The. median, range, and mode for the following numbers:8,7,12,7,11,10,7,12

The equation of the circle with the centre (5,7) and containing the point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]

The equation for a circle in standard form is [tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex]  = [tex]r{2}[/tex], where (x, y) denotes arbitrary coordinates on the circle's perimeter, r denotes the circle's radius, and (x1, y1) denotes the coordinates of the circle's centre.

The equation of a circle with centre (x1,y1)

[tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex]  = [tex]r{2}[/tex]

we know the centre , which is (5,7) so the equation changes to:

[tex](x-5){2}[/tex]+ [tex](y-7){2}[/tex]  = [tex]r{2}[/tex]

putting the values of the point p we get

[tex](1-5){2}[/tex] [tex]+ (9-7){2}[/tex][tex]= r{2}[/tex]

r=[tex]\sqrt{20}[/tex]

so the equation of the circle will be:

[tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]

Therefore the equation that satisfies the given condition of a circle with centre (5,7) and containing point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]

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1.0000 percent is the probability that all 12 flights will arrive on time.

So, the problem meets all requirements for a binomial experiment, written as:

[tex]P(X=x)\left(\begin{array}{l}n \\x\end{array}\right) p^x(1-p)^{n-x}[/tex]

Now, p=0.85 and n=14, the probability that precisely 14 people arrived on time are calculated as follows:

[tex]\begin{aligned}&P(X \geq 1)=1-P(X=0) \\&=1-\left(\begin{array}{c}12 \\0\end{array}\right) 0.85^0(1-0.85)^{12} \\&=1-1.297 \times 10^{-10} \\&=1.0000\end{aligned}[/tex]

Therefore, 1.0000 percent is the probability that all 12 flights will arrive on time.

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The complete question is given below;
Your flight has been delayed: At Denver International Airport, 85% of recent flights have arrived on time. A sample of 14 flights is studied. Round the probabilities to at least four decimal places. Find the probability that all 12 of the flights were on time.

Part 1

[tex)400+30x=4900[/tex]

Part 2

[tex]30x=4500 \\ \\ x=150[/tex]

So, the answer is 150 ft².

We would find the percentage of those knowing neither Hindi nor English in the population using set theory,

Percentage of population knowing English (A) = 46%

Percentage of  population knowing Hindi (B) = 34%

Percentage of population who know both languages (A U B) = 23%

therefore,

Applying set theory,

A U B = A + B - (A ∩ B)

23% = 36% + 46% - ( A ∩ B)

A ∩ B = 80% - 23% = 57% population knows either Hindi OR English.

So, Population who neither know Hindi or English = 100% - 57% = 43%

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The value of d after addition or subtraction is 7.5

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every discipline of mathematics, including trigonometry, calculus, and coordinate geometry.

Given that : the equation is 5.5 = −2+d

5.5 = −2+d

5.5 + 2 = d

7.5 = d

The value of d after addition or subtraction is 7.5

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The correct answer is 20%

We know,

1 m = 100 cm

thus 1.5 m will be 150 cm (1.5 x 100 = 150cm)

now, to find 30 cm as a percentage :

(30/150) x 100

=20 %

Thus, 30cm 1.5 can be expressed, as  20%.

What do you understand by percentage?

percentage- "a relative value indicating hundredth parts of any quantity." Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

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there are no restrictions other than 2 x + 1 > 81 on the radical inequality.

We are given the radical inequality as:

⁴√ 2 x + 1 > 3

We need to find the restriction on this inequality.

For this we will first put x on one side and other constant on the other side.

So, we get that:

2 x + 1 > 3⁴

2 x + 1 > 81

So, the restriction is not from the given options.

But, the value of 2 x + 1 should be greater than 81 for the inequality to be true.

Therefore, we get that, there are no restrictions other than 2 x + 1 > 81 on the radical inequality.

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In a case whereby the area of a trapezoid is given by the formula A=12(b1+b2)h then the equation for b2 is b2= (A - 12hb1)/12h.

The formula for the  trapezoidis given as A=12(b1+b2)h , where the value of term b2 is been exdpected to be found.

firstly, we need to open the bracket as :

A=12(b1+b2)h

A= 12hb1 + 12hb2

Then this can be simplified as  12hb2= (A - 12hb1)

Then we can try to make the b2 the subject of the formula as

b2= (A - 12hb1)/12h.

Therefore, the value of the term b2 can be written as b2= (A - 12hb1)/12h.

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Answer:

It is the setup.

