A circular swimming pool is 12 feet across and is enclosed by a fence. How long is the fence? (Round your answer to one decimal place.)

Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Answer:

histogram

Step-by-step explanation:

The difference in the addition of both fractions is that they have different lowest common multiples.

We want to add the fraction expression given as:

¹/₂ + ¹/₄

Taking the Lowest common multiple of 8, we have:

(4 + 2)/8 = 6/8

However, for the second fraction expression, we have:

¹/₂ + ¹/₃

Taking the lowest common multiple which is 6, we have:

(3 + 2)/6 = 5/6

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The distance, In feet, from the base of the ladder to the base of the wall is 4.2 ft.

He needs to move the ladder 0.1 ft closer to the base of the building.

The situation forms a right angle triangle.

Right angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.

The length of the ladder is the hypotenuse of the triangle formed. Therefore, the distance, In feet, from the base of the ladder to the base of the wall can be calculated as follows;

cos 65° = adjacent / hypotenuse

cos 65° = d / 10

d = 10 × 0.42261826174

d = 4.22618261741

d = 4.2 ft

She needs to move the ladder so it reached a window 9.6 feet above the ground. Therefore, the distance from the base of the ladder and the wall is as follows;

cos 65 = d / 9.6

d = 9.6 × 0.42261826174

d = 4.05696

d = 4.1

Therefore, he needs to move the ladder 0.1 ft closer to the building.

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A (-12, 14)

B (8, 8)

C (-12, -4)

D (0, -14)

E (14, 0)

F (0, 0)

Answer:

A (-12,14)

B ( 8,8)

C (-12,-4)

D (0,-14)

E (14,0)

F (0,0)

Step-by-step explanation:

(X,Y)

X coordinates go before Y coordinates in a given coordinate pair hope this helps!

Answer:

1. 232.35 cm²

2. 52.81 cm²

3. 373.25 cm²

Step-by-step explanation:

1. Area of circle = πr²

radius (r) = 8.6

Area = π*8.6²

Area = 232.35 cm²

2. Area of circle = πr²

radius (r) = 4.1 cm

Area = π*4.1²

Area = 52.81 cm²

3. Area of circle = πr²

radius (r) = 10.9 cm

Area = π*10.9²

Area = 373.25 cm²

The height of domino #7 is approximately 6.89 cm tall.

The formula for the nth term of a geometric progression is:

\(a_n = a * r^(^n^-^1^)\)

where:

a is the first term (the height of the smallest domino, 4.00 cm),

r is the common ratio (the growth rate, 1.12), and

n is the term number (for domino #7, n = 7 + 1 = 8, because the sequence starts with domino #0).

Let's plug these values into the formula:

\(a_8 = 4.00 cm * (1.12)^7\)

(Note that we're using 7, not 8, because the first domino is #0, not #1.)

Now, compute the value:

\(a_8 = 4.00 cm * (1.12)^7\)

=  6.89 cm

So, domino #7 is approximately 6.89 cm tall.

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Answer:

16 boxes will be needed for 122 books.

Step-by-step explanation:

Given that,

Each box can hold 8 books.

We need to find the number of boxes needed for 122 books. It can be calculated as follows :

\(\dfrac{122}{8}\) = 15.25

It means 15 boxes can be filled and 16 boxes will be needed for 122 books.

The number of Jim's model car is 48

From the question, we have the following parameters that can be used in our computation:

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

huh?

Step-by-step explanation:

Reflect over the y-axis, reflect over the x-axis, rotate 180°

A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting a figure in a line or a point.

Every point of a figure is translated to an image across a fixed line via a reflection. The fixed line is referred to as the reflection line.

Given:

ABCD is a triangle which is being reflected. with coordinates

A(-4, 1)

B( -3, 2)

C( -1, 2)

D(0 ,1)

First,

Rotate 180°, reflect over the x-axis, reflect over the line y=x

the last transformation should be : reflect with respect to the y-axis

Second, Reflect over the x-axis, rotate 180°, reflect over the x-axis

the transformation should be : reflect with respect to the y-axis

Third,

Rotate 180°, reflect over the y-axis, reflect over the line y=x

last transformation should be : reflect with respect to the x-axis

Fourth,

Reflect over the y-axis, reflect over the x-axis, rotate 180°

last transformation should be : rotate 180° CORRECT!

Hence, Reflect over the y-axis, reflect over the x-axis, rotate 180°

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Answer:

a) 3:4

b) It is proportional because for the glacier advances 3 feet every 4 days in both January and February

Hope this helps!

As a result, the experimental probability of landing on heads is 48%, probability which means that we should expect heads approximately 48 times out of 100 coin flips.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.

