There are adults and children in a cinema.
There are 48 adults.
25% of the people at the cinema are children.
Work out the total number of people at the cinema.

The answer is sin(y) = 4/sqrt(16 - 16x^2).

We can use the following identity:

sin(y) = sqrt\((1 - cos^2(y))\)

Since x = cos(y), we can substitute to get:

sin(y) = sqrt\((1 - x^2)\)

We are given that 0 < x < 1/4. This means that \(x^2\) < \(\frac{1}{16}\)Therefore, we can simplify the expression for sin(y) as follows:

sin(y) = sqrt(\((1 - x^2)\) = sqrt(\(1 - \frac{1}{16}\) = sqrt(\(\frac{15}{16}\)) = 4/sqrt(\(16 - 16x^2\))

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Answer:

Step-by-step explanation:

Answer:

when x=-3 then from the graph the value of y is -2

Answer:

Step-by-step expla

The statistical technique that combines results of a large number of studies is called meta-analysis.

It means that you will take data from various sources, such as studies, combine them together, and then create this mixture of various results that you can use in your own research. If something occurs often in those studies, it means that it is good and reliable information.

Answer: 9 1/3%

Step-by-step explanation:

By forming and solving equations, we know that the speed of the runner is 4 miles per hour.

So, we need to form an equation to get the speed of the runner:

'x' is the speed of the runner. Now, solve for x as follows:

Therefore, by forming and solving equations, we know that the speed of the runner is 4 miles per hour.

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To rewrite the integral ∫(2x)\(e^{4x^{2} }\)dx using integration by parts, we'll consider the function f(x) = (2x) and g'(x) = \(e^{4x^{2} }\).

Integration by parts states that ∫u dv = uv - ∫v du, where u and v are functions of x.

Let's assign:

u = (2x) => du = 2 dx

dv = \(e^{4x^{2} }\) dx => v = ∫\(e^{4x^{2} }\) dx

To evaluate the integral of v, we need to use a technique called the error function (erf). The integral cannot be expressed in terms of elementary functions. Hence, we'll express the integral as follows:

∫\(e^{4x^{2} }\) dx = √(π/4) × erf(2x)

Now, we can rewrite the integral using integration by parts:

∫(2x)\(e^{4x^{2} }\) dx = uv - ∫v du

= (2x) × (√(π/4) × erf(2x)) - ∫√(π/4) × erf(2x) × 2 dx

= (2x) × (√(π/4) × erf(2x)) - 2√(π/4) × ∫erf(2x) dx

The integral ∫erf(2x) dx can be further simplified using substitution. Let's assign z = 2x, which implies dz = 2 dx. Substituting these values, we get:

∫erf(2x) dx = ∫erf(z) (dz/2) = (1/2) ∫erf(z) dz

Therefore, the final expression becomes:

∫(2x)\(e^{4x^{2} }\) dx = (2x) × (√(π/4) × erf(2x)) - √(π/2) × ∫erf(z) dz

Please note that the integral involving the error function cannot be expressed in terms of elementary functions and requires numerical or tabulated methods for evaluation.

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Answer:

115.7 km/h

Step-by-step explanation:

velocity = distance/time

velocity = (0.9 km)/(28 s) = 0.032143 km/s

The velocity is 0.032143 k/s. The question is answered, but since km/s is not a common unit of speed, we can convert to a more common unit of speed such as km/h.

velocity = (0.9 km)/(28 s)[(3600 s)/(1 h)] = 115.7 km/h

The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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the answer choice is B.

Answer: 15 x 9 = 135

Answer:

3

Step-by-step explanation:

The probability that none of them are between 46 cm and 48 cm is 0.422

From the given data,

A botanist wanted to know if the stem lengths of daffodils differed depending on which side of a building they grew on.

South side of the building

First quartile Q1 = 43

Median Q2 = 46

Third quartile Q3 = 48

As we know that first quartile Q1 is 25% mark , Median id 50% mark and third quartile Q3 is 75% mark

25% data's lie between Q1 and Q2 and next 25% between Q2 and Q3.

So the percentage data point lying between median and Q3 is 25% or 0.25.

In a sample of 3 let X be the random variable defining numbers of daffodils lying between 46 cm and 48 cm.

Then X follows Binomial (3 P=0.25)

So, P(X=0)=\({ }^3 \mathrm{C}_0 \times 0.25^0 \times(1-0.25)^3=\frac{3 !}{3 !} \times 1 \times 0.75^3=0.421875 \approx 0.422$\)

Therefore, the probability that none of them are between 46 cm and 48 cm is 0.422

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Answer:

Domain is how many units between the farthest point on x axis.

Step-by-step explanation:

I need to see the graph to give you the domain in Interval notation.

As a result, the correct transformation sequence is: c. a centre translation  circle of 5 units to the left and 2 units up, followed by a dilation with centre (-5, 2) and scale factor 3.

A circle appears to be a double component that is defined as the collection of all points in a jet that are equidistant as from hub. A circle is typically depicted with a capital "O" for the centre and a lower section "r" for the diameter, which refers to the distance from where it began to any point on that circle. The formula 2r gives the girth (the distance of the circle), where (pi) is a conformity constant roughly equivalent to 3.14159. The formula r2 computes the circumference of a circle, which refers to the amount of space inside the circle.

To demonstrate the similarity of Circle A and Circle B, we must find a series of transformations that maps Circle A onto Circle B while preserving their shape. Because a dilation and a translation both preserve shape, we must determine the correct dilation centre and scale factor, as well as the translation direction and distance.

Option a. suggests translating Circle A's centre 5 units to the right and 2 units up, followed by a dilation with centre (0, 0) and scale factor 3. This transformation sequence does not map Circle A onto Circle B because it does not consider Circle B's position.

Option b. proposes a 5 unit to the right and 2 unit down translation of Circle A's centre, followed by a dilation with centre (0, 0) and scale factor. This transformation sequence does not map Circle A to Circle B because the translation direction is incorrect.

Option c. suggests translating Circle A's centre 5 units to the left and 2 units up, followed by a dilation with centre (-5, 2) and scale factor 3. Because it translates the centre of Circle A to the centre of Circle B and dilates Circle A with respect to the centre of Circle B, this transformation sequence maps Circle A onto Circle B. As a result, option c is the correct transformation sequence.

As a result, the correct transformation sequence is:

c. a centre translation of 5 units to the left and 2 units up, followed by a dilation with centre (-5, 2) and scale factor 3.

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Answer:

Step-by-step explanation:

EFD = 90* (straight line = 180, and other angle is 90)

EHF = 180-52 = 128* (again straight line)

HFG = 90-32 = 58* (its a right angle (can tell by the square angle) = 90*)

G = 180 - 52 - 58 = 70* (angles in triangle = 180)

E = 180 - 32 - 128 = 20* (angles in triangle = 180)

We simplify the expression -2√15(-8 + 10√15) = 150 + 16√15

To answer the question, we need to know what surds are

Surds are square roots of positive integers.

Since we have  -2√15(-8 + 10√15), we simplify the expression

So, -2√15(-8 + 10√15) = -2√15 × (-8) + 10√15 × √15 (expanding the bracket)

= -2× (-8) × √15 + 10 × √(15 × 15)

=  16 × √15 + 10 × √15²

=  16 × √15 + 10 × 15

=  16√15 + 150

=  150 + 16√15

So, we simplify the expression -2√15(-8 + 10√15) = 150 + 16√15

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Answer:

√3+√2 = 3.15

Step-by-step explanation:

because you can't square root those two so it will be a decimal

Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

The probability that the sample mean will be less than 200 pounds is approximately 0.9015 or 90.15%.

Step-by-step explanation:

To solve this problem, we can use the central limit theorem, which states that the sampling distribution of the mean of a large sample (n >= 30) will be approximately normal, regardless of the distribution of the population.

We are given that the population mean is 196 pounds and the standard deviation is 22 pounds. The sample size is 50, which is large enough to apply the central limit theorem.

To find the probability that the mean of the sample will be less than 200 pounds, we need to standardize the sample mean using the formula:

z = (x - mu) / (sigma / sqrt(n))

where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (200 - 196) / (22 / sqrt(50)) = 1.59

Now we need to find the probability that a standard normal variable is less than 1.59. We can use a standard normal table or calculator to find this probability, which is approximately 0.944.

Therefore, the probability that the mean of the sample will be less than 200 pounds is 0.944 or 94.4% (rounded to one decimal place).

So, we can say that there is a 94.4% chance that the mean weight of 50 randomly selected individuals will be less than 200 pounds.

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Step-by-step explanation:

Probability Density Function(PDF) is a statistical

expression that defines a probability distribution for a descrent random variable as opposite to a continuous random variable.

Answer:

U ARE A QUEEN

Step-by-step explanation:

HAY BESTIE

Answer:

i need points sorry ;(

Step-by-step explanation:

Answer: A. \(9x^2 - 16y^2\) .

Step-by-step explanation:

From all the options only option A has both terms square and they minus sign between them.

Also, \(9x^2 - 16y^2= (3x)^2-(4y)^2=(3x+4y)(3x-4y)\)

Here a= 3x and b= 4

Hence, the correct answer is A. \(9x^2 - 16y^2\) .

Answer:

A

Step-by-step explanation:

Answer:

it is 19000 hope this helps!

Answer:

19,000

Step-by-step explanation:

Basically add 2 zeros to 190

Hope this helps!

Answer:

what  question?

Step-by-step explanation:

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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Answer:

3

Step-by-step explanation:

The equation of line for given coordinated will be 7x + 5y = 20

Y = m x + c is the general equation for a straight line, where m is the gradient and c is the y intercept. By determining the gradient and the y intercept, and then utilizing these values in the equation, we may determine the equation of a straight line.

Given,

point = (5, -3)

slope =  -7/5

the equation of line = y-y1 = m(x - x1)

where m = slope

so the equation of line will be -

⇒ y + 3 = -7/5 (x - 5)

⇒ 5y + 15 = -7x + 35

⇒ 7x + 5y = 35-15

⇒ 7x + 5y = 20

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Answer:

104

Step-by-step explanation:

8·[7-2·(6-9)]

= 8·[7-2·(-3)]

= 8·[7 + 6]

= 8·[13]

= 104

Answer:

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

4x - 8 = 4x + 10 (subtract 4x on both sides)

-8 = 10

The answer is -8 = 10 No solution

Hope this helps ya!!