Step-by-step explanation:

Only 6 is negative. The 11 also needs to be negative.

According to the solution Angle 3 is measured at 48 degrees.

Adjacent angles seem to be two angles that share a side and then a vertex but do not overlap at all (corner point). It is clear what is meant when the term "adjacent angles" is broken down; they are just two angles that seem to be close to one another.

Adjacent angles seem to be two angles that do not overlap but share a vertex and a side. In the figure, angles 1 and 2 are close by. Both their common side and vertex are the same.

Angle 3 and angle 132 degrees are nearby angles in this scenario.

Consequently,

angle3 plus 132 degrees equals 180 degrees.

angle 3 = 48 degree

angle 3 = 180-132 degree

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In 13 days they will travel 1904 miles altogether.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

Multiplication in action or in progress. The multiplication of 8 and 3 is the same as the sum of 8+8+8, which is a mathematical operation that takes two numbers and returns an answer that is equal to the sum of a column in which one of the numbers is repeated the amount of times of the other number.

Given Data

they travel 238 miles a day for 13 days

1 day = 238 miles

13 days = 238 (13)

13 days = 1904

In 13 days they will travel 1904 miles altogether.

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A round plane figure whose boundary ( circumference) consists of the points equidistant from a fixed point (the center). In the above question Pedro was wrong.

All the points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in plane draws to keep its distance from a specific point constant.

The tactic Pedro frequently used is ineffective since applying strict transformation to one figure and then onto another will only demonstrate whether the figures are congruent, not whether they are comparable.

Keep in mind that resemblance, as opposed to congruence, is about the proportionality between the dimensions of those figures. Therefore, when we overlay the figures, they won't match.

Pedro should divide each set of matching coordinates to demonstrate similarity; if all divisions provide the same outcome, the figures are said to be comparable.

Therefore, Pedro was not wrong.

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Answer: 33.6

Step-by-step explanation:

Answer:

33.6

Step-by-step explanation:
4.20 x 8 = 33.6

The number of pipes that are made of chrome according to the prediction by Patty are 120.

It is given in the question that :-

Number of pipes in stock at Patty's hardware store = 600

Number if pipes randomly selected by Patty = 40

Number of pipes of chrome = 8

Hence, we can write,

Probability of chrome pipes = 8/40 = 1/5

Therefore, we can write,

Number of pipes that are made of chrome according to the prediction by Patty = (1/5)*600 = 120

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

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Answer:25.8184143223

1+1+278*67/782

1+1+18626/782

2+23.8184143223

25.8184143223

1. Month for assistance caregivers is 14 months.

Month for senior caregivers will be 14 months.

2. After 2 month, there will be 14 of each types of caregiver.

What is an expression?

Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.  

Given that;

A daycare center in Hillsdale currently has 12 assistant caregivers and 6 senior caregivers.

On high demand the owner is going to be hiring 1 assistant caregiver per month and 4 senior caregivers per month.

Let m is number of months.

Then, Each month has 12+ m for assistant caregivers and 6 + 4m for senior caregivers.

By given condition we formulate;

12 + m = 6 + 4m

12 - 6 = 4m - m

6 = 3m

3m = 6

m = 2

Thus, 12 + m = 12 + 2 = 14

And, 6 + 4m = 6 + 4 x 2 = 14

So, After 2 month, there will be 14 of each types of caregiver.

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The distance when F = 0.029 based on the computation is 5.1 meters.

From the information, the force, F between two objects is inversely proportional to the square of the distance.

This willilk be illustrated as:

F = k / D²

We will find the value of k. This will be:

F = k / D²

0.084 = k / 3²

0.084 = k / 9

Cross multiply

k = 9 × 0.084 = 0.756

Therefore, the distance when F = 0.029 will be:

D² = k / F

D² = 0.756 / 0.029.

D² = 26

D = ✓26

D = 5.1

The distance is 5.1 meters.

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Answer:

0.3,1/2,26%

Step-by-step explanation:

ascending order if arranging from smallest to highest .In this case, 0.3 Is the smallest followed by 1/2 and then 26%.

The unit rate is 10 minutes per meters.

What is rate of time?

Time is in units of seconds, minutes, hours, or years. Rate is distance per time, so its units could be mph, meters per second, or inches per year.

rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute.

Given,

she fills 4/5 meters in 8 minutes.

let x be the time she fills minutes per liter.

4/5 meters ⇔ 8 minutes

1 meter ⇔ x minutes

Cross multiplying

4/5*x = 1*8

x = 5*8/4

x = 10 minutes

The unit rate is 10 minutes.

