A square playground has a perimeter of 100 feet. What is the area of the playground?
*

200 square feet
625 square feet
2,500 square feet
10,000 square feet

In the parallelogram ABCD the value of DF is 13.33 metres or DF = 40/3 metres (rounded to two decimal places).

In the parallelogram ABCD, we can draw a diagonal AC that splits the parallelogram into two congruent triangles, namely, △ABC and △ADC.

Let x be the length of DF. We can use similar triangles to find x.

Notice that △BCE and △DFE are similar triangles, since they share the same angle at E and the angles at B and D are congruent due to opposite angles in a parallelogram. Therefore, we can write the following proportion:

BC/CE = DF/FE

Substituting the given values, we have:

16/8 = x/(20-x)

Simplifying this equation, we get:

2 = x/(20-x)

2(20-x) = x

40 - 2x = x

3x = 40

x = 40/3

Therefore, DF = 40/3 meters or 13.33 meters (rounded to two decimal places).

To learn more about parallelogram refer to:

brainly.com/question/29147156

#SPJ4

Answer:

what term?

Step-by-step explanation:

Explain the question.

[tex]t_2023[/tex] will be equal to the expression[tex]: t_2023 = [k*t_2022 + 1] / [k^2 * t_2021][/tex]. in terms of k.

The sequence given is defined by the recurrence relation:  [tex]t_n[/tex] = [tex][kt_(n−1)+ 1] /[k^2 t_(n−2)] for n ≥ 3,with t_1 = 1[/tex] and [tex]t_2[/tex] = 2, and [tex]t_3=(2k+1)/k^2[/tex], and [tex]t_4=(3k+1)/2k^3[/tex], and [tex]t_5=(k+1)/2k^2[/tex], and [tex]t_6[/tex]=1 and [tex]t_7[/tex]=2 and [tex]t_8=(2k+1)/k^2, t_9=(3k+1)/2k^3[/tex]. To find the value of [tex]t_2023[/tex], we need to find the values of the previous two terms, [tex]t_2022[/tex] and [tex]t_2022[/tex] . We can do this by using the recurrence relation, starting at n = 3 and going up until n = 2022.

Therefore,[tex]t_2022 = [k*t_2021 + 1] / [k^2 * t_2020][/tex].

Similarly, [tex]t_2021 = [k*t_2020 + 1] / [k^2 * t_2019[/tex]].

We can now plug in the values of [tex]t_2021[/tex] and [tex]t_2020[/tex], which can be found by continuing to work backwards in the recurrence relation until n = 9, and then we have the initial conditions of the sequence. Once we have the values of [tex]t_2021[/tex] and [tex]t_2021[/tex] , we can substitute them into the recurrence relation for[tex]t_2023[/tex] to get the desired result. Therefore, [tex]t_2023 = [k*t_2022 + 1] / [k^2 * t_2021].[/tex]

To know more about recurrence relation click here:

https://brainly.com/question/9521757

#SPJ11

Donovan scored 6 points, Jeremy scored 18 points, and Kolby scored 12 points.        

Let's denote the number of points scored by Donovan as "D".    

According to the problem, Jeremy scored triple the number of points as Donovan, so he scored 3D points.

Similarly, Kolby scored double the number of points as Donovan, so he scored 2D points.

We also know that the total number of points scored by all three boys is 36. So we can write an equation:

D + 3D + 2D = 36

Simplifying this equation, we get:

6D = 36

Dividing both sides by 6, we get:

D = 6

So Donovan scored 6 points.

Using the values we found for Donovan's score, we can find the scores of Jeremy and Kolby:

Jeremy scored 3D = 3(6) = 18 points

Kolby scored 2D = 2(6) = 12 points

Therefore, Donovan scored 6 points, Jeremy scored 18 points, and Kolby scored 12 points.

To learn more about equation:

https://brainly.com/question/10413253

#SPJ4

After answering the provided question, we can conclude that Therefore, the answer of quadratic equation is  D) [tex]$-3x^{2}+7$[/tex]

A quadratic equation is x ax² + bx + c = 0, so it's a single variable quadratic polynomial. a 0. Because this regression is of second order, the Fundamental Principle of Algebra helps to ensure that it includes at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic calculation.

