Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new housing project to a processing plant The city does not want the sewer line to cross the farm land. Can a direct line be installed?
● Let 1 unit = 100 feet.
● The entry to the sewer plant is at (2,3)
● The sewage exit from the housing project is at (12,6)
● The sprinkler system extends 200 ft and the center of the land is at (8,3)
Questions: (1) Will the sewer line cross the farmland? If so then at what points?
(2) If the farmer wants to maximize the farming area and does not want to cross the sewer line, what is the longest sprinkler system that could be installed?

Answer: 47°

Step-by-step explanation:

Answer:

standard deviation sign is σ

mean sign is x , and sometimes it have a hyphen directly above x.

Step-by-step explanation:

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

It is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list. To find the mean, add up all the values in the set. Then divide the sum by how many values there are.

The symbol ∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern.

21 % is the answer.

Problem is that the height of this plant 6.3 and 7.8 cm

P (6.3 <x< 7.8)

12 -5 = 7cm

7.8 - 6.3 = 1.5cm

1.5 / 7 = 0.21

=21%

Probability is a field of mathematics that deals with the numerical description of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the impossibility of the event and 1 indicating certainty.

Probability is a measure of the likelihood that an event will occur. Many events cannot be predicted with absolute certainty. You can only predict the probability that an event will occur.

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Answer:

555 m

Step-by-step explanation:

Because the model should have identical proportions to the real-life tower, the ratio between the height and shadow length of both diagrams should be the same.

Height (model)             Height (real)
-------------------------  =  ------------------------
Shadow (model)         Shadow (real)

Math:

 0.9 meters                   x
--------------------  =  ----------------------               <----- Ratio
 0.2 meters           123.3 meters

4.5 = x / 123.3 meters                                  <----- Divide 0.2 from 0.9

555 meters = x                                            <----- Multiply both sides by 123.3

Answer:

1)  4x + 5y = 20         4x + 5y = 20  

  -2x + 3y = 12  -->  2(-2x + 3y) = 2(12)

2) 4x + 5y = 20  

  -4x + 6y = 24

3) 4x + 5y = 20  

   -4x + 6y = 24

   0x + 11y = 44

4) 11y = 44

5) y = 4

6) 4x + 5y = 20  

   4x + 5(4) = 20  

7) 4x + 20 = 20

8) 4x = 0

9) x = 0

10) The solution is the point (0, 4)

The probability that they win both contracts is 33% if there is a 45% probability of winning the first contract and the probability of winning the second contract after winning the first contract.

Probability is the rate of successful outcomes to the total outcomes of an event.

P(E) = n(E)/n(S)

Where E -event, n(E) - successful/favorable outcomes of event E, and n(S) - total outcomes of the event.

It is given that,

An aerospace company has submitted bids on two separate federal government defense contracts.

The probability of winning the first contract is - 45%

The probability of winning the second contract if they win the first contract is  - 73%

The probability of winning the second contract if they lose the first contact is - 45%

So, the probability that they win both contracts is

= (probability of winning the first contract) × (probability of winning the second contract)

= 0.45 × 0.73

= 0.3285 ≅ 0.33

⇒ 33%

Therefore, the probability that they win both contracts is 33%.

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The polynomial expression that represents the profit of selling x tablets is 10x - 100

profit = revenue – cost

= (100 + 30x) - (20x + 200)

= 100 + 30x - 20x - 200

Profit = 10x - 100

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Answer:

Option D is correct

Step-by-step explanation:

there were no corn muffins sold.

Answer:

No corn muffins were sold at the bake sale :)

Step-by-step explanation:

Lets go thru each answer choice to see why it is incorrect/correct :)

A.

A is incorrect because more cookies were sold than muffins! that is why A is incorrect :)

B.

This calls for adding! lets do that now :)

Chocolate chip: 5

Oatmeal: 1

Peanut: 3

6 + 1 + 3 = 10

10 < 11

10 is not greater than 11 so B is incorrect!! :)

C.

We need to add again so lets do that now!

Corn: 0

Muffin: 2

2 + 0 = 2

2 < 3

2 is less than 3 so C is incorrect!! :)

D.

It is true that 0 corn muffins were sold at the bake sale so D is our answer!! :D

Have an amazing day!!

Please rate and mark brainliest!!

The total number of bars of kitkat Mr hassell had in total is 3 1/2 bars

Total bars of KitKat = 6 × 3/4

= (6×3)/4

= 18/4

= 9/2

= 4 1/2 bars

Number of bar remaining after eating 1 bar = 4 1/2 - 1

= 3 1/2 bars

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Using the dimensions of a reduced rectangle and one given measurement of an original rectangle:

Reduction is a type of dilation that reduces the size of an original figure to form a new figure that is similar to the original. The corresponding lengths of both figures are therefore proportional.

Assuming the dimensions of the reduced rectangle are 10 cm by 4 cm, and the length of the original rectangle is given as 8 cm, to find the missing measure (x), do the following:

Set up a proportion using the corresponding parts

10/8 = 4/x

Solve the proportion using cross products to find x:

10x = (8)(4)

10x = 32

x = 32/10

x = 3.2 cm

The missing length is 3.2 cm.

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Answer:

Using the given measurements of both figures, set up a proportion that has the corresponding parts in the same position. Then solve the proportion using cross products to find the value for the unknown.

Step-by-step explanation:

Answer:

large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 la

or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, Root Tissues

Identify the root tissues. Record your answer under "Slide 5" on your lab report.

Answer:

Step-by-step explanation:

A cone has a circular base. So, the answer to your question is B for circle.

Using the unit circle, the coordinates of the terminal point corresponding to [tex]\theta = 120^\circ[/tex] is: (-0.5, 0.866).

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

In this problem, the angle is of [tex]\theta = 120^\circ[/tex], hence:

Hence the terminal point is:

(-0.5, 0.866).

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Answer:

(-4,-4)

Step-by-step explanation:

If the point is moved 2 units to the rights then we add 2 to the x value: -6+2 = -4

(-4,-4)

Answer:

1. (x + 8)(x + 3)

2. (x - 9)²

Step-by-step explanation:

Given trinomials:

1. [tex]x^2+11x+24[/tex]

2. [tex]x^2-18x+81[/tex]

..................................................................................................................................................

When factoring trinomials of the form ax² + bx + c:

..................................................................................................................................................

1) x² + 11x + 24

Step 1: Multiply the leading coefficient (1) and the last term (24).

[tex]\implies 1 \times 24 = \boxed{24}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (11).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:24 & \sf Sum\:of\:factors\\\cline{1-2} 1, 24\ \| -1, -24 & 25\ \| -25 \\\cline{1-2} 2, 12\ \| -2, -12 & 14\ \| -14 \\ \cline{1-2} 3, 8\ \| -3, -8 & 11\ \| -11 \\\cline{1-2} 4, 6 \ \| -4, -6 & 10\ \| -10 \\\cline{1-2}\end{array}[/tex]

[tex]\implies 3x+8x=11x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2+3x+8x+24[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2+3x)}^x+\overbrace{(8x+24)}^8\ \ \textsf{[ Factor out $x$ and $8$. ]}[/tex]

[tex]\implies x\overbrace{(x+3)}^{\textsf {Factor out}}+8(x+3)[/tex]

[tex]\implies \boxed{(x+8)(x+3)}[/tex]

The factored form of the given trinomial is [tex](x+8)(x+3)[/tex].

..................................................................................................................................................

2) x² - 18x + 81

Step 1: Multiply the leading coefficient (1) and the last term (81).

[tex]\implies 1 \times 81 = \boxed{81}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (-18).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:81 & \sf Sum\:of\:factors\\\cline{1-2} 1, 81\ \| -1, -81 & 81\ \| -81 \\\cline{1-2} 3, 27\ \| -3, -27 & 30\ \| -30 \\ \cline{1-2} 9, 9\ \| -9, -9 & 18\ \| -18 \\\cline{1-2}\end{array}[/tex]

[tex]\implies (-9x)+(-9x)=-18x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2-9x-9x+81[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2-9x)}^x+\overbrace{(-9x+81)}^{-9}\ \ \textsf{[ Factor out $x$ and $-9$. ]}[/tex]

[tex]\implies x\overbrace{(x-9)}^{\textsf {Factor out}}-9(x-9)[/tex]

[tex]\implies (x-9)(x-9)[/tex]

[tex]\implies \boxed{(x-9)^2}[/tex]

The factored form of the given trinomial is [tex](x-9)(x-9)\ \textsf{or}\ (x-9)^2[/tex].

A certain journey by train takes 5 hours at the speed of 45 km/h. What will be the speed of the train to complete the same journey in 3 hours?

Answer:

Journey taken time 5 hour at speed of 45km/hr

So,

 1 hour=45/5=9km/hr

Therefore,3 hour=(9x3)km/hr.

(please mark me brainliest if my answer was good)

The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2

We want to find the equivalent quotient of the given expression; √16 / √8

Now, we know that the square root of 16 is equal to 4 i.e. √16 = 4

Thus, applying that to our expression gives;

√16/√8 = 4/√8

Now, square root of 8 which is √8 can also be expressed as; 2√2

Thus;

4/√8  = 4/2√2 = 2/√2

The steps to rationalize the denominator, to get rid of all radicals that are in the denominator are as follows;

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.

Step 2: Make sure all radicals are simplified.

Step 3: Simplify the fraction if needed.

If we rationalize the denominator of our expression, we have;

2/√2 × √2/√2 = 2√2/ 2 = √2

Also, 2/√2 can be expressed as √4 /√2

Therefore, The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2

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The price of the turkey based on the percentage given is $15.81.

It was stated that the cost is $15.50 but that there was a 2% increment in price.

Therefore, the new price will be:

= $15.50 + (2% × $15.50)

= $15.50 + $0.31

= $15.81

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The length of the side QR in the task content can be determined as; 12.22cm.

It follows from the task content that 2 lengths and one included angle are given in the task content. It therefore follows that the length of side QR can be evaluated by the cosine rule as follows;

QR² = 13² + 4² - (2×4×13×cos70)

QR = √149.4

QR = 12.22cm

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Answer:

no

Step-by-step explanation:

Take the prime factorization of [tex]x[/tex].

[tex]x = 7\times24\times48 = 7\times(2^3\times3)\times(3\times2^4) = 2^7\times3^2\times7[/tex]

If [tex]xy[/tex] is a perfect cube, then the smallest [tex]y[/tex] that makes this happen is [tex]y=2^2\times3\times7^2 = \boxed{588}[/tex]. We "complete" the cube by introducing just enough factors to get each prime power to be a multiple of 3.

Answer: 588

Step-by-step explanation:

Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -10/2(-1)

Xmax = 5.

Thus, the maximum height on the vertical axis is given by:

h(x) = -x² + 10x + 9.5

h(5) = -(5)² + 10(5) + 9.5

h(5) = -25 + 50 + 9.5

h(5) = 34.5 feet.

Therefore, the spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.

Also, the spray reaches all the way to the ground at about:

Maximum distance = √34.5 + 5

Maximum distance = 10.87 feet.

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Complete Question:

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.

1. The irrigation system is positioned____ feet above the ground to start.

2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.

3. The spray reaches all the way to the ground at about_____ feet away​

Answer:

2x⁴-45x-8

Step-by-step explanation:

Answer:

222

Step-by-step explanation:

Hey there!

250 - {(135 + 34) ÷ (46 - 33)} - 15 

= 250 - 169/(46 - 44) - 15

= 250 - 169/13 - 15

= 250 - 13 - 15

= 237 - 15

= 222

Therefore, your answer should be:

222

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The quantity with the fewest number of significant figures.

What is significant figures?

When multiplying two measured values the number of significant figures should be equal to the?

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Triangle ABC is dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Triangle ABC has vertices at A(-3, -1), B(2, -2) and C(-1, -4). It is then dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)

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Rosa is providing home-based tutoring.

What is Home-based tutoring?

Therefore, Rosa is providing home-based tutoring.

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Answer:

<x = 55 degrees

<y = 55 degrees

<z = 70 degrees

Step-by-step explanation:

The 125 degree angle and x are supplementary since they form a straight line, which means that their degrees add up to 180. To find x, the interior angle, we must subtract 125 from 180.

180 - 125 = 55

Angle x is 55 degrees. Since the sides opposite x and y are marked with lines, they are congruent, and since the sides are congruent, the angles must be, too. So, y is also 55 degrees.

Finally, the angles in any triangle add up to 180 degrees. To find z, we must subtract the values of x and y from 180.

180 - 55 - 55 = 70, so z is 70 degrees.

Brainliest, please :)

❄Hi there,

the external angle & the interior angle form a linear pair, which means, if you add these angles together, you'll arrive at 180°.

Using this knowledge let's set up an equation and find x:

[tex]\triangleright \ \sf{125+x=180}[/tex]. We let x be the desired angle.

[tex]\triangleright \ \sf{x=180-125=55}[/tex]

So the interior angle is [tex]\angle\sf{55}\textdegree[/tex].

❄