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3 years ago

What is the period of the sinusoidal function? Enter your answer in the box.

Mathematics

1 answer:

muminat3 years ago

3 0

Answer:

ANSWER:

The period of the sinusoidal function is 2π.

Step-by-step explanation:

EXPLANATION:

The sinusoidal function is a periodic function.It goes one unit up and one unit down with an amplitude of one and it repeats itself after this time interval.So,the period of the sine function is 2π

A sine or sinusoidal loop is a perpetual swing. It is called after the role sine. It happens frequently in tentative and practiced math, science, physics, engineering, signal processing, and other disciplines. Its utmost fundamental pattern as a role of time (t).

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⦁ Find the sum of the series . 15 sigma n=1, (2n-1) Show your work

sergejj [24]

Answer:

225

Step-by-step explanation:

The sum of this series is given by the formula:

$S_n=\frac{n}{2}[2a+(n-1)d]$

Where

S_n is the sum

a is the first term (we get this by plugging in n = 1 into "2n-1", we have 2(1) - 1 = 1)

n is the number of terms (the sum is defined for n = 1 to n = 15, so 15 terms)

d is the common different (the difference is successive terms. Here, 2nd term would be 2(2) - 1 = 3, and first term was 1, so d = 3 -1 = 2)

plugging in the info, we will get the sum:

$S_n=\frac{n}{2}[2a+(n-1)d]\\S_{15}=\frac{15}{2}[2(1)+(15-1)(2)]\\=225$

The sum is 225

4 0

3 years ago

Is the sequence {4, 7, 10, 13, 16, ...} a function? Explain.

jek_recluse [69]

Step-by-step explanation:

tricky, as the sequence does not define the input values.

by we can assume that the corresponding input values are 1, 2, 3, 4, 5, ... as it is usual for a sequence.

in that sense, b is the correct answer.

3 0

2 years ago

How would you simplify the expression represented by the diagram below?

luda_lava [24]

6 + 3c is the correct answer

3 0

3 years ago

Read 2 more answers

What is six less than three raised to the third power?

Nataliya [291]

Answer:

Step-by-step explanation:

Three raise to third power can be written as $3^3$ . In this three is the base which is raised to third power.

$3^3 = 3*3*3 = 27$

Next we need to subtract 6 from Three raise to third power(i.e from 27)

which can be written mathematically as

$3^3 - 6 = 3*3*3 - 6 \\=> 27 - 6 = 21$

Hence 6 less than three raised to the third power is 21 as explained above.

4 0

3 years ago

It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell

Mademuasel [1]

Answer:

a) 75

b) 4.33

c) 0.75

d) $3.2 \times 10^{-13}$ probability that no one in a simple random sample of 100 young adults owns a landline

e) $6.2 \times 10^{-61}$ probability that everyone in a simple random sample of 100 young adults owns a landline.

f) Binomial, with $n = 100, p = 0.75$

g) $4.5 \times 10^{-8}$ probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.

This means that $p = 0.75$

(a) On average, how many young adults do not own a landline in a random sample of 100?

Sample of 100, so $n = 100$

$E(X) = np = 100(0.75) = 75$

(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.75)(0.25)} = 4.33$

(c) What is the proportion of young adults who do not own a landline?

The estimation, of 75% = 0.75.

(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?

This is P(X = 100), that is, all do not own. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 100) = C_{100,100}.(0.75)^{100}.(0.25)^{0} = 3.2 \times 10^{-13}$

$3.2 \times 10^{-13}$ probability that no one in a simple random sample of 100 young adults owns a landline.

(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?

This is P(X = 0), that is, all own. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{100,0}.(0.75)^{0}.(0.25)^{100} = 6.2 \times 10^{-61}$

$6.2 \times 10^{-61}$ probability that everyone in a simple random sample of 100 young adults owns a landline.

(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?

Binomial, with $n = 100, p = 0.75$

(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?

This is P(X = 50). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 50) = C_{100,50}.(0.75)^{50}.(0.25)^{50} = 4.5 \times 10^{-8}$

$4.5 \times 10^{-8}$ probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

8 0

3 years ago