This means there is at least yet another word that must be squared. The formula "ax² + bx + c = 0" is a common solution for quadratic equations. where a, b, and c are arithmetical coefficients or constants. where the parameter "X" is unidentified.

To find g(h(x))

[tex]$\begin{array}{l}{{h(x)=3x^{2}-2}}\\ {{g(h(x))=g(3x^{2}-2)}}\\ {{g(3xA^2))=-3x^2-2}+5}}\\ {{g(h(x))=-3x^{2}+7}}\end{array}$[/tex]

Therefore, the answer is D) [tex]$-3x^{2}+7$[/tex]

To know more about quadratic equation visit:

brainly.com/question/30098550

#SPJ1

Answer:

We know that 120 can be factored as 2^3 * 3 * 5, so its totient function value can be found as follows:

φ(120) = φ(2^3) * φ(3) * φ(5)

= 2^2 * 2 * 4

= 16

Therefore, there are 16 numbers less than or equal to 120 that are relatively prime to 120

Answer:

Side 3 is:  5x^3 - 4x^2 +3x - 12

Note that the answer options do not include this result, but it is likely that the second option is simply missing the square term for the -4x, and it should read -4x^2.

Step-by-step explanation:

The perimeter is the sum of all three sides.  To find Side 3, subtract Sides 1 and 2 from the perimeter:

5x^3 - 2x^2 +3x - 8 - (3x^2-4x-1) - (4x-x^2+5)      = Side 3

  Perimeter             -      Side 1    -     Side 2        = Side 3

5x^3 - 2x^2 +3x - 8 - 3x^2+4x+1 - 4x+x^2-5        [Remove parentheses]

5x^3 - 3x^2 +x^2 - 2x^2 +3x +4x - 4x - 8 +1 -5     [Combine like terms]

5x^3 - 4x^2 +3x - 12                       [Simplify]       = Side 3

Answer: Scootering is faster

Step-by-step explanation: If it takes 20 minutes to go around walking going through the middle would technically split the time in half and 20 divided by 2 is 10 which is more than 8 therefore scootering is faster.

The sample space is 20, 24, 28, 32, 36, 40. There are 6 outcomes in the sample space.  In this case, the sample space is {20, 24, 28, 32, 36, 40}.

The sample space of the probability experiment is the set of all possible outcomes that can occur when randomly choosing a number from the multiples of 4 between 20 and 40, inclusive.

To determine the number of outcomes in the sample space, we simply count the number of elements in the set. In this case, there are 6 outcomes in the sample space.

Therefore, the sample space is {20, 24, 28, 32, 36, 40} and there are 6 outcomes in the sample space. After Randomly choosing a number from the multiples of 4 between 20 and 40, these values are found.

Know more about  probability here:

https://brainly.com/question/30034780

#SPJ11

The value of the probability P(A ∪ B) if the events are independent events is  0.55

The formula for the probability of the union of two events is:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Since the events A and B are independent, the probability of their intersection is simply the product of their individual probabilities:

P(A ∩ B) = P(A) × P(B)

Substituting the given values, we have:

P(A ∩ B) = 0.4 × 0.25 = 0.1

Now we can use the formula for the union:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

So, we have

P(A ∪ B) = 0.4 + 0.25 - 0.1

This gives

P(A ∪ B) = 0.55

Therefore, the probability of the union of events A and B is 0.55.

Read more about probability at

https://brainly.com/question/251701

#SPJ1

If A, B, and C lie on a straight line, the sum of angles y, x, and z will be 180 degrees:

y + x + z = 180

Substituting the values given in the problem:

95 + x + 330 = 180

Simplifying:

425 + x = 180

Subtracting 425 from both sides:

x = -245

Therefore, x is -245 degrees.

However, since x represents an angle on a straight line, we can add 180 degrees to get an equivalent angle:

x + 180 = -245 + 180 = -65

Therefore, x is -65 degrees.

