1/2 of a 360
circle in degrees

The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

Learn more about polygons at: https://brainly.com/question/1592456

#SPJ1

The correct answer is option A. 2 1/8 when reduced to the lowest terms.

To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.

Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.

Learn more about Lowest Terms:

https://brainly.com/question/233783

#SPJ4

A logical argument cannot have a true conclusion and all true premises. A logical argument cannot have all true premises if it has a false conclusion. So at least one of the premises must be untrue.

If the premises and conclusion are connected in such a way that if the premises were true, then the conclusion would also have to be true, then the argument is considered valid.

FALSE. A strong argument has all true premises and is valid. Since a good argument is valid, it follows that the conclusion must also be true if all of the premises are true. A sound argument must have a true conclusion since a sound argument also has all true premises.

Hence we get the required answer.

Learn more about Arguments here:

brainly.com/question/860494

#SPJ4

Step-by-step explanation:

d+q =12

.25q + .10d = 1.95

d = 12-q

substitute

.25q + .10(12 -q) =1.95

.25q + 1.2 - .1q = 1.95

.15q = .75

q = 5. quarters

d + 5 = 12

d = 7 dimes

Answer:

5 quarters and 7 dimes

Step-by-step explanation:

5 quarters = $1.25

7 dimes = $0.70

7 + 5 = 12

$1.25 + 0.70 = $1.95!!

I hope this helped :)

Also, this answer was calculated by g00gle.

Answer:

\( \huge \boxed{ \boxed{1675}}\)

Step-by-step explanation:

according to the question

population decreases in 1 year

\(2500 \times 3\% \\ 2500 \times \frac{3}{100} \\ 25 \times 3 \\ 75\)

population will decrease in 11 years

so the population of the town after 11 years will be

2500-825

Answer:

6.11km/hr

Step-by-step explanation:

Let the speed that Kelli swims be represented by Y

Speed of the river = 5km/hr

Distance = Speed × Time

Kelli swam upstream for some distance in one hour

Swimming upstream takes a negative sign, hence:

1 hour ×( Y - 5) = Distance

Distance = Y - 5

She then swam downstream the same river for the same distance in only 6 minutes

Downstream takes a positive sign

Converting 6 minutes to hour =

60 minutes = 1 hour

6 minutes =

Cross Multiply

6/60 = 1/10 hour

Hence, Distance =

1/10 × (Y + 5)

= Y/10 + 1/2

Equating both equations we have:

Y - 5 = Y/10 + 1/2

Collect like terms

Y - Y/10 = 5 + 1/2

9Y/10 = 5 1/2

9Y/ 10 = 11/2

Cross Multiply

9Y × 2 = 10 × 11

18Y = 110

Y = 110/18

Y = 6.1111111111 km/hr

Therefore, Kelli's can swim as fast as 6.11km/hr still in the water.

PT.1     Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?

Choose the most logical value for the variable to represent.

Let x = Kelli's swimming speed in still water

PT.2    Which expression represents the distance Kelli traveled upstream?

1(x – 5)

PT.3     Which expression represents the distance Kelli traveled downstream?

0.1(x + 5)

PT.4     Solve the equation x – 5 = 0.1(x + 5) for x. Round your answer to the nearest hundredth.  Kelli can swim about 6.11  km/hour.

84 minutes

1) Since we are dealing with the average then we need to plug all those 4 durations on this formula:

Note that in the question there were two trips whose duration was 78 minutes.

2) Hene, the 5th trip was 84 minutes long

2 multipled by the sum of 3 and 4

Answer:

16 mph

Step-by-step explanation:

Givens:

4 hours total time

48 miles total distance

So our equation should look like this.

48 = 2x(2) + x(2)

Where x = speed second half of trip.

x = 8

x*2 = 16 mph

Answer:

A plant with yellow leaves and stunted growth is likely deficient in nutrients such as nitrogen, iron, magnesium or sulfur. It could also be affected by a viral or fungal infection, or an environmental stressor such as too much or too little water, poor soil quality or exposure to extreme temperatures. A soil test or analysis of the plant's symptoms can help identify the specific cause of the deficiency and appropriate treatment or management practices.

Step-by-step explanation:

Any value calculated from this survey would be considered a statistic.

