Make A the subject of the formula
r = squareroot A/3

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

learn more about exterior angle theorem from

https://brainly.com/question/17307144

#SPJ1

Step-by-step explanation:

when scaling a model or a map or ... there is airways the same scaling factor applied for every dimension of the object.

in other words, length and width of the plane must be multiplied by the same factor.

the length is first scaled by going from feet to inches. and then scaled by the factor 1/2, as 27/2 = 13.5.

we need to do the same for the width. feet to inches and then half : 18/2 = 9 in

Step-by-step explanation:

1.A

2.A

3.A

4.C

5.A

6.A

7.C

8.D

9.A

10.C

11.C

12.C

13.D

14.B

15.B

16.A

17.C

18.A

19.B

20.C

21.B

22.D

23-27 Write in

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Let's solve ~

\(\qquad \sf  \dashrightarrow \: ( - 3 {p}^{3} + 5 {p}^{2} - 2 p) + ( - p {}^{3} - 8 {p}^{2} - 15p)\)

\(\qquad \sf  \dashrightarrow \: - 3 {p}^{3} + 5 {p}^{2} - 2 p - p {}^{3} - 8 {p}^{2} - 15p\)

\(\qquad \sf  \dashrightarrow \: - 3 {p}^{3} -p³+ 5 {p}^{2} - 8 {p}^{2} -2p - 15p\)

\(\qquad \sf  \dashrightarrow \: - 4{p}^{3} -3 {p}^{2} - 17p \)

Account C will earn more interest than Account S after 10 years due to compounding, with a difference of $457.17.

Account S earns simple interest, which is calculated based on the initial deposit, interest rate, and time. Using the formula for simple interest, Account S will earn $220 after 10 years.

On the other hand, Account C earns compound interest, which takes into account the compounding effect over time. The formula for compound interest considers the initial deposit, interest rate, compounding frequency, and time. Assuming interest is compounded annually, Account C will accumulate a final amount of $677.17 after 10 years.

The difference in interest earned between the two accounts is $457.17 ($677.17 - $220), making Account C the more lucrative option.

Learn more about Compound interest click here :brainly.com/question/26367706

#SPJ11

The candidate key for the relation schema R(A,B,C,D,E): A→B, C→B, D→A, D→B, D→C, C→D, D→E.

Candidate key for the given relation: To find the candidate key for the relation schema R(A,B,C,D,E), we need to follow the below steps:

Here, we have the following functional dependencies: A→B, C→B, D→ABC, AC→D, D→E.

Step 1: To normalize the given dependencies, we have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To check for the minimal dependency, we can eliminate the redundancy by eliminating D→ABC. Therefore, we have the following dependency:

A→B, C→B, D→A, D→B, D→C, D→E.

Step 3: Find the closure on each attribute, which is as follows:

1. A+ = {A,B}

2. B+ = {B}

3. C+ = {B}

4. D+ = {A,B,C,D,E}

5. E+ = {E}

Step 4: The combination of attributes that have all attributes of the relation schema, and it will be a candidate key is AD. Therefore, the candidate key is AD.

Compute the minimal cover of F:

Minimal Cover: The minimal set of dependencies that is equivalent to the given set of dependencies is the minimal cover.

We have the following functional dependencies:

A→B, C→B, D→ABC, AC→D, D→E.

The process to compute the minimal cover of F is as follows:

Step 1: To find the redundant dependencies, we need to split the dependencies. We have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E  becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To eliminate the dependencies with three attributes, we can use the following steps:

If X→YZ, then X→Y and X→Z.

Therefore, we have the following dependency:

D→A, D→B, D→C.

Step 3: To eliminate the dependency with two attributes, we can use the following steps:

If X→Y and Y→Z, then X→Z.

We have the following dependency: AC→D, C→D.

Step 4: Therefore, the minimal cover of F is A→B, C→B, D→A, D→B, D→C, C→D, D→E.

Know more about the dependency

https://brainly.com/question/4294556

#SPJ11

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Using the information above, we test it out to see if it is true

4+8 >9

4+9>8

9+8>4

Since the sum of two sides is greater than the third side. Therefore the answer is possible.