The equation of the graphed function, which is composed of translations to f(x) = x³, is given as follows:

B. y = f(x + 3) - 2.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The turning point of f(x) = x³ is at the origin, while for the graphed function it is at point (-3,-2), hence the translations are given as follows:

Hence the graphed function is defined as follows:

B. y = f(x + 3) - 2.

More can be learned about translations at brainly.com/question/28174785

#SPJ1

Answer:a

Step-by-step explanation:its simple

The percentage decrease in the population after on year is found to be 19%.

The percentage decrease can be found by using the formula,

Percentage decrease = change in population/initial population x 100.

Now change in population in one year is given as final population - initial population.

Putting values, change in population = 252000 - 204120

Change in population = 47880

Now, putting all the value in the formula,

percentage decrease = 47880/252000 x 100

percentage decrease = 19%

So, the decrease in the population is found to be 19%.

To know more about percentage increase or decrease, visit,

https://brainly.com/question/11360390

#SPJ4

Answer:

The required amount Ahmet needs to pay after 6 years is $1619.14.

What is compound interest?

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,

From the given data,

P = 700, r = 15% and t = 6 (n =1)

Now,

Amount = principal[1 + r/n]ⁿᵃ

Amount = 700(1 + 0.15)⁶

Amount = $1619.14

Thus, the required amount Ahmet needs to pay after 6 years is $1619.14.

Step-by-step explanation:

Hence, in answering the stated questiοn, we may say that If yοu're unitary methοd  satisfied with yοur line plοt, save it and distribute it as needed.

The unit technique is a prοblem-sοlving apprοach that invοlves finding the value οf a single unit and then multiplying that value by the needed value. Tο put it simply, the unit technique is used tο extract a single unit value frοm a given multiple. 40 pens, fοr example, wοuld cοst 400 rupees, οr the cοst οf οne pen. The prοcess fοr achieving this may be standardized. A single cοuntry. anything that has an identity element. Its adjοint and reciprοcal are equal in mathematics and algebra.

a general methοd fοr prοducing a line plοt:

First, cοllect yοur data. Stοck prices, temperature readings, and survey results are all examples οf this. The crucial thing is that yοu have a set οf values tο plοt οn a graph.

Enter yοur x and y values intο the plοt. The exact prοcedure depends οn the graphing prοgrammed yοu're using, but yοu shοuld be able tο enter yοur values intο a data table οr spreadsheet.

Make any changes yοu want tο yοur plοt. Adding labels tο the x and y axes, tweaking the plοt's scale, changing the line cοlοur οr thickness, οr adding a title are all pοssibilities.

If yοu're satisfied with yοur line plοt, save it and distribute it as needed.

To know more about unitary method  visit:

brainly.com/question/28276953

#SPJ1

Complete question:

The lowest common denominator, 20, can be used to represent any fraction that can be stated as a ratio of integers with factors of 2 and 5 in the denominator. eg. 1/4, 1/2, 2/5 and 7/10

To find all the fractions that have 20 as the lowest common denominator, we need to identify all the prime factors of 20, which are 2, 2, and 5.

Then, we can express each fraction with these prime factors in the denominator, by multiplying the numerator and denominator by the missing factors. For example, for the fraction 1/4, we need to multiply both the numerator and denominator by 5 to get:

1/4 = 5/20

Similarly, for the fraction 3/5, we need to multiply both the numerator and denominator by 2 to get:

3/5 = 6/10 = 12/20

By doing this for all fractions, we can express them with the same denominator of 20. Here are some examples:

1/4 = 5/20

3/5 = 12/20

1/2 = 10/20

2/5 = 8/20

7/10 = 14/20

Therefore, any fraction that can be expressed as a ratio of integers with factors of 2 and 5 in the denominator can be written with 20 as the lowest common denominator.

To learn more about lowest common denominator click here

brainly.com/question/17092436

#SPJ4

Complete Question

Write any two fractions which have 20 as the LCD (lowest common denominator)?