To determine whether the given value is a statistic or a parameter, consider the following:

A statistic is a numerical value calculated from a sample of the population, while a parameter is a numerical value that describes a characteristic of the entire population.

In this case, the health and fitness club surveys 40 members. This is a sample of the population, not the entire population.

Know more about statistic here:

https://brainly.com/question/31577270

#SPJ11

Answer:

\(m = \frac{16 - 8}{3 - 6} = - \frac{8}{3} \)

(a) The function f(x, y) does not have a limit at (0,0). (b) No information is provided to determine the limit for f2(x, y).

(a) For the function f(x, y) = 5ry²/(3x² + y²), we can analyze the behavior as (x, y) approaches (0,0). Since the denominator 3x² + y² becomes zero as (x, y) approaches (0,0), we cannot directly evaluate the function at this point. However, by considering the parabola z = -y², we can observe that the function does not approach a specific value and thus does not have a limit at (0,0).

(b) The function f2(x, y) = Vel + Vsin(y) is not well-defined as no information or context is provided for the variables Vel, V, and U. Without this information, it is not possible to determine the limit of the function at (0,0) or any other point.

Therefore, for (a), the function f(x, y) does not have a limit at (0,0), and for (b), no information is given to determine the limit for f2(x, y).

To learn more about “variable” refer to the https://brainly.com/question/28248724

#SPJ11

Answer:

-4x

Step-by-step explanation:

3-7=-4 just add a x

Heuristics refers to rules of thumb that simplify the decision-making process. Heuristics are mental shortcuts that help individuals make decisions quickly, often relying on previous experience or intuition rather than a more systematic approach.

While heuristics can be useful, they can also lead to biases and errors in judgment if they are applied too broadly or without careful consideration. It is important to be aware of these heuristics and how they can affect decision-making processes, especially in complex or high-stakes situations where careful consideration is necessary.

The answer is C.

To learn more about Heuristics : brainly.com/question/29793101

#SPJ11

Answer:

5.25

Step-by-step explanation:

Answer:

your pretty whatsbyour name

Answer:

Amount of money saved  25 35 45 55 65 75 85

Step-by-step explanation:

Explanation:  On week 1 you have the $25 you already saved plus the $10 for that week, so $35.  

For every week after that add $10 to the money saved for the additional $10 saved that week.

On the 8th week the total amount of money saved is 95+10, or $105.

Answer:

D) 6.8 inches

Step-by-step explanation:

1.7 x 4 = 6.8 inches

Answer:

x = 2

Step-by-step explanation:

-5(4x - 2) = -2(3 + 6x)

-20x + 10 = -6 - 12x            Distribute -5 to 4x and -2 and distribute -2 to 3 and

                                           6x

10 = -6 + 8x                        Add 20x to both sides

16 = 8x                                Add 6 to both sides

2 = x                                   Divide 8 to both sides

Answer:

-0.5

Step-by-step explanation:

-5(4x-2) = -2(3+6x)

-20x-10 = -6-12x

-10 = -6+8x

-4 = 8x

-0.5 = x

The solution to the given differential equation is \(y(x) = -x^4/25 + x^2/15 - (3/25)e^(-3x) + (1/2)x^4cos(x) + (1/2)x^2sin(x) + C1e^(-3x) + C2\), where C1 and C2 are arbitrary constants.

To solve the given differential equation using the method of undetermined coefficients, we assume a particular solution of the form \(y_p = A(x^4 + Bx^2e^(-3x) + Csin(x))\), where A, B, and C are undetermined coefficients.

Step 1:

Differentiating y_p with respect to x, we obtain \(y_p' = 4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x).\)

Taking the second derivative, we have \(y_p" = 12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x).\)

Step 2:

Substituting y_p, y_p', and y_p" into the given differential equation, we get:

\((12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x)) + 5(4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x)) = 2x^4 + x^2e^(-3x) + sin(x).\)

Simplifying the equation and grouping the like terms, we have:

\((12A + 20Ax^3) + (-6B + 10Bx)e^(-3x) + (-15Bx^2 + 9Bx^3) + (12A + 10C)cos(x) + (-C + 2Bx)sin(x) = 2x^4 + x^2e^(-3x) + sin(x).\)

Comparing the coefficients of the terms on both sides, we can determine the values of A, B, and C. Equating the coefficients of each term, we obtain:

\(12A + 20Ax^3 = 2x^4,\)

\(-6B + 10Bx = x^2e^(-3x),\)

\(-15Bx^2 + 9Bx^3 = 0,\)

12A + 10C = 0,

-C + 2Bx = sin(x).

