a theatre has the capacity to seat people accross two levels, the circle and the stalls.
the ratio of the number of seats in the circle to the number of seats in the stalls is 2:5
Last friday the audience occupied all the 528 seats in the circle and 2/3 of the seats in the stalls.
work out the percentage of occupancy of the theatre last friday.
give your answer to 2 significant figures.
show working out.


Please help me with this question, finding it very hard,
thanks.

Let's assume the first odd integer is x. Since the next odd integer would be consecutive, we can represent it as x + 2.

According to the problem, the product of these two consecutive odd integers is 399:

x * (x + 2) = 399

Expanding the equation:

x^2 + 2x = 399

Rearranging the equation into a quadratic form:

x^2 + 2x - 399 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 2, and c = -399.

x = (-2 ± √(2^2 - 4 * 1 * -399)) / (2 * 1)

Simplifying:

x = (-2 ± √(4 + 1596)) / 2

x = (-2 ± √1600) / 2

x = (-2 ± 40) / 2

Now, we can calculate the two possible values for x:

x = (-2 + 40) / 2 = 38 / 2 = 19

x = (-2 - 40) / 2 = -42 / 2 = -21

Since we are looking for consecutive odd integers, we take the positive value of x, which is 19. The next consecutive odd integer would be 19 + 2 = 21.

Therefore, the two consecutive odd integers whose product is 399 are 19 and 21.

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Yes, even if you don't know how many handshakes there were overall, you can be sure that there were at least two guests who had the same number.

Assume that the gathering will have n visitors. With the exception of oneself, each person may shake hands with n-1 additional individuals. For each guest, this means that there could be 0, 1, 2,..., or n-1 handshakes.

There will be the following number of handshakes if each guest shakes hands with a distinct number of persons (i.e., no two guests will have the same number of handshakes):

0 + 1 + 2 + ... + (n-1) = n*(n-1) divide by 2

The well known formula for the sum of the first n natural numbers . The paradox arises if n*(n-1)/2 is not an integer since we know that the actual number of handshakes must be an integer. The identical number of handshakes must thus have been shared by at least two other visitors.

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When the region enclosed by y = xex and the x-axis on the interval [0, 1] is revolved about the y-axis, a solid with the volume 2(3 + 2e) is produced.

To find the volume of the solid of revolution generated when the region bounded by y = xe^x and the x-axis on the interval [0, 1] is revolved about the y-axis, we can use the method of cylindrical shells.

The volume of the solid of revolution can be calculated using the formula: V = 2π ∫[a,b] x f(x) dx,

In this case, the curve is defined by f(x) = xe^x, and the interval of integration is [0, 1]. Therefore, the formula becomes:

V = 2π ∫[0,1] x(xe^x) dx.

V = 2π ∫[0,1] x^2e^x dx.

Integrating by parts, we can choose u = x^2 and dv = e^xdx:

du = 2x dx, v = ∫e^x dx = e^x.

Using the integration by parts formula, ∫u dv = uv - ∫v du, we have:

V = 2π [x^2e^x - ∫2xe^x dx]

 = 2π [x^2e^x - 2∫xe^x dx].

Integrating ∫xe^x dx by parts again, we choose u = x and dv = e^xdx:

du = dx, v = ∫e^xdx = e^x.

Using the integration by parts formula once more, we have:

V = 2π [x^2e^x - 2(xe^x - ∫e^xdx)]

 = 2π [x^2e^x - 2(xe^x - e^x)].

V = 2π [x^2e^x - 2xe^x + 2e^x]

 = 2π [(x^2 - 2x + 2)e^x].

Now, we can evaluate the volume using the upper and lower limits of integration:

V = 2π [(1^2 - 2(1) + 2)e^1 - (0^2 - 2(0) + 2)e^0]

 = 2π [1 - 2 + 2e - 0 + 0 + 2]

 = 2π (3 + 2e).

Therefore, the volume of the solid of revolution generated when the region bounded by y = xe^x and the x-axis on the interval [0, 1] is revolved about the y-axis is 2π(3 + 2e).

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Answer:

The answer is 10%.

Step-by-step explanation:

Solution:

To get the percentage decrease of the price of the shirt, you have to subtract 46.58 - 41.92 = 4.66 .

Then the divide 4.66 / 46.58 = 0.10004294 .

Then round the decimal and you will get 0.10 .

Then move 2 steps from the decimal then you will get the percentage 10.

So the answer  is 10%.

Answer: 48

Step-by-step explanation: just got it right on ap3x

Step-by-step explanation:

(i) Here in ∆ AED and ∆ CEB ,

Hence by AAS congruence congruence condition ,

Also ,

==========================================

(ii) In ∆ AEB and ∆CED ,

Hence by SAS condition ,

===========================================

(iii) Here ,

Since these two angles are alternate interior Angles and equal . Hence the lines will be parallel . Also since ∆AEB is congruent to ∆CED , the corresponding sides will be equal . Hence AB = CD .

The mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides

Inequalities are expressions that have unequal values, when compared

The inequality is given as

-4x > 120

When 4 is added to both sides, the inequality becomes

4 - 4x > 120 + 4

The above is not the solution to the inequality.

The solution is as follows:

We have:

-4x > 120

Divide both sides inequality by -4

x < -30

Hence, the mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides

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The value(s) of 'c' such that the area of the region bounded by the parabolas y = z² - c² and y = c² - x² is 576 are c = ±6. The area of the region is 2304 sq. units.

Given parabolas are y = z² - c² and y = c² - x². We need to find the value(s) of 'c' such that the area of the region bounded by these parabolas is 576.

Now,

Firstly, we need to sketch the region on the xy plane. Here is the required sketch:

Region bounded by parabolas y = z² - c² and y = c² - x²

Next, we need to find the intersection points of these parabolas:

y = z² - c² = c² - x²z² + x² = 2c² ⇒ z² = 2c² - x²

Now, equating the above equation to find the points of intersection, we get:z² - (2c² - z²) = 0 ⇒ 2z² - 2c² = 0 ⇒ z = ± c

Now, when z = c, x = 0 from the above equation z² = 2c² - x².

Hence, the point of intersection is (0, c).

Similarly, when z = -c, x = 0 from the above equation z² = 2c² - x².Hence, the point of intersection is (0, -c).

Now, we need to find the value(s) of 'c' such that the area of the region bounded by these parabolas is 576.

Using the concept of integration, the area of the region is given by the following formula: A = 2∫[0, c] (c² - x²) dx - 2∫[0, c] (z² - c²) dz

Thus, we need to calculate the above integrals to find the value(s) of 'c'.

∫[0, c] (c² - x²) dx = c²x - (x³/3)|[0, c] = (2/3)c³

Similarly, ∫[0, c] (z² - c²) dz = (z³/3 - c²z)|[0, c] = (2/3)c³ - 2c⁴/3

Now, substituting these values in the area formula, we get: A = 2[(2/3)c³] - 2[(2/3)c³ - 2c⁴/3] = 8c⁴/3

For area = 576, we get:8c⁴/3 = 576 ⇒ c⁴ = 216 ⇒ c = ± 6

When c = 6, the area of the region is 8c⁴/3 = 8(6⁴)/3 = 2304 sq. units.

When c = -6, the area of the region is 8c⁴/3 = 8(6⁴)/3 = 2304 sq. units.

Therefore, the value(s) of 'c' such that the area of the region bounded by the parabolas y = z² - c² and y = c² - x² is 576 are c = ±6.

The area of the region is 2304 sq. units.

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Answer:

15 I just stared so I am bad but I think I am correct

Answer:

The 4th graph.

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

f(2)=4 means when x=2. F(x) or you may call it y, equals 4, so find the one that when x=2, y=4, then its your answer.

Answer:

At least 15 hours

Step-by-step explanation:

First, subtract the $75 that her parents will contribute:

250 - 75

= 175

So, from babysitting, she will have to raise $175

Divide this by 12 to find how many hours she has to babysit:

175/12

= 14.583

We have to round this up to a whole number, which will be 15.

So, Missy will have to babysit for a minimum of 15 hours

Please find attached the drawing of the unit circle in degrees showing the angle of rotation of 60°, created with MS Word.

A unit circle is a circle that has a radius of 1 unit, and which is centered at the origin of the coordinate plane.

An angle of 60°, can be drawn on a unit circle, with the angle 0° corresponding to the horizontal x-axis and the arm rotated 60° counterclockwise from the positive x-axis

Cos(60°) = 1/2, therefore, the tip of the rotated harm coincides with the line x = 0.5

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There are n different values that the remainder r can take on when \(n^2\) is divided by n 4.

We can use the Remainder Theorem to solve this problem. The Remainder Theorem states that when a polynomial f(x) is divided by (x-a), the remainder is f(a).

Using this theorem, we can see that \(n^2\) divided by n 4 leaves a remainder of \(n^2 - kn 4\), where k is some integer. We want to find how many different values r can take on, which is the same as finding how many different values \($n^2 - kn 4$\) can take on.

Let's rewrite \(n^2 - kn 4 as n(n - k 4)\). This expression tells us that n and n - k 4 have the same remainder when divided by n 4. Therefore, n - k 4 can only take on n different values, namely \(0, n, 2n, \ldots, (n-1)n.\)

For each of these n values, we can find a corresponding value of k that satisfies\($n^2 - kn 4 \equiv r \pmod{n 4}$\), namely \(k = (n^2 - r)/(n 4).\) Therefore, there are exactly n different values that r can take on.

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For the construction of an inscribed circle the required construction that must be known is the angle bisector. The correct option is (A).

The angle bisector is a line that divides an angle into two equal parts. For a circle inscribed in a triangle the line joining the center to the vertex is the angular bisector of the interior angle.

The diagram for the given case can be drawn as follows,

For the circle inscribed in the circle, all the sides are tangents.

By the property of tangents to a circle ∠ODB and ∠OFB are right angles.

Now, in ΔODB and ΔOFB the relation is obtained as,

∠ODB = ∠OFB  (right angles)

OB = OB           (Common sides)

And, OD = OF  (radius of the circle)

⇒ ΔODB ≅ ΔOFB (by RHS criteria)

This implies that ∠ODB ≅ ∠OFB.

Thus, the line joining the centre and the vertex of triangle bisects its angles.

Hence, for the given case the required construction to be known is the angle bisector of triangle.

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Answer:

D) 140

Step-by-step explanation:

140% of 10 is 14 and 14 added to ten is 24

Answer: 12

Step-by-step explanation:

The value of the expression 7 to the power of negative 2 is 1/49.

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(7^{-2}\)

The value of this expression.

= 1/7²

= 1/49

Thus,

The value \(7^{-2}\) is 1/49.

Option B is the correct answer.

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Diversity encompasses multiple dimensions such as life experiences, educational background, geographic origin, and age that is option E.

Diversity encompasses a range of factors including life experiences, educational background, geographic origin, and age. It goes beyond a single dimension and encompasses various aspects that contribute to differences among individuals. By embracing diversity in all its forms, organizations and communities can benefit from a wider range of perspectives, ideas, and talents.

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The volume of the cylinder is approximately 6058.73 cubic meters.

A cylinder is a three-dimensional geometric shape that is similar to a tube. It has two parallel bases that are circular in shape, and its lateral surface is a rectangle. The height of the cylinder is the distance between the two bases. The cylinder has a top base and a bottom base, and these are both circles with the same diameter. The volume of a cylinder can be found by multiplying the area of one of its circular bases by its height. The surface area of a cylinder can be found by adding up the areas of the two circular bases and the lateral surface. Cylinders are widely used in mathematics, engineering, and physics, and they play an important role in the study of various geometric and physical concepts.

Given the diameter of a cylinder is 34m and its height is 27m, we can find the volume of the cylinder using the formula:

Volume = π × (diameter / 2)² × height

Plugging in the values, we get:

Volume = 3.14 × (17 / 2)² × 27

Volume = 3.14 × (8.5)² × 27

Volume = 3.14 × 72.25 × 27

Volume = 6058.73 cubic meters

So, the volume of the cylinder is approximately 6058.73 cubic meters.

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Answer:

$842.98 * 107.25/100 =  $904.10

107.25% = 107.25/100

Step-by-step explanation:

The price is at 842.98 before adding the taxes of 7.25%

if that is the price then it represents 100% of the price. By adding the sales taxes the full price after taxes will be at 100%+7.25% = 107.25 % of the previous price.

The price after sales taxes will be at

$842.98 * 107.25/100 =  $904.10

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width =

2×(x + 10y) + 2×(7x² - x + 9y) =

2x + 20y + 14x² - 2x + 18y =

14x² + 38y

Answer:

$12.43

Step-by-step explanation:

Given :

Mean = $8.52

Standard deviation, = $2.38

Stock price which falls beyond 0.05 of the distribution is at the 95th percentile

The 95th percentile distribution has a Pvalue of 1.645 (standard normal table)

We obtain the value of x, with z = 1.645

Using the Zscore relation :

Zscore = (score - mean) / standard deviation

1.645 = (score - 8.52) / 2.38

Cross multiply :

1.645 * 2.38 = score - 8.52

3.9151 = score - 8.52

Score = 8.52 + 3.9151

Score = $12.4351

Stock price beyond 0.05 is $12.43

Answer:

8

Step-by-step explanation:

bababooey

Answer:

$34.51

Step-by-step explanation:

To find 19% of 29, you first want to change the 19% to a decimal.

19% to a decimal is 0.19

Then you multiply the 0.19 by 29

29•0.19= 5.51

Now just add the 5.51 to the 29 to get the total

5.51+29=$34.51

In a fictional alphabet with 20 letters, there are 8,000 different 3-letter words possible.

To solve this problem, we can use the formula for permutations, which is n!/(n-r)!, where n is the number of letters in the alphabet and r is the number of letters in the word.

In this case, n = 20 and r = 3, so the formula would be 20!/(20-3)!. Simplifying the equation, we get:

P = 20!/(17!)

P = (20*19*18)/(1*1*1)

P = 8,000

Therefore, there are 8,000 different 3-letter words possible in a fictional alphabet with 20 letters.

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194 member voted against the bill whereas 241 members voted in favour of the bill.

A bill usually refers to a piece of paper money, such as a dollar bill or a euro bill.

To solve this problem, we can use algebra. Let's call the number of members who voted against the bill "x". Then, the number of members who voted in favor of the bill would be "x + 47" (since there were 47 more members voting in favor than against).

We know that the total number of members who voted (either for or against) was 435. So, we can write an equation:

x + (x + 47) = 435

Simplifying this equation, we get:

2x + 47 = 435

Subtracting 47 from both sides:

2x = 388

Dividing both sides by 2:

x = 194

So, 194 members voted against the bill, and the number of members who voted in favor would be:

x + 47 = 194 + 47 = 241

Therefore, 241 members voted in favor of the bill.

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Answer:

87.407

Step-by-step explanation:

circumference = 2*pie*r

= 2*pie*17

=106.8/2

=53.4

53.4+(17*2)

=87.4

Answer:

Step-by-step explanation:

it 87.38

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