Find the length of arc in cm.​

To simplify the expression, we need to rationalize the denominator:

7_4√3 + 1 ÷ 7_4√3

= (7_4√3 + 1) ÷ 7_4√3 (since division is the same as multiplication by the reciprocal)

= (28 + 4√3 + 1) ÷ 28 (multiplying the numerator and denominator of the first fraction by the conjugate of the denominator)

= (29 + 4√3) ÷ 28

So the simplified expression is (29 + 4√3) ÷ 28.

Answer:

Let's represent the width of the flag with 'w'. Then, according to the problem, the length would be 'w + 90'.

We know that the perimeter of a rectangle is given by:

P = 2(length + width)

Substituting the values from the problem, we get:

500 = 2(w + w + 90)

Simplifying, we get:

250 = 2w + 90

2w = 160

w = 80

So, the width of the flag is 80 feet.

And the length of the flag would be:

w + 90 = 80 + 90 = 170 feet.

The value of [tex]x _{238} = 111.1875 _{238}[/tex] for the given equation in congruence.

Congruence is an equivalence relation that is applied to compare numbers in discrete or modular arithmetic. If the difference between two numbers, a and b, is divisible by n, then the two numbers are said to be congruent modulo n (abbreviated as a b mod n). In other words, when a and b are divided by n, the remainders are equal. A key idea in number theory, congruence has a wide range of uses in domains like computer science and encryption.

For the given expression we have:

[tex]2142 . x _{238} = 442 _{238}\\x _{238} = 442 _{238} / 2142 _{238}\\x _{238} = 111.1875 _{238}[/tex]

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The length of the lake is solved to be

The length of the lake is solved by subtraction of length obtained using angle of depression of 68 degrees from the length obtained solving using angle of depression of 32 degrees

Using angle of depression of 68 degrees

The complimentary angle is 22 degrees

sin 22 = length / 250

length = sin 22 x 250

length = 93.65

Using angle of depression of 32 degrees

The complimentary angle is 58 degrees

sin 58 = length / 250

length = sin 58 x 250

length = 212.01

The length of the lake

= 212.01 - 93.65

= 118.36 m

= 118 m to the nearest m

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Answer: 10 feet wide

Step-by-step explanation:

If there is 50 feet long on either side, then the perimeter of the length is 100 feet.  That would mean that there is 20 feet left. If there is 20 feet for 2 sides, we would divide that in half. 20 / 2 = 10.

So, for all of the tiles to be used, the pool would have to be 10 feet wide.

The solution to the system of equation is (29, 75).

The given simultaneous equation is expressed as shown below:

3x-y=12 ............ 1

y=2x+17 ............ 2

We need to determine the unknown values of x and y

Substitute equation 2 into 1 to have:

3x-y=12

3x- (2x + 17) = 12

3x - 2x - 17 = 12

x - 17 = 12

x = 12 + 17

x = 29

Substitute x = 29 into equation 2;

y=2(29)+17

y = 58 + 17

y = 75

Hence the solution to the system of equation is (29, 75)

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The composite figure has an area of 74 square centimeters.

In this question we find the representation of a composite figure formed by two rectangles, whose area has to be computed. The area formula for a rectangle is:

A = b · h

Where:

Now we proceed to determine the area of the composite figure:

A = (8 cm) · (3 cm) + (5 cm) · (2 cm) + (8 cm) · (5 cm)

A = 24 cm² + 10 cm² + 40 cm²

A = 74 cm²

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Answer: Your answer is 23.5in²

Hope it helped :D

Good Luck!

The condition of equal variability of residuals across all values of the predictor variable (homoscedasticity) does not appear to be satisfied.

Based on the residual plot, the condition for inference for the slope of the regression line that does not appear to be satisfied is the assumption of constant variance (also known as homoscedasticity).

This condition states that the variability of the residuals should be roughly the same at all levels of the predictor variable (in this case, the number of people in the dining party).
If the residual plot shows a pattern, such as a widening or narrowing of the points, it indicates that the constant variance assumption might not hold.

This could affect the accuracy of the linear regression analysis and the validity of the conclusions drawn from it.

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At 15 years old, her height is 70 inches.

The height she will never achieve is the horizontal asymptote of the function.

To find the teenager's height, plug in x=0 into the function: f(0) = -1/0 + 2 + 68.

Since division by zero is undefined, the function is not valid at 15 years old.

The height she will approach but never achieve is the horizontal asymptote of the function.

As x approaches infinity, the -1/x term approaches 0.

Therefore, the height approaches 2+68 = 70 inches.

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Answer:

6

Step-by-step explanation:

2 x 3 = 6

The maximum height reached by each stone is 40.5 meters.

The height of each stone above the ocean is given by the function:

h = -2t² + 2t + 40

This is a quadratic function in standard form, with a = -2, b = 2, and c = 40.

The maximum height reached by the stone occurs at the vertex of the parabolic curve described by this function.

The t-coordinate of the vertex is given as:

t = -b / 2a

Substitute the values of a and b,

t = -2 / (2×(-2)) = 0.5

So the maximum height is reached 0.5 seconds after the stone is thrown.

To find the maximum height, substitute the value of t into the function:

h = -2(0.5)² + 2(0.5) + 40 = 40.5 meters

Therefore, the maximum height reached by each stone is 40.5 meters.

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Answer: N′(−9, −2), M′(−6, −1), O′(−9, −5)

Step-by-step explanation: N=S -9+7+9+23x52=N′(−9, −2), M′(−6, −1), O′(−9, −5)

Answer: 112km

Step-by-step explanation:

SA rectangular prism = 2 (lh +wh + lw )

= 2 ((4x2)+(8x4)+(2x8))

= 2 (8+32+16)

= 2(56)

= 112km

Jeff can use the Pythagorean Theorem to check if the corner of the room forms a right triangle, indicating a right angle between the walls.

Jeff can use the Pythagorean Theorem to determine if the walls form a right angle by following these steps:

1. Identify the two sides adjacent to the angle in question: the side that is 3 inches from the corner (Side A) and the side that is 4 inches from the corner (Side B).

2. Measure the distance between the two marks along the floor (Side C). This distance will act as the hypotenuse of the right triangle.

3. Apply the Pythagorean Theorem: A² + B² = C². In this case, A = 3 inches and B = 4 inches. Calculate A² + B², which equals 3² + 4² = 9 + 16 = 25.

4. Compare the calculated value (25) to the square of the measured distance (C²). If A² + B² equals C², then the walls form a right angle, and the corner is a right triangle.

5. If the values match, it confirms that the angle between the two walls is a right angle (90 degrees), meaning the corner forms a right triangle. If the values do not match, then the walls do not meet at a right angle.

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Answer:

1.44444444444

Step-by-step explanation:

Answer: 1.44 square miles

Step-by-step explanation:

Set up a proportion, convert 2 hours and 15 min by putting 15/60=

[tex]\frac{3.25}{2.25} =\frac{x}{1}[/tex]

x=1.44 square miles

The slope of the least-squares regression line for math is 0.68 and for English is 0.68. Then the correct option is A.

Given that:

English (x)    450    470   510   520   540   570   590   620   670   680

Math (y)        490    480  500   580  550   540    610    590  620   650

The slope of the least-squares regression line represents the rate of change between two variables. To find the slope of the line, we need to use linear regression analysis.

The slope of the line turns out to be 0.68, which means for each additional point in the English score, the math score is predicted to increase by 0.68 points.

Therefore, the correct answer is:

0.68, which means for each additional point in the English score, the math score is predicted to increase by 0.68 points.

Thus, the correct option is A.

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Answer:  A=a2

Here are the steps to finding the square root using factoring:

Find the factors. Factors are the numbers you multiply to find the total under the square root symbol. ...

Separate the factors into their own square roots. ...

Solve for the individual squares. ...

Finish solving the equation.

The correct answers are:

• 3642yd² explanation on bottom.

The given options represent the possible answers for the area of the square. To find the correct answer, we need to look for the option that matches the given area. The area is given in square units of yards, which means the answer will also be in square yards. Out of the given options, only "3642yd²" matches the given area of 3642 square yards. Therefore, the correct answer is "3642yd²".

• Another way to get the answer.

The given image shows a square with four sides equal in length. The area of a square is equal to the product of its sides. Among the given options, the area of the square is either 7242 yd², 36 yd², 72 yd², or 3642 yd². To determine the area of the square, we need to identify the correct measurement of its side, which is equal to 6 yd. We can then use the formula A = s², where A is the area and s is the length of each side, to find that the area of the square is 36 yd².

If you share 7 apples equally with 3 people, then there are 2 1/3 apples for each people when 7 divided by 3.

Given that,

7 apples are shared with 3 people.

Total number of apples = 7

Total number of people = 3

Number of apples each people get = 7/3 = 2 1/3

Here 2 means that 2 whole apples.

7 is not divisible by 3. So the number near to 7 which is divisible by 3 is 6.

6/3 = 2

Then the remaining 1 is divided in to 3 and 2 + 1/3 parts is given to each people.

Hence If you share 7 apples equally with 3 people, then there are 2 1/3 apples for each people.

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Using probability, the expected number of pears to be sold if a total of 30 pieces of fruit are sold during the day is 12.

Given that,

When a total of 20 fruits are sold in a day,

Number of pears sold = 8

So the probability of selling pears can be calculated as,

Probability = 8/20 = 0.4

Percentage = 40%

40% of the total fruits sold will be pears.

Expected number of pears sold if the total fruits sold is 30 is,

Expected number = 30 × 0.4 = 12

Hence the expected number of pears sold if the total fruits sold is 30 is 12.

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Answer: 94.2

Step-by-step explanation:

30 x 3.14

For a more accurate answer, multiply by the π symbol

30 x π = 94.25

The attributes, measurements used, and observations of the data are given below as per the average age of the score.

Attributes:

The table is given in the attached image below.

Measurements used:

Number of players (count)

Average score per game (mean)

The average age of players (mean)

Observations:

There are six basketball teams denoted by A, B, C, D, E, and F.

Team A has 12 players, with an average score per game of 74 and an average age of 13.5.

Team B has 15 players, with an average score per game of 50 and an average age of 12.8.

Team C has 14 players, with an average score per game of 63 and an average age of 12.2.

Team D has 17 players, with an average score per game of 38 and an average age of 13.1.

Team E has 11 players, with an average score per game of 51 and an average age of 12.7.

Team F has 16 players, with an average score per game of 60 and an average age of 11.

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The surface area of the pyramid is given by -

[tex]$A = lw\;+l\sqrt{(\frac{w}{2})^{2} +h^{2} } +w\sqrt{(\frac{l}{2})^{2} +h^{2} }[/tex].

The pyramid is not given. So, we will discuss some important points regarding the pyramids along with its surface area.

The surface area of the pyramid is given by -

[tex]$A = lw\;+l\sqrt{(\frac{w}{2})^{2} +h^{2} } +w\sqrt{(\frac{l}{2})^{2} +h^{2} }[/tex]

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The homeowner needs to work for roughly 3 weeks to save up for the cost of the fence.

Option B is correct.

We have the following values:

Length of walkway gate = 5 feet

Length of driveway gate = 15 feet

The total reduction in length = 5 + 15 = 20 feet

the Length of property = 150 feet

Width of property = 60 feet

Perimeter of property = 2(150 + 60) = 420 feet

We can calculate that Length of fence after subtracting gates is given as  = 420 - 20

= 400 feet

So in order to calculate the amount of time needed to save up for the fence:

we have:

Total cost after tax / Hourly wage = ?

where

Hourly wage = $30.66

Total cost after tax = $3,688.10

therefore the  amount of time  =

$3,688.10 / $30.66 = 120.14 hours

So it takes the homeowner 120.14 hours / 40 hours/week = 3.004 weeks to save up for the cost of the fence if they make $30.66/hour after taxes and are saving 100% of their income.

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The requried, difference in monthly pension payments is the second offer pays $64.50 more per month. Option B is correct.

To calculate the monthly pension payment for the second offer, we need to know the number of years of service the welder plans to work at each company. Let's assume the welder plans to work for 18 years at each company (the same number of years used for the first offer).

For the first offer, the monthly pension payment is given as $1,893.

For the second offer, the pension rate is 1.5% per year of service, so the total pension rate after 18 years of service is:

1.5% * 18 = 27%

The monthly pension payment is calculated as a percentage of the average annual wage, which is $87,000 for the second offer. So the monthly pension payment for the second offer is:

27% * ($87,000 / 12) = $1,956.25

The difference in monthly pension payments is:

$1,956.25 - $1,893 = $64.50

So the answer is that the first offer pays $63.25 less per month than the second offer. Rounded to the nearest 10 cents, the answer is that the second offer pays $64.50 more per month than the first offer.

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The obtained inequality be 5x + 9 < 4.

The given inequality is,

5x + 6 < 1

To obtain the required expression,

Add 3 in both sides of inequality

⇒5x + 6 + 3 < 1 + 3

⇒5x + 9 < 4

Hence,

The inequality which is required be

5x + 9 < 4

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Answer:[tex]f(x)=2x^{2} +3x-2[/tex]

Step-by-step explanation:

f[tex]f(1)=3\\\\ax^{2} +b+c=3 (1)\\f(2)=12\\4a+2b+c=12 (2)\\f(3)=25\\9a+3b+c=25(3)\\(2)-(1)= 3a+b=9 (4)\\(3)-(2)=5a+b=13 (5)\\(5)-(4)= > 2a=4 = > a=2\\(4)= > b=3\\(1)= > c=-2\\f(x)=2x^{2} +3x-2[/tex]

Answer:

C. The volume is multiplied by 8

Step-by-step explanation:

1*1*1=1

1+1=2

1+1=2

1+1=2

2*2*2=8

Answer:

in the picture

Step-by-step explanation:

we multiply the side by two and find the new volume, unfolding and calculations in the figure

Answer:

Step-by-step explanation:

The maximum and minimum values of f(x, y, z) subject to the given constraint can be found by substituting the values of x, y and z in the function f(x, y, z).

What is function?
Function is an operation that takes one or more inputs and produces an output, or a set of outputs, depending on the type of function. Functions are commonly used in mathematics and computer science, and are essential for solving a wide range of problems.

We are given a function f(x, y, z) = xyz and the constraint x2 + 2y2 + 3z2 = 96. To find the maximum and minimum values of f(x, y, z) subject to the given constraint, we can use the method of Lagrange multipliers.

Let λ be the Lagrange multiplier. Then, the Lagrange function is given by:

L(x, y, z, λ) = xyz + λ (x2 + 2y2 + 3z2 - 96)

We will now calculate the partial derivatives of L with respect to x, y, z and λ.

∂L/∂x = yz + 2xλ = 0
∂L/∂y = xz + 4yλ = 0
∂L/∂z = xy + 6zλ = 0
∂L/∂λ = x2 + 2y2 + 3z2 - 96 = 0

Solving the above equations, we get:
2xλ = -yz
4yλ = -xz
6zλ = -xy
x2 + 2y2 + 3z2 = 96

Substituting the values of λ in the first three equations, we get:
2x(-xz/4y) = -yz
2x2z/4y = -yz
x2z/2y = -yz

From the fourth equation, we get:
x2 + 2y2 + 3z2 = 96

Substituting the values of x2, y2 and z2 from the above equation in the fifth equation, we get:
(96 - 2y2 - 3z2)z/2y = -yz
96z/2y - yz - 3z3/2y = 0

Solving for z, we get:
z = (96/4y) ± √(962/16y2 - 3y2)

Substituting the values of z from the above equation in the fourth equation, we get:
x2 + 2y2 + 3 (96/4y)2 ± √(962/16y2 - 3y2)2 = 96

Solving for y, we get:
y = ±√(96/14 - 3z2/2)

Substituting the values of y from the above equation in the third equation, we get:
x = ± 2z √(14z2/96 - 1/3)

Hence, the maximum and minimum values of f(x, y, z) subject to the given constraint can be found by substituting the values of x, y and z in the function f(x, y, z).

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A two-dimensional graph, also known as a coordinate plane or Cartesian plane, is divided into four quadrants. The quadrants are numbered in a counterclockwise direction, starting from the top-right quadrant and going around to the other quadrants.

To name the quadrants on a graph:

Point C is in the fourth quadrant. We can verify this because it is located at a positive x-coordinate and a negative y-coordinate. (4,-4)