28775 tickets are sold for a football match. Children’s tickets cost £15. The ratio of children to adults is 9:16.
If the total ticket sales makes £615785, what is the difference between the price of an adults ticket and a children’s ticket?

The coefficient of x^4 y^7 in the expansion of (x y)^11 is:

(11 choose 4) = 330.

The binomial expansion of (x y)^11 is given by the formula:

(x y)^11 = (11 choose 0) x^11 y^0 + (11 choose 1) x^10 y^1 + (11 choose 2) x^9 y^2 + ... + (11 choose 11) x^0 y^11

To find the coefficient of x^4 y^7 in this expansion, we need to look at the term (11 choose 4) x^4 y^7. The coefficient of this term is given by the binomial coefficient (11 choose 4), which is calculated as:

(11 choose 4) = 11! / (4! * (11-4)!) = 330

Therefore, the coefficient of x^4 y^7 in the expansion of (x y)^11 is 330.

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The measure of angle ABD is 76° and the measure of angle DBE is 104°.

Given that, the measure of angle ABE is 180°.

∠ABC=3x+5 and ∠CBE=2x+10.

Here, ∠ABC+∠CBE=∠ABE

3x+5+2x+10=180°

5x+15=180°

5x=165°

x=33°

So, ∠ABC=3x+5=104° and ∠CBE=2x+10 = 76°  

Angle CBE = Angle ABD = 76°

Angle ABC = Angle DBE = 104°

Therefore, the measure of angle ABD is 76° and the measure of angle DBE is 104°.

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Answer:

\(\Huge \fbox{72 mph}\)

Step-by-step explanation:

Step 1:

Convert \(\bold{32 m/s}\) to \(\bold{km/h}\) by multiplying by 3.6 (since \(\bold{1 m/s}\) = \(\bold{3.6 km/h}\))

\(\large \text{32 m/s $\times$ 3.6 = 115.2 km/h}\)

Step 2:

Convert \(\bold{115.2 km/h}\) to \(\bold{mph}\) using the given conversion factor of \(\bold{8 km/h = 5 mph}\)

\(\large \text{115.2 km/h $\div$ 8 km/h = 14.4}\\\text{14.4 $\times$ 5 mph = 72 mph}\)

Therefore, \(\bold{32 m/s}\) is equivalent to \(\bold{72 mph}\).

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In the standard conversion unit, 32 m/s equals 72 mph in mph

The conversion equation is given as

\(\sf 8 \ km/h = 5 \ mph\)

Convert 8 km to meters

So, we have the following equation

\(\sf 8 \times 1000 \ m/h = 5 \ mph\)

Evaluate the products

So, we have the following equation

\(\sf 8000 \ m/h = 5 \ mph\)

Convert 1 hour to seconds

So, we have the following equation

\(\sf 8000 \ m/3600 s = 5\ mph\)

Evaluate the quotient

So, we have the following equation

\(\sf \dfrac{20}{9} \ m/s = 5 \ mph\)

Multiply both sides by 9/20

\(\sf 1 \ m/s = \dfrac{9}{20} \times 5 \ mph\)

Multiply both sides by 32

\(\sf 32 \times 1 \ m/s = 32 \times \dfrac{9}{20} \times 5 \ mph\)

Evaluate the products

\(\sf 32 \ m/s = 72 \ mph\)

Hence, the equivalent of 32 m/s in mph is 72 mph

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Answer:

178.570

Step-by-step explanation:

Answer:

it stays the same so 178.572

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

1 hour = 60 minutes

1200 riders = 60 minutes: divide by sixty to set equal to 1

20 riders = 1 minute

Just divide 1,200 by 60 because there are 60 minutes in 1 hour.

Just think about it this way: If you eat 1 banana a minute, you eat 60 bananas an hour. The amusement park ride goes around once a minute. In one hour it goes around 60 times. Each time it carries the same amount of people.

1,200 divided by 60 is...

20!

The ride can carry 20 riders each ride, and each ride lasts a minute.

We then applied the formula for factoring perfect square trinomials to obtain the fully factored form, which is 4(2x - 3)2.

To factor 16x2 - 48x + 36 completely, we can first factor out the greatest common factor of 4:

16x2 - 48x + 36 = 4(4x2 - 12x + 9)

Now,

we can see that the expression inside the parentheses is a perfect square trinomial, which can be factored as:

4x2 - 12x + 9 = (2x - 3)2

Therefore, putting the pieces together, we have:

16x2 - 48x + 36 = 4(4x2 - 12x + 9) = 4(2x - 3)2

Hence, the fully factored form of the given expression is 4(2x - 3)2, which is option D).

The reason why we can recognize 4x2 - 12x + 9 as a perfect square trinomial is because it has the form a2 - 2ab + b2, where a = 2x and b = 3. This form can always be factored as (a - b)2, which in this case gives (2x - 3)2. The factor of 4 in the final answer comes from the fact that we initially factored out a 4 from the given expression.

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Answer:

A) The fish was out of water for 0.6875 seconds.

B) Maximum height = 5.672

Step-by-step explanation:

Height is modeled by;

y = -16t² + 11t

A) To find total time of the fish out of water, we need to find the x - intercept. That is the points where y = 0

So, 0 = -16t² + 11t

So the roots of this equation are;

t = 0 or 0.6875

Thus,the fish was out of water for 0.6875 seconds.

B) y = -16t² + 11t

The x coordinate of the vertex is at - b/2a

For y = -16t² + 11t

a = -16, b = 11, c = 0

So, -b/2a = -11/(2*-16) = 11/32

The maximum height will be at the y-coordinate of the vertex.

Thus, we need to find f(11/32)

f(11/32) = -16(11/32)² + 11(11/32) = 1.890625 + 3.78125 = 5.671875 ≈ 5.672

Answer: 6(u-2)+2=6u-10

Step-by-step explanation:

Then, any value of u makes the equation true.

The other side of this equation 6 (u-2) + 2 is 6u - 10 and is true for all values of u.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

6 (u-2) + 2

Simplify the above expression as shown below,

6 × u - 6 × 2 + 2  (Use distributive property)

6u - 12 + 2    (Add constant terms)

6u - 10

Thus, 6 (u-2) + 2  = 6u - 10

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Heritability is typically divided into two categories, namely broad sense and narrow sense heritability.

The following formulas are used to calculate heritability in the broad sense:

H² = Vg / Vp

Where,

H² = Heredity

Vg = Genotypic Variance

Vp = Phenotypic Variance

FOR BACK FAT:

Vg = 13.7

Vp = 28.9

H² = Vg / Vp

H² = 13.7 / 28.9

H² = 0.474

FOR BODY LENGTH:

Vg = 27.2

Vp = 49.1

H² = Vg / Vp

H² = 27.2 / 49.1

H² = 0.553

These formulas are used to calculate narrow sense heredity:

H² = Vg / Vp

Where,

H² = Heredity

Vg = Genotypic Variance

Va = Additive Genetic Difference

FOR BACK FAT:

Vp = 28.9

Va = 7.98

H² = Va / Vp

H² = 7.98 / 28.9

H² = 0.276

FOR BODY LENGTH:

Vp = 49.1

Va = 12.4

H² = Va / Vp

H² = 12.4 / 49.1

H² = 0.252

Because back fat has a high narrow sense of heredity and a low broad sense of heritability, it is the best pick. Additionally, heritability in the restricted sense has good breeding value.

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First, we convert 1/2% to a decimal.

Similarly:

Answer:

B/6

Step-by-step explanation:

is this what you mean

B= ammount of candie

1/6= the piles she divided

so

\(\frac{b}{6}\)

Paper Company will make the following entry:

Debit: Notes Receivable - Dame Company $4,700

Credit: Accounts Receivable $4,700

What is an entry?

An "entry" in accounting refers to the recording of a financial transaction or event in the company's books or accounting system. It is the process of documenting the impact of a transaction on the financial statements.

1. Debit: Notes Receivable - Dame Company ($4,700) - This account represents the amount owed to Paper Company by Dame Company and is classified as a noncurrent asset since it will be settled in more than one year.

2. Credit: Accounts Receivable ($4,700) - This account represents the open accounts receivable from Dame Company, which is now being settled through the promissory note.

By making this entry, Paper Company acknowledges the receipt of the promissory note and removes the outstanding accounts receivable from their books, replacing it with a notes receivable asset.

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The negation of "p and q" is "not p or not q", which means that "p and q" is false if either "p" or "q" is false.

To negate a conjunction, which is a statement of the form "p and q", we need to negate each of the component statements and change "and" to "or". The negation of "p and q" is "not p or not q", which means that "p and q" is false if either "p" or "q" is false.

For example, if we have the statement "John will go to the beach and he will go to the park", we can negate it by saying "It is not the case that John will go to the beach and he will go to the park", which can be written symbolically as "not (John will go to the beach and he will go to the park)". Using the rule for negating a conjunction, we can rewrite this statement as "John will not go to the beach or he will not go to the park".

Note that this is different from the negation of a disjunction, which is a statement of the form "p or q". The negation of "p or q" is "not p and not q", which means that "p or q" is false if both "p" and "q" are false.

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Answer:

  6√3 square units

Step-by-step explanation:

The ratios of side lengths in a 30°-60°-90° triangle are 1 : √3 : 2. Using this fact, we can find the lengths of the orthogonal sides of the triangle to be ...

  3(2/√3) = 2√3 . . . . side AB in the attached figure

and

  2·3 = 6 . . . . . . . . . . side AC in the attached figure

Then the area of the triangle is ...

  A = 1/2bh

  A = 1/2(6)(2√3) = 6√3 . . . . square units

Arc DC specifically corresponds to a 90° angle in this scenario.

In circle O, if DC is intercepted by diameter AC, the measure of arc DC is 90°. This is because any arc intercepted by a diameter in a circle forms a right angle, which is always 90°.

Therefore, the correct answer is 90°. It is important to note that the given choices of 40°, 140°, and 220° are incorrect in this context. Arc DC specifically corresponds to a 90° angle in this scenario.

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Answer:

You multiply each term inside the parentheses by -1 in order to subtract each term, since subtraction is the additive inverse.

Step-by-step explanation:

Subtraction is the additive inverse. We multiply each term in parentheses by -1  in order to open the parentheses and start adding the resulting terms.

In the equation 3(x + 2) + 4x = 6x + 8 + x

the number to be changed in y = 7x + 6 is 6

the number to be used instead is 8

Simplifying the equation,3(x + 2) + 4x = 6x + 8 + x

3(x + 2) + 4x = 6x + 8 + x

3x + 6 + 4x = 6x + 8 + x

7x + 6 = 7x + 8

the two equations are not equal however for

y = 7x + 6 and y = 7x + 8 to make infinitely many solutions 6 in y = 7x + 6 should be changed to 8 or

"8" in y = 7x + 8 in should be changed to 6

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Answer: 5700

Step-by-step explanation: 5.7 ×10³=5.7x1000=5700

Answer:

3

Step-by-step explanation:

The chances that the coin is unbiased are 0.08 or 8%.

Probability is the measure of the likelihood of an event occurring.

Probability is calculated by dividing the number of successful events by the total number of possible events.

The probability of an event ranges between 0 and 1.

An event with a probability of 0 has no chance of occurring, whereas an event with a probability of 1 is certain to occur.

In the given question, a coin was tossed 500 times.

The result was heads 230 times and tails 270 times.

Let us calculate the probability of getting heads when the coin is tossed.

P(h) = Probability of getting heads = Number of heads/Total number of tosses = 230/500 = 0.46

Similarly, let us calculate the probability of getting tails when the coin is tossed.

P(t) = Probability of getting tails = Number of tails/Total number of tosses = 270/500 = 0.54

The coin is unbiased if the probability of getting heads is equal to the probability of getting tails when the coin is tossed.

P(h) = P(t)0.46

= 0.54 0.54 - 0.46

= 0.08

Thus, the chances that the coin is unbiased are 0.08 or 8%.

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Answer:

18 1/2

Step-by-step explanation:

1/2z = 9 1/4

1/2z = 37/4

z = 74/4 (Multiplied on both sides by 2 to get of the 1/2)

z = 18 1/2

The probability of selecting a black card first and a red card second from a standard deck of 52 playing cards without replacement is 13/51.

The probability of selecting a black card on the first draw is 26/52, or 1/2, since there are 26 black cards in a standard deck of 52 playing cards.

After the first card is drawn, there are 51 cards remaining, of which 26 are red. Therefore, the probability of selecting a red card on the second draw, given that a black card was selected on the first draw, is 26/51.

To find the probability of both events happening (selecting a black card followed by a red card), we multiply the probabilities of each event:

P(black card first, red card second) = P(black card first) × P(red card second | black card first)

P(black card first, red card second) = (1/2) × (26/51)

P(black card first, red card second) = 13/51

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Answer:

x = 2, y = -3

Step-by-step explanation:

Since both equations are set equal to y,

\(-x+5=-2x+7 \\ \\ x=2 \\ \\ \implies y=-2+5= - 3\)

To determine how many times the spinner will land on blue or green, we need to know the number of sections that are shaded blue or green.

Let's assume the spinner has 8 sections in total, with 3 sections shaded blue, 4 sections shaded green, and the remaining sections shaded red.

Out of 24 spins, the probability of landing on blue or green can be calculated as the sum of the individual probabilities. The probability of landing on blue is 3/8, and the probability of landing on green is 4/8 (since there are 4 green sections out of 8 in total).

Therefore, the expected number of times the spinner will land on blue or green in 24 spins is:

(3/8 + 4/8) * 24 = (7/8) * 24 = 21.

So, the spinner is expected to land on blue or green approximately 21 times out of the 24 spins.

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1. Irrelevancy Result 1: Modigliani-Miller Theorem

The Modigliani-Miller theorem states that, under certain assumptions, the value of a firm is independent of its capital structure. This result is achieved under the assumptions of perfect capital markets, no taxes, no transaction costs, and no information asymmetry. In this case, the theorem shows that the way a firm finances its operations, whether through debt or equity, does not affect its overall value.

Irrelevancy Result 2: Capital Structure Irrelevance

This result builds upon the Modigliani-Miller theorem and states that the specific mix of debt and equity used to finance a firm's operations is irrelevant in determining its value. This result holds true as long as the overall cost of capital remains constant. In other words, different capital structures may lead to different returns for equity holders and debt holders, but the total value of the firm remains the same.

Irrelevancy Result 3: Dividend Irrelevance

The dividend irrelevance result, also known as the Miller-Modigliani dividend irrelevance proposition, states that the dividend policy of a firm does not affect its value. This result is based on the assumption that investors can reinvest dividends at the same rate of return as the firm. Therefore, whether a firm pays dividends or retains earnings for reinvestment purposes, the total value of the firm remains unchanged.

2. These irrelevancy results collectively suggest that, under specific assumptions, certain financial decisions or factors do not have a significant impact on the value of a firm. The results highlight the importance of underlying assumptions and perfect market conditions in arriving at these conclusions.

When discussing valuation issues, these results emphasize the need to consider the relevant assumptions and market conditions that apply to a particular situation. Real-world factors such as taxes, transaction costs, and information asymmetry can significantly impact the valuation of a firm and may invalidate the assumptions underlying these irrelevancy results.

Therefore, while these results provide valuable insights, it is crucial to carefully analyze the specific context and consider additional factors when conducting valuations in practical settings.

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As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.

Here,

If the two angles are congruent, then they must have the same measure.

So we can set the expressions for the measures of the two angles equal to each other and solve for y:

3y + 11 = 11y + 15

Subtracting 3y from both sides:

11 = 8y + 15

Subtracting 15 from both sides:

-4 = 8y

Dividing both sides by 8:

y = -1/2

Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

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Answer:

45/4 inches closer 11

Step-by-step explanation:

16/9 = 20/x

9/4= x/5

45/4 inches = x

11< x< 12

Answer:

Each ride costs $1.25

Step-by-step explanation:

$20 - $13.75 = $6.25

$6.25 / 5 = $1.25

Answer:

1.25 per ride

Step-by-step explanation:

Subtract 13.75 from 20. You get 6.25. Divide 6.25 by 5.