How much is The cost per ticket it $7.50 for five tickets

Integration of dx/3sin^2 -4

Scilla [17]

Answer:

= 1/2 tan^(-1)(2 cot(x)) + constant

Step-by-step explanation:

Take the integral:

integral1/(3 sin^2(x) - 4) dx

Multiply numerator and denominator of 1/(3 sin^2(x) - 4) by -sec^2(x):

= integral-(sec^2(x))/(4 sec^2(x) - 3 tan^2(x)) dx

Prepare to substitute u = tan(x). Rewrite -(sec^2(x))/(4 sec^2(x) - 3 tan^2(x)) using sec^2(x) = tan^2(x) + 1:

= integral-(sec^2(x))/(tan^2(x) + 4) dx

For the integrand -(sec^2(x))/(tan^2(x) + 4), substitute u = tan(x) and du = sec^2(x) dx:

= integral-1/(u^2 + 4) du

Factor out constants:

= - integral1/(u^2 + 4) du

Factor 4 from the denominator:

= - integral1/(4 (u^2/4 + 1)) du

Factor out constants:

= -1/4 integral1/(u^2/4 + 1) du

For the integrand 1/(u^2/4 + 1), substitute s = u/2 and ds = 1/2 du:

= -1/2 integral1/(s^2 + 1) ds

The integral of 1/(s^2 + 1) is tan^(-1)(s):

= -1/2 tan^(-1)(s) + constant

Substitute back for s = u/2:

= -1/2 tan^(-1)(u/2) + constant

Substitute back for u = tan(x):

= -1/2 tan^(-1)(tan(x)/2) + constant

Which is equivalent for restricted x values to:

Answer: = 1/2 tan^(-1)(2 cot(x)) + constant

6 0

3 years ago

How do u write 5(2x - 1) in a distributive property

Nookie1986 [14]

Answer:

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

Step-by-step explanation:

The distributive property states that multiplying a sum or difference of two terms by a number is equal to multiplying the same number with each term of the sum or difference separately and then adding the products.

It can be written as:

a(b+c) = ab + ac

or

a(b-c) = ab - ac

So, for the given question,

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

5 0

3 years ago

Hope Amelia Solo, the American soccer goalkeeper, World Cup champion and two-time Olympic gold medalist, allows goals at a rate

Nuetrik [128]

Answer:

3.70% probability she allows more than one goal

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

X~Pois(0.3)

This means that $\mu = 0.3$

In her next match, what is the probability she allows more than one goal?

Either she allows at most one goal, or she allows more than one goal. The sum of the probabilities of these events is decimal 1. So

$P(X \leq 1) + P(X > 1) = 1$

We want $P(X > 1)$ . So

$P(X > 1) = 1 - P(X \leq 1)$

In which

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.3}*(0.3)^{0}}{(0)!} = 0.7408$

$P(X = 1) = \frac{e^{-0.3}*(0.3)^{1}}{(1)!} = 0.2222$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.7408 + 0.2222 = 0.9630$

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.9630 = 0.0370$

3.70% probability she allows more than one goal

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B%205x%20%2B%202y%20%3D%201%7D%20%5Catop%20%7B4x-%20y%20%3D%20-7%7D%7D

yuradex [85]

Answer: x = -1, y = -11

4 0

3 years ago

One positive integer is 1 less than twice another. The sum of their squares is 106. Find the integers.

neonofarm [45]

They give us 2 pieces to the puzzle. Both are positive numbers...x and y.
1.) 1 number is 1 less than twice another number. (x = 2y -1)...and
2.) the sum of their squares is 106. (x^2 + y^2 = 106).

substitute the value for x into the second equation.

(2y-1)^2 + y^2 = 106
(2y-1) (2y-1) + y^2 = 106 (use distributive property)
4y^2 - 2y - 2y + 1 + y^2 = 106 (subtract 106 from both sides)
4y^2 - 2y - 2y + 1 + y^2 - 106 = 106 - 106 (combine like terms)
5y^2 - 4y - 105 = 0 (factor)
(y-5) (5y-21) = 0 (set to 0)
y - 5 = 0
y = 5

substitute the 5 into the equation for y (x = 2(5) - 1)
x = 9 if we square 9, we get 81.
subtracted from 106 we have 25...the square root of 25 is 5.

our answers are 5 and 9.

8 0

4 years ago