The population of rabbits by the year 2023  is 13985.

We have to use the following exponential function. This will be:

y = a b^t

In 2008 means, t=0

So we have 7100 = a b^0

a = 7100

y = 7100b^t

In 2013 means t = 2013-2008 =5

8900 = 7100 b⁵

b⁵ = 89/71

b = 1.046

So the equation will be

y = 7100 (1.046)^t

For 2023, t=2023-2008= 15

y = 7100(1.046)¹⁵

= 13985

The population is 13985.

Learn more about exponential function in:

https://brainly.com/question/2456547

#SPJ1

Answer:

180 ft cubed.

Step-by-step explanation:

The formula for volume is V = lwh

6 is the height, 10 is the length, and 3 is the width.

So then you would multiply 6, 10 and 3, which equals 180.

Answer:

Hopefully, I am correct is it 1/4??

Step-by-step explains:

(Sorry If I am wrong I just guessed.)

In spherical coordinates, the equation \(5z^2 = 6x^2 + 6y^2\) can be written as: \(ρ^2sin^2(φ) = 6ρ^2sin^2(θ)cos^2(φ) + 6ρ^2sin^2(θ)sin^2(φ)\)

Spherical coordinates are a system of coordinates used to represent points in three-dimensional space. In this coordinate system, a point is described by three parameters: ρ (rho), θ (theta), and φ (phi).

ρ (rho) represents the radial distance from the origin to the point.

θ (theta) represents the azimuthal angle, which is the angle measured in the xy-plane from the positive x-axis to the line connecting the origin and the point.

φ (phi) represents the polar angle, which is the angle measured from the positive z-axis to the line connecting the origin and the point.

In spherical coordinates, a point in 3D space is represented using three parameters: ρ (rho), θ (theta), and φ (phi).

ρ (rho) represents the radial distance from the origin to the point.

θ (theta) represents the azimuthal angle, which is the angle measured in the xy-plane from the positive x-axis to the line connecting the origin and the point.

φ (phi) represents the polar angle, which is the angle measured from the positive z-axis to the line connecting the origin and the point.

To express the equation\(5z^2 = 6x^2 + 6y^2\)in spherical coordinates, we need to convert the variables x, y, and z to their corresponding spherical coordinate representations.

In spherical coordinates, the conversions are as follows:

x = ρsin(φ)cos(θ)

y = ρsin(φ)sin(θ)

z = ρcos(φ)

Substituting these values into the equation, we have:

5(ρcos(φ))^2 = 6(ρsin(φ)cos(θ))^2 + 6(ρsin(φ)sin(θ))^2

Simplifying the equation further by expanding the terms and using trigonometric identities, we can obtain the equation in spherical coordinates:

\(ρ^2sin^2(φ) = 6ρ^2sin^2(θ)cos^2(φ) + 6ρ^2sin^2(θ)sin^2(φ)\)

This equation relates the variables ρ, θ, and φ in spherical coordinates and represents the same relationship as the original equation in Cartesian coordinates.

To know more about Spherical coordinates refer here:

https://brainly.com/question/4465072

#SPJ4

Answer:

Start at 5 and move 8 units to the left

Step-by-step explanation:

5 -8

Start at 5 on the number line

We are subtracting 8

Move 8 units to the left

You will end of at -3

(ignore this answer, i cant delete it srry..)

Answer:

It takes them 45 minutes

Step-by-step explanation:

Let's say that x is the amount of work in one hour that zina does

so the amount of work that rachel does in the same hour is 1/3x, because 3 times slower

so we have

x+1/3x=100%

what does that mean?

it means the amount of hours taken to complete a skycraper

so we solve for x

x=75%

so we need to figure out how much hours does zina takes to complete 75% of the skycraper

1 hour ----- 100%

x hours ---- 75%

1 hour *75%/100%=x hours

1 hour (3/4)=x hours

60 minutes (3/4)= x minutes

x=45 minutes

Answer:

They are the same

Step-by-step explanation:

A to B is 3cm = S to T is 3cm

B to C is 4.5 cm = T to U is 4.5 cm

A to C is 110 degrees = U to S is 110 degrees

you can also just rotate the STU to make ABC

Step-by-step explanation: Answer is 10

For this type of problem, we need to create a slope intercept equation for both.

