Which fraction is equivalent to 0.16 repeating

x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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In the given scenario ladder is 6.52 feet long.

Given that,

The angle between ground and ladder = 62 degree

The distance of ladder from ground and ladder = 3 feet

We have to find the length of  ladder.

Since we know that,

The trigonometric ratio

cosθ = adjacent/ Hypotenuse

Here we have,

Adjacent =  3 feet

Hypotenuse = length of ladder

Thus to find the length of ladder we have to find the value of hypotenuse.

Therefore,

⇒ cos62 = 3/ Hypotenuse

⇒    0.46 = 3/ Hypotenuse

⇒ Hypotenuse =  3/0.46

                          = 6.52

Thus,

length of ladder  = 6.52 feet.

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Answer:

c=15.7

Step-by-step explanation:

c=2(pi)(r)

pi=3.14 in this question

r=2.5

c=2(2.14)(2.5)

Answer:

15.70 cm

Step-by-step explanation:

The formula for circumference is \(c = 2\pi r\), where r = radius. We are using 3.14 instead of pi here.

The radius is shown to be 2.5 cm, simply plug that into the equation and solve.

To solve, you must first carry out \(2.5*2 = 5\).

Then, multiply that product by pi, or, in this case, 3.14: \(5*3.14 = 15.7\)

So, the answer exactly  is 15.7. When rounded, it's technically 15.70 but that is absolutely no different than the exact answer.

Answer:

75

Step-by-step explanation:

87-12= 75

edg2020

Answer:

397

Step-by-step explanation: you placed 325 already and earned 19  you add 325  19 50 3 you get your final product which is 397 which is what you will earn or get out of your savings

Answer:

46

Step-by-step explanation:

Angle CED and GHE are equal as the lines are parallels. Also, the line rom D to F will be a total of 180.

Therefor, substract the angle FEC from 180 and you get the angle CED which is equal to GHE

Answer: 1. 4

2. 12

3. 6

4. 8

Step-by-step explanation:

Answer:

24 + 12 = 36

Step-by-step explanation:

find the volume of the upper left part by finding the dimensions

it already gives 2 side lengths: 2 and 2. To find the 3rd side length you can take 5 - 2 to get 3. 3*2*2 = 12

find the volume of the bottom portion by finding the dimensions. we are given 2 sides again: 2 and 2. to get the upper long side, we can do 4 + 2 to get 6. 6*2*2 = 24

24+12= 36cm^3

Answer:

Step-by-step explanation:

should be 1110

Answer:

1110

Step-by-step explanation:

Answer:

C. 5.8

Step-by-step explanation:

We use the Pythagoras theorem here. which is a²+b²=c².

a and b are the replacements for the 5miles and  3miles here.

They are a and b because a  and b are always on the right angle side.

The longest side of this triangle is called a hypotenuse which is the c in this case.

the other sides (a and b) are called the adjacent and the opposite.

it doesn't matter if you use adjacent or opposite for a and b in this case.

the only important thing is the hypotenuse here.

So it's a²+b²=c², which is 5²+3²=c².

5² is 25 and 3² is 9, so we add them and we get 34.

so c²=34, we don't want the square on c  so we send it to 34 which becomes √34.

√34 gives us 5.8 miles which is up to just only one decimal place.

You might need to use calculators for square roots because they take long to calculate.

To determine if two hexadecimal numbers can be consecutive in gray code, you need to convert them to binary and then compare their corresponding bits.

Gray code is a binary numeral system where two consecutive numbers differ by only one bit. Therefore, if two hexadecimal numbers can be consecutive in gray code, their binary representations must differ by only one bit as well. To convert a hexadecimal number to binary, simply convert each hexadecimal digit to its corresponding 4-bit binary representation. For example, the hexadecimal number 3A would be converted to 0011 1010 in binary.

Here is a step-by-step guide to determine if two hexadecimal numbers can be consecutive in gray code:
1. Convert the first hexadecimal number to binary. For example, if the first hexadecimal number is 3A, convert it to 0011 1010 in binary.
2. Convert the second hexadecimal number to binary using the same method as step 1.
3. Compare the corresponding bits of the two binary numbers. If there is only one bit that differs between the two binary numbers, then the original hexadecimal numbers can be consecutive in gray code.
4. If there is more than one bit that differs between the two binary numbers, then the original hexadecimal numbers cannot be consecutive in gray code.

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The measure of Angle f from the the figure is \(53^{o}\).

On a shared plane, parallel lines do not cross one another. Now, if a transversal crosses two parallel lines at two separate sites, four angles are created at each location. The characteristics of parallel lines with respect to transversals are therefore listed below.