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2.5 m/s²  is the distance between the traffic lights .

Defining acceleration Short response?

   from the picture V = 15 m/s

                           t = 6 sec

  a = Δv/Δt  = 15/6  ⇒ 2.5 m/s²

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The most appropriate choice for similarity of figures will be given by

Volume of cylinder B is 720 [tex]cm^2[/tex]

What is similarity of figures?

Two figures are said to be similar if they have same shape but different sizes.

Actually sides of similar figures are proportional

Ratio of heights of cylinder A and B = 5 : 10

                                                            = 1 : 2

Ratio of areas of cylinder A and  cylinder B = [tex]1 ^2 : 2^2[/tex]

                                          = 1 : 4

Area of cylinder A = [tex]18[/tex] [tex]cm^2[/tex]

Area of  cylinder B = [tex]18 \times 4\\[/tex]

                                = [tex]72[/tex] [tex]c[/tex][tex]m^2[/tex]

Height of  cylinder B = [tex]10 cm^2[/tex]

Volume of cylinder B = Area of cylinder B [tex]\times[/tex] Height ofcylinder B

                     = [tex]72 \times 10[/tex]

                     = [tex]720[/tex] [tex]cm^2[/tex]

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Complete Question

The image of the question has been attached with this question.

Step-by-step explanation:

Splitting the middle term

8a^2 +16a + 2a+4 =0

8a (a+2) +2(a+2) = 0

(8a+2) (a+2)

8a=-2 , a = -2

a= -2/8

a= -1/4

a ( -1/4 , -2)

The dimensions of the college basketball court with a perimeter of 96 meters are:

The dimensions of a rectangular perimeter, like a basketball court, are the two sides (length and width).

The perimeter of a rectangle measures the four sides, that is, the two long sides and two wide sides.

The perimeter is given by the perimeter equation, P = 2(a+b).

The perimeter of the basketball court = 96 meters

The perimeter = 2(Length + Width)

2(Length + Width) = 96 meters

Length = 14 meters more than the width

The total difference of the two lengths = 28 meters (14 x 2)

Width = 17 meters (96 - 28)/2

Length = 31 meters (17 + 14)

Check:

Perimeter = 2(Length + Width)

96 meters = 2(31 + 17)

96 = 62 + 34

96 = 96

Thus, the college basketball court with a perimeter of 96 meters has the following dimensions: 31 meters in length and 17 meters in width.

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The total terms that in the following sequence 7, 10, 13,..., 391, 394 is 130

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + (n-1)d

Where;

a = 7

Tn = 394

d = 3

Substitute the value in the formula, we have;

394 = 7 + ( n -1) 3

expand the bracket

394 = 7 + 3n - 3

collect like terms

394 - 4 = 3n

find the difference

390 = 3n

Make 'n' the subject of formula

n = 390/3

n = 130

Hence, the number is 130

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Answer:

Mike is not correct.

Step-by-step explanation:

The opposite of 5 is in fact -5, but the absolute value of 5 is not -5. The absolute value of 5 is 5.

hope this helps. . .....

The cost of the polishing, £C, is given by C = 6πr² + 300/r​.

The volume of the solid cylinder is 75 m³.

Formula for volume of cylinder = πr²h.

Where R is rhe radius of cylinder and h is the height of the cylinder.

So we can write,

πr²h = 75

h = 75/πr².

So the height of the cylinder is 75/πr² centimeters.

Curved surface area of the cylinder is 2πrh m².

Cost of polishing the curved surface area is £2/cm².

Total cost of polishing the curved surface area = £2×2πrh

Area of the base and the top is 2(πr²).

Cost of polishing base and top is £3/cm².

Cost of polishing 1m² of the base and top,

Cost of area of base and top = £3/cm².

Total Cost of polishing base and top area = £3×2(πr²)

The total cost C of polishing the whole glass,

C = 4πrh + 6πr²

Puting the value of h = 75/πr²

C = 4πr(75/πr²) + 6πr²

C = 6πr² + 300/r.

Hence it is proved that the total cost of polishing is,

C = 6πr² + 300/r.

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Answer:

82°

Step-by-step explanation:

 The exterior angle of triangle equals the sum of opposite interior angles.

 ∠C + ∠B = 143°

  61+ ∠B  = 143

         ∠B  = 143 - 61

         ∠B = 82°

Answer:

i Used the standard form to find the vertices.

Vertex

1: (5,−1+4√2)

Vertex

2: (5,−1−4√2)

Step-by-step explanation: