Hello! Can someone please help me. I am in trouble, hope ypu help me guys, with complete answer! THANK YOU​

Answer:

  A.  4.33 minutes

  B.  it will be about 11% less than the initial time (4.85 -0.54)

Step-by-step explanation:

You want to know the team's final time if it decreases by 5 1/2% on each of two runs after their initial run time of 4.85 minutes. And you want to know how to check the answer for reasonableness.

If the time decreases by 5.5% on each run, it is multiplied by (1 -5.5%) = 0.945 on each run. The time after 2 more runs will be ...

  (4.85 min)(0.945)(0.945) ≈ 4.33 min

The team's time on the final run was about 4.33 minutes.

For small percentages, the product of small percentage changes is nearly the same as the sum of the percentage changes. That is, two changes by -5.5% will be about the same as a change of 2 × (-5.5%) = -11%.

Of course a decrease of 11% is a decrease of 10% and another decrease of 1%. This makes the estimated time be ...

  4.85 -0.485 -0.0485 ≈ 4.85 -0.54 = 4.31

The estimate is a larger change than the actual change, so the computed value of 4.33 is judged to be reasonable. (The actual effect of two -5.5% changes is about a -10.7% change.)

__

Additional comment

This "add the percentages" is a suitable way to check the reasonableness of all sorts of problems involving percent changes, including problems involving investments or loan interest.

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Through proportionality, we find out that the value of [tex]y[/tex] is 25/4 when [tex]x[/tex] is doubled, 25/9 when [tex]x[/tex] is tripled, 25/36 when [tex]x[/tex] is increased to 5 times its original value, 1 when [tex]x[/tex] is increased by 5 times its original value, and 400 when [tex]x[/tex] is reduced by 75%.

It is given to us that -

[tex]y[/tex] is inversely proportional to [tex]x^{2}[/tex]

This implies that -

[tex]y[/tex] ∝ [tex]\frac{1}{x^{2} }[/tex]

[tex]= > y=\frac{k}{x^{2} }[/tex] ----- (1)

where, [tex]k[/tex] = Constant of proportionality

It is also given to us that for a particular value of [tex]x[/tex], [tex]y[/tex] is 25.

From equation (1) and from the above statement, it can be said that -

[tex]x^{2} =\frac{k}{y} \\= > x^{2} =\frac{k}{25}\\= > x=\frac{\sqrt{k} }{5}[/tex] ------ (2)

Now, we have to find out the value of [tex]y[/tex] when [tex]x[/tex] -

a) is doubled

=> [tex]x_{1} = 2x[/tex] ---- (3)

Using equation (3) in equation (1),

[tex]= > y=\frac{k}{(x_{1}) ^{2} }\\= > y=\frac{k}{(2x)^{2} }\\= > y=\frac{k}{4x^{2} }[/tex]---- (4)

Substituting the value of [tex]x[/tex] from equation (2) in equation (4), we have

[tex]y=\frac{k}{4x^{2} }\\= > y=\frac{k}{4(\frac{\sqrt{k} }{5} )^{2} } \\= > y=\frac{25k}{4k}\\ = > y=\frac{25}{4}[/tex]

Thus, the value of [tex]y[/tex] is 25/4 when [tex]x[/tex] is doubled.

b) is tripled

=> [tex]x_{2}=3x[/tex] ---- (5)

Using equation (5) in equation (1),

[tex]= > y=\frac{k}{(x_{2} )^{2} } \\= > y=\frac{k}{(3x)^{2} } \\= > y=\frac{k}{9x^{2} }[/tex]------ (6)

Substituting the value of [tex]x[/tex] from equation (2) in equation (6), we have

[tex]y=\frac{k}{9x^{2} }\\= > y=\frac{k}{9(\frac{\sqrt{k} }{5} )^{2} } \\= > y=\frac{25k}{9k} \\= > y=\frac{25}{9}[/tex]

Thus, the value of [tex]y[/tex] is 25/9 when [tex]x[/tex] is tripled.

c) increased to 5 times its original value

[tex]x_{3}= x+5x\\= > x_{3}=6x[/tex]

From equation (2),

[tex]x_{3}=6x\\= > x_{3}=6(\frac{\sqrt{k} }{5} )\\= > x_{3}=\frac{6\sqrt{k} }{5}[/tex]----- (7)

Using equation (7) in equation (1),

[tex]y=\frac{k}{(x_{3}) ^{2} } \\= > y=\frac{k}{(\frac{6\sqrt{k} }{5} )^{2} } \\= > y=\frac{25k}{36k} \\= > y = \frac{25}{36}[/tex]

