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alina1380 [7]
3 years ago
11

What is the general equation of a sine function with an amplitude of 6, a period of StartFraction pi Over 4 EndFraction, and a h

orizontal shift of StartFraction pi Over 2 EndFraction?
y = sine (8 (x minus StartFraction pi Over 2 EndFraction))
y = 8 sine (4 (x minus StartFraction pi Over 2 EndFraction))
y = 6 sine (8 (x minus StartFraction pi Over 2 EndFraction))
y = 6 sine (8 x) + StartFraction pi Over 2 EndFraction
Mathematics
2 answers:
Juliette [100K]3 years ago
7 0

Answer:

The answer is C, above was correct.

Step-by-step explanation: edge 2021

Katen [24]3 years ago
3 0

Answer:

C: y = 6 \sin (8(x-\frac{\pi}{2} ))

Step-by-step explanation:

Amplitude is changed by multiplying the entire trig function by a number, by default the amplitude is 1, so multiplying by 6 is necessary; eliminate A and B

Horizontal shift is going through the x axis, so it must be subtracted from the x value. This is only seen in choice C of the remaining answers.

Calculating the period isn't necessary because we already found the right answer but in case you need it in the future; the period is by default 2pi, to get to pi/4, it had to be 8 times smaller, so multiplying x and translations on x by 8 will get you the correct period.

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Answer: 6

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A study indicates that 62% of students have have a laptop. You randomly sample 8 students. Find the probability that between 4 a
Scrat [10]

Answer:

72.69% probability that between 4 and 6 (including endpoints) have a laptop.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they have a laptop, or they do not. The probability of a student having a laptop is independent from other students. So we use the binomial probability distribution 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.

A study indicates that 62% of students have have a laptop.

This means that n = 0.62

You randomly sample 8 students.

This means that n = 8

Find the probability that between 4 and 6 (including endpoints) have a laptop.

P(4 \leq X \leq 6) = P(X = 4) + P(X = 5) + P(X = 6)

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

P(X = 4) = C_{8,4}.(0.62)^{4}.(0.38)^{4} = 0.2157

P(X = 5) = C_{8,5}.(0.62)^{5}.(0.38)^{3} = 0.2815

P(X = 6) = C_{8,6}.(0.62)^{6}.(0.38)^{2} = 0.2297

P(4 \leq X \leq 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.2157 + 0.2815 + 0.2297 = 0.7269

72.69% probability that between 4 and 6 (including endpoints) have a laptop.

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1,156 and 1,225 are not equal, so these 3 numbers
<em>can</em> be the sides of a triangle, but it's not a right one.

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Answer:

Step-by-step explanation:

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