Solving these equations, we find A = -1/25, B = 1/15, and C = 0.

Therefore, the particular solution is \(y_p = (-1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

To obtain the general solution, we add the particular solution y_p to the complementary function y_c, where y_c is the solution of the homogeneous equation y" + 5y' = 0. The general solution is given by y(x) = y_c + y_p.

The complementary function can be found by solving the homogeneous equation:

y" + 5y' = 0.

The characteristic equation associated with the homogeneous equation is r^2 + 5r = 0. Solving this quadratic equation

, we find two distinct roots: r = 0 and r = -5.

Therefore, the complementary function is \(y_c = C1e^(-5x) + C2\), where C1 and C2 are arbitrary constants.

Finally, the general solution to the given differential equation is:

\(y(x) = C1e^(-5x) + C2 - (1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

Learn more about differential equation

brainly.com/question/32524608

#SPJ11

The average rate of change of the given function is 20.

It quantifies how much the function changed per unit on average throughout that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.

The average rate of change of a function f(x) over the interval [a,b] is given by the formula:

(f(b) - f(a)) / (b - a)

So, for the function f(x) = x² + 2 as x changes from 5 to 15, we can plug in the values to find the average rate of change:

(f(15) - f(5)) / (15 - 5) = (15² + 2 - 5² - 2) / (15 - 5) = (225 - 25) / 10 = 200 / 10 = 20

So the average rate of change of the function is 20.

To learn more about the average rate of change click here:

brainly.com/question/23715190.

#SPJ1

The root locus plot is symmetrical around the real-axis as there are no poles/zeros in the right half of the s-plane. There will be 2 root loci which proceed to end at infinity. There is no break-away/break-in point as there are no multiple roots on the real-axis. At K = 61.875, the system is marginally stable.

The transfer function is G(s) = K (s + 5) / s(s + 1)(s + 2). We have to determine the Root Locus plot of the given unity feedback system.

(a) The root locus plot is symmetrical around the real-axis as there are no poles/zeros in the right half of the s-plane. Hence, all the closed-loop poles lie on the left half of the s-plane.

(b) Number of root loci proceeding to end at infinity = Number of poles - Number of zeroes. In the given transfer function, there is one zero (s = -5) and three poles (s = 0, -1, -2). Therefore, there will be 2 root loci which proceed to end at infinity.

(c) There is no break-away/break-in point as there are no multiple roots on the real-axis.

(d) The angle of arrival is given by (2q + 1)180º, and the angle of departure is given by (2p + 1)180º. Where, p is the number of poles and q is the number of zeroes located to the right of the point under consideration. Each asymptote starts at a finite pole and ends at a finite zero.

The angle of departure from the finite pole is given by

Angle of departure = (p - q) x 180º / N

(where, N = number of asymptotes).

The angle of arrival at the finite zero is given by

Angle of arrival = (q - p) x 180º / N.

(e) The poles of the system are s = 0, -1, -2. The system will be marginally stable if one of the poles of the closed-loop system lies on the jω axis. Estimate the value of K when the system is marginally stable:

The transfer function of the system is given by,

K = s(s + 1)(s + 2) / (s + 5)

Thus, the closed-loop transfer function is given by,

C(s) / R(s) = G(s) / (1 + G(s))

= K / s(s + 1)(s + 2) + K(s + 5)

Therefore, the closed-loop characteristic equation becomes,

s³ + 3s² + 2s + K(s + 5) = 0

The system will be marginally stable when one of the poles of the above equation lies on the jω axis.

Hence, substituting s = jω in the above equation and equating the real part to zero, we get,

K = 61.875 (approx.)

Therefore, at K = 61.875, the system is marginally stable.