Thus, the value of [tex]y[/tex] is 25/36 when [tex]x[/tex] is increased to 5 times its original value.

d) increased by 5 times its original value

[tex]x_{4}=5x\\= > x_{4}=5(\frac{\sqrt{k} }{5}) \\= > x_{4}=\sqrt{k}\\[/tex]------ (8)

Using equation (8) in equation (1),

[tex]= > y=\frac{k}{(x_{4}) ^{2} }\\= > y=\frac{k}{(\sqrt{k} )^{2} } \\= > y=1\\[/tex]

Thus, the value of [tex]y[/tex] is 1 when [tex]x[/tex] is increased by 5 times its original value.

e) reduced by 75%

[tex]= > x_{5}= x-(\frac{75}{100} )x\\= > x_{5}=\frac{100x-75x}{100}\\ = > x_{5}=\frac{25x}{100} \\= > x_{5}=0.25x[/tex]

Substituting the value of [tex]x[/tex] from equation (2) in the above equation,

[tex]x_{5}=0.25x\\= > x_{5}=0.25(\frac{\sqrt{k} }{5} )\\= > x_{5}=0.05\sqrt{k}[/tex]----- (9)

Using equation (9) in equation (1),

[tex]= > y=\frac{k}{(x_{5}) ^{2} }\\= > y=\frac{k}{(0.05\sqrt{k}) ^{2} } \\= > y= \frac{1}{0.0025}\\ = > y= 400[/tex]

Thus, the value of [tex]y[/tex] is 400 when [tex]x[/tex] is reduced by 75%.

Therefore, through proportionality, we find out that the [tex]y[/tex] is 25/4 when [tex]x[/tex] is doubled, 25/9 when [tex]x[/tex] is tripled, 25/36 when [tex]x[/tex] is increased to 5 times its original value, 1 when [tex]x[/tex] is increased by 5 times its original value, and 400 when [tex]x[/tex] is reduced by 75%.

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17.5 miles is the runner training distance in the tenth week.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given,

The first​ week, she runs 4 miles during each training session

Each​ week, she increases her distance by 1.5 miles.

4,5.5,7,8.5....

The given sequence is a Arithmetic sequence, a is the first term and d is common difference

a=4,d=5.5

We need to find the distance in the tenth week.

n=10

aₙ=a+(n-1)d

a₁₀=4+(10-1)(1.5)

a₁₀=4+9(1.5)=4+13.5=17.5

Hence 17.5 is the runner training distance in the tenth week.

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In the tenth week, the runner will run 17.5 miles.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, A runner is training for a marathon.

The first​ week, she runs 4 miles during each training session.

Here a₁ = 4.

Each​ week, she increases her distance by 1.5 miles.

d = 1.5

We know the nth term of an AP is aₙ = a₁ + (n - 1)d.

∴ In tenth week which is a₁₀ the runner will run,

a₁₀ = a₁ + (10 - 1)×1.5

a₁₀ = 4 + 9(1.5).

a₁₀ = 4 + 13.5.

a₁₀ = 17.5 miles.

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The lengths of the sides of the rectangular field in order to minimize the cost will be length = 6000 feet and width = 4000 feet  .

In the question ,

it is given that ,

the area that farmer need to fence = 24 million square feet

let the length of  field be [tex]=[/tex]"x"   and

let the width  of rectangular field be  [tex]=[/tex]"y"  .

So , the area of the rectangular field = x.y = 24

So , y = 24/x  .

given that the field is divided into half ,

So , the required fencing will be

S = 2x + 3y

Substituting y = 24/x in the equation,

we get ,

S = 2x + 3(24/x)

S = 2 + 72/x

Differentiating the equation "S [tex]=[/tex] 2 [tex]+[/tex] 72/x" with respect to "x" ,

dS/dx = 2 - 72/x²

to minimize the cost of fencing , we equate ds/dx to 0 ,

we get

2 - 72/x² = 0

x² = 36 million feet

x² = 36000000

x = 6000 feet

and y = 24/x = 24million/6000

= 24000000/6000

= 4000 feet

Therefore , The length of the rectangular field is 6000 feet and the width of the rectangular field is 4000 feet .

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About 20% of the time Aaron tunes in to his favored station, there will be a commercial playing.

Given info;

The assumption is that over a significant number of days, 20% of the time he tunes in to his favorite station, an ad will be playing. This is based on the idea of relative frequency.

The relative frequency of event A, which is calculated by dividing the number of desired outcomes by the total outcomes, will be off over a large number of experiments, according to the likelihood of an outcome A of a%.

When he dials into his preferred station, there is a 0.2 probability that a commercial will start playing.

