The drawing plan for an art studio shows a rectangle that is 11.2 inches by 8 inches. The scale in the plan is 4 in.: 5 ft. Find the length and width of the actual studio. Then find the area of the actual studio.

The length is ________ feet, the width is _____ feet, and the area is _______ square feet.

It is not possible to make paper quilts with 24 paper squares in 5 rows because the quilt shape would be incomplete.

To make a quilt with paper squares we must establish the averages we want for our quilt. In this case we want a quilt with 5 rows of paper squares. Additionally, we have 24 square pieces of paper.

In that case we would have to divide the number of pieces of paper available in the number of rows to find out how many pieces we should put in each row.

According to the above, it is not possible to make a quilt with 24 square pieces of paper because the shape would be incomplete. Therefore, we must use more square pieces of paper. In this case, it could be 25 pieces of square paper.

To make a 5 row quilt, where each row has 5 square pieces of paper, we would have 25 square pieces of paper and the quilt shape would be complete.

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2x + 6y when x is -4/5 and y is 1/3

Evaluate:

2(-4/5) + 6(1/3)

= 2/5 or 0.4(decimal form)

2/5 or 0.4 would be your answer.

Hope this helps!

The average velocity would be,

[tex]V_{avg}= \frac{-10h^2 - 80h + 8t -32}{h}[/tex]

We know that the average velocity is nothing but the total displacement/ total time taken.

As we know the average velocity over the time interval [t1, t2] is given by, 

[tex]v_{avg}= \frac{s(t_2) - s(t_1)}{ t_2 - t_1}[/tex]

Here, we have been given the disaplcement function s(t) = -10t² + 8t + 4

And time interval is [4, 4 + h]

For t = 4,

s(4) =  -10(4)² + 8(4) + 4

s(4) = -10(16) + 32 + 4

s(4) = -160 + 32 + 4

s(4) = -124

For t = 4 + h

s(4 + h) =  -10(4 + h)² + 8t + 4

s(4 + h) = -10(16 + 8h + h²) + 8t + 4

s(4 + h) = -160 - 80h - 10h² + 8t + 4

s(4 + h) = -10h² - 80h + 8t - 156

Using abova formula the average velocity V_(ave) would be,

[tex]V_{avg}= \frac{s(4+h) - s(4)}{ 4+h - 4}\\\\V_{avg}=\frac{-10h^2 - 80h + 8t - 156 - (-124)}{h} \\\\V_{avg}=\frac{-10h^2 - 80h + 8t - 156 + 124}{h} \\\\V_{avg}= \frac{-10h^2 - 80h + 8t -32}{h}[/tex]

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Answer:

I am not sure I hope this helps!

Selling price- $500.00

Rate of discount- 20%

Discount- $100.00 (20% of $500.00)

Sale price- $400.00 ($500.00 - $100.00)

Answer:

Step-by-step explanation:

1.4

Answer:

1 2/5

Step-by-step explanation:

simplified: 1.4

Answer:

Simplify the following:

(10 x)^(-3)

Multiply each exponent in 10 x by -3:

1/(10^3 x^3)

10^3 = 1000:

Answer: 1/(1000 x^3)

Step-by-step explanation:

The area of the sector with theta as π/12 radian and radius as 4 is 2 / 3π.

A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them.

The sector has the central angle as π/2 radian and a radius of 4 units. Therefore, let's find the area of the sector using the formula as follows:

area of a sector = ∅ / 2 r²

where

Therefore,

∅ = π / 12

r = 4 units

Hence,

area of a sector = π / 12 × 1 / 2 × 4²

area of a sector = π / 4 × 16

area of a sector = 16 / 24 π

area of a sector = 2 / 3π

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The equations for the perpendicular and parallel lines are obtained as y = 2/3x + 12 and y = -3/2x - 15/2 respectively.

A straight line can be written in the slope-intercept form as, y = mx + c.

In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.

The equation of the line is given as y = -3/2x + 6.

(a) Compare the given equation with y = mx + c to obtain,

m = -3/2

Then, the slope of the perpendicular line is given as,

⇒ -1 ÷ -3/2 = 2/3

Plug x = -9 and y = 6 in y = mx + c to get,

6 = 2/3 × -9 + c

⇒ c = 12

Thus, the required equation can be given as y = 2/3x + 12.

(b) The slope of the line parallel to y = -3/2x + 6 is -3/2.

Plug x = -9 and y = 6 in y = mx + c to get,

6 = -3/2 × -9 + c

⇒ c = -15/2

Thus, the required equation can be given as y = -3/2x - 15/2.

Hence, the equations of the lines for both part are given as  y = 2/3x + 12 and y = -3/2x - 15/2 respectively.

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The minimum sample size required for the estimate is 7.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Mean = 10.3

Standard deviation = S.D = 2.2

Sample size = n = 0.18

90% confidence interval Z value = 1.65

Now,

( {Mean - Z value (S.D/√n)}, {Mean + Z value (S.D/√n} )

( {10.3 - 1.65 (2.2/√0.18), 10.3 + 1.65 (2.2/√0.18} )

( {10.3 - 8.64}, 10.3 + 8.64} )

(1.66, 18.94)  

Minimum value:

= 1.66

= 7

Thus,

The minimum sample size is 7.

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Answer:

Step-by-step explanation:

100/50=2

so 10 x 2 = 20

they walk 20 feet

An equivalent fraction with a rational denominator can multiply the original fraction by a fraction with a rational denominator.

To produce an equivalent fraction with a rational denominator, you can multiply the original fraction by a fraction with a rational denominator. For example, if the original fraction is [tex]$\frac{3}{5}$[/tex] , you can multiply it by [tex]$\frac{2}{2}$[/tex]  to get the equivalent fraction [tex]$\frac{3 \cdot 2}{5 \cdot 2} = \frac{6}{10}$[/tex]  . The denominator of this equivalent fraction, 10, is a rational number.

In general, to produce an equivalent fraction with a rational denominator, you can multiply the original fraction by a fraction with a rational denominator. The specific fraction you choose will depend on the desired denominator.

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Multiplying [tex]\frac{3}{\sqrt{17}-\sqrt{2} }[/tex] by  [tex]\frac{\sqrt{17}+\sqrt{2}}{5}[/tex] will produce an equivalent fraction with a rational denominator.

Consider given  expression [tex]\frac{3}{\sqrt{17}-\sqrt{2} }[/tex]

First we rationalize a denominator of  fraction [tex]\frac{3}{\sqrt{17}-\sqrt{2} }[/tex]

To rationalize the denominator, multiply and divide the expression by [tex]{\sqrt{17}+\sqrt{2} }[/tex]

So given fraction would be,  

[tex]\frac{3}{\sqrt{17}-\sqrt{2} }\\\\= \frac{3\times (\sqrt{17}+\sqrt{2})}{(\sqrt{17}-\sqrt{2})\times (\sqrt{17}+\sqrt{2}) }\\\\= \frac{3\times (\sqrt{17}+\sqrt{2})}{(\sqrt{17}^2-\sqrt{2}^2) }\\\\ = \frac{3\times (\sqrt{17}+\sqrt{2})}{(17-2) }\\\\= \frac{3\times (\sqrt{17}+\sqrt{2})}{15 }\\\\= \frac{3\times (\sqrt{17}+\sqrt{2})}{3\times 5 }\\\\= \frac{\sqrt{17}+\sqrt{2}}{5 }[/tex]

Therefore, the required fraction is:  [tex]\frac{\sqrt{17}+\sqrt{2}}{5}[/tex]

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A complete question is:

Multiplying 3/sqrt 17 - sqrt 2 by which fraction will produce an equivalent fraction with a rational denominator

When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression

A linear function which has the greatest y-intercept include the following: D. y = 3x + 4

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Based on the information provided regarding the equations and graphs, the y-intercept are as follows:

Therefore, y = 3x + 4 is a linear function with the greatest y-intercept.

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Complete Question:

Which linear function has the greatest y-intercept?

y = 6x + 1

On a coordinate plane, a line goes through points (0, 2) and (5, 0).

On a coordinate plane, a line goes through points (1, 2) and (0, negative 3).

y = 3x + 4

The area of the regular hexagon will be 216√3 square units. Then the correct option is C.

Let 'a' be the apothem and 'p' be the perimeter of the regular polygon.

Then the area of the regular polygon will be

A = (1/2) × a × p

A regular hexagon has a side length of 12. Then the perimeter of the regular hexagon is given as,

P = 6 x 12

P = 72

Then the length of the apothem will be given as,

a = 6 x tan 60

a = 6√3

Then the area of the regular hexagon will be given as,

A = (1/2) x (6√3) x (72)

A = 216√3

A regular hexagon has a side length of 12. Then the area of the regular hexagon will be 216√3 square units. Then the correct option is C.

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The value of x to the nearest tenth is option D) 11.00

What is the angle bisector theorem?

The Angle Bisector Theorem, also known as the "Median and Altitude Theorem" states that in a triangle, the ratio of the length of a median (a line segment drawn from a vertex of a triangle to the midpoint of the opposite side) to the length of the side it bisects is equal to the ratio of the length of the other median to the length of the side it bisects.

First Let us take the △ as ABC. And AD is the angle bisector (Given) we will solve this using the angle bisector theorem

Then BD/DC = AB/AC

Here, BD = 5.1, DC = 4.6, AB = 12.2, AC = ?

Now, 5.1/4.6 = 12.2/x

5.1 X x = 12.2 X 4.6

x = 56.12/5.1

Hence, the value of x to the nearest tenth 11.00

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Answer:

domain = {6,16,41,49}

range = {4,-10,7}

A Perpendicular bisector is a line that divides a given line segment exactly into two halves forming 90 degrees angle at the intersection point.

A line known as a perpendicular bisector divides a specified line segment precisely in half, creating a 90° angle at the intersection. The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler. On both sides of the line segment being divided, it forms a 90° angle.

Step 1: Sketch a line segment of any appropriate length, XY.

Step 2: Using a compass, draw arcs above and below the line segment, with X serving as the center and XY's width is greater than 50%.

Step 3: Carry out Step 2 but use Y as the center.

Step 4: Write "P" and "Q" next to the junction points.

Step 5: Join the points 'P' and 'Q'. The point at which the perpendicular bisector PQ intersects the line segment XY is its midpoint. Label it as 'O'.

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The midpoint of the line segment is (4, -3).

The slope of the line segment is -2/5.

The equation of the perpendicular bisector is y = 5/2x - 13.

To find the equation of the perpendicular bisector of a line segment, we need to determine two things:

The midpoint of the line segment and the slope of the perpendicular bisector.

Midpoint:

The midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the formula:

[(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Using the endpoints (-1, -1) and (9, -5), we can find the midpoint:

x = (-1 + 9) / 2 = 4

y = (-1 - 5) / 2 = -3

Slope:

The slope of the line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the endpoints (-1, -1) and (9, -5), we can find the slope:

m = (-5 - (-1)) / (9 - (-1))

= (-5 + 1) / (9 + 1)

= -4 / 10

= -2 / 5

Perpendicular Bisector:

The slope of the perpendicular bisector will be the negative reciprocal of the slope of the line segment.

The slope of the perpendicular bisector will be 5/2.

Using the midpoint (4, -3) and the slope 5/2, we can find the equation of the perpendicular bisector using the point-slope form:

y - y₁ = m(x - x₁)

Plugging in the values, we have:

y - (-3) = 5/2(x - 4)

y + 3 = 5/2(x - 4)

y + 3 = 5/2x - 10

y = 5/2x - 10 - 3

y = 5/2x - 13

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Answer:

14

Step-by-step explanation:

because ab means 2(5), then add 4 you get your answer as 14

The trigonometric identity 1 - sin²θ/(1 + cosθ) = cosθ is true since L.H.S = R.H.S

Trigonometric identities are equations that shows the relationship between trigonometric ratios.

Given the trigonometric identity

1 - sin²θ/(1 + cosθ) = cosθ

We need to show that the left hand side (L.H.S) equals the right hand side (R.H.S) of the equation

So, we proceed as follows

Given that

1 - sin²θ/(1 + cosθ) = cosθ

Starting with the left hand side

L.H. S = 1 - sin²θ/(1 + cosθ)

Taking the L.C.M, we have that

[(1 + cosθ)  - sin²θ]/(1 + cosθ) = [1 + cosθ  - sin²θ]/(1 + cosθ)

Using the trigonometric identity sin²θ + cos²θ = 1

Substituting this into the equation, we have that

[1 + cosθ  - sin²θ]/(1 + cosθ) =  [sin²θ + cos²θ + cosθ  - sin²θ]/(1 + cosθ)

= [cos²θ + cosθ + sin²θ - sin²θ]/(1 + cosθ)

= [cos²θ + cosθ + 0]/(1 + cosθ)

= [cos²θ + cosθ]/(1 + cosθ)

Factorizing out cosθ from the numerator, we have that

= [cos²θ + cosθ]/(1 + cosθ) = cosθ(cosθ + 1)/(1 + cosθ)

= cosθ(1 + cosθ)/(1 + cosθ)

= cosθ

= R.H.S

So, 1 - sin²θ/(1 + cosθ) = cosθ

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Answer:

= cos θ

Step-by-step explanation:

A trigonometric identity that we already know is

[tex]\sin {}^{2} \theta + \cos {}^{2} \theta = 1[/tex]

From the question given we want to prove that the left side equals the right side:

[tex]1 + \frac{\sin {}^{2} \theta }{1 + \cos \theta }[/tex]

Let's rewrite sin²θ using the identity sin²θ+cos²θ=1 by subtracting cos²θ:

sin²θ=1-cos²θ, so we can write 1-cos²θ in place of sin²θ to give:

[tex]1 - \frac{1 - \cos {}^{2}\theta }{1 + \cos \theta }[/tex]

Now that everything is in terms of cos, we can solve this fraction.

1-cos²θ can be written as a difference of two squares which is (1+cosθ)(1-cosθ):

[tex]1- \frac{(1+cos \theta)(1-cos \theta)}{1+cos \theta}[/tex]

We can cancel out 1+cosθ from the fraction to give:

[tex]1 - (1 - cos \theta)[/tex]

Expand the brackets out:

[tex]= 1 - 1 + cos \theta[/tex]

= cos θ

Moment of inertia is [tex]I_{1} = \frac{5Ir^{2} }{4}[/tex] for rotation about a diameter.

What is momentum ?

Whenever you toss a ball at someone as well as it smacks him square in the face. It indicates how difficult it would have been to stop the thing. A baseball is swooping through the air. A large truck is moving. A bullet discharged from such a firearm. Momentum is important in Physics because it describes the relationship between speed, mass and direction. It also describes the force needed to stop objects and to keep them in motion. A seemingly small object can exert a large amount of force if it has enough momentum.

Have given ,

radius of a sphere = r and moment of inertia = [tex]I_{1}[/tex]

[tex]I = \frac{1}{2} Mr^{2}[/tex]

∵ [tex]M = \frac{5}{2} Mr^{2}[/tex]

∴ [tex]I_{1} = \frac{5Ir^{2} }{4}[/tex]

Hence , Moment of inertia is [tex]I_{1} = \frac{5Ir^{2} }{4}[/tex] for rotation about a diameter.

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Answer:

hard question

Step-by-step explanation:

100 meters was he under the sea at the end of the 10 minutes. This can be solved using the concept of multiplication.

Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. Multiply in arithmetic refers to the continuous addition of equal-sized groups.

Multiplication in mathematics is the addition of equal groups. The number of items there in group expands while we multiply. An example of a multiplication issue would be the product and the two components. The components in the multiplication problem 8 x 9 = 72 are the numbers 8 and 9, while the result is the number 72.

At the end of 10 minutes, the deep-sea diver would have been at a depth of 100 meters under the sea.

This is because 10 meters per minute multiplied by 10 minutes

=  100 meters.

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The linear function rule to model how many inches of water w are in the bucket after any number of minutes will be w = (1/3)t + 14

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario. An equation expresses the relationship between the variables that are given

In this situation, At time t=0, water begins to drip out of a pipe into an empty bucket. After 42 minutes, there are 14 inches of water in the bucket

The linear function rule to model how many inches of water w are in the bucket after any number of minutes will be:

w = (14/42)t + 14

w = (1/3)t + 14

Therefore, based on the calculation, the equation that can be used to represent the information will be w = (1/3)t + 14

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Using the algebraic approach, the solution to the inequality, 5x - 1 < 2x + 11 is: D. x < 4.

An inequality is a mathematical statement that says that two values are not equal. It is written using one of the following symbols:

For example, the inequality "x > 5" means that the value of x is greater than 5. "y ≤ 3" means that the value of y is less than or equal to 3.

Given the inequality, 5x - 1 < 2x + 11, solve for the value of x algebraically as shown below:

5x - 1 < 2x + 11 [given]

Combine like terms:

5x - 2x < 1 + 11

3x < 12

3x/3 < 12/3 [division property of equality]

x < 4

The solution is: D. x < 4.

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a) The function is increasing on these following intervals: (0,1), (3,5).

b) The function is decreasing on these following intervals: (1,3) and (5,6).

c) The extremas are given as follows:

The function is increasing when the derivative is positive, hence the intervals are given as follows:

(0,1) and (3,5).

The function is decreasing when the derivative is negative, hence the intervals are given as follows:

(1,3) and (5,6).

The relative extremas are the values for which the derivative is of zero, hence:

The graph of the derivative is given by the image presented at the end of the answer.

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Answer:

The scale factor is 4

Step-by-step explanation:

Assuming that the center of the dilation is the origin (0,0).  I hope the picture is clear enough to read.

Answer:

Mixed Number: 4 9/20
Decimal Form: 4.45

If this help please set brainliest.

Explanation:
To add these fractions, we first need to find a common denominator. 4 and 5 have a common multiple of 20, so we can express each fraction using a denominator of 20:

-4/5 = (-8)/20

5 1/4 = 21/4 = (215)/(45) = 105/20

Now we can add the fractions:

(-8)/20 + 105/20 = (105 - 8)/20 = 97/20

To express the result as a mixed number, we can divide 97 by 20 to get the integer part, which is 4 with a remainder of 17. The fraction part is 17/20, which can be simplified to 9/20 by dividing both the numerator and denominator by 8. The final result is:

4 9/20

This fraction can be simplified to 4.45 by dividing both the numerator and denominator by 5:

4 9/20 = (4*4 + 9)/(20/5) = (16 + 9)/4 = 25/4 = 6.25/1 = 6.25

So the final result is 4.45.

This is because the Pythagorean Theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

Pythagorean Theorem is an essential mathematical principle that has been used for centuries. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is named after the ancient Greek mathematician Pythagoras. Using this theorem, one can calculate the length of any side of a right triangle if the lengths of the other two sides are known.

This relationship between the side lengths and the angle measures can be used to calculate the exact angle measures when all three side lengths are known.

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