The following formula can be used to calculate the relative frequency or experimental probability of landing on heads:

Number of Heads / Total Number of Flips = Experimental Probability of Heads

The number of heads in this case is 48, and the total number of flips is 100. Therefore,

Heads Experimental Probability = 48 / 100 = 0.48

We can multiply this by 100 to get a percentage:

Heads Experimental Probability = 0.48 * 100 = 48%

As a result, the experimental probability of landing on heads is 48%, which means that we should expect heads approximately 48 times out of 100 coin flips.

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The x and y intercepts of the given graph of the function are 3/2 and -1 respectively.

Intercepts of the line

The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called the x-intercept. If a point crosses the y-axis, then it is called the y-intercept.

Given equation of the line:

y = (2/3)x - 1

To find the y -intercept, putting x = 0, we get,

y = (2/3)*0 - 1

y = 0 - 1

y = -1

Hence, the y - intercept is -1.

To find the x -intercept, putting y = 0, we get,

0 = (2/3)x - 1

1 = (2/3)x

x = 3/2

Hence, the x - intercept is 3/2.

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The surface area of the triangular prism is B. 1,008 \(cm^{2}\)

Triangular Prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.

How to determine this

The surface area of the triangular prism =  Area of the front Triangle + Area of the triangle + Each sides of the triangle by the length of the triangular prism.

Area of the front and back triangle will be the the same given the same base and height

To find the area of the triangle = 1/2 * Base * Height

Where base = 12 cm

Height = 9 cm

Area = 1/2 * 12 cm * 9 cm

Area = 6 * 9 \(cm^{2}\)

Area of the one triangle = 54 \(cm^{2}\)

So, by multiplying each sides of the triangle by the length

= Base * Length

= 12 cm * 25 cm

= 300\(cm^{2}\)

Height * Length

= 9 cm * 25 cm

= 225 \(cm^{2}\)

Then, Hypotenuse * Length

= 15 cm * 25 cm

= 375 \(cm^{2}\)

Surface area = 54\(cm^{2}\) + 54\(cm^{2}\) * 300\(cm^{2}\) + 225\(cm^{2}\) + 375\(cm^{2}\)

Surface Area = 1,008\(cm^{2}\)

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When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

What is division?

A division in mathematics is the process of dividing a specific amount into equal parts. The division is the inverse of multiplication.

We can find a division fact if we know a multiplication fact: For instance, 3 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Here given that,

We have to divide 87/7,

By dividing,

we know that 8/7 gives reminder 1, and a quotient of 1.

Then divide 14 by 7,

which gives reminder 0 and quotient 2.

So by dividing 84 / 7 we get reminder 0 with a quotient of 12.

Therefore the correct option is option A. With a quotient of 12.

Hence, When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

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The stars in order from the closest one to the farthest one are:

0.883, 0.886, 0.89, 1.25

so, the answer is A.

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

To put the given distances in order from the closest one to the farthest one, we need to arrange them in ascending order.

That means we need to start with the smallest value and move toward the largest value.

Looking at the given distances, we see that the smallest value is 0.883, followed by 0.886, then 0.89, and finally 1.25, which is the largest value.

Putting the given distances in ascending order, we get:

0.883, 0.886, 0.89, 1.25

Therefore, the stars in order from the closest one to the farthest one are:

0.883, 0.886, 0.89, 1.25

so, the answer is A.

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The answer to your question is DG.

Answer:

acute angle

Step-by-step explanation:

Answer:

Acute Angle!

Step-by-step explanation:

Picture in 1st answer! <3

Answer: I'd be happy to help you with these problems!

1a.

i. Cardinal: There were 10 apples in the basket.

ii. Ordinal: He came in first place in the race.

iii. Nominal: My favorite color is blue.

i. 1997 in Roman numerals is MCMXCVII.

ii. 15-03-2023 in Roman numerals is XV-III-MMXXIII.

2a.

2√128 - √243 + 5√125 + √27 - √80 - 162 + √98

First, simplify the square roots:

2√64·2 - 3√81·3 + 5√25·5 + √9·3 - √16·5 - 162 + √49·2

Next, simplify further:

2·8√2 - 3·3√3 + 5·5√5 + 3√3 - 4√5 - 162 + 7√2

Combine like terms:

15√2 - √3 + 8√5 - 162 - 4√5 + 7√2

Simplify further:

22√2 + 4√5 - √3 - 162

b.

1.3555555555.... can be written as 1.36 in 7º.

c.

Village A has a funeral every 10 days, so it will have a funeral on March 4th, March 14th, March 24th, etc.

Village B has a funeral every 15 days, so it will have a funeral on March 4th, March 19th, April 3rd, etc.

Village C has a funeral every 20 days, so it will have a funeral on March 4th, March 24th, April 13th, etc.

