If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room? (5 points) a Length = 16 feet, width = 12 feet b Length = 10 feet, width = 8 feet c Length = 32 feet, width = 24 feet d Length = 14 feet, width = 12 feet

The formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl; is true

What is the Surface Area of a Pyramid?

The total area of a pyramid's faces is referred to as the pyramid's surface area. In other terms, a pyramid's surface area is the whole area that the pyramid's surface occupies. Typically, it is measured in square units like m2, cm2, in2, and so forth.

The pyramid's two types of surface areas are:

Regular Pyramid Lateral Surface Area = (1/2) Pl Square Units

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True, the formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl.

The total area of a pyramid's faces is referred to as the pyramid's surface area. In other terms, a pyramid's surface area is the whole area that the pyramid's surface occupies. Typically, it is measured in square units like m², cm², in², and so forth.

The pyramid's two types of surface areas are:

Refer to the attachment.

The base area of the pyramid is, B = a2

The base perimeter of the pyramid is, P = 4a

The area of each of the side faces = (1/2) × base × height = (1/2) × (a) × l

Therefore, the sum of all side faces = 4 [(1/2) × (a) × l] = (1/2) × (4a) × l

= (1/2) Pl.

Regular Pyramid Lateral Surface Area = (1/2) Pl Square Units

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cash from operations is $140 when net income = $200 , depreciations = $10, and working capital went up by $70.

Cash from Operations = Net Income + Depreciation - Change in Working Capital

Plugging in the values:

Cash from Operations = $200 + $10 - $70

Cash from Operations = $140.

So, cash from operations is $140.

Cash from operations can be calculated by adding non-cash items such as depreciation and subtracting changes in working capital.

This means that the company generated $140 in cash from its operations during the given period. It is important to understand the cash from operations as it represents the cash generated from the day-to-day operations of the business and provides an indication of its ability to generate cash in the future.

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Answer:

1 because,

(2*4+82-18)/8*9

(8+82-18)/72

(90-18)/72

72/72

1

Answer:

Step-by-step explanation:

2 x 4 + 82 - 18 / 8 x 9

We want to use the PEMDAS rule for working math problems with more than one operation.

P = Parentheses first

E = Exponents second

M/D = Multiplication and division third

A/S= Addition and subtraction last

There are no parentheses, so we look for exponents next and there are none.

The next operations are multiplication and division.

Step 1

2 x 4 = 8

8 + 82 - 18 / 8 x 9

Step 2

8 x 9 = 72

Step 3

8 + 82 - 18 / 72

Before we can divide by 72, we need to add and subtract the top numbers from left to right.

Step 4

8 + 82 - 18 = 72

72/72

Now divide 72 by 72

Step 5

72/72 = 1

Answer:

The mother is now 20 years old and the daughter is 8 years old. Let the mother's age be x and the daughter's age be y. We can write the equation x - 12 = y and x - 4 = 4y. Solving these equations simultaneously gives us x = 20 and y = 8.

Step-by-step explanation:

Answer: - 14.4

Step-by-step explanation:

Matrices are used to represent data in rows and columns. The values of x and y are 9 and -14.4 respectively.

Matrix A is represented as: ( x -5, y -8)

Calculate A2: A2: (x 5, y  -8) x (x 5, y  -8)

 Recall that A2 = A

This means that: (x2 + 5y, 5x - 40)  = (x  5)

                             ( xy - 8y, 5y + 64) = (y  -8)

So, by comparison:

5x - 40 = 5

5x = 40 + 5

5x = 45

x = 9

Similarly:

5y + 64 = -8

5y = -64 - 8

5y = -72

y = -14.4

Hence, the values of x and y are 9 and -14.4 respectively.

The equation a² = a is true, when the value of  "x = 1" and "y = 1".

An equation is a mathematical statement that asserts that two expressions are equal.

When we are given an equation like

=> a² = a

it means that the value of a² on the left side is equal to the value of "a" on the right side.

Here we need to find the values of "x" and "y" for which this equation is true.

Let's start by assuming that the value of "a = 1".

In that case, the equation

=> a² = a

=> 1² = 1.

And since 1 raised to the power of 2 is equal to 1, this equation is true. Therefore, we have found a solution for the equation: "a = 1".

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The relationship on the table is an exponential function

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

x | 2 9 16 23

y | 4 8 16 32

For a fucttion to be a linear function:

A change in the x value must correspond to a change in the y values

In the function

When x increases by 7, y doubles

So, it is not linear

Instead, it is an exponential function because is has a common ratio

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The length DL of the rhombus is 24 units

The figure that completes the question is added as an attachment

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

DA = 4x

AL = 5x - 3

This means that

DA = A:

So, we have

5x - 3 = 4x

Evaluate the like terms

x = 3

So, we have

DL = 2 * DA

This gives

DL = 2 * 4 * 3

Evaluate

DL = 24

Hence, the length is 24 units

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Answer:

26582

Step-by-step explanation:

Using the distributive and double negation laws, the given statement can be simplified to ¬n.

The given expression can be simplified to ¬n using Boolean algebra. This can be shown by first using the distributive property to distribute the negation operator to the term (n ∧p). This will result in the expression ¬n ∨¬p. Then, using the commutative law of conjunction (∧), the expression can be reordered to (¬n ∧¬p) ∨p. Then, using the associative law of conjunction (∧), the expression can be reordered to ¬n ∧(¬p ∨p). Since the negation of a disjunction is the conjunction of the negations, then (¬p ∨p) simplifies to 1, which in turn simplifies the expression to ¬n ∧1, which is then simplified to ¬n. Therefore, the simplified expression is ¬n.

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Sum of angles at 5 corners of a polygonal path abcdea is 360 degrees (assuming convex polygon).

What is vector ?

Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

The sum of the angles at the corners of a polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon. In this case, n = 5, so the sum of the angles at the corners is (5-2) * 180 = 360 degrees.

However, this assumes that the polygon is convex. Since abcde is not a convex pentagon, need to calculate the angles at each corner separately.

The angle between two lines can be calculated using the dot product formula:

cos(θ) = (u⋅v) / (||u|| * ||v||)

where u and v are the vectors representing the lines, and ||u|| and ||v|| are their magnitudes. The angle θ is between 0 and 180 degrees.

For example, to find the angle between the lines ab and bc,use the vectors b-a and c-b:

cos(θ) = (b-a⋅c-b) / (||b-a|| * ||c-b||)

Sum of angles at 5 corners of a polygonal path abcdea is 360 degrees (assuming convex polygon).

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The sum of these five numbers is 66.59 degrees.

To find the sum of the angles turned at each corner, we need to find the angle between each pair of adjacent sides.

First, we find the slope of the line segment between each pair of points:

AB: slope = (2-0)/(7-0) = 2

BC: slope = (4-2)/(3-7) = -2

CD: slope = (7-4)/(3-3) = 3

DE: slope = (5-(-1))/(-1-3) = -6

EA: slope = (0-5)/(0-(-1)) = 5

Next, we find the angle between each line segment using the inverse tangent function (atan).

AB: angle = atan(2) = 63.43 degrees

BC: angle = atan(-2) = -63.43 degrees

CD: angle = atan(3) = 71.57 degrees

DE: angle = atan(-6) = -84.97 degrees

EA: angle = atan(5) = 79.56 degrees

Adding up all the angles, we get:

63.43 + (-63.43) + 71.57 + (-84.97) + 79.56 = 66.59 degrees

So the sum of the five angles is 66.59 degrees.

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The volume of the solid can be found by using the general slicing method which involves slicing the solid into multiple thin slices, computing the volume of each slice.

The general slicing method can be used to find the volume of the solid with a semicircular base of radius 9 whose cross section is a triangle. This method involves slicing the solid into multiple thin slices, computing the volume of each slice, and then summing up the volumes of all the slices. To find the volume of each slice, we first need to determine the area of the cross-section for each slice. The area of the cross-section can be found by multiplying the base of the triangle by its height. For each slice, the base of the triangle is equal to 2πr/N, where r is the radius of the semicircle and N is the number of slices. The height of the triangle is equal to the thickness of each slice. Once the area of the cross-section is calculated, we can find the volume of each slice by multiplying the area by the thickness of the slice. Finally, the volume of the solid is equal to the sum of the volumes of all the slices.

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The area of the shaded regions in the given figure is 4.56 cm².

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

From the given figure,

Here, ΔLMN is isosceles triangle, ML=MN=4 cm

Now, area of a ΔLMN =1/2 ×Base×Height

= 1/2 ×4×4

= 8 cm²

By using Pythagora's theorem, we have

LN²=LM²+MN²

LN²=4²+4²

LN²=32

LN=4√2 cm

Area of semicircle = πr²/2

Here, radius =2√2 cm

Now, 3.14×(2√2)²/2

= 12.56 cm²

Area of shaded region = 12.56-8

= 4.56 cm²

Therefore, the area of the shaded regions in the given figure is 4.56 cm².

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The soccer team sold 25 pizzas.

Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.

The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).

We can represent this situation using the following system of equations:

5x + 3(x + 11) = 233

Expanding the second equation:

5x + 3x + 33 = 233

Combining like terms:

8x + 33 = 233

Subtracting 33 from both sides:

8x = 200

Dividing both sides by 8:

x = 25

So, the soccer team sold 25 pizzas.

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The soccer team sold 25 pizzas.

Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.

The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).

We can represent this situation using the following system of equations:

5x + 3(x + 11) = 233

Expanding the second equation:

5x + 3x + 33 = 233

Combining like terms:

8x + 33 = 233

Subtracting 33 from both sides:

8x = 200

Dividing both sides by 8:

x = 25

So, the soccer team sold 25 pizzas.

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The prices of the two stocks will be the​ same after 3 hours from noon.

A stock, also known as equity, is a security that represents the ownership of a fraction of the issuing corporation.

Given that, The price of Stock A at 9 A.M. was $12.71. Since​ then, the price has been increasing at the rate of $0.12 each hour. At noon the price of Stock B was $13.46. It begins to decrease at the rate of $0.13 each hour.

Let the hours when they equalize at h, then we have:

12.71 + 0.12h = 13.46 - 0.13h

0.25h = 0.75

h = 3

Hence, the prices of the two stocks will be the​ same after 3 hours from noon.

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The triangle is 2.98142 meters high.

The height of a triangle is the perpendicular tracing from one side to the other of the triangle. The height of the triangle is also referred to as the altitude, which joins the base to form a right-angle triangle.

The formula h = xy, where x and y are the bases of the two analogous triangles formed when the height of the right triangle is drawn from one vertex to its hypotenuse, can be used to determine the altitude of a right triangle.

A line segment connecting a triangle's vertex to its opposite side is known as the triangle's altitude. In relation to the base or the side it touches, it is perpendicular. It is possible to draw three altitudes in a triangle because it has three sides. The Orthocenter is the location where the three heights of a triangle intersect.

 s = a + b +c\2

 hb = √ -a4 +2(ab)² + 2 (ac)² - b4 +2 (bc)² - c4/2b

      =√-3 4 +2 .(3.6)² +2.(3.7)² - 6 4 +2.(6.7)²-7 4 / 2.6

      =2.98142

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a) Compa a = compa b is occurs when the two vectors are proportional

b) Proja b = proja a is occurs when the two vectors are parallel.

A vector is a mathematical object with both magnitude and direction.

In the context of vectors, "comp" refers to the scalar (or dot) product and "proj" refers to the projection. The scalar product of two vectors is a scalar that measures the degree to which two vectors are pointing in the same direction. The projection of a vector is a vector that represents the component of the vector in a specific direction.

(a) The scalar product of two vectors is equal if and only if the two vectors are proportional. In other words, if a and b are nonzero vectors such that compa b = compb a, then the two vectors must be pointing in exactly the same direction.

(b) The projection of a vector is equal if and only if the two vectors are parallel. In other words, if a and b are nonzero vectors such that proja b = projb a, then the two vectors must be parallel, or pointing in exactly the same direction.

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The next term in the sequence is 1.5

It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.

The sequence given is: 12,6,3

We have to find the ratio or constant amount to find the next term:

12/2 = 6

6/2 = 3

We can see the successive term is half of the preceding one, so the general formula will be:

A(n+1)=A(n)/2

For the next term we get:

A(4th)= A(n)/2

A(4th) = 3/2

A(4th) = 1.5

The sequence is: 12, 6 ,3 , 1.5

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Correctly written question:

What is the next term of the following sequence? 12, 6, 3, ...

The ratio of red to yellow pots of flowers in three different ways are

16 : 12, 8 : 6, and 4 : 3

As per the given data Sylvia while walking with her dog, she noticed that the 32 houses had a pot of red flowers on their front step.

Also, 24 houses had a pot of red flowers on their front step.

Here we have to determine that the ratio of red pots of flowers to yellow pots of flowers in three different ways.

The three different ways will be part a part b and part c.

The ratio of red to yellow pots of flowers.

32 : 24

Simplify the above ratio.

16 : 12

Also, we have to simplify further.

We get:

8 : 6

Then:

4 : 3

Therefore the ratios are 16 : 12, 8 : 6, and 4 : 3

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10 ,  [ -3 , 4 ] and  [ 0 , 0 ] are the values in linear equation .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                        The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

a = [ 3, -4 ]

b = [ -3,4 ]

a + b =  [ 3, -4 ] +  [ -3,4 ]

     = [ 0 , 0 ]

2a + 3b  = 2  [ 3, -4 ] + 3 [ -3,4 ]

             = [6 , -8 ] + [-9 , 12 ]

             = [ -3 , 4 ]

l a - b l = l [ 3, -4 ] -  [ -3,4 ]

          = l [ 6 , -8 ] l

           = √36 + 64

           = √100

             = 10

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Answer:

Answer:

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

To find out, we use the formula for direct variation:

A = kwh

Where A is the area, k is the constant of proportionality, w is the width, and h is the height.

From the information given, we can find k:

6 = k (4)(3)

6 = 12k

k = 0.5

So, the area when width is 6 and height is 4 is:

A = kwh = 0.5 (6)(4) = 9

Answer:

Step-by-step explanation:

Answer:

To graph the line using slope and y-intercept, we can follow these steps:

Identify the slope and y-intercept:

The slope of the line is -1/3.

The y-intercept is -7.

Plot the y-intercept:

Plot the point (0, -7) on the coordinate plane, since this is the point where the line intersects the y-axis.

Plot additional points using the slope:

Choose a convenient value for x (such as x = 1) and use the equation of the line to find the corresponding value of y.

Plot this point on the coordinate plane.

Repeat the process for several more values of x to obtain additional points on the line.

Connect the dots:

Draw a line through the points that you have plotted, connecting them to form the graph of the line.

Note: The line y = -1/3x - 7 will have a negative slope and will decrease as x increases, which means that the line will slope downward from left to right.

Answer:

y=-1/3x+1

Step-by-step explanation:

3x+9y=9

First take your x and transfer it to the other side of the = by doing the opposite.

3x+9y=9

-3x -3x

9y=9-3x

You must then switch the -3x and 9 so that it stays in y intercept form

9y=-3x+9

Then you need to get y by itself by dividing both sides by 9.

y=-3x/9+1

Lastly simplify the fraction left from the division.

y=-1/3x+1

The amount of feet saved is given as follows:

24 feet.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

Applying the Pythagorean Theorem, the diagonal length for this problem is given as follows:

d² = 35² + 50²

d = square root (35² + 50²)

d = 61 feet.

Without the diagonal, the distance would be of:

35 + 50 = 85 feet.

Hence the amount saved is given as follows:

85 - 61 = 24 feet.

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Team A needs to sell 255 bags of popcorn to reach their goal of $100.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Team A will sell the bags of popcorn for $0.50 each.

Team B will sell the cotton candy for $0.75 per stick.

Let the number of bags of popcorn sold by Team A be "x".

So, the total cost for the popcorn machine rental and supplies is

= $15 + 0.05x.

To reach their goal of $100

$100 = 0.5x - ($15 + 0.05x)

$100 = 0.5x - $15 - 0.05x

$115 = 0.45x

x = $115 / 0.45

x = 255 bags of popcorn

Thus, Team A needs to sell 255 bags of popcorn.

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18 meters = 59.0551 foot. Meter to Feet Conversion : One meter is approximately equal to 3.28084 feet. To convert meters to feet, multiply the given meter value by 3.28084 feet.

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As a result, the confidence level widens as the sample size shrinks, indicating an inverse connection between the confidence interval and sample size.

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The measure of angle R is 106.5 degrees approximately when the

sides of the triangle are given.

If ABC is a triangle, then as per the statement of the Law of Cosines, we have: a2 = b2 + c2 – 2bc cos α, where a,b, and c are the sides of triangle and α is the angle between sides b and c.

Here PQR is a triangle, then as per the statement of cosine law,

we will have:  p2 = q2 + r2 – 2pqcos R,

where p, q  and r are the sides of triangle and R is the angle between sides q and p.

therefore, [tex]28^{2} = 17^{2} +15^{2}[/tex] - 2(28)(17)cos R

              cos R = -270/952

                        = -0.284

                    R = cos-1(-0.284)

              therefore, R = 106.499 = 106.5 approximately.

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Answer: 10

step by step explenation