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3 years ago

Please explain your answer as well. THX!!

Mathematics

2 answers:

ehidna [41]3 years ago

8 0

Answer:

Step-by-step explanation:

sec(x)*cos(x) + cos(x)-1/(sec(x))

We know that sex(x) = 1/(cos(x))

substitute it in our expression.

1/(cos(x)) * cos(x) + cos(x) - 1/(1/cos(x)) = 1+cos(x) - cos (x)= 1

Sedaia [141]3 years ago

8 0

ANSWER

A. 1

EXPLANATION

The given trigonometric expression is

$\sec(x) \cos(x) + \cos(x) - \frac{1}{ \sec(x) }$

Recall and use the following reciprocal identities.

$\frac{1}{ \sec(x) } = \cos(x)$

and

$\sec(x) = \frac{1}{ \cos(x) }$

When we apply these identities, we get

$\frac{1}{ \cos(x) } \times \cos(x) + \cos(x) - \cos(x)$

This simplifies to:

$1 + 0 = 1$

The correct choice is A

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The number of people arriving at a ballpark is random, with a Poisson distributed arrival. If the mean number of arrivals is 10,

Stella [2.4K]

Answer:

a) 3.47% probability that there will be exactly 15 arrivals.

b) 58.31% probability that there are no more than 10 arrivals.

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.

If the mean number of arrivals is 10

This means that $\mu = 10$

(a) that there will be exactly 15 arrivals?

This is P(X = 15). So

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

$P(X = 15) = \frac{e^{-10}*(10)^{15}}{(15)!} = 0.0347$

3.47% probability that there will be exactly 15 arrivals.

(b) no more than 10 arrivals?

This is $P(X \leq 10)$

$P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

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

$P(X = 0) = \frac{e^{-10}*(10)^{0}}{(0)!} = 0.000045$

$P(X = 1) = \frac{e^{-10}*(10)^{1}}{(1)!} = 0.00045$

$P(X = 2) = \frac{e^{-10}*(10)^{2}}{(2)!} = 0.0023$

$P(X = 3) = \frac{e^{-10}*(10)^{3}}{(3)!} = 0.0076$

$P(X = 4) = \frac{e^{-10}*(10)^{4}}{(4)!} = 0.0189$

$P(X = 5) = \frac{e^{-10}*(10)^{5}}{(5)!} = 0.0378$

$P(X = 6) = \frac{e^{-10}*(10)^{6}}{(6)!} = 0.0631$

$P(X = 7) = \frac{e^{-10}*(10)^{7}}{(7)!} = 0.0901$

$P(X = 8) = \frac{e^{-10}*(10)^{8}}{(8)!} = 0.1126$

$P(X = 9) = \frac{e^{-10}*(10)^{9}}{(9)!} = 0.1251$

$P(X = 10) = \frac{e^{-10}*(10)^{10}}{(10)!} = 0.1251$

$P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.000045 + 0.00045 + 0.0023 + 0.0076 + 0.0189 + 0.0378 + 0.0631 + 0.0901 + 0.1126 + 0.1251 + 0.1251 = 0.5831$

58.31% probability that there are no more than 10 arrivals.

8 0

3 years ago

Given the sequence 12, 9, 6, 3,........ where x = 0, 1, 2......,

Nitella [24]

Answer:

f(x) = -3x + 12

Step-by-step explanation:

The chart could be represented like this:

x y

0 12

1 9

2 6

3 3

Suppose that f(x) = y

And substitute x values.

y = -3x + 12

"x = 0"

y = -3(0) + 12

y = 0 + 12

y = 12

"x = 3"

y = -3(3) + 12

y = -9 + 12

y = 3

From the results, it corresponds to the function.

4 0

3 years ago

Pierre uses 30 grams of chocolate to make

Travka [436]

Pierre can make 3 liters of chocolate sauce from 450 grams of chocolate.

Step-by-step explanation:

Given,

Chocolate used to make 200 ml of chocolate sauce = 30 grams

Ratio of chocolate to milliliters of chocolate sauce = 30:200

Let,

x be the milliliters of sauce made from 450 grams of chocolate

Ratio of chocolate to ml of sauce = x:450

Using proportion;

Ratio of chocolate to ml of sauce:: ratio of chocolate to ml of sauce

$30:200::450:x$

Product of extreme = Product of mean

$30*x=200*450\\30x=90000$

Dividing both sides by 30

$\frac{30x}{30}=\frac{90000}{30}\\x=3000$

450 grams of chocolate will make 3000 milliliters of chocolate sauce.

We will convert this in liters.

1 liter = 1000 ml

3000 ml = $\frac{3000}{1000}$ = 3 liters

Pierre can make 3 liters of chocolate sauce from 450 grams of chocolate.

Keywords: ratio, proportion

Learn more about proportion at:

#LearnwithBrainly

3 0

3 years ago

Please lemme know soon, ty

Mrac [35]

Answer:

PHOTO IS BLACK . SO , I CAN'T ANSWER UR QUESTION

4 0

3 years ago

What all needs to be known in 8th grade math?

Firlakuza [10]

Answer:

Technically, it depends on which school you attend, which state, city, or area you live in, and if you have an honor-based program or just the basic class. Although, in the basic level of 8th grade, you will learn measurements, a bit of geometry, algebra, and probability.

Hope this helps and good luck!

4 0

2 years ago