Let's start by making one for plan a. We know that there is 20 dollars per month, this is the y intercept. Now, although it says per month which can change by x, the problem is mainly asking for minutes.

Remember, a slope intercept equation is

y=mx+b

M is the slope, and x is multiplied to the slope. The slope for an example can be used for this, adam eats 5 apples per day or x, how many apples can he eat in 5 days? We are wanting to know how many he can eat in 5 days, so we of course would multiply 5 by 5. This is basically a slope equation.

So, for plan a, we have y=0.05x+20 where x is minutes

For plan b, we should get

y=0.10x+15 where x is also minutes. The problem is asking use to find which value that we plug in will make both plan a and b correct. Basically, the value we find is x, so we solve for x by setting the two equations equal.

0.05x+20=.10x+15 Use inverse operations

20=.05x+15

5=.05x

x=10

We know if we plug in 10 for x, both would equal the same or 21 dollars.

The relationship between the incidence angle θ₁ and refraction angle θ₂ can be plotted using Snell's Law in MATLAB or Microsoft Excel.

The plot will vary depending on the refractive indices of the two mediums involved. The cases to consider are when n₁ = 1.2 × n₂, n₁ = n₂, and n₁ = 0.8 × n₂. The plot should also mark the angle of total internal reflection.

Snell's Law describes the relationship between the angles of incidence and refraction when light passes through the interface of two different mediums.

It can be expressed as n₁sin(θ₁) = n₂sin(θ₂), where n₁ and n₂ are the refractive indices of the first and second mediums, respectively, and θ₁ and θ₂ are the angles of incidence and refraction.

To plot the relationship, you can start by selecting a range of incidence angles, θ₁, and calculate the corresponding refraction angles, θ₂, using Snell's Law. Then, plot θ₁ on the x-axis and θ₂ on the y-axis. Repeat this process for each case: n₁ = 1.2 × n₂, n₁ = n₂, and n₁ = 0.8 × n₂.

When n₁ = 1.2 × n₂, you will observe a plot where the refraction angle θ₂ is smaller than the incidence angle θ₁ for all values. This indicates that the light is bending less when passing from the first medium to the second medium.

When n₁ = n₂, the plot will show a linear relationship between θ₁ and θ₂. The refraction angle will be proportional to the incidence angle, and the slope of the line will be determined by the refractive index.

When n₁ = 0.8 × n₂, you will observe a plot where the refraction angle θ₂ is greater than the incidence angle θ₁ for all values. This indicates that the light is bending more when passing from the first medium to the second medium.

To mark the angle of total internal reflection, you need to find the critical angle. The critical angle is the incidence angle at which the refraction angle becomes 90 degrees.

Beyond this angle, total internal reflection occurs, meaning the light is completely reflected back into the first medium. In this case, you can calculate the critical angle using the equation sin(θ_c) = n₂/n₁. On the plot, mark the critical angle as well as any incidence angles beyond the critical angle where total internal reflection occurs.

By plotting the relationship between the incidence angle and refraction angle using Snell's Law, you can visualize how light bends as it passes through different mediums and observe the occurrence of total internal reflection at specific angles.

Learn more about Snell's Law here:

brainly.com/question/31432930

#SPJ11

44 x 15 = 660

660/2 = 330

330cm^2

Answer:

330

Step-by-step explanation:

area of a triangle = 1/ 2 × base× height

base = 44 m

height = 15 m

area = 1/ 2 × 44× 15

= 22 × 15

= 330 Sq. m

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

The equation of the line that passes through (-4,1) and is perpendicular to the line y= -1/2x + 3​.

We are given that;

Point= (-4,1)

Equation y= -1/2x + 3​

Now,

To find the y-intercept, we can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point on the line. Substituting the values we have, we get:

y - 1 = 2(x - (-4))

Simplifying and rearranging, we get:

y = 2x + 9

Therefore, by the given slope the answer will be y= -1/2x + 3​.