Learn more about the root locus plot from the given link-

https://brainly.com/question/33280195

#SPJ11

Answer: 1 2/3

Step-by-step explanation:

3 1/3 - 1 2/3

We know that you can't subtract the numerators 1 and 2 so you have to borrow from the whole number, 3 becomes a 2, and the numerator (which is 1) becomes a 4. You need to add the denominator to the numerator to get the 4. Then 4-2 =2 which is you numerator, denominator stays the same and 201 is 1 so then its 1 2/3

Step-by-step explanation:

The given relation is :

\(y=-0.11x+24.9\) ...(1)

We need to describe this relationship in words.​

The general equation of a line is given by :

y = mx +c ...(2)

comparing equations (1) and (2).

m = -0.11 and c = 24.9

It shows that the slope of the line is -0.11 and the y-intercept is 24.9.

The ratio of the number of unshaded to shaded squares is 7 : 3.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

It is also defined as the fraction of one quantity with respect to other.

The ratio of a and b is denoted as a : b.

Given is a grid of squares which is given below.

Total number of squares = 10

Of that,

Number of shaded squares = 3

Number of unshaded squares = 7

We have to find the ratio of unshaded to shaded squares in the grid which is 7 / 3 or 7 : 3.

Ratio of unshaded squares to shaded squares = 7 : 3

Hence 7 : 3 is the ratio of unshaded to shaded.

Solve more problems about Ratio here :

https://brainly.com/question/19761366

#SPJ9

The probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution.

To calculate the probability, we need to assume that the sample proportion follows a normal distribution. This assumption holds true when the sample size is sufficiently large and the conditions for the central limit theorem are met.

First, we need to calculate the standard error of the sample proportion. The standard error is the standard deviation of the sampling distribution of the sample proportion and is given by the formula sqrt(p(1-p)/n), where p is the estimated proportion and n is the sample size.

Next, we convert the sample proportion range into z-scores using the formula z = (x - p) / SE, where x is the given proportion and SE is the standard error. In this case, we use z-scores of 0.2 and 0.42.

Once we have the z-scores, we can use a standard normal distribution table or a statistical software to find the corresponding probabilities. The probability of the sample proportion falling between 0.2 and 0.42 is equal to the difference between the two calculated probabilities.

Alternatively, we can use the z-table to find the individual probabilities and subtract them. The z-table provides the cumulative probabilities up to a certain z-score. By subtracting the lower probability from the higher probability, we can find the desired probability.

In conclusion, the probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution and z-scores. This probability represents the likelihood of observing a sample proportion within the specified range.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

The probability that both marbles are of the same color is 31/66

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

5 red and 7 green marbles.

We have to calculate the probability of two marbles being drawn consecutively without replacing them.

The first is that if we define events R to be two red marbles, and G to be two green marbles, then we can verify that:

P(R) = (5/12)(4/11)

P(G) = (7/12)(6/11)

Then, P(R ∪ G) = P(R) + P(G)

                        = (5/12)(4/11) +  (7/12)(6/11)

                        = 5/33 + 7/22

                        =  31/66

Hence, the probability that both marbles are of the same color is 31/66

To learn more about the probability from the given link

https://brainly.com/question/24756209

#SPJ9

Answer:

B

Step-by-step explanation:

The sugar is already dissolved, so we know it's not C, We know it's not A, because if the water was impure, wouldn't the problem tell us in the first place?

I hope this helps, plz let me know!

Answer:

x = -1.5 , y = 5.17

Step-by-step explanation:

Solve the system of equation using ELIMINATION (solve for x)

x + 3y = 14

-x + y = 10

Solution

x + 3y = 14 ------- equation 1  * 1

-x + y = 10 ------- equation 2  * 3

x + 3y = 14 ------- equation 3

-(-3x + 3y = 30)------ equation 4

Using the ELIMINATION METHOD.

x-(-3x) + 3y-3y = 14-30

4x = -6

x = \(\frac{-6}{4}\)

x = -1.5

Substuting -1.5 into equation one

x + 3y = 14

-1.5 + 3y = 14

Adding 1.5 to both sides

-1.5 + 1.5 +3y = 14 +1.5

+3y = 15.5

Dividing by the coeffient of y

\(\frac{3y}{3} = \frac{15.5}{3}\)

y = 5.166666666666

y =5.17

Therefore x = -1.5 , y = 5.17

Answer:

They would need to sell 42

Step-by-step explanation:

You would do 500/12 which is 41.6 but you need to round up the .6 so that would be 42.

Hope this helps. Sry if I get it wrong