Sylvia wants to cover the floor of a room with carpet. She will need exactly 36 square yards of carpeting to cover the floor. When Sylvia arrives at the store to purchase the carpet, she is told that she must place her order in square feet. Assuming no waste, how many square feet of carpet does Sylvia need to order to have the exact amount necessary to cover the floor?

Step-by-step explanation:

what is the formula for the whole surface area of a sphere ?

\(a = 4 \times \pi \times {r}^{2} \)

that would give us the whole surface area all 360 degrees or 2×pi arc length all around the sphere.

but we don't need all 360 degrees. we only need the Theta'th (that is the specified angle) part.

in radians the arc length of that angle segment on the "equator" of the sphere

s = r×Theta

and the whole equator circumference is

c = 2×pi×r

so, the Theta'th part is then

r×Theta / 2×pi×r = Theta / 2×pi

we only need that part of the whole sphere surface area, so the formula would look like

\(lune = theta \times 4 \times \pi \times {r}^{2} \div (2 \times \pi)\)

=>

\(lune = theta \times 2 \times {r}^{2} \)

Answer:

4x - 5y = -10

Step-by-step explanation:

Your Welcome :)

Answer:0.8p+1 and 1+0.8p

Step-by-step explanation:

0.5p+0.3p=0.8p

7-6=+1

0.8p+1

and

Swap both numbers

(0.5p+7)+(0.3p-6)=1+0.8p

Answer:

I would say its a 16.5 %

Step-by-step explanation:

The number that contains the letters f, g, e, i, t, h exists 6759208.

The variable is known as the letter. Finding the number that can replace the variable and make the equation true is the aim of algebra. Knowing that 3 + 7 = 10 in the aforementioned example Thus, x = 7 would be the solution. (The equation is true if the x is replaced with a 7).

Both of them appear to be merely meaningful writings. However, between the ages of four and five, as kids begin to understand what these symbols actually mean, they begin to understand that numbers and letters convey completely distinct sorts of information: numbers express quantity, while letters make words.

The number that contains the letters f, g, e, i, t, h exists 6759208.

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The equation is  \(g(x) = -\frac{1}{16} (x - 1)^2 + 2\)  Graphing this equation below, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.

To graph function g, we need to find its equation that satisfies the given properties. We know that the y-intercept of g is less than that of f, so we can choose it to be 1. Also, the parabola of g opens downwards and its vertex is between the two x-intercepts, which are at x = -2 and x = 4. We can use these points to find the equation of the parabola in the standard form: g(x) = a(x - h)² + k. Using the fact that g(0) = 1 and the x-intercepts, we can solve for a, h, and k. The resulting equation is:

\(g(x) = -\frac{1}{16} (x - 1)^2 + 2\)

Graphing this equation, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

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The probability of flipping heads is 1/2, and the probability of rolling an even number is 1/2 (since there are three even numbers and three odd numbers on the cube). To find the probability of both events happening (flipping heads and rolling an even number), we multiply the probabilities together:

1/2 x 1/2 = 1/4

So the probability that Olive flipped heads and rolled an even number is 1/4 or 25%.

Answer: 1/4

Step-by-step explanation:

840 different numbers can be created selecting 4 of the digits from the number

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

Number =  8712395

Digits = 4

The count of digits in the number is 7

Using the above as a guide, we have the following:

So, we have

Numbers = 7 * 6 * 5 * 4

Evaluate

Numbers = 840

Hence, 840 numbers can be formed

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Answer:

x=1.7099

Step-by-step explanation:

2x³=10

x³=10/2

x³=5

x=∛5

x=1.7099

The solution to the equation 3 / 5x-2 = 2 / 3x-1 is x = 1.

Given the equation in the question;

3 / 5x-2 = 2 / 3x-1

To solve for x, cross multiply the equation

3 / 5x-2 = 2 / 3x-1

3( 3x - 1 ) = 2( 5x - 2 )

Apply distributive property

3( 3x - 1 ) = 2( 5x - 2 )

3×3x + 3×-1 = 2×5x + 2×-2

9x - 3 = 10x - 4

Subtract 10x from both sides

9x - 10x - 3 = 10x - 10x - 4

9x - 10x - 3 = - 4

Add 3 to both sides

9x - 10x - 3 + 3 = - 4 + 3

9x - 10x  = - 4 + 3

-x = -1

Divide both sides by -1

-x/-1 = -1/-1

x = 1

Therefore, the value of x is 1.

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Step-by-step explanation:

\( \tt \: \frac{1}{2} + 2 \frac{3}{4} - \frac{3}{8}\)

\( = \tt \: \frac{1}{2} + \frac{11}{4} - \frac{3}{8}\)

\(= \tt \: \frac{4}{8} + \frac{22}{8} - \frac{3}{8}\)

\(= \tt \: \frac{(4 + 22 - 3)}{8}\)

\(= \tt \: \frac{23}{8}\)

\(= \tt \red{3 \frac{7}{8}}\)

At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.

To find the total revenue at each price, we can multiply the price by the corresponding quantity.

Price        Quantity          Total Revenue

$6                0                      $0

$5                 1                       $5

$4                 2                       $8

$3                 3                        $9

$2                 4                         $8

$1                  5                          $5

To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.

In this case, the highest total revenue is $9, which occurs when the price is $3.

At a price of $3, the company will sell 3 units (as indicated in the Quantity column).

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The result of the expression 20 - 6 is 14.

To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.

Step 1: Start with the given expression, 20 - 6.

Step 2: Evaluate the subtraction operation: 20 - 6 = 14.

Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.

This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Given data:

V = 72w

Dimension = 9 inches long , 8 inches wide and 10 inches high.

Volume = long x wide x hight

Now, by the given question volume is given by

V = 72 w , that means height of the water in container changes.

And volume depend upon the height of the water contained.

Thus, the height of the container is the independent variable.

The answer is , height of the container is independent.

Answer:

Add equations A and C to eliminate y and add B and C to eliminate y

Step-by-step explanation:

From the equation given, we can see that the coefficient of y in A and C are alternating values 5 and  -5 which cancels out on adding same for B and C. Hence t eliminate y, we will add B and C and A and C

Therefore the correct answer will be to eliminate add equations A and C to eliminate y and add B and C to eliminate y

Answer:

The mass of wood is 4309.65 kg.

Step-by-step explanation:

Volume of a cylinder is:

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

Where \(r\) is the radius of base of cylinder

and \(h\) is the height of the cylinder

\(r=\dfrac{d}{2}\)

\(d\) is the diameter of base of cylinder.

A tree's trunk is in the shape of cylinder only. And we are given the following details:

\(d = 0.5m\\\Rightarrow r = \dfrac{0.5}{2} m\)

\(h =36 m\)

\(V = \pi (\dfrac{0.5}{2})^2 \times 36\\\Rightarrow V = 7.065\ m^3\)

Density of wood of tree = 610 kg per cubic meter

Mass of trunk = Volume \(\times\) density

\(\Rightarrow 610 \times 7.065\\\Rightarrow 4309.65\ kg\)

Hence, mass of trunk is 4309.65 kg.

Answer:

31 and 13

Step-by-step explanation:

let the 2 numbers be x and y , with x > y , then

x + y = 44 → (1)

y = x - 18 → (2)

Substitute y = x - 18 into (1)

x + x - 18 = 44

2x - 18 = 44 ( add 18 to both sides )

2x = 62 ( divide both sides by 2 )

x = 31

and

y = 31 - 18 = 13

The 2 numbers are 31 and 13

Answer:

A)The required linear demand equation ( q ) = -4500p + 41500

B) $4.61

   $95680.55

C) No it would not have been possible by charging a suitable price

Step-by-step explanation:

A)  find the linear demand equation

given two points ; ( 3, 28000 ) and ( 5, 19000 )

slope ( m ) = ( y2 - y1 ) / ( x2 - x1 )

                 = ( 19000 - 28000 ) / ( 5 - 3 )  = -4500

slope intercept is represented as ; y = mx + b

where y( 28000) = -4500(3) + b

  hence b = 41500  

hence ; y = -4500x + 41500

The required linear demand equation ( q ) = -4500p + 41500   ----- ( 1 )

p = price per ride

B ) Determine the price the company should charge to maximize revenue from ridership  and corresponding daily revenue

Total revenue ( R ) = qp

                               = p ( -4500p + 41500 )

  hence R = -4500p^2 + 41500p  ------ ( 2 )

To determine the price that should maximize revenue from ridership we will equate R = -4500p^2 + 41500p  to a quadratic equation R(p) = ap^2 + bp + c

where a = -4500 ,  b = 41500 , c = 0

hence p = \(-\frac{b}{2a}\)  = \(- \frac{41500}{2(-4500)}\) =  4.61

$4.61 is the price the company should charge to maximize revenue from ridership

corresponding daily revenue = R = -4500p^2 + 41500 p

where p = $4.61

hence R = -4500(4.61 )^2 + 41500(4.61) = $95680.55

C) No it would not have been possible by charging a suitable price

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

x = length of one side.

1,232in^2 = x^2

Take the sqrt of both sides.

35.1 in = x

The length of one side = 35.1 in

Step-by-step explanation:

We know that,

area of square = a²

→ 1,232 = a²

→ a = √1232

→ a = 35.0 in

Nearest 10th = 35.1 in

Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners.

Therefore option A is correct.

The college degree is described as a qualification awarded to students after completing the requirements for a specific course of study of which the two most common types of degrees are the Bachelor of Arts and Bachelor of Science.

With reference to the table, the occupations that do not require a college degree are:

We were able to conclude that Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners with a rate of 24.6%.

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Answer:

0.0384

Step-by-step explanation:

Given that:

Mean (m) = 6.0

Standard deviation (s) = 2.0

Sample size (n) = 50

Probability that average amount is greater than 6.5

P(x > 6.5)

Obtain the Zscore using the relation :

Zscore = (x - m) / (s / sqrt(n))

Zscore = (6.5 - 6.0) / (2 / sqrt(50))

Zscore = 0.5 / 0.2828427

Zscore = 1.7677

Zscore = 1.77

P(Z > 1.77) = 1 - P(Z < 1.77)

P(Z > 1.77) = 1 - 0.9616

P(Z > 1.77) = 0.0384

Answer:

4.2%

Step-by-step explanation:

n=50, X=6.0, δ=2.0

Z=\(\frac{6.5-6.0}{2.0}\)  =  0.25

F(Z)= 4.2% based on the chart in the FE Handbook

Answer:

Answer is...D)

Step-by-step explanation:

If you have the area just divide it by 4 and that will give you the answer .

A square has all equal sides

Hope This Helps<3

The side of the length will be x = √m square inches.

The area of the square and rectangle is -

Square = [x]²           {x is the side of a square]

Rectangle = L x B    {L is the length and B is breadth}

Given is Lisa who is decorating outside edge of a square picture frame. She needs to know the side length of the frame. The area of the frame is [m] square inches.

It is given that the the area of the square is [m] square inches.

Assume that the length of the side is [x] inches.

x² = m

x = ±√m

Side cannot be negative. Therefore, the side of the length will be -

x = √m

Therefore, the side of the length will be x = √m square inches.

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In order to determine if the given point satisfies the equation, replace the values of the coordinates of the points, and veify if the left side matches with the right side of the equation, as follow:

5x + 5y = 5

point: (0,1)

x = 0

y = 1

5(0) + 5(1) = 5

0 + 5 = 5

5 = 5

The previous result is consistent, then, the answer is YES.

Step-by-step explanation:

its 2!! hope this helps

Answer:

3

Step-by-step explanation:

A rectangular prism is thought of as being created by stacking congruent polygons.

A solid (3-dimensional) object which has six faces that are rectangles. It has the same cross-section along a length, which makes it a prism.

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Stacking congruent figures means arranging the congruent figures on the top of the other until it become a large pile.

According to the given question.

We have to stack the congruent polygons.

As we know that stacking up means ​to keep increasing in quantity until we get a large pile.

Since, when we piled up of stack the congruent polygons we will get a prism.

For example when we stack congruent squares we will get cube or we can say a rectangular prism.

If we stack congruent octagons we will get an octagon prism.

Hence, a rectangular prism is thought of as being created by stacking congruent polygons.

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68% of states have an infant mortality rate between 5.36 and 8.60 percent.

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.

In this problem, we have that:

Assuming that the distribution is normal, what percentage of states have an infant mortality rate between 5.36 and 8.60 percent (per 1,000 live births)?

\(\sf 5.36 = 6.98 - 1\times1.62\)

So, 5.36 is one standard deviation below the mean.

\(\sf 8.60 = 6.98 + 1\times1.62\)

So 8.60 is one standard deviation above the mean.

Therefore, by the Empirical Rule, 68% of states have an infant mortality rate between 5.36 and 8.60 percent.

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