm³

Therefore, the amount of water that is needed to fill 50 cups will be:

= 153.86 × 50

= 7693cm

Answer:

here the answer! There is the  proof it's right. :)

Step-by-step explanation:

Answer:

1/3 = 2/6

Step-by-step explanation

Edu correct

At the given rate at which the pump pumps at ten-minute intervals then there will be a total of 2,990 gallons in the tank after 90 minutes.

Because the interval is every 10 minutes, we will use 10 and multiply it to each rate and get the sum total.

= 42*10 + 40*10 + 38*10 + 35*10 + 35*10 + 32*10 + 28*10 + 20*10 + 19*10 + 10*10

= 420 + 400 + 380 + 350 + 350 + 320 + 280 + 200 + 190 + 100

= 2,990

If a tank is being filled with water using a pump that is old, and at the given rate at which the pump pumps at ten-minute intervals then There will be a total of 2,990 gallons in the tank after 90 minutes.

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-------- Correct question format is given below in image -------

Answer:

Angle RST is a translation of Angle UVW

Step-by-step explanation:

Answer:

aw man I wanted brainly

Step-by-step explanation:

Step-by-step explanation:

2.1--3<7.

--0,9<7

true

5--3< 8

2<8

true

Answer:

Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):

2.6

Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.

In short: 2.6 rounded to the nearest whole number is 3.