The conclusion is that over a long number of days, an advertisement will be playing about 20% of the time he tunes in to his preferred station.

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Answer:

answer is 5

Step-by-step explanation:

If ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)°  and ∠HFI= (x+1), the measure of x will be 29°.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that, ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)°  and ∠HFI= (x+1),

Complementary angles are those where the sum of the two angles is 90 degrees. In other words, two angles are considered complementary if they combine to form a right angle. The two angles are said to complement one another in this context.

Since ∠EFH and ∠HFI are complementary angles,

∠EFH + ∠HFI = 90

(2x + 2)+ (x+1) =90

3x+3=90

x+1=30

x=29°

Thus, if ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)°  and ∠HFI= (x+1),the measure of x will be 29°.

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The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2.

From the question, we have

2x -3+x>x+1

⇒3x-3>x+1

Subtract x from both sides, we get

⇒3x-3-x>x+1-x

⇒2x-3>1

⇒2x>4

⇒ x > 2

The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2.

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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The equation can be proved by taking Pythagorean Triplets into consideration, therefore 5^{2} + 12^{2} = 13^{2}

What are Pythagorean Triplets?

The "Pythagorean Triple" is a collection of three positive numbers, a, b, and c, that satisfy the following rule:

a^{2} + b^{2} = c^{2}

From the figure two in the attached image it can be very well observed that 5,12 and 13 are making a pythagorean triplets, therefore it can be said 5^{2} + 12^{2} = 13^{2}

Hence Proved.

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[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-10}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-8)}}} \implies \cfrac{-18}{1 +8} \implies \cfrac{ -18 }{ 9 } \implies - 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-8)}) \implies y -8 = - 2 ( x +8) \\\\\\ y-8=-2x-16\implies {\Large \begin{array}{llll} y=-2x-8 \end{array}}[/tex]

The value is 5/2 and 35/2 pounds.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.

Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire.

The ratios of  the given table

Table 10,

[tex]\begin{aligned}&\Rightarrow \frac{5}{3}=\frac{1}{x} \\&\Rightarrow x=\frac{3}{5} \\&\Rightarrow \frac{5}{3}=\frac{12}{x}=\frac{12+3}{15} \\&\Rightarrow x=\frac{12}{5}\end{aligned}[/tex]

Table 9,

[tex]\begin{aligned}&\frac{10}{4}=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{1} \\&x=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{7} \\&x=\frac{35}{2}\end{aligned}[/tex]

[tex]\begin{array}{rccc}\text { 9) pounds } & 10 & \frac{5}{2} & \frac{35}{2} \\\text { Weeks } & 4 & 1 & 7 \\\text { 10) tons } & 5 & 1 & 12 \\\text { days } & 3 & \frac{3}{5} & \frac{12}{5}\end{array}[/tex]

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Answer:

34

Step-by-step explanation:

Triangle is an isosceles triangle, where two angles are the same. BA=BC

Answer:34

Step-by-step explanation:

its an isosceles triangle because two sides are equal

The null and alternative hypothesis are H0 : μ = 444; Ha : μ < 444.

In the given question we have to determine the decision rule for rejecting the null hypothesis.

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting.

[tex]\mu_{0}[/tex] = 444

A 9 bag sample had a mean of 441 grams with a standard deviation of 25.

A level of significance of 0.025 will be used.

There have claim that the machine is underfilling the bags.

So , the null and alternative hypothesis are

H0 : μ = 444

Ha : μ < 444

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The correct answer is:  " 4096 x⁶ " .

Step-by-step explanation:

Given:   [(4x)³] ² ;  Simplify.

Method 1)
Note the following multiplication property of exponents:
    ⇒ (aᵇ)ᶜ  = a⁽ᵇ*ᶜ⁾  ;

As such:

   [ [(4x)³] ²  = (4x)⁽²ˣ³⁾ = (4x)⁶ ;

Now; note the following property of exponents:
   (ab)ᶜ  = aᶜ * bᶜ  ;

As such:  (4x)⁶ = 4⁶ * x⁶ ;

Now; we can simplify 4⁶  ;  by using a calculator:
  →  4⁶  = 4096 ;

Or:  4⁶  =  4 * 4 * 4 * 4 * 4 * 4 ;

            =  (4 * 4) * 4 * 4 * 4 * 4 ;

            = 16 * 4 * 4 * 4 * 4 * ) ;

            = (16 * 4) * 4 * 4 * 4 ;

            =  64 * 4 * 4 * 4 ;  

            =   (64 * 4) * 4 * 4 ;

            =   (126 * 4) * 4    

            =  (256) * 4 ;

            =  4096 .
_______

or:   4⁶  = 4 * 4 * 4 * 4 * 4 * 4 ;

             =  (4 * 4) * (4 * 4) * (4 * 4) ;

             = 16 * 16 * 16 ;

             =  (16 * 16) * 16 ;

             = (256) * 16 ,   =  4096.

_______
So:       [(4x)³] ²  =  4⁶  *  x⁶  =  4096 x⁶ ;
_______
Method 2) Given: [(4x)³] ² ;

 (4x)³     =  4x * 4x * 4x ;

 [(4x)³]²  =  (4x * 4x * 4x)²

              = (4x * 4x * 4x) * (4x * 4x * 4x) ;

              =    (4 * 4 * 4 * x * x * x * 4 * 4 * 4 * x * x * x ;

              =   4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;

 ⇒ (4 * 4 * 4 * 4 * 4 * 4)  = 4⁶  = 4096 ; (see Method 1 above).
 ⇒ (x * x *  x * x * x * x)  = x⁶ ;

                      ⇒  [(4x)³] ² =  4⁶ * x⁶ =  4096 x⁶ ;
_______
Method 3)
 [(4x)³] ²  = (4x)⁽²ˣ³⁾  = (4x)⁶ ;

      (4x)⁶ = 4x * 4x * 4x * 4x * 4x * 4x ;

              = 4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;

              = (4 * 4 * 4 * 4 * 4 * 4) * (x * x * x * x * x * x) ;

⇒ (4 * 4 * 4 * 4 * 4 * 4) = 4⁶ = 4096 ; [see Method 1 above].
⇒  (x * x * x * x * x * x)  = x⁶ ;

                      ⇒   [(4x)³] ² =  4⁶ * x⁶ =  4096 x⁶ .

_______
The correct answer is:  " 4096 x⁶ " .

_______
Hope this is helpful.

  Best wishes in your academic endeavors!
_______

Answer:

Simplify (4x to the power of 3) power of 2

Step-by-step explanation:

The school I go to tells me to do this:

(4x^3)^2

(4x^3)(4x^3)

(4)(4) - 16

(x^3)(x^3) - x^6 bc you add the exponents

16x^6 which is correct bc my teacher has checked us on that before in class bc we have had equations like that ^_^

Answer:

Yes.

Step-by-step explanation:

if 6s=24, s = 4 because 6 x 4 = 24

so

6s divided by 6 = 24 divided by 6 because 6 x s = 24

SOO

24 divided by 6 = 24 divided by 6

If in a class of 25 students, 14 are boys and 11 are girls. On a unit test, 6 boys and 6 girls made an A grade. If a student is chosen at random from the class, The probability of choosing a boy or an A student 4 / 5

From the question, we have the following data

Total number of students = 25

The total number of boys = 14

The students that are A male students = 6

Then we would have probability of having an A male student to be:

Total boys + A male students / total

= 14 + 6 / 25

= 4 / 5

Hence the probability is 4 / 5

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Answer:

The highest power of a variable in a function is known as its degree.

Step-by-step explanation:

Examples:

x + 5 is 1st degree, since x is to the power of 1.

5[tex]x^{3}[/tex] + 3x + 5 is 3rd degree.

[tex]x^{21}[/tex] +99 is 21st degree.

An equation for the constant of proportionality is (b) y = kx

From the question, we have the options to represent the given parameters

An equation that represents a constant of proportion passes through the origin

So, we have the following points

(x, y) = (0, 0) and (x, y)

The slope (k) is then calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

k = (y - 0)/(x - 0)

Evaluate the difference

k = y/x

Make y the subject

y = kx

Hence, the constant of proportionality has an equation of (b) y = kx

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So, lets think about the information we are given.

Sammy earns 23,400 in a given year.

In a year, he works 52 weeks.

Per week, he works 30 hours.

Find hours -> find pay.

To find hours, multiply number of weeks by hours

52 * 30 = 1560

He works 1560 hours per year.

To find hourly income, divide total money per year by hours per year.  He makes 15 dollars per hour.

Find $ per week.

Hourly rate by hours per week

15 * 30 =450 per week

Hope this helps :)

Answer:

Sami had an hourly pay rate of $15 an hour

Step-by-step explanation:

Multiply 52 by 30 and you get 1,560, this is the total number of hours sami worked in a year.

If Sami made $23,400 in one year and worked 1,560 hours, you divide the total amount of hours work and total amount of money made to get an hourly pay rate of $15 an hour.

According to algebra, we can break 12 into parts such that each X value when multiplied by 6 gives a total of 72. Thus, the 2nd option is correct.

Divide the quantity "12" into parts (the number of parts is not specified) and multiply each part by 6.

If you don't want to divide 12, the straight forward way is to simply multiply 12 by 6. 12 x 6 = 72

If we decompose 12 into 12 parts,

X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂

In this case X₁ represents the first unit of the number 12. X₂ represents the second unit of the number 12. X₁₂ represents the last unit of the number 12. Therefore, X₁ + X₂ + X₃ + X₄ + X5 + X₆ + X₇ + X₈ + X₉ + X₁₀ + X₁₁ + X₁₂ = 12

Each X value is the number 1. There are 12 locations and each case has its own identity. Multiplying each X value by 6 gives a total of 72.

According to algebra, we can break 12 into parts such that each X value when divided by 6 gives a total of 72. Thus, the 2nd option is correct.

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The statement “A teacher compares the pretests and posttest scores of students” is an example of matched pairs design.

Given data;

A teacher contrasts the results of her class's standardized test with the entire country's results. An instructor contrasts the results of the students' pre-and post-tests. A teacher computes the average grade received by students on two tests and checks to see if it is greater than 80%. An instructor contrasts the results of students who were taught using a computer-based method with those of post-students whose students ought to use a more conventional approach.

⇒

The statement “A teacher compares the pretests and posttest scores of student” using here would be approach-test because the sample “the students’ scores” are being compared with the two different treatments” and pretest and posttest scores.

A matched pairs design is demonstrated with the sentence "A teacher compares the pretests and posttest scores of students."

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Answer:

55x+36y

Step-by-step explanation:

1. Group similar terms: 14x+41x+9y+27y
2. Add: 55x+36y

The domain and range of the function is given by D:{x|∞<x<∞} and

R:{y|∞<y<∞}

In the given graph we can see that the graph is of straight line .

We know that the straight line graph of the function is of the form

y = mx + c

Now we can say that the graph of the given function is of that form.

The graph passes through (-7,0) and (-5,3)

Slope of the line= 3 / 2

Equation of the line is

y-3 = -3/2(x+5)

or, 2y+3x+9 = 0

Here the domain will be all possible values of x and range will be all possible values of y.

Domain : {x|∞<x<∞}  

Range : {y|∞<y<∞}

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.

A is the domain and B is the co-domain if a function f: A →B exists that maps every element in A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R.

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The diameter of his circular field is 18miles

What is sprinkler?

A sprinkler irrigation system is a tool used to irrigate (water) lawns, gardens, golf courses, and other areas. They are also utilised for cooling and dust control in the air. Sprinkler irrigation is a technique for applying water in a way that is similar to rainfall: it is controlled. Pumps, valves, pipes, as well as sprinklers are just a few of the possible components of the network used to distribute the water. Sprinklers for irrigation can be used in residential, commercial, and agricultural settings. Both sandy soil and uneven terrain with insufficient water supply can benefit from it. The rotating nozzle-topped perpendicular pipes are linked to the main pipeline at regular intervals. Water leaks from the rotating nozzles when it is pressurised and forced through the main pipe.

The irrigation sprinkler in this instance is angled.

θ = 50 = 50 π/ 180 rad.

It mists a sphere-shaped area.

A = 2/(2 miles).

If the sprinkler's length is

miles, L. It will be watered within the circle's radius.

Hence,

L^2 = A when divided by two in radians.

⇒ L = √ (2 A / θ)

= √ [(2 x 2 x 180) /40 π]

≈ 18 miles

Hence, The diameter of his circular field is 18 miles

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192.5  the length of the longest side of triangle DEF .

What do you mean by congruent?

Triangle ABC ~ Triangle DEF.

SO, both triangle sides are equal .

7/17.5 = 9/22.5  = 11/x

1/17.5 = 11/x

x = 11 * 17.5

x = 192.5

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Answer:

A: AC/AE = BC/BD

Answer:

hundreds would say the hundreds because they're both in the 8000s and you want to look at the first different digits ihni so i hope this helps

Step-by-step explanation:

Answer:

angle a = 74 degrees

angle b = 106 degrees

angle c = 106 degrees

angle d = 65 degrees

angle e = 65 degrees

Step-by-step explanation:

Angle a:

the Alternate Interior Angles Theorem makes angle a equal to 74 degrees

Angle b:

First find angle c, and angle b is equal to angle c because angle b and c are Corresponding angles

Angle c:

angle c = 180 degrees - 74 degrees

angle c = 106 degrees

Angle d:

angle d corresponds with 65 degrees, therefore the are the same.

Angle e:

angle d and e are opposite angles, therefore they are the same.