Tank #2
Step 1: Calculations
Main Show Tank Calculation:
1. The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized lank?
Round your answer to the nearest whole number. You must explain your answer using words,
and you must show all work and calculations to receive credit.
Holding Tank Calculations:
2. The holding tanks are congruent in size, and both are in the shape of a cylinder that has beer
in half vertically. The bottom of the tank is a curved surface What is the volume of both

The total cost C as a function of the number of units produced is C(x) = 248000 + 68.28x, the revenue function is R(x) = 98.96x and the profit function is P(x) = 98.96x - 248000 - 68.28x

The given parameters are

Fixed cost = $248,000

Variable cost = $68.28

Hence, the total cost C as a function of the number of units produced is C(x) = 248000 + 68.28x

Here, we have

Selling price = $98.96

This means that

R(x) = Selling price * x

Hence, the revenue function is R(x) = 98.96x

This is calculated as:

P(x) = R(x) - C(x)

So, we have:

P(x) = 98.96x - 248000 - 68.28x

Hence, the profit function is P(x) = 98.96x - 248000 - 68.28x

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Answer: Choice D

The graph will be discrete because there is no such thing as a partial person to sign up, and the booth is set up once each day for sign ups.

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Explanation:

Let's start with the independent variable d. This acts as the variable x. It's the input. The value of d only takes on positive whole numbers (eg: d = 1, d = 2, d = 3, etc). We cannot have something like d = 2.718

So this bit of evidence shows that our function is discrete. Discrete input values (d) plug into the function to produce corresponding discrete output values (m).

Furthermore, we know that m is discrete because the number of people cannot be a fractional or decimal number. We can't have half a person for instance.

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A quick way to see if a set is discrete or continuous is to ask the question: "is it possible to apply the midpoint formula for ANY two values, and have the output make sense?"

So a set like {1,2,3,4,5,...} is discrete because the midpoint of 2 and 3 is 2.5, but that value is not in the set mentioned.

In other words, discrete sets have "gaps" so to speak, while continuous ones do not.

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Another useful property is that let's say that a < x < b, and x is drawn from the domain set. This reduced set will be finite if we're dealing with discrete data. Eg: The set {1,2,3,4,5,...} has the subset {2,3,4} which is finite and discrete.

In contrast, the subset of real numbers x such that \(2 \le x \le 4\) is continuous and this subset is infinitely large (has infinitely many members) because we could have things like 2.718 or 3.14 etc

Answer:

2x-3

Step-by-step explanation:

You use polynomial division to solve this, I tried to write down a little bit of my thinking process but I cant write everything out

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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When t=3, the velocity of the object is -11 m/s. This means the object is moving backward at a rate of 11 meters per second. The acceleration at t=3 is -6 m/s².

Given the velocity function v(t) = 20 - t², we need to find the velocity when t=3. Plugging in t=3 into the equation, we get v(3) = 20 - 3² = 20 - 9 = 11. Therefore, when t=3, the velocity of the object is 11 m/s. The positive value indicates that the object is moving in the negative direction.

To find the acceleration at t=3, we differentiate the velocity function with respect to time. Taking the derivative of v(t) = 20 - t², we get a(t) = -2t. Plugging in t=3, we have a(3) = -2 × 3 = -6. Thus, the acceleration of the object at t=3 is -6 m/s².

In conclusion, at t=3, the velocity of the object is -11 m/s, indicating it is moving backward at a rate of 11 meters per second. The acceleration at t=3 is -6 m/s².

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Answer:

her equation should be a² + 3² = 4²

Step-by-step explanation:

a² + 3² = 4²

a² + 9 = 16

a² = 7

a = \(\sqrt{7}\)

a ≈ 2.6 inches

The coordinates of the other endpoints are

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

Midpoint and Endpoint

The coordinates of the other endpoint given one endpoint and the midpoint is calculated as

(x₂, y₂) = (2Mx - x₁, 2My - y₁)

Using the above as a guide, we have the following:

(a) midpoint (5,8), endpoint (13,10)

(x, y) = (2 * 5 - 13, 2 * 8 - 10)

(x, y) = (-3, 6)

(b). midpoint (−7,6), endpoint (−9,9)

(x, y) = (2 * -7 + 9, 2 * 6 - 9)

(x, y) = (-5, 3)

(c). midpoint (12,6), endpoint (19,16)

(x, y) = (2 * 12 - 19, 2 * 6 - 19)

(x, y) = (5, -7)

(d). midpoint (−9,8), endpoint (−16,9)

(x, y) = (2 * -9 + 16, 2 * 8 - 9)

(x, y) = (-2, 7)

(e). midpoint (a,b), endpoint (p,q)

(x, y) = (2 * a - p, 2 * b - q)

(x, y) = (2a - p, 2b - q)

(f). midpoint (6a,6b), endpoint (3a,5b)

(x, y) = (2 * 6a - 3a, 2 * 6b - 5b)

(x, y) = (9a, 7b)

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Answer:

1,920

Step-by-step explanation:

A=L x W

so we have to multiply each number

24*8=192

192*10=1,920

To approximate the area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method, we can use the following formula:

Approximate Area = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

where Δx is the width of each subinterval and xi represents the right endpoint of each subinterval.

In this case, the interval [2, 4] is divided into four equal subintervals, so Δx = (4 - 2) / 4 = 0.5.

Now, let's evaluate the function at the right endpoints of the subintervals:

f(2.5) = 1/(2.5)^2 = 0.16

f(3) = 1/(3)^2 = 0.1111

f(3.5) = 1/(3.5)^2 = 0.0816

f(4) = 1/(4)^2 = 0.0625

Substituting these values into the formula:

Approximate Area = 0.5 * [0.16 + 0.1111 + 0.0816 + 0.0625]

Approximate Area = 0.5 * 0.4152

Approximate Area = 0.2076

Therefore, the approximate area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method is approximately 0.2076.

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Answer:

pro video is my work and my

Step-by-step explanation:

vision is pro

Answer:

The Correct answer is

57°

Answer:

Step-by-step explanation:

Let's use Law of Sines to find  angle X

recall   Sin(A) / a = Sin(B) / b

where A = 118 and a =  30 m

X = B   and b = 18  m

then

Sin(118) / 30 = Sin(B)  / 18

0.0294315 =  Sin(B) / 18

18 * 0.0294315 = Sin(B)

0.529768 = Sin(B)

arcSin(0.529768) = arcSin(Sin(B) )

31.9898 = B

x =32°

then since we know 2 of the 3 angles inside the triangle and we know they add to 180 , then

180 = 118 +32 + y

30 = y

y = 30°

Let's use law of Sines once more to find side z

so Sin(A) / a = Sin(B) / b    

where A= 30 and a = z

and B = 118   and b = 30

( notice how I reassigned things for this new problem ? )

Sin(30) / z = Sin(118) / 30

0.5 /  z  = 0.0294315

0.5 / 0.0294315 = z

16.988 = z

z = 17 m

You are done, for now.   Hope this  is helping you  "get this"  :)

Answer:

$13.70

Step-by-step explanation:

20 - 2.25 x 2.8

20-16.3 = 13.7

Answer:

It is the second choice.

Step-by-step explanation:

Divide both side by pi r squared. Boom.

Answer:

h = V/πr²

Step-by-step explanation:

Its asking you to isolate h. You can simply divide on the right besides h on both sides.

V = πr²h

V/πr² = h

Your answer should be - 84.

Explanation:

Starting equation: \(2\:+\:8\:-\:2\:\left[32\:+\:5\:\left(1\:+\:2\right)\right]\)

-Calculate within parentheses [32 + 5 (1+2)] = 47.

Remaining equation: 2 + 8 - 2 x 47

-Multiply and divide (left to right) 2 x 47 = 94

Remaining equation: 2 + 8 - 94

-Add and subtract (left to right) 2 + 8 - 94 = -84

Your final answer is -84

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Hope this helps!

Have a great day and God bless! :)

Answer:

Pontiac's Rebellion, which came closely on the heels of the French and Indian War, made the British seek more peaceful relations with Native Americans in the Ohio Valley. They issued the Proclamation of 1763, which prohibited colonists from settling in the region, as a way to avoid further conflict.

Step-by-step explanation:

Answer:

The answer is A.

Step-by-step explanation:

You have to apply :

\( {(a - b)}^{2} ⇒ {a}^{2} - 2ab + {b}^{2} \)

So for this question :

\( {(3a - b)}^{2} \)

\( = {(3a)}^{2} - 2(3a)(b) + {(b)}^{2} \)

\( = 9 {a}^{2} - 6ab + {b}^{2} \)

Answer:

see below

Step-by-step explanation:

sqrt(77)

8^2 = 64

9^2 = 81

It is closer to 9

We know it is between 8.5 and 9

8.8^2 = 77.44

This is a good approximation

Answer:

Katie will have 7 dollars left over.

Step-by-step explanation:

100

She buys a book so subtract 23 from 100.

100-23= 77

Katie has 77 dollars and wants to donate $10 to as much charities. 10 can go into 77, 7 times, which means she can only donate to 7 charities in $10.

a _______________________________

Answer:

a

Step-by-step explanation:

2 x 4 is 8

2.5 x 4 is 10

3 x 4 is 12

Answer:

0.8

Step-by-step explanation:

-4/4 + 160% + 1/5 =

= -1 + 1.6 + 0.2

= 0.8

The opportunity cost of cheese in the home country is 2 gallons of wine per pound of cheese, while in the foreign country, it is 0.5 pounds of cheese per gallon of wine.

The opportunity cost of a good represents the value of the next best alternative that must be given up producing or consume that good. In the home country, producing 1 pound of cheese requires giving up the opportunity to produce 2 gallons of wine. Therefore, the opportunity cost of cheese in the home country is 2 gallons of wine per pound of cheese. In the foreign country, producing 1 gallon of wine requires giving up the opportunity to produce 0.5 pounds of cheese. Hence, the opportunity cost of cheese in the foreign country is 0.5 pounds of cheese per gallon of wine.

To construct the world relative supply (RS) curve, we need to compare the relative labor requirements of cheese and wine production between the home and foreign countries. The relative labor requirement is obtained by dividing the labor requirement for one good by the labor requirement for the other good. In this case, we divide the unit labor requirements of cheese by the unit labor requirements of wine. For the home country, the relative labor requirement is 1 hour of cheese per 2 hours of wine, and for the foreign country, it is 2 hours of cheese per 1 hour of wine.

The world relative supply (RS) curve shows the combinations of cheese and wine that can be produced globally given the available labor supply in both countries. It is derived by combining the relative labor requirements of the two countries. By plotting different combinations of cheese and wine production on the RS curve, we can observe the trade-off between the two goods and the potential gains from trade.

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The expected value is the long-term average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability and summing them up. In simpler terms, it represents the average value we expect to get over many trials.

The expected value is a concept in probability and statistics that represents the long-term average outcome of a random variable. It is also known as the mean or average. To calculate the expected value, we multiply each possible outcome by its probability and sum them up.

For example, let's say we have a fair six-sided die. The possible outcomes are numbers 1 to 6, each with a probability of 1/6. To find the expected value, we multiply each outcome by its probability:

Summing up these values gives us:

1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 21/6 = 3.5

Therefore, the expected value of rolling a fair six-sided die is 3.5. This means that if we roll the die many times, the average outcome will be close to 3.5.

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Answer:

it should be cost, because when there is more quantity of something there will be less price.

Answer:

the spent on food would be $23

And for clothes it would be = $23 + $24 = $47

Step-by-step explanation:

Let us assume the food be x

So for clothes it would be  x + $24

And, the total spent on food and clothes is $70

So the equation is

x + x + $24 - $70

2x = $70 - $24

2x = $46

x = $23

So, the spent on food would be $23

And for clothes it would be = $23 + $24 = $47

In the top right corner is -7x since we multiply the x and -7

In the bottom row, we'll have 5x for the first box and -35 for the second box. Each box is the result of multiplying the outer values.

In the top left corner, the x^2 is from multiplying the two copies of x.

Answer:2.8

Step-by-step explanation:

2.8

Answer:

C

Step-by-step explanation:

f(x) - g(x)

= \(\sqrt{x}\) - x - (2x³ - \(\sqrt{x}\) - x) ← distribute parenthesis by - 1

= \(\sqrt{x}\) - x - 2x³ + \(\sqrt{x}\) + x ← collect like terms

= - 2x³ + 2\(\sqrt{x}\)

Answer:

D. 5.5

Step-by-step explanation:

Answer: 5.5

Step-by-step explanation:

KM=LN

6x+16=49

6x=33, x=5.5