To determine the next time all three villages will have a funeral on the same day, find the least common multiple of 10, 15, and 20.

10 = 2 x 5

15 = 3 x 5

20 = 2 x 2 x 5

The least common multiple is 2 x 2 x 3 x 5 = 60.

So, the next time all three villages will have a funeral on the same day is 60 days after March 4th, which is May 3rd, 2023.

Comment if you have any more questions.

Answer:

x = 4

Step-by-step explanation:

we are given the equation

x/h + 1 = 2

we are also given a the value of h = 4

we are told to find x

let's use the equations and substitute in what we have first

x/h + 1 = 2  ➔  x/4 + 1 = 2

now we can solve for x

x/4 + 1 = 2

lets begin by subtracting one from both sides

now we are left with

x/4 = 1

now do the inverse of division which is multiplication

so we multiply both sides by the denominator 4

now we have

x = 4  

Hope this helps!! :)

The confidence interval based on the given values (x = 45, n = 96, Confidence level = 95%.

The confidence level (95%), sample size (n = 96), and sample mean (x = 45), we can calculate the margin of error and the confidence interval. Here's how:

1. Margin of Error:

The margin of error represents the maximum expected difference between the true population parameter and the sample estimate. It depends on the confidence level and the standard deviation (which we don't have in this case).

Since the standard deviation is unknown, we can use the t-distribution to estimate it. With a sample size of n = 96, the degrees of freedom are (n - 1) = 95. Considering a 95% confidence level, the critical value for a two-tailed test is approximately 1.984 (referencing a t-distribution table or calculator).

The margin of error (E) can be calculated using the following formula:

E = critical value * (standard deviation / sqrt(n))

However, since we don't have the standard deviation, we can't compute the margin of error in this case.

2. Confidence Interval:

The confidence interval represents a range of values within which the true population parameter is likely to fall.

The confidence interval can be calculated using the formula:

CI = x ± (critical value * standard deviation / sqrt(n))

The confidence interval based on the given values (x = 45, n = 96, confidence level = 95%.

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The value of length of side AB is,

⇒ AB = 5 units

We have to given that;

The figure is shown a trapezoid.

Hence, By using Pythagoras theorem we get;

⇒ AB² = 4² + (5.25 - 2.25)²

⇒ AB² = 16 + 3²

⇒ AB² = 16 + 9

⇒ AB² = 25

⇒ AB = √25

⇒ AB = 5 units

Therefore, The value of length of AB is,

⇒ AB = 5 units

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Answer:

[0, -7, 1]

[0, 3, 4]

Answer:

the answer is 2

Step-by-step explanation:

Bcz u choseine option and lose the next bet benefit

Answer:

20

Step-by-step explanation:

firstly let's find out the side lengths of the triangle using formula

\(length \: = \: \sqrt{(y₂-y1) + ( y₂-y1)}\)

length of AB

\( \sqrt{( - 6 - 2) {}^{2} + ( - 4 - 1) {}^{2} } = \sqrt{89} \)

length of AC

\( \sqrt{( - 6 - 2) {}^{2} + (1 - 1) {}^{2} } = 8\)

length of BC

\( \sqrt{( - 6 - ( - 6)) {}^{2} + (1 - ( - 4)) {}^{2} } = 5\)

Now we have all three side lengths:

a =√89 b = 8 and c = 5

using this formula to find the semi perimeter where a, b and c are the side lengths, input them in

\(s \: = \: \frac{a + b + c}{2} \)

\(s = \frac{ \sqrt{89} + 8 + 5 }{2} = \frac{13 + \sqrt{89} } {2} \)

Use heron's formula

\(area = \sqrt{s(s - a)(s - b)(s - c)} \)

\(area = \sqrt{ \frac{13 + \sqrt{89} }{2}(\frac{13 + \sqrt{89} }{2} - \sqrt{89})( \frac{13 + \sqrt{89} }{2} - 8)(\frac{13 + \sqrt{89} }{2} - 5 } = 20\)

area = 20

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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a. Sketch the region of integration in the XY-plane.

b. Reverse the order of integration.

c. Evaluate the integral.

(a) The integral is a double integral, which means that the region of integration is a region in the XY plane. The region of integration is defined by the limits of integration for x and y. However, since the limits of integration are not given, it's not possible to sketch the region of integration in the XY plane.

(b) The integral is already written with the order of integration reversed.

(c) Without the limits of integration, it is not possible to evaluate the integral. The limits of integration are necessary to determine the region of integration, and thus the range of values for x and y over which the integral is to be taken. Without this information, it is not possible to carry out the evaluation of the integral.

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Answer:

42

Step-by-step explanation:

Answer:62 7/20

Step-by-step explanation: