An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. The yard has 3 sprinkler heads that each cover a circular area with no overlap. What is the approximate total area that will be watered? 1963. 5 ft 1963. 5 ft² 5890. 5 ft 5890. 5 ft².

Using the z-distribution, the 95% confidence interval is (0.1279, 0.1921), and it means that we are 95% sure that the proportion for the entire population is between these two values.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem:

Hence:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.16 - 1.96\sqrt{\frac{0.16(0.84)}{500}} = 0.1279[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.16 + 1.96\sqrt{\frac{0.16(0.84)}{500}} = 0.1921[/tex]

The 95% confidence interval for the true proportion of households that have experienced property damage due to crime is (0.1279, 0.1921), and it means that we are 95% sure that the proportion for the entire population is between these two values.

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Rotation involves moving the rectangle ABCD around a fixed point

The length of side A'B' is 4 units, if AB was 4 units

From the question, we have the following transformations

Both transformations are rigid transformations, and they do not change the length of the shape

Hence, the length of side A'B' is 4 units, if AB was 4 units

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The value of ac is 36 and the value of b is 13. Then the value of ac + b is 49. The two numbers are 4 and 9.

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

Consider the trinomial 6x² + 13x + 6.

Compare with the standard equation, we have

ax² + bx + c

Then we have

a = 6

b = 13

c = 6

The product of ac will be

ac = 6 × 6 = 36

The sum of ac and b will be

ac + b = 36 + 13 = 49

The two numbers that have a product of ac and a sum of b are 4 and 9.

More about the polynomial link is given below.

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Answer:

36,13,9

Step-by-step explanation:

Just took the test 2022

The computation of the angle given simply shows that the value of angle x is 109°.

From the information given, it can be noted that two numbers are given and there's a subtraction sign between the numbers given.

Therefore, in this scenario, one simply just has to subtract the numbers. Therefore, thus goes thus:

x = 304 - 115

x = 189

The value of x is 189°.

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Answer:

x=1

Step-by-step explanation:

3x1+2=5

Answer:

I'm assuming you're trying to find x.

In this problem, x = 1

Step-by-step explanation:

3x + 2 = 5

    -2     -2    Subtract 2 from each side

3x = 3

3x/3 = 3/3    Divide each side by 3

x = 1

Answer:

Solving steps:

18) 16a²b - 8abc + 4ab²c²

=> 4ab(4a - 2c + bc²)

19) 3x³ + 3x² - 3x

=> 3x(x² + x - 1)

20) 2abx² + 3abx³ - 4abx[tex] {}^{4} [/tex]

=> abx²(2 + 3x - 4x²)

Answer:

x = 1.28t^2 > 5.5

Answer:

[tex]t\le \:7.04[/tex]

Step-by-step explanation:

[tex]1.28\ge \cfrac{t}{5.5}\:(\bold{Switch \: sides})[/tex]

[tex]\cfrac{t}{5.5}\le \:1.28[/tex]

[tex]\cfrac{5.5t}{5.5}\le \:1.28\cdot \:5.5\:(\bold{ Multiply\: both\:sides\:by\: 5.5})[/tex]

[tex]t\le \:7.04[/tex]

~

A) x=6

B) 50

Step-by-step explanation:

[tex]8x + 2 + 70 + 60 = 180[/tex]

[tex]8x = 180 - 132[/tex]

[tex]8x = 48[/tex]

[tex]x = 6[/tex]

~

[tex] \angle \: b = 8x + 2[/tex]

[tex]8(6) + 2[/tex]

[tex]50[/tex]

[tex] \angle \: b = 50[/tex]

~

Answer:

On average, 2 out of 10 adults visited the museum most frequently

Step-by-step explanation:

Answer:

KL = 3.4

Step-by-step explanation:

[tex]\frac{LI}{HE} =\frac{KL}{HG}[/tex]

[tex]\frac{5}{16} =\frac{KL}{11}[/tex]

[tex]KL=11(\frac{5}{16} )=55/16=3.4375[/tex]

Hope this helps

Answer:

54:45

6:5

this is the scale factor

Answer:

A, C, and D, are correct

Step-by-step explanation:

We can find the answer to each of these by simply doing the math for each one

[tex]3*\sqrt{2} = 4.24\\\frac{1}{2} *\sqrt{68} = 4.123\\\sqrt{17} = 4.123[/tex]

Answer:

A, C, and D

Step-by-step explanation:

A is 4.24

B is 3.54

C is 4.12

D is 4.12

E is 5.29

Answer:

Part A: 18 cups

Part B: 56 biscuits

Part C: $0.16

Step-by-step explanation:

Part A

72 * 1/4 = 18

Part B

18 total cups/ 2 cups/biscuit = 9 cups able to be used (dk how else to explain it)

6 * 9 = 56 biscuits

Part C

$6.48/56 = $0.16

Answer:

3.6g

Step-by-step explanation:

the protein thats in 125g of yoghurt is 4.5g

the protein thats in 1g of yoghurt is 4.5/125

the protein thats in 100g of yoghurt is

4.5/125 x 100

0.036 x 100

3.6g

Answer:

1

Step-by-step explanation:

What ever is in the parenthesis needs to be substituted into the equation

So,

3(-2)  + 7 =

-6 + 7

1

f(-2) = 1

Answer:

f(-2) = 1

Step-by-step explanation:

1. Replace x with -2

f(-2) = 3(-2) + 7

2. Multiply 3 by -2

f(-2) = -6 +7

3. Add -6 and 7

-6 + 7 = 1

f(-2) = 1

Answer:

Step-by-step explanation:

Answer:

B = 48°

b = 29.7

c = 39.1

Step-by-step explanation:

You have made a Mistake which is C = 102° Not 120°

So, Lets begin with the Problem

Since the Sum of Interior Angles of the Triangle = 180 °

Then A+B+C=180

Then 30+B+102=180

Then  B+132=180

Subtract 132 from Both sides

B = 180 - 132 = 48°

Applying Law of Sines

[tex]\frac{a}{sinA} =\frac{b}{sinB}=\frac{c}{sinC}[/tex]

by substituting

[tex]\frac{20}{sin30} =\frac{b}{sin48}=\frac{c}{sin102}[/tex]

Then   [tex]b=\frac{20sin48}{sin30} =29.7[/tex]

Then   [tex]c=\frac{20sin102}{sin30} =39.1[/tex]

Answer:

x=4

Step-by-step explanation:

both angles add up to 90* because it is a right angle

10x + 12x + 2 = 90

22x + 2 = 90

subtract 2 from both sides of the equation

22x = 88

divide both sides by 22

x = 4

System of equations helps to solve real-life problems. The system of equations will not have no solution.

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

The two of the system of equations given to us are,

[tex]y+x=19-x^2[/tex]

[tex]x+y = 80[/tex]

Now,

1. The first step is to isolate one variable in the system of equations,

[tex]y=19-x^2-x[/tex]

[tex]y=80-x[/tex]

2. The second step is to substitution to create a one-variable equation.

[tex]80-x=19-x^2-x\\x^2-x+x=19-80\\x^2 = -61[/tex]

Now, since the value of x  is the negative square root. therefore, the system of equations will not have a real number of solutions.

If we plot the two equations on the graph, then the line of the system of equations will not intersect any point, therefore, the system of equations will have no solution.

Hence, the system of equations will not have no solution.

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Answer:

0 solutions

Step-by-step explanation:

Edge 2022

Answer:

65°

step-by-step explanation:

solve for x:

116x - 1 = 114x + 1

116x - 114x = 1 + 1

2x = 2

x = 1

Find angle C:

m∠C + 116(1) - 1 = 180°

m∠C = 180° - 115

m∠C = 65°

Solution:

We know that:

This means that:

Step-1: Find the value of x.

[tex]116x - 1 = 114x + 1[/tex]

[tex]\rightarrow 116x - 114x = 1 + 1[/tex]

[tex]\rightarrow 2x = 2[/tex]

[tex]\rightarrow \bold{x = 1}[/tex]

Step-2: Solve for ∠C.

[tex](116x - 1) + (114x + 1) + \angle C + \angle C = 360\°[/tex]

[tex]\rightarrow (116x - 1) + (114x + 1) + \angle C + \angle E = 360\°[/tex]                           [∠C = ∠E]

[tex]\rightarrow 116x - 1 + 114x + 1 + 2\angle C = 360\°[/tex]                                  

[tex]\rightarrow 230x + 2\angle C = 360\°[/tex]                                        

[tex]\rightarrow 230(1) + 2\angle C = 360\°[/tex]                                                                 [x = 1]

[tex]\rightarrow 230 + 2\angle C = 360\°[/tex]                                                                          

[tex]\rightarrow 2\angle C = 360 - 230[/tex]

[tex]\rightarrow 2\angle C = 130[/tex]

[tex]\rightarrow \boxed{\bold{\angle C = \frac{130}{2} = 65\°}}[/tex]                                                      

Answer:

grafic 2

Step-by-step explanation:

Using proportions, it is found that about 175 trees are oak.

A proportion is a fraction of a total amount.

For the four samples, the proportions are: {0.3, 0.15, 0.26, 0.29}.

Hence, the mean proportion is given by:

M = (0.3 + 0.15 + 0.26 + 0.29)/4 = 0.25

Out of 700 trees:

700 x 0.25 = 175.

About 175 trees are oak.

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Answer:

About 5 meters

Step-by-step explanation:

v= πr² h/3

r= √3 v/πh= 3•314/ π•12= 4.99873 rounded which then rounds to 5

Answer:

y=2x-1

Step-by-step explanation:

Since it is parallel to y=2x-5, they have the same slope of 2.

Now you're going to plug the point and slope into the following equation: y-(y value of point) = slope ×(x-(x value of point))

y-5= 2 (x-3)

Now you simplify:

y-5=2x -6

y=2x-1

Answer:

x=-3 im pretty sure

Step-by-step explanation:

so if y=4 and 4 is something plus 7, 7+-3=4 so im abut 98% its -3