The pair of alternative internal angles are equal when two parallel lines are crossed by a transversal.

When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional.

In the problem angle

a = \(119^{o}\)

e = \(66^{o}\)

Now , c = e ( alternate angles, interior)

⇒ c = \(66^{o}\)

a + b = \(180^{o}\) ( as sum of angles on a straight line is \(180^{o}\) )

b = \(180^{o}\) - \(119^{o}\) = \(61^{o}\)

f + b+ c = \(180^{o}\)                [sum of angles of a Triangle is \(180^{o}\) ]

f = \(180^{o}\)  - \(61^{o}\) - \(66^{o}\) = \(53^{o}\).

The measure of Angle f from the the figure is \(53^{o}\).

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Answer:

AD = 9, BC = 5

Step-by-step explanation:

Tangents to a circle from an external point are congruent, then

AD = 5 + 4 = 9 units

BC = 3 + 2 = 5 units

The requried Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR. Option A is correct.

A straightforward method of expressing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, with a vertical line inside to indicate the median value.

Here,
Burger Quick is able to estimate its wait time more consistently because it has a smaller interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The smaller the IQR, the more consistent the data is around the median, which is represented by the line within the box in the box plot.

In this case, Burger Quick has a smaller IQR (8.0) compared to Super Fast Food (7.0), indicating that the wait times at Burger Quick are more consistent around the median. The range, which is the difference between the maximum and minimum values, is not a good measure of consistency as it is affected by outliers.

Therefore, based on the given information, Burger Quick is able to estimate its wait time more consistently because it has a smaller IQR.

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The area of the figure given, which seems to have two semi - circles removed, is 85. 71 cm ²

The area of the figure can be found by finding the area of the rectangle and then subtracting the area of the two semicircles.

The area of the rectangle is :

= 17 x 8

= 136 cm ²

The area of the two semi circles is :

= ( π x radius ² x 2 semicircles ) x 1 / 2 circle

= π x 4 ² x 2 x 1 / 2

= 50. 29 cm ²

The area of the figure is:

= 136 - 50. 29

= 85. 71 cm ²

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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There are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

1. First we need to identify the total number of seats in the lecture hall which is 200.

2. Then we need to identify the number of seats with folding arm tablets that are designed for wheelchair users which is 30.

3. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats.

4. Therefore, 200 - 30 = 170, which means there are 170 seats with folding arm tablets that are not designed for wheelchair users.

The lecture hall in question has a total of 200 seats, with 30 of those seats having folding arm tablets that are designed for wheelchair users. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats. This means that 200 - 30 = 170, which means there are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

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Step-by-step explanation:

y=57x-8y=-12

so we put the Y

y=-12

-12=57x-8y

57x-8x(-12)=-12

(-36/19,-12)<---- answer

We know that n^2 is a multiple of both 24 and 108, which means it must be a multiple of their least common multiple (LCM). The LCM of 24 and 108 is 216.

So, n^2 must be a multiple of 216. This means that n must be a multiple of the square root of 216, which is 6√6.

Therefore, every integer n in s must be of form 6√6 * k, where k is a positive integer.

To find the divisors of every integer n in s, we need to find the common factors of all such expressions.

We can express 6√6 as 2√6 * 3. So, every integer n in s can be written as 2√6 * 3 * k.

The divisors of every integer n in s must be factors of 2√6 and 3.

The factors of 2√6 are 1, 2, √6, and 2√6.

The factors of 3 are 1 and 3.

Therefore, the integers that are divisors of every integer n in s are 2 and 3, which are both positive integers.

So, the correct answer is none of the given options (a, b, c, d).

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Answer:

y = \(-\frac{1}{2}\)x + 1

Step-by-step explanation:

y = mx + c

Find the reciprocal and change the sign of the gradient (m), which is -\(\frac{1}{2}\)

so

y = \(-\frac{1}{2}\)x + c

Put in your point that you want it to intersect (4,-1):

-1 =   \(-\frac{1}{2}\)(4) + c

-1 = -2 + c

-1 + 2 = c

1 = c

y = \(-\frac{1}{2}\)x + 1

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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Answer:

(1, 2), (1,4), (1, 6)

Step-by-step explanation:

They're adding the Y-axis

The statements which must be true from the given statements are :

Base angles of Quadrilateral Z are congruent.

Opposite angles of quadrilateral C are congruent.

Opposite angles of quadrilateral L are congruent.

Consecutive angles of quadrilateral Z are congruent.

Consecutive angles of quadrilateral L are congruent.

Opposite angles of quadrilateral C are supplementary.

Opposite angles of quadrilateral T are supplementary.

Given are,

Quadrilateral C has 4 congruent sides.

So this must be a square and thus all angles are equal which is equal to 90°.

Opposite angles are thus congruent.

Opposite angles of a quadrilateral is always supplementary.

Quadrilateral L has two pairs of parallel sides and congruent diagonals.

So it must be a rectangle or a square.

So, opposite angles are congruent, each equal to 90 degrees.

Also, consecutive angles are equal, since each angle equal to 90°.

Quadrilateral T has at least one pair of parallel sides that are also congruent.

If at least one pair of parallel sides are congruent, then the other pair of sides are also parallel and congruent.

S it can be rectangle, square, parallelogram or rhombus.

If it is parallelogram or rhombus, base angles will not be equal.

Opposite angles are supplementary.

Quadrilateral Z has exactly one pair of parallel sides that are not congruent. The other pair of sides are congruent.

This must be an isosceles trapezium.

Base angles of an isosceles trapezium are equal and thus congruent.

So consecutive angles are congruent.

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The exponential equation is \(y=ab^x\). Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = \(ab^{x}\) . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = \(ab^{x}\) . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = \(ab^{x}\)

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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Answer:

x≥9

Step-by-step explanation:

Pretend the Less than or equal to sign is just an equals sign

-7x+7=-56 Solve:

-7x=-56-7

-7x=-63

For the last step, if you divide a negative number, the Sign switches. So not the sign is greater than or equal to.

x>=9

Answer:

o resultado é 961

foi mal se erei

Answer:

D. \(9(y+3) and 27+9y\)

Step-by-step explanation:

The first expression for each set is using the distributing propety. We can start with the first one. We notice right away that 3 sets of 3y is 9y, when the other expression is 6. So, that is incorrect. Next we see the second one does have a correct y-value, but the integer value of 6 is not the same, since 3*3=9, not 6. For C we can tell that 9*3=27, which is not equal to 12. Therefore, D must be the answer.

Answer:

\(\frac{dh}{dt}\approx0.08622\text{ ft/min}\)

Step-by-step explanation:

We know that the conical water tank has a radius of 13 feet and is 21 feet high.

We also know that water is flowing into the tank at a rate of 30ft³/min. In other words, our derivative of the volume with respect to time t is:

\(\frac{dV}{dt}=\frac{30\text{ ft}^3}{\text{min}}\)

We want to find how fast the depth of the water is increasing when the water is 17 feet deep. So, we want to find dh/dt.

First, remember that the volume for a cone is given by the formula:

\(V=\frac{1}{3}\pi r^2h\)

We want to find dh/dt. So, let's take the derivative of both sides with respect to the time t. However, first, let's put the equation in terms of h.

We can see that we have two similar triangles. So, we can write the following proportion:

\(\frac{r}{h}=\frac{13}{21}\)

Multiply both sides by h:

\(r=\frac{13}{21}h\)

So, let's substitute this in r:

\(V=\frac{1}{3}\pi (\frac{13}{21}h)^2h\)

Square:

\(V=\frac{1}{3}\pi (\frac{169}{441}h^2)h\)

Simplify:

\(V=\frac{169}{1323}\pi h^3\)

Now, let's take the derivative of both sides with respect to t:

\(\frac{d}{dt}[V]=\frac{d}{dt}[\frac{169}{1323}\pi h^3}]\)

Simplify:

\(\frac{dV}{dt}=\frac{169}{1323}\pi \frac{d}{dt}[h^3}]\)

Differentiate implicitly. This yields:

\(\frac{dV}{dt}=\frac{169}{1323}\pi (3h^2)\frac{dh}{dt}\)

We want to find dh/dt when the water is 17 feet deep. So, let's substitute 17 for h. Also, let's substitute 30 for dV/dt. This yields:

\(30=\frac{169}{1323}\pi (3(17)^2)\frac{dh}{dt}\)

Evaluate:

\(30=\frac{146523}{1323}\pi( \frac{dh}{dt})\)

Multiply both sides by 1323:

\(39690=146523\pi\frac{dh}{dt}\)

Solve for dh/dt:

\(\frac{dh}{dt}=\frac{39690}{146523}\pi\)

Use a calculator. So:

\(\frac{dh}{dt}\approx0.08622\text{ ft/min}\)

The water is rising at a rate of approximately 0.086 feet per minute.

And we're done!

Edit: Forgot the picture :)