Solve the following initial value problem. dy 2. = 32t + sec^ t, v(tt) = 2 dt The solution is a (Type an equation. Type an exact answer, using a as needed.)

The amount of fabric that is needed for the tent is 18350 in² (optionC)

A prism is a solid shape that is bound on all its sides by plane faces. The surface area of a prism is expressed as ;

SA = 2B +pH

where B is the base area , p is the perimeter of the base and H is the height of the prism.

Base area =1/2bh

= 1/2 × 50× 70

= 25 × 70

= 1750in²

Perimeter of the base = 74+74+50

= 198 in

height = 75in

Therefore SA = 2×1750 +198 × 75

= 3500 + 14850

= 18350 in²

therefore the amount of fabric that will be needed nis 18350 in²

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Answer:

40 dollars and 12 cents

Step-by-step explanation:

So since there are more than 8 people on the table, we can say that there will be an 18% gratuity that will be added to the final bill.

510+18%(510)

510+0.18×510

510+91.8

601.8$ is the total bill

since there are 15 people

601.8/15=40.12

The relation R is transitive, as demonstrated through the matrix method where every pair (x, y) and (y, z) in R implies the presence of (x, z) in R, based on the matrix representation.

To demonstrate this using the matrix method, we construct the matrix representation of the relation R. Let's denote the elements of the set {a, b, c, d} as rows and columns. If an element exists in the relation, we place a 1 in the corresponding cell; otherwise, we put a 0.

The matrix representation of relation R is as follows:

\(\left[\begin{array}{cccc}1&1&1&1\\1&1&1&1\\0&0&1&0\\1&1&1&1\end{array}\right]\)

To check transitivity, we square the matrix R. The resulting matrix, R^2, represents the composition of R with itself.

\(\left[\begin{array}{cccc}4&4&3&4\\4&4&3&4\\2&2&1&2\\4&4&3&4\end{array}\right]\)

We observe that every entry \(R^2\) that corresponds to a non-zero entry in R is also non-zero. This verifies that for every (a, b) and (b, c) in R, the pair (a, c) is also present in R. Hence, the relation R is transitive.

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The pool can contain 10492 gallons of water

What is volume of cylinder?

The capacity of a cylinder, which determines how much material it can carry, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, may be immersed in it uniformly. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.

Right circular cylinder: A cylinder with circular bases and a lateral curved surface with each line segment perpendicular to the bases.

Oblique Cylinder: A cylinder with sides that are inclined over the base at a different angle than a right angle.

An elliptic cylinder is a cylinder with ellipses at its bases.

Two right circular cylinders tied together inside of one another form a right circular hollow cylinder.

volume of cylinder= (π)\(r^2h\)

diameter= 18feet

radius = 9 feet

height = 5.5 feet

volume= 3.14*(\(9^2\))*5.5

     = 1398.87 \(feet^3\)

volume in gallons = 1398.87 * 7.5

                 = 10492 gallons

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Answer:

15, 17, 19 and 21 it mst b them

Answer:

sinZ=opposite/hypotenuse

the opposite is 48,the hypotenuse is 50

therefore sinZ=48/50

simplified to 24/25

I hope this helps

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The value of the trigonometric ratio, Sin(∠Z) is 24/25.

The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

Sin(θ) = Perpendicular/Hypotenuse

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

In ΔXYZ, for ∠Z, YZ is the base side, and XY is the perpendicular side. Therefore, the trigonometric ratio for ∠Z can be written as,

Sin(∠Z) = (XY)/(XZ)

Sin(∠Z) = 48/50

Sin(∠Z) = 24/25

Hence,  the value of the trigonometric ratio, Sin(∠Z) is 24/25.

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Roses: 6

Daisies: 15 - 6

= 9

The ratio of all flowers to all rose flowers.

15:9

The ratio of roses to daisies.

6:9

2:3 (simplified)

9514 1404 393

Answer:

Step-by-step explanation:

The function puts a minus sign on 3 times the magnitude of the input.

1. y = -|3×17| = -51

2. y = -|3×10| = -30

3. y = -|3×20| = -60

4. -6 = -|3x|

  2 = |x| . . . . divide by -3

  x = ±2 . . . . two possibilities

Answer:

10/5 is 2 this is because you want to see how many fives can fit in 10 so the answer is 2

Geordi's transition from working for the government to joining an engineering firm that advocates for increased government funding is an example of the "revolving door" phenomenon.

The "revolving door" refers to the movement of individuals between government positions and jobs in the private sector that are closely related to government affairs. In this case, Geordi's shift from a government job to an engineering firm involved in lobbying for government funding reflects this phenomenon.

The revolving door can raise concerns about potential conflicts of interest and the influence of special interest groups on government policies and decisions. While Geordi's move is not inherently unethical or illegal, it highlights the close relationship between government entities and private industries, and the potential for individuals to leverage their expertise and connections for personal or corporate gain.

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Answer:

60°

Step-by-step explanation:

the triangle need to have 180°. The up right corner is 60 because 120 + 60 = 180. Then I extended to rhombus where you have two sets of same angles. 125 + 55 = 180. 125 + 125 = 250. 360 - 250 = 110. 110 ÷ 2 = 60

Answer:

Step-by-step explanation:

let x be the unknown volume

5/7=50/x

x=70

Answer:

137.2 m³

Step-by-step explanation:

Given the ratio of sides a : b , then

ratio of volumes = a³ : b³

Here ratio of sides = 5 : 7 , then

ratio of volumes = 5³ : 7³ = 125 : 343

let x be the volume of the larger prism then by proportion

\(\frac{50}{125}\) = \(\frac{x}{343}\) ( cross- multiply )

125x = 17150 ( divide both sides by 125 )

x = 137.2

That is volume of larger prism is 137.2 m³

The person being interviewed in the Bureau of Transportation Statistics omnibus household survey is asked to respond to the following statement: "Public transportation is an important mode of travel for me."

They are then asked to indicate their level of agreement or disagreement with the statement using a rating scale. The purpose of this question is to gather information about the perception and usage of public transportation among households in the United States. The responses collected from this survey help the U.S. Department of Transportation understand the importance and effectiveness of public transportation in different regions and make informed decisions regarding transportation policies and investments. The survey is conducted annually to track changes and trends in public transportation usage and perception over time. The Bureau of Transportation Statistics uses the information gathered from the omnibus household survey to create reports and provide valuable insights to policymakers, researchers, and transportation planners.

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Answer:

f(x) = x² - 13x + 42

Step-by-step explanation:

given zeros are x = 6 and x = 7 then the corresponding factors are

(x - 6) and (x - 7)

the quadratic function is then the product of the factors , that is

f(x) = (x - 6)(x - 7) ← expand using FOIL

     = x² - 13x + 42

Answer:

I think it would be 2 miles

Step-by-step explanation:

This is because 1/4 of an hour is 15 minutes

so in 15 minutes he swims half a mile

4 x 15 = 60 minutes

so 4 x 1/2 = 2miles

Answer: x = 3 or -13/3

Step-by-step explanation: if you sub in 3 for x, you'll get 9+2 =11, which is true. -13/3 is also correct since subbing it in will give you -13+2, which equals -11. The absolute value of -11 is 11. So both of them work

By using the concept of array, it can be concluded that-

struct Sample[10] is the correct option

Fourth option is correct.

What is an array?

An array is a collection of elements with the same data type, which are stored at a particular memory location. Array is of single dimensional as well as double dimensional.

Here,

Size of array = 10

The array is of type Sample

The correct statement for creating an array of size 10  of type Sample

is struct Sample [10]

Fourth option is correct

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Complete Question

The complete question has been attached

Answer:

32

Step-by-step explanation:

f(x) = 7, so:

5 · 7 - 3= 35 - 3 = 32

Answer:

x = 2

Step-by-step explanation:

f(x) = 5x - 3    

7 = 5x - 3

10 = 5x

2 = x

So, x = 2

Answer: x = 12.51

Step-by-step explanation:

Answer:

Exact Form:

1 /216

Step-by-step explanation:

The probability that both selected people like bananas is: (0.68) * (0.89) = 0.6052

We want to find the probability that both of the selected people like bananas

Let's define the following sets:

A: Set of people who like apples.

B: Set of people who like bananas.

O: Set of people who like oranges.

We are given the following information:

|A ∩ B ∩ O| = 12 (The number of people who like all three fruits is 12)

|A| = 34 (The number of people who like apples is 34)

|A ∩ B - O| = 7 (The number of people who like apple and banana but not oranges is 7)

|B ∩ O| = 16 (The number of people who like bananas and oranges is 16)

|A' ∩ B' ∩ O'| = 4 (The number of people who don't like any of the fruits is 4)

|O| = 25 (The number of people who like oranges is 25)

|O - (A ∪ B)| = 0 (All people who like oranges also like at least one other fruit)

To calculate the probability that both selected people like bananas, we need to find the probability of selecting two individuals who both like bananas out of the total population of 50 people.

Let's calculate the probability step by step:

1. Calculate the probability of selecting the first person who likes bananas:

  P(B) = |B| / 50

  P(B) = 34 / 50

  P(B) = 17 / 25

  P(B) = 0.68

2. Calculate the probability of selecting the second person who likes bananas given that the first person already likes bananas:

  P(B|B) = (|B| - 1) / (50 - 1)

  P(B|B) = (34 - 1) / 49

  P(B|B) = 33 / 49

  P(B|B) = 0.89

3. Calculate the overall probability of both selected people liking bananas:

  P(B and B) = P(B) * P(B|B)

  P(B and B) = (17 / 25) * (33 / 49)

  P(B and B) = 0.68 * 0.89

  P(B and B) = 0.6052

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It would be: D) Increased recycling of waste

Your Welcome

Answer:

85%

Step-by-step explanation:

Because we can see that only 15% of the class obtained A's, and the question only refers to those that did not receive A's, we can subtract the 15% of the 100% whole to get 85%. This can also be written as 85/100 or 17/20(simplified).

a) To find the volume of the torus using the shell method, the integral can be set up as ∫2πy(2πr)dy.

b) To find the volume of the torus using the washer method, the integral can be set up as ∫π(R²-r²)dx.

c) The volume of the torus can be found by evaluating one of the two integrals obtained in parts (a) and (b).

a) The shell method involves considering cylindrical shells with height dy and radius y. Since the torus is formed by revolving a circle of radius 3 centered at (8,0) about the y-axis, the radius of each shell is y and the height is 2πr, where r is the distance from the y-axis to the circle. Therefore, the integral to find the volume of the torus using the shell method is ∫2πy(2πr)dy.

b) The washer method involves considering infinitesimally thin washers with inner radius r and outer radius R. In the case of the torus, the inner radius is the distance from the y-axis to the circle, which is y, and the outer radius is the radius of the circle, which is 3. Therefore, the integral to find the volume of the torus using the washer method is ∫π(R²-r²)dx.

c) To find the volume of the torus, one of the two integrals obtained in parts (a) and (b) can be evaluated. The specific integral to evaluate depends on the chosen method (shell or washer). By substituting the appropriate values into the integral and evaluating it, the volume of the torus can be calculated.

Note: The specific calculations to find the volume of the torus and the corresponding numerical result were not provided in the question, so the final answer in cubic units cannot be determined without further information.

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Answer:

A café owner wants to determine the average pay per week for all his employees. The mean should be calculated using population (μ).

A cattle rancher weighs each of his cattle every six months. He calculates the average weight. The mean should be calculated using population (μ).

Step-by-step explanation:

Answer:

The correct options are the café owner, psychology student, and the catlle rancher.

Step-by-step explanation:

because it is I promise you

As per the side splitter theorem, the segment length would complete the proportion is GJ

In math, the side splitter theorem states that "if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally".

Here we have to find the segment length that would complete the proportion by using the side splitter theorem.

According to this theorem and by using the following diagram, we can elaborate the following proportion

=> GH/HE = GJ/JF

Here we have identifies that the segment that completes the proportion is GJ, because it must be used according to the theorem.

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Answer:

x = 144⁰

y = 36⁰

z = 54⁰

Step-by-step explanation:

x = 54° + 90° (The exterior angle of a triangle is equal to the sum of the two opposite interior angles)

Therefore, x = 144°

y is the same as the angle beside x

(alternate angles are equal)

The angle beside x added to x equals 180° (angles on a straight line)

Therefore, the angle beside x = 180 - 144

= 36°

Since the angle beside x is the same as y, therefore y = 36°

z = 54° (alternate angles are equal)

Answer:

45 and 20

Step-by-step explanation:

Numbers divisible by 5 must end in 0 or 5.

Hope this helped, have a good day!