The perimeter of the rectangle is (x² + 30x + 104) in² while The area of the rectangle is (x² + 30x + 104) in²

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The rectangle have a length of (0.5x + 13) and width of (2x + 8)

1) Perimeter = 2(length + width)

Perimeter = 2(0.5x + 13 + 2x + 8) = 2(2.5x + 21) = (5x + 42) inches

The perimeter of the rectangle is (x² + 30x + 104) in²

2) Area = length * width

Area = (0.5x + 13) * (2x + 8) = x² + 4x + 26x + 104

Area = (x² + 30x + 104) in²

The area of the rectangle is (x² + 30x + 104) in²

Find more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

1219.5 more centimeters of fabric

Step-by-step explanation:

First, we need to convert 12.5 meters to centimeters, since the given amount of fabric is in centimeters.

12.5 meters = 12.5 x 100 centimeters/meter = 1250 centimeters

Now we can find the difference between what Ray needs and what he has:

1250 centimeters - 30.5 centimeters = 1219.5 centimeters

Therefore, Ray needs 1219.5 more centimeters of fabric.

By alternately multiplying 2(n-2) by 1 and -1 for odd and even values of n, respectively, this formula yields the nth term of the sequence.

A sequence is a list of objects that is in order in mathematics. (or events). Similar to a set, it has members. (also called elements, or terms). The length of the sequence is the number of many ordered elements (potentially infinite).

Given :

The ratio between consecutive terms in the above sequence is not constant, hence it is not a geometric sequence. The series does, however, appear to rotate between positive and negative numbers.

The explicit formula for the nth term in this sequence is as follows:

a = (-1)^(n+1) * 2^(n-2) (n-2)

By alternately multiplying 2(n-2) by 1 and -1 for odd and even values of n, respectively, this formula yields the nth term of the sequence. For instance, when n is 1, we obtain:

n = 2 results in:

so forth.

To know more about sequence visit:

https://brainly.com/question/30262438

#SPJ9

Answer:

1.  C.

2. D.

3. D.

Step-by-step explanation:

A.  Round both dimensions the nearest whole number. 8 1/3 rounds to 8,     6 3/4 rounds to 7. Multiply these two and your estimate for the tarp area is 56 sq yds. Option C.

B. Convert both mixed numbers to improper fractions. Multiply whole number by divisor and add the dividend. (8*3) + 1 = 25. First number is 25/3.(6*4) + 3 = 27. Second number is 27/4. Multiply these two numbers fractions  and get 225/4. Convert to a mixed number, 56 1/4. Option D.

C. This answer is reasonable. 56 1/4 is pretty close to our estimate of 56 sq yds. Or just choose the option that corresponds to your estimate from part A. Option D.

The probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1/1.

The reason for this is that if any letter of the alphabet is selected at random, the probability of getting an "r" is 1/26, or 0.0385. Since letters can be used more than once, this probability remains the same regardless of how many letters are selected. Thus, the probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1.

In summary, the probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1. This is because, when a letter is selected at random, each letter has an equal chance of being chosen (1/26), and since the probability of selecting an "r" remains the same regardless of how many letters are selected, the probability of getting at least one "r" is also 1.

Know more about probability here:

https://brainly.com/question/13604758

#SPJ11

Answer: To find the total area of the grass that Yuri's dad needs to fertilize, we need to calculate the area of the back yard and the area of the front yard, and then add them together.

Area of the back yard:

The back yard measures 55 feet by 30 feet, so the area is:

55 feet x 30 feet = 1650 square feet

Area of the front yard:

The front yard is a square with a length of 42 feet on each side, so the area is:

42 feet x 42 feet = 1764 square feet

Total area:

To find the total area, we add the area of the back yard and the area of the front yard:

1650 square feet + 1764 square feet = 3414 square feet

Therefore, Yuri's dad needs to fertilize a total area of 3414 square feet.

Step-by-step explanation:

The initial amount of salt in the tank is 60 kg, calculated using the formula M = ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank.

