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qwelly [4]
3 years ago
12

Write an equation for a cosine function with an amplitude of 5, a period of 3, a phase shift of 2, and a vertical displacement o

f 2.
y = 5 cos 2π x-2/3 + 2

y = 3 cos π (x-2) - 5

y = 3 cos 2π (x-5) + 2

y = 5 cos 2π x+2/2 + 2
Mathematics
1 answer:
kramer3 years ago
8 0

Answer:

y = 5 cos ((2π/3)x - 2) + 2

Step-by-step explanation:

Cosine function takes a general form of  y = A cos (Bx + C) + D

Where

A is the amplitude

2π/B is the period

C is the phase shift ( if -C, then phase shift right, if +C phