All categories

2 years ago

Use complete sentences to describe the range of the sine function.

1 answer:

3 0

The Range of a function is the set of all values that that function can take.

Given the sine function f(x)=sinx,

This function is the function which calculates the sine of the values of x.

According to the definition of the sine of an angle x in the unit circle,

$-1 \leq sinx \leq 1$ ,

so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.

This means that the values that the sine function takes are any values between -1 and 1, inclusive.

This determines the Range of the sine function.

So the Range of the sine function is [-1, 1]

You might be interested in

In a room there are a mixture of people and dogs. there are 72 heads, and 200 legs. how many dogs are in the room?

IRINA_888 [86]

There are a total of 9 dogs

6 0

2 years ago

Which of the following are solutions to the equation sinx cosx = 1/4? Check all that apply.

N76 [4]

The solution is <span>B. π/12+nπ

</span>proof
sinx cosx = 1/4 is equivalent to 2 <span>sinx cosx = 1/2 or sin2x =1/2
so 2x = arcsin(1/2) = </span>π/6 + 2nπ, so x = π/12+nπ

8 0

2 years ago

Read 2 more answers

The organizers of a talent show have budgeted $1800 to buy souvenir clothing to sell at the event. They can buy shirts for $10 e

ki77a [65]

Let s represent number of shirts and h represent number of hats.

We have been given that the organizers of a talent show have budgeted $1800 to buy souvenir clothing to sell at the event. They can buy shirts for $10 each and hats for $8 each.

The cost of s shirts would be $10s$ and cost of h hats would be $8h$ . The cost of s shirts and h hats should be less than or equal to 1800. We can represent this information in an inequality as:

$10s+8h\leq 1800$

We are also told that organizers plan to buy at least 5 times as many shirts as hats. This means that number of shirts should be greater than or equal to 5 times hats. We can represent this information in an inequality as:

$s\geq 5h$

Therefore, the second inequality should be $s\geq 5h$ and option C is the correct choice.

6 0

2 years ago

Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small

Greeley [361]

Answer:

(a) $\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....$

(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.

(c) The probability that n ≥ 4 is 0.018.

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.

Step-by-step explanation:

We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.

Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,

Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

So, the probability distribution of the geometric distribution is given by;

$\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....$

where, p = probability that the residents are of Hawaiian ancestry = 74%

(b) The probabilities that n = 1, n = 2, and n = 3 is given by;

$\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}$

P(1) = $\text{0.74} \times \text{(1 - 0.74)}^{1-1}$ = 0.74

P(2) = $\text{0.74} \times \text{(1 - 0.74)}^{2-1}$ = 0.192

P(3) = $\text{0.74} \times \text{(1 - 0.74)}^{3-1}$ = 0.050

(c) The probability that n ≥ 4 is given by = P(n ≥ 4)

P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)

= 1 - 0.74 - 0.192 - 0.050

= 0.018

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)

We know that the mean of the geometric distribution is given by;

Mean = $\dfrac{p}{1-p}$ = $\dfrac{0.74}{1-0.74}$

= $\dfrac{0.74}{0.26}$ = 2.85 or 3 (approx).

4 0

2 years ago

A high percentage of people who fracture or dislocate a bone see a doctor for that condition. Suppose the percentage is 99%. Con

marishachu [46]

Answer:

(i) 0.15708

(ii) 0.432488

(iii) 3

Step-by-step explanation:

Given that, 99% of people who fracture or dislocate a bone see a doctor for that condition.

There is only two chance either the person having fracture or dislocation of bone will either see the doctor or not.

As per previous data, if one person got a fracture or dislocation of bone, the chance of seeing the doctor is 0.99. Assuming this chance is the same for every individual, so the total number of people having fractured or dislocated a bone can be considered as Bernoulli's population.

Let p be the probability of success represented by the chances of not seeing a doctor by any one individual having fractured or dislocated a bone.

So, p=1-0.99=0.01

According to Bernoulli's theorem, the probability of exactly r success among the total of n randomly selected from Bernoulli's population is

$P(r)=\binom{n}{r}p^r(1-p)^{n-r}\cdots(i)$