Learn more about slope here:

https://brainly.com/question/2503591

#SPJ1

Representative sample is especially important in frequency claims because they ensure the findings accurately reflect the larger population.

When making frequency claims, researchers aim to generalize their findings to a larger population. Representative sample consists of individuals who closely mirror the characteristics of the target population. By selecting a representative sample, researchers increase the likelihood that the sample's frequencies and proportions will accurately reflect those of the larger population. This ensures that the frequency claim made based on the sample data is more likely to be valid and reliable.

Representative samples help minimize bias and enhance the generalizability of the findings. If a sample is not representative, it may over- or under-represent certain groups or characteristics within the population. This can lead to misleading frequency claims that do not accurately reflect the reality of the population as a whole. For example, if a study on voting preferences only surveys young adults, the findings may not accurately represent the voting patterns of the entire electorate.

Using a representative sample is crucial to increase the external validity of frequency claims. It allows researchers to make more accurate inferences and generalizations about the target population based on the characteristics and behaviors observed in the sample. By ensuring the sample is representative, researchers can enhance the credibility and applicability of their frequency claims, providing more reliable information for decision-making, policy development, or further research.

Learn more about Representative sample

brainly.com/question/28331703

#SPJ11

The "zero of a function" refers to the input value that makes the function's output equal to 0.

Answer:

Hello! answer: x = 19

Step-by-step explanation:

This is a supplementary angle! So it will add up to 180 degrees 180 - 123 = 57 so we know something multiplied by 3 will equal 57 and 19 × 3 = 57 so x = 19 Hope this is a good explanation!

Answer:

68.54 dollars is you answer you would do 63 times .088 and add 63 to your answer

Step-by-step explanation:

The auditing software can identify 63.7% of misreporting issues in accounting ledgers. The probability that no misreported transactions are found is 1 - 63.7% = 36.3%. The probability that at least half of the transactions are misreported is 1 - P(X  25) = 1 - P(X  24) P(X  24) = _(i=0)24 (50C_i) (0.363)i (1 - 0.363)(50 - i)  0.0001. The expected monetary gain is approximately -$49.8.

Given that an auditing software can identify 63.7% of misreporting issues in accounting ledgers. Let X be the number of accounting misreporting transactions identified by the software among 50 randomly selected transactions for the last 3 months.Probability that no misreported transactions are found:X follows a binomial distribution with n = 50 and p = 1 - 63.7% = 36.3%.P(X = 0) = (1 - p)^n = (1 - 0.637)^50 ≈ 0.0002Probability that less than 10 misreported transactions are found:

P(X < 10) = P(X ≤ 9)P(X ≤ 9)

= P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)P(X ≤ 9)

= ∑_(i=0)^9 (50C_i ) (0.363)^i (1 - 0.363)^(50 - i) ≈ 0.99

Probability that at least half of the transactions are misreported:

P(X ≥ 25)P(X ≥ 25)

= P(X > 24)P(X > 24)

= 1 - P(X ≤ 24)P(X ≤ 24)

= ∑_(i=0)^24 (50C_i ) (0.363)^i (1 - 0.363)^(50 - i) ≈ 0.0001

Expected monetary gain:Let Y be the amount of money that the firm gets to earn or pay. The probability distribution of Y can be shown below:Outcomes: $200, -$50, -$100

Probabilities: P(X = 0), P(0 < X < 10), P(X ≥ 25)P(X = 0)

= 0.0002P(0 < X < 10)

= 0.99 - 0.0002 = 0.9898P(X ≥ 25)

= 0.0001E(Y)

= ($200 x P(X = 0)) + (-$50 x P(0 < X < 10)) + (-$100 x P(X ≥ 25))E(Y)

= ($200 x 0.0002) + (-$50 x 0.9898) + (-$100 x 0.0001)≈ -$49.8

Therefore, the expected monetary gain is approximately -$49.8.

To know more about probability Visit:

https://brainly.com/question/31828911

#SPJ11

Answer:  7

7x2 = 49 then find square root = 7

To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

Learn more about assets on:

https://brainly.com/question/25746199

#SPJ1