If ∃ a in the naturals and ∃ b in the integers, then ∀ = c is a rational number.

Which of the following statements are equivalent to this definition?

a.) If "c" is a rational number, then every two different natural numbers divide c.

b.) ∀ "c" that is a rational number, then ∃ natural number "a" divides it.

c.) If "c" is a rational number then "a/b = c."

d.) If ∃ "a" in the naturals and ∃" b" in the integer numbers then "a*b = c" where "c" is any rational number.

e.) ∀ rational number "c", it is the case that ∃ a natural number "a" and ∃ an integer number "b" such that "a" divided by "b" is equal "c".

f.) ∀ rational number "c", it is the case that there exists some "a" and "b" such that "a" divided by "b" is equal to "c".

g.) None of the above

Explain your reasoning.

Answers

Answer 1

Statement e) "For every rational number 'c', there exists a natural number 'a' and an integer number 'b' such that 'a' divided by 'b' is equal to 'c'." this is equivalent to the given definition.

Statement a) "If 'c' is a rational number, then every two different natural numbers divide c."

This statement is not equivalent to the given definition. The original definition talks about the existence of specific natural and integer numbers, whereas statement a) talks about any two different natural numbers dividing 'c' without specifying the values of 'a' and 'b'.

Statement b) "For every 'c' that is a rational number, there exists a natural number 'a' that divides it."

This statement is not equivalent to the given definition. The original definition states the existence of both a natural number 'a' and an integer 'b', whereas statement b) only mentions the existence of a natural number 'a'.

Statement c) "If 'c' is a rational number, then 'a/b = c'."

This statement is equivalent to the given definition. It correctly states that if 'c' is a rational number, then it can be expressed as the ratio of 'a' divided by 'b', which aligns with the original definition.

Statement d) "If there exists 'a' in the naturals and 'b' in the integer numbers, then 'a*b = c' where 'c' is any rational number."

This statement is not equivalent to the given definition. It talks about the product of 'a' and 'b' equaling 'c' for any rational number 'c', without specifying the relationship between 'a' and 'b' as in the original definition.

Statement e) "For every rational number 'c', there exists a natural number 'a' and an integer number 'b' such that 'a' divided by 'b' is equal to 'c'."

This statement is equivalent to the given definition. It states that for any rational number 'c', there exists a specific natural number 'a' and integer 'b' such that 'a' divided by 'b' is equal to 'c', which matches the original definition.

Statement f) "For every rational number 'c', there exists some 'a' and 'b' such that 'a' divided by 'b' is equal to 'c'."

This statement is equivalent to the given definition. It expresses the same idea as statement e) in slightly different wording, stating the existence of 'a' and 'b' such that 'a' divided by 'b' equals 'c'.

Learn more about the rational number at

https://brainly.com/question/17450097

#SPJ4


Related Questions

Alinear trendline used to forecast sales for a given time period takes the form y = b+ bil. increases by , then the estimated y value all else e tone period, increases, b1; constant o tone period, increases, bo, constant bione period, increases; bo constant bi: one period, increases bi: constant

Answers

The linear trendline used to forecast sales for a given time period takes the form y = b0 + b1t, where y represents the estimated sales, b0 is the constant term, b1 is the coefficient of the time period variable (t), and t is the time period.

In this equation, the coefficient b1 determines the relationship between the time period and the estimated sales. If b1 increases, it means that for each additional time period, the estimated sales will also increase. On the other hand, if b1 is constant, it implies that the estimated sales do not change with each additional time period.

To know more about linear trendlines here: brainly.com/question/31313926

#SPJ11

bro I NEED HELP FAST

Answers

It’s D 2 1/3 because 1/3 each 3 days is 3/3 and then plus another one is 6/3 and plus one more is 9/3

The sum of two nonnegative numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible.
a. The numbers are 10 and 10.
b. The numbers are 0 and 20.
c. The numbers are 1 and 19.
d. The numbers are 20 and 0.

Answers

Option D. The numbers are 20 and 0.

Let the two nonnegative numbers be x and y such that x + y = 20. We know that the sum of the squares of the two nonnegative numbers x and y is as large as possible and as small as possible.

x + y = 20, or y = 20 - x (Since the numbers are non-negative, x, y ≥ 0)

Substituting y = 20 - x into x² + y² = P (for the sake of simplicity), we get x² + (20 - x)² = Px² + 400 - 40x + x² = P

We will take the first derivative with respect to x now: 2x - 40 = 0x = 20

Therefore, one of the nonnegative numbers is 20, and the other is zero. Consequently, the smallest possible sum of squares is 400 (since 20² + 0² = 400).Option D. The numbers are 20 and 0.

To know more about derivative visit:

https://brainly.com/question/23819325

#SPJ11

Given, the sum of two nonnegative numbers is 20.

The problem asks us to find the numbers if the sum of their squares is as large as possible; as small as possible.

Therefore, let's find the sum of their squares at first.If 'x' and 'y' are two numbers, then the sum of their squares is given by:

[tex]x^2 + y^2[/tex]

If the sum of two nonnegative numbers is 20, then one number can be written as x and the other number can be written as y in terms of x.

Thus,y = 20 − xNow, the sum of their squares:

[tex]x^2 + y^2 = x^2 + (20 - x)^2[/tex]
= [tex]x^2 + 400 + x^2 - 40x[/tex]
= [tex]2x^2 - 40x + 400[/tex]
The above expression represents a parabola which opens upward because the coefficient of x^2 is positive.

Therefore, the sum of the squares of the two numbers will be maximum at the vertex of the parabola.

The x-coordinate of the vertex can be found as

:−b/2a = −(−40)/(2.2) = 10Hence, x = 10 and y = 10.

Substituting x = 10 and y = 10, we get

[tex]x^2 + y^2 = 200.[/tex]

Now, to find the smallest value of the sum of their squares, we can observe that the smallest value of x is 0, and the largest value of y is 20.

Thus, if x = 0 and y = 20, we get x^2 + y^2 = 400.

Answer:  The numbers are 10 and 10. The numbers are 0 and 20.

To know more about squares, visit:

https://brainly.com/question/14198272

#SPJ11

Hang was trying to factor 10x^2 + 5x she found that the greatest common factor of these terms was 5x and made an area model what is the width of the area model

Answers

Width of Heng's area model is  2x + 1

Step-by-step explanation:

Given:

Greatest common factor is 5x

To Find:

The width = ?

Solution:

let the  be the area

And  5x be the length

Then area  = length  x  width

Now rewriting the formula for width, we get

Width =  

Substituting the values in the above formula

Width =

Width = 2x + 1

A pool manager balances the pH level of a pool. The price of a bucket of chlorine tablets is $90, and the price of a pH test kit is $11. The manager uses a coupon that applies a 40% discount to the total cost of the two items. How much money does the pool manager pay for each item?

Answers

Answer:

The chlorine tablets are $36 and the pH test kit is $4.40.

Step-by-step explanation:

So what I first did was add 90+11 (because $90 for the chlorine tablets and $11 for the pH kit). The answer you should get is 101.  From their I did 101 multiplied by 40% or 101 multiplied by .40 (40% and 0.40 are the same thing). You now get $40.4.  

Now I did 90·40%. I got $36

Then I did 11·40%. I got 4.4

I added them up and got $40.4 which was my new price so now we know that the chlorine tablets are $36 and the pH test kit is $4.40.

6(x-2)=-18 what does x=

Answers

Answer:

x = -1

Step by step explanation:

Distribute 6

6x-12= -18

Add 12 to both sides

6x= -6

Divide both sides by 6

x= -1

Hope this helps

The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with 100 and 11. The proportion of adults with scores above 110 is closest to 0.25 b.0.33. c0.14. 4.0.18 Colleges often rely heavily on raising money for an "annual fund" to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's smal income is a good predicar of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. In the stadies described a annual income is an explanatory variable. b the correlation between annual income and the size of the donation is positive. c the size of the donation to the annual fund is the response variable. d. All of the answer options are correct.

Answers

The proportion of adults with scores above 110 is 0.1841.

Here, we have,

It should be noted that from the information illustrated, Wechsler Adult Intelligence Scale scores are approximately Normal, with a mean of 100 and a standard deviation of 11.

The formula to use will be:

P(a < Z < b) = P(Z < b) – P(Z < a)

a = lower value

b = higher value

Z = z value

It should be noted that the proportion of adults with scores above 110 will be:

= P(x > 110)

= P(z > 110 - 100/11)

= P(z > 0.90)

= 1 - 0.8159

= 0.1841

Therefore, this illustrates those that has scores of more than 110.

Learn more about normal curve on:

brainly.com/question/4079902

#SPJ4

The population of a city is 218720.
The population has been increasing at the rate of 2% per year.
What was the population 3 years ago?​

Answers

Correct Answer is 205,857

Work out
1/8
of 760

please help​

Answers

Answer: 95

Step-by-step explanation:

Think of 1/8 times 760 as 760/8 because it’s the same thing.

Show the enteiws to close $2000 in expense, $5000 in revenue, and
$500 in dividens.

Answers

To close the $2,000 in expenses, $5,000 in revenue, and $500 in dividends, we need to transfer these amounts to the appropriate accounts and close the temporary accounts at the end of the accounting period. Here are the journal entries to close these amounts:

Close Expenses:

Date | Account | Debit | Credit

End of Year | Expenses | $2,000 |

| Income Summary | | $2,000

Close Revenue:

Date | Account | Debit | Credit

End of Year | Income Summary | $5,000 |

| Revenue | | $5,000

Close Dividends:

Date | Account | Debit | Credit

End of Year | Retained Earnings | $500 |

| Dividends | | $500

After these closing entries, the balances of the temporary accounts (Expenses, Revenue, and Dividends) will be zero, and their respective amounts will be transferred to the Income Summary and Retained Earnings accounts. The Income Summary account will show the net income (revenue minus expenses) for the period.

Please note that the specific account titles may vary depending on the company's chart of accounts, so make sure to use the appropriate account titles according to your specific chart of accounts.

Learn more about entries at: https://brainly.com/question/18042491

#SPJ11

Subject:Mathematics ​

Answers

Answer:F : 13 1/2

Step-by-step explanation:27 divided by 2 is 13 1/2

Osing Trig to Find a Side Apr 06, 5:40:44 PM In AOPQ, the measure of ZQ=90°, the measure of Z0=26°, and QO = 4.9 feet. Find the length of PQ to the nearest tenth of a foot. P (hypotenuse) X (opp. of 20) 2009 Q 4.9​

Answers

Answer:5.4

Step-by-step explanation:

A scalene triangle has sides measuring 200 feet, 107 feet, and 221 feet. What is the
perimeter of the triangle?

Answers

Answer:

P = 528

Step-by-step explanation:

P = a + b + c = 200 + 107 + 221 = 528

Which point is a solution to the inequality in this graph

Answers

Given:

The graph of an inequality.

To find:

The point which is a solution of the given graph of inequality.

Solution:

From the given graph it is clear that the boundary line of the graph is a dotted line. It means the points lie in shaded region are in the solution set but the points on the line are not included in the solution set.

The points (3,2) and (-3,-6) are lie on the boundary line. it means they are not the solution of the inequality represented by the given graph.

Point (5,0) lies on the positive x-axis at the distance of 5 units from the origin and it doesn't lies in the shaded region. So, (5,0) is not a solution.

Point (0,5) lies on the negative y-axis at the distance of 5 units from the origin and it lies in the shaded region. So, (0,5) is a solution.

Therefore, the correct option is B.

What is the name of the blue dot located inside the curve of the parabola
below?
O A. Focus
B. Center
O C. Directrix
D. Vertex

Answers

The blue dot located inside the curve of the parabola is Focus.

What are Parts in Parabola?

The essential feature of a parabola is that all of its points are the same distance from a point called the focus and a line called the directrix. The vertex, axis, latus rectum, and focal length are also key components of a parabola.

The latus rectum, also known as the focal diameter, is the line segment that runs through the focus and parallel to the directrix. The focal diameter's endpoints are located on the curve.

A parabola is the set of all points ( x, y ) in a plane that are the same distance from a fixed line called the directrix and a fixed point not on the directrix (the focus).

A parabola will have three key components: a focus, a directrix, and a vertex. This upward-opening parabola demonstrates that all points,, along the parabola's curve will be the same distance from the focus and the directrix.

Thus, the blue dot located inside the curve of the parabola is Focus.

Learn more about Parabola here:

https://brainly.com/question/21685473

#SPJ7

Help Please! Find The Circumference Of A Circle With R=12.3.

Answers

Answer:

77.28

Step-by-step explanation:

c=π2r

12.3 times 2 =

24.6π

=77.28317928

=77.28

Answer:

77.3

Step-by-step explanation:

I’ll mark you brainlieist

Answers

1. Divide by 4
x < 5

2. Subtract 4
x < 21

3. Add 8
x > 40

4. divide by -4( flip inequality sign b/c dividing by negative) so > turns into >
x < -6

The rest using the same concept. Try them yourself and ask for help if you need it

Please help if you wantbbrainleist! :(

Answers

Box 2 I believe is correct because 3 x 1 x 2 is 6.

Claim: the average age of online students is 32 years old. Can you prove it is not? What is the null hypothesis? o What is the alternative hypothesis? What distribution should be used? o What is the test statistic? o What is the p-value? o What is the conclusion? o How do we interpret the results, in context of our study? • Claim: the proportion of males in online classes is 35%. Can you prove it is not? o What is the null hypothesis? o What is the alternative hypothesis? o What distribution should be used? o What is the test statistic? o What is the p-value? o What is the conclusion? o How do we interpret the results, in context of our study?

Answers

To predict a linear regression score, you first need to train a linear regression model using a set of training data.

Once the model is trained, you can use it to make predictions on new data points. The predicted score will be based on the linear relationship between the input variables and the target variable,

A higher regression score indicates a better fit, while a lower score indicates a poorer fit.

To predict a linear regression score, follow these steps:

1. Gather your data: Collect the data p

points (x, y) for the variable you want to predict (y) based on the input variable (x).

2. Calculate the means: Find the mean of the x values (x) and the mean of the y values (y).

3. Calculate the slope (b1): Use the formula b1 = Σ[(xi - x)(yi - y)]  Σ(xi - x)^2, where xi and yi are the individual data points, and x and y are the means of x and y, respectively.

4. Calculate the intercept (b0): Use the formula b0 = y - b1 * x, where y is the mean of the y values and x is the mean of the x values.

5. Form the linear equation: The linear equation will be in the form y = b0 + b1 * x, where y is the predicted value, x is the input variable, and b0 and b1 are the intercept and slope, respectively.

6. Predict the linear regression score: Use the linear equation to predict the value of y for any given value of x by plugging in the x value into the equation. The resulting y value is your predicted linear regression score.

To know more about linear regression scores:- brainly.com/question/30670065

#SPJ11

how many square miles does ATC and radar services attempt to cover? How many aircraft at any given time is ATC monitoring, and spread over how many airports within the USA?

Answers

The work of providing air traffic control and radar services in the United States falls under the purview of the Federal Aviation Administration (FAA). ATC and radar services that  cover all airspace over the United States, regardless of whether flights are domestic or international.

What is the radar services

FAA provides ATC and radar services in the US. ATC and radar services cover all US airspace, including domestic and international flights. The FAA manages the NAS, covering 29.5 million sq mi. This includes airspace over the entire United States, including Alaska, Hawaii, Guam, Puerto Rico. VI ATC monitors varying number of aircraft based on time, weather, and traffic.

The FAA deals with 44k flights daily in the US. Note that this number may increase during peak travel periods. The FAA manages ATC for 13k+ US airports. Incl. international, regional, gen. aviation & priv. airstrips. The number can vary due to new or old airports.

Learn more about radar services  from

https://brainly.com/question/28331231

#SPJ4

let x equals negative 14 times pi over 3 period part a: determine the reference angle of x. (4 points) part b: find the exact values of sin x, tan x, and sec x in simplest form. (6 points)

Answers

The exact values  of sin x, tan x and sec x in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.

To solve this problem, we'll work with the angle x, which is equal to -14π/3. Part a: Determine the reference angle of x. The reference angle is the positive acute angle formed between the terminal side of the angle and the x-axis. To find the reference angle, we ignore the negative sign and convert the angle to its equivalent positive angle within one revolution.

The positive equivalent angle can be obtained by adding 2π (or 360 degrees) repeatedly until we obtain a positive angle. In this case, we have: -14π/3 + 2π = -14π/3 + 6π/3 = -8π/3. The reference angle of x is 8π/3. Part b: Find the exact values of sin x, tan x, and sec x in simplest form. sin x = sin(-14π/3) = -sin(14π/3) (Using the symmetry of sine function)

= -sin(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)

= -sin(2π/3) (Sine of an angle 2π/3 is known) = -√3/2.

tan x = tan(-14π/3) = tan(14π/3) (Using the symmetry of tangent function)

= tan(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)

= tan(2π/3) (Tangent of an angle 2π/3 is known)= √3. sec x = sec(-14π/3) = sec(14π/3) (Using the symmetry of secant function)= sec(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)= sec(2π/3) (Secant of an angle 2π/3 is known)= -2/√3. Therefore, the exact values in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.

To learn more about reference angle, click here: brainly.com/question/30989987

#SPJ11

Answer: The exact values  of sin x, tan x and sec x in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.

Step-by-step explanation: To solve this problem, we'll work with the angle x, which is equal to -14π/3. Part a: Determine the reference angle of x. The reference angle is the positive acute angle formed between the terminal side of the angle and the x-axis. To find the reference angle, we ignore the negative sign and convert the angle to its equivalent positive angle within one revolution.

The positive equivalent angle can be obtained by adding 2π (or 360 degrees) repeatedly until we obtain a positive angle. In this case, we have: -14π/3 + 2π = -14π/3 + 6π/3 = -8π/3. The reference angle of x is 8π/3. Part b: Find the exact values of sin x, tan x, and sec x in simplest form. sin x = sin(-14π/3) = -sin(14π/3) (Using the symmetry of sine function)

= -sin(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)

= -sin(2π/3) (Sine of an angle 2π/3 is known) = -√3/2.

tan x = tan(-14π/3) = tan(14π/3) (Using the symmetry of tangent function)

= tan(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)

= tan(2π/3) (Tangent of an angle 2π/3 is known)= √3. sec x = sec(-14π/3) = sec(14π/3) (Using the symmetry of secant function)= sec(4π + 2π/3) (Dividing by 4π to obtain an angle within one revolution)= sec(2π/3) (Secant of an angle 2π/3 is known)= -2/√3. Therefore, the exact values in simplest form are: sin x = -√3/2, tan x = √3, sec x = -2/√3.

please help me .........​

Answers

Answer: the answer is b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

first add them together. the y cancels out and your left with 3x=15. divide by 3 on both sides and you get x=5. The only answer with positive 5 as an x value is b

The volume of a rectangular prism is 1,560 cm3. The height is 12 cm. The width is w and the length is w + 3. Find w.

Answers

Volume = w * h * l
w = w, h = 12, l = w + 3
1,560 = w * 12 * w + 3
1,560 = 12w^2 + 3
-12w^2 = 3 - 1,560
-12w^2 = -1557
w^2 = 519/4
w = 11.39079 cm
You can round it if you want

Answer:

w=10 cm

Step-by-step explanation:

The formula for the volume of a rectangular prism is V=whl.

So in this case, the equation would be 1560=w·12·(w+3). Then, we can simplify this equation.

1. Divide 12 to both sides of the equation. 1560/12=130. The equation becomes 130=w(w+3).

2. Distribute w through the parentheses, the equation becomes 130=w²+3w.

3. Then, -130 from both sides of the equation, so we can get the quadratic: w²+3w-130=0.

4. Factor the quadratic. w²+3w-130=(w-10)(w+13).

5. (w-10)(w+13)=0. w=10 or w=-13. However, w is the width of a rectangular prism, can the width of a shape be negative? No. So we can ignore the solution w=-13. Therefore, w=10cm.

6. To make sure our answer is correct, let's substitute the values back into the volume of a rectangular prism formula: V=whl. w=10; h=12; l=10+3=13; V=10(12)(13)=120*13=1560 cm³. As a result, our answer is correct, w=10 cm.

Hope this helps, have a nice day.

Let {N(t),t > 0} be a renewal process. Derive a renewal-type equation for E[SN (1)+1).

Answers

The renewal-type equation for E[SN(1)+1] is E[SN(1)+1] = 2, indicating that the expected value of the sum of the number of renewals by time 1 plus 1 is equal to 2.

To derive a renewal-type equation for E[SN(1)+1], we can use the renewal-reward theorem.

Let Tn be the interarrival times of the renewal process, where n represents the nth renewal. The random variable N(t) represents the number of renewals that occur by time t.

Using the renewal-reward theorem, we have:

E[SN(1)+1] = E[T1 + T2 + ... + TN(1) + 1]

Since the interarrival times are independent and identically distributed (i.i.d.), we can express this as:

E[SN(1)+1] = E[T] * E[N(1)] + 1

Now, we need to compute the expressions for E[T] and E[N(1)].

E[T] represents the expected interarrival time, which is equal to the reciprocal of the renewal rate. Let λ be the renewal rate, then E[T] = 1/λ.

E[N(1)] represents the expected number of renewals by time 1. This can be calculated using the renewal equation:

E[N(t)] = λ * t

Therefore, E[N(1)] = λ * 1 = λ.

Substituting these expressions back into the renewal-type equation, we have:

E[SN(1)+1] = (1/λ) * λ + 1 = 1 + 1 = 2

Hence, the renewal-type equation for E[SN(1)+1] is E[SN(1)+1] = 2.

To know more about renewal-type equation refer here:

https://brainly.com/question/31971995#

#SPJ11

Roy received math test scores of 05, 90, 90, and 85.
7. What is Roy's median test score?
8. What score would Roy need to get on
his next test to have a mean of 92

Answers

Median = 87.5 Sorry about the other one

7. 90

8. I maybe the other p help

Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.)
f(x) = 3x2/3 − 2x
I keep getting stuck at taking the first derivative and solving for critical points. So please show all work and even some of the tedious algebra bits included so I can see where I'm messing up?

Answers

The function f(x) = 3x²/3 - 2x has no intercepts, a relative minimum at (1, -1), no points of inflection, and no asymptotes.

Intercepts: To find the x-intercepts, we set f(x) equal to zero and solve for x:

0 = 3x²/3 - 2x

0 = x² - 2x

0 = x(x - 2)

x = 0 or x = 2

Therefore, both x = 0 and x = 2 are not actual x-intercepts, but rather double roots.

Relative Extrema: To find the relative extrema, we take the derivative of f(x) and set it equal to zero,

f'(x) = 2x - 2

0 = 2x - 2

2 = 2x

x = 1

Substituting x = 1 back into the original function, we find f(1) = -1. Therefore, the relative minimum occurs at (1, -1).

f''(x) = 2

Since the second derivative is a constant, it never equals zero. Therefore, there are no points of inflection for this function.

Asymptotes: To determine if there are any asymptotes, we examine the behavior of the function as x approaches positive or negative infinity. Since the highest power of x in the function is 2, the graph does not approach any vertical asymptotes.

For horizontal asymptotes, we look at the limits as x approaches positive or negative infinity:

lim(x→∞) f(x) = lim(x→∞) (3x²/3 - 2x) = ∞

The limits approach positive infinity in both cases, indicating that there are no horizontal asymptotes. Graphically, the function represents a parabola that opens upwards, with a relative minimum at (1, -1).

To know more about asymptote of functions, visit,

https://brainly.com/question/4138300

#SPJ4

Find the area of a sector with central angle 27/8 rad in a circle of radius 4 m.

Answers

The area of the sector with a central angle of 27/8 radians in a circle of radius 4 meters is 27 square meters.

To find the area of a sector, you can use the formula:

Area of Sector = (θ/2π) * πr²

where θ is the central angle in radians and r is the radius of the circle.

Given:

Central angle (θ) = 27/8 radians

Radius (r) = 4 meters

Substituting the given values into the formula, we have:

Area of Sector = (27/8 * 1/(2π)) * π * (4)^2

Simplifying the expression:

Area of Sector = (27/8 * 1/2) * (4)^2

Area of Sector = (27/16) * 16

Area of Sector = 27 square meters

Therefore, the area of the sector with a central angle of 27/8 radians in a circle of radius 4 meters is 27 square meters.

To know more about area of a sector: https://brainly.com/question/22972014

#SPJ11

Please help, Im stuck on this part of a review and Im really confused asap

Answers

Answer:

( 6, -1 )

Step-by-step explanation:

When you rotate 1 from the x axis by 90° it becomes -1 from the y axis.

When you rotate 6 by 9° from thr y axis, it becomes again 6 on the x axis

Your new x value is 6 and y is -1

So (6,-1)

Answer:

(-6, 1)

Step-by-step explanation:

To find the point obtained by rotating point P = (1, 6) counterclockwise by an angle of 90 degrees (r₉₀°), we can use the rotation formula:

x' = x * cos(θ) - y * sin(θ)

y' = x * sin(θ) + y * cos(θ)

In this case, θ is 90 degrees.

Substituting the values into the formula:

x' = 1 * cos(90°) - 6 * sin(90°)

y' = 1 * sin(90°) + 6 * cos(90°)

cos(90°) = 0 and sin(90°) = 1, so we have:

x' = 1 * 0 - 6 * 1 = -6

y' = 1 * 1 + 6 * 0 = 1

Therefore, r₉₀°(P) = (-6, 1). The point P = (1, 6) rotates counterclockwise by 90 degrees to the point (-6, 1).

#SPJ1

I need help with short sides of the triangles on Pythagorean theorem

Answers

Answer:

5

Step-by-step explanation:

13² - 12² = 25

√25 = 5

Have a great day <3

Which equation represents a line which is perpendicular to the line
7x + 3y = -18?

Answers

Answer:

c y=6x+4

Step-by-step explanation:

c y=6x+4
Hope this helps you
Other Questions
Frankl states that "mans search for meaning is the primary motivation in his life and not a "secondary rationalization" of instinctual drives. This meaning is unique and specific in that it must and can be fulfilled by him alone; only then does it achieve a significance which will satisfy his own will to meaning." So, my question is do you think that mans search for meaning can change over time if it "satisfy his own will to meaning? president eisenhowers secretary of defense, charles wilson, stated his belief that "what was good for ________ was good for the country." Volkan Company has cash of $10,000, Accounts payable of $24,000, inventory of $16,000, and, equipment of $40,000. The company has short-term loan of $10,000, Accounts receivable of $14,000, Salary payable of $6,000 and Long-term loan of $10,000.The current ratio for Volkan Company is _____.Do not copy from Chegg and give complete answer with explanation PLEASE HELP IM ON A TIMEFRAME What is a wetland?A]an ecosystem that is made up of salt water at least part of the yearB]an ecosystem in which plant roots are submerged during some part of the yearC]an ecosystem in which half the area is wet and the other half is dryD]an ecosystem with running water at least part of the year Describe one way World War I influence colonized states This is a term project, TOPIC :Growth Dynamics. kindly type the answer and only any if you know the topic. thumbs up be given, Note less than 1500 words ,INCLUDE background ,importance, Literature of review(books, research article), Objectives, Research question, data source and methodology(highlight data used (primary/secondary), Techniques for analyzing e.g correlation/regression, indicate the variables used, technique used in collection of the data, analysis and finding ,conclusion and Discussion , reference and Abstract. Y'all I have. Crush and we like each other but I feel like I don't deserve him........he so sweet and is so respectful he is christan which makes it all easier.....I don't know what to do he's so amazing I feel like I don't deserve him...... What is the area of this 3) use the graphic organizer below to identify the effects of the war on the american workforce: Solve this question for brainlest What is an amortization schedule used for?A To show how much of a loan payment goes to the principal and how much goes to pay interest.B To apply standard accounting rules specifying material vs. immaterial assets.C To set rules for which asset purchases will be recorded as assets.D To track the value of a fixed asset over time. URGENT WILL GIVE BRAINLIEST!!!! 2x + 7 = 15What does x equal? Rachel makes $38.25 in 3 hours.How much money did she makeper hour?4HELPPPPP 10 points I NEED IT NOW What is the definition of media literacy?A. Media literacy is the ability to read books aloud.B. Media literacy is the ability to create media for your computer.C. Media literacy is the ability to put together a bike using the instruction manual.D. Media literacy is the ability to "read" critically the messages behind the various media withwhich you interact on a daily basis. A taxi driver wrote a formula to represent the mileage and fee for his last customer. He wrote the equation 3.00 + 0.50 m = 9.50, where m represents the number of miles traveled.Which statement shows the meaning of the drivers equation? Select two options.Three dollars added to $0.50 is the same as $9.50.Three dollars plus $0.50 times the number of miles is equal to nine dollars and fifty cents.Three dollars more than the quotient of $0.50 and the number of miles is nine dollars and fifty cents.The product of the number of miles and the sum of $3 and $0.50 is equal to $9.50.The sum of three dollars and the product of 50 cents times the number of miles is nine dollars and fifty cents. Two ways by which people are related as family which civilization had the most influence on the structure of the u.s. government? responses a.rome b.egypt c.china d.india Smelly Perfume Company manufactures and distributes several different products. The company currently uses a plantwide allocation method for allocating overhead at a rate of $7 per direct labor hour. Cindy is the department manager of Department C which produces Products J and P. Department C has $16,200 in traceable overhead. Diane is the department manager of Department D which manufactures Product X. Department D has $11,100 in traceable overhead. The product costs (per case of 24 bottles) and other information are as follows: J P XDirect materials $100.00 $ 72.00 $48.00Direct labor 42.00 31.50 12.00Overhead 28.00 21.00 14.00 $170.00 $124.50 $74.00Machine hours 4 2 3Number of cases (per year) 300 500 6001. If Smelly changes its allocation basis to machine hours, what is the total product cost per case for Product P?a. $163.50b. $144.00c. $138.15d. $117.152. If Smelly changes its overhead allocation to departmental rates, what is the product cost per case for Product P assuming Departments C and D use direct labor hours and machine hours as their respective allocation bases?a. $117.15b. $163.50c. $131.50d. $138.15