Initially, the tank contains 60 kg of salt and 2000 liters of water. The amount of salt in the tank can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The density of salt is 2270 kg/m3. Assuming the tank has a constant volume, the mass of the salt in the tank is 60 kg.

The amount of salt in the tank changes due to the addition of pure water and mixing of the solution. The amount of salt in the tank at any given time can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The rate at which the salt is added to the tank is equal to the rate at which the salt-water solution is drained from the tank.

Therefore, the rate of change of the mass of the salt in the tank is equal to 8 liters/minute of pure water entering the tank minus 4 liters/minute of salt-water solution draining from the tank. Thus, the amount of salt in the tank initially is 60 kg.

Learn more about volume of the tank here:

https://brainly.com/question/27819222

#SPJ4

Answer:

the answer to ur question is: 36

The expected value and standard deviation of x are 1.6 and 0.66, respectively.

Given that:

Jimmy volunteers at events at the hospital each year.

The random variable x is the number of hospital events Jimmy works at each year.

We understand that he does not work for more than two events in a year

So, x can take on the values 0, 1, or 2.

From the question, we have:

Over the past ten years

So, the table is

X P(X)

0 0.1

1 0.2

2 0.7

To find the expected value, we take the sum of the products of x and P(x)

So, we have

E(x) = 0(0.1) + 1(0.2) + 2(0.7)

E(x) = 1.6

To find the standard deviation, we need to first calculate the variance:

Var(X) = E(x^2) - [E(x)]^2

Where

E(x^2) = 0^2(0.1) + 1^2(0.2) + 2^2(0.7)

E(x^2) = 3

So, we have

Var(X) = 3 - (1.6)^2

Var(X) = 0.44

This means that

SD(x) = √0.44

SD(x) = 0.66

Hence, the standard deviation is 0.66

Read more about probability distribution at

https://brainly.com/question/24756209

#SPJ1

Answer:

6 hours

Step-by-step explanation:

[tex]\frac{1}{6}[/tex] of Total battery life = [tex]\frac{1}{6} * 3600 = 600[/tex]milliamps

Assuming the battery takes 100 Milliamps per hour,

Time = Battery Capacity / Current hours

Time = 600 / 100 Mah = 6H

Answer:

1

explanation in head

A proportional connection exists when two values may be expressed as y = kx, where k is a constant. To discover which ordered pairings have a proportionate connection with (0.2, 0.3).

We must find a value of k for each pair that makes this equation true. Let us begin with option A: (1.2, 2.3). If we wish to represent this combination as y = kx, we must discover the value of k that results in 2.3 = k. (1.2). When we solve for k, we get: k = 2.3 / 1.2 ≈ 1.92 As a result, (1.2, 2.3) does not have a proportionate connection with (0.2, 0.3) since the value of k is different for both couples. This procedure can be repeated for each of the others. options. Option B: (2.7, 4.3) yields: k = 4.3 / 2.7 ≈ 1.59 Option C: (3.2, 4.8) yields: k = 4.8 / 3.2 = 1.5 Option D: (3.5, 5.3) yields: k = 5.3 / 3.5 ≈ 1.51 Option E: (5.2, 7.8) yields: k = 7.8 / 5.2 = 1.5 As a result, alternatives C and E are proportional to (0.2, 0.3) since they can be represented in the form y = kx with the same k value. k = 1.5 in both situations.

learn more about equation  here:

https://brainly.com/question/29657988

#SPJ4

The point one tick mark to the left of negative 3 on the number line is -3.25.

Number lines are horizontal straight lines in math where the intervals between the integers are equal. A number line can be used to show all of the numbers in a sequence. At both ends, this line continues indefinitely.

Each tick mark on the number line represents one-fourth of a unit, so the distance between negative 4 and negative 3 can be divided into 4 parts, each with a length of one-fourth of a unit. Starting from negative 4, the tick marks would be labeled as -4, -3.75, -3.5, -3.25, -3, and so on. Therefore, the point one tick mark to the left of negative 3 is at -3.25 on the number line.

Learn more about Number Line:

https://brainly.com/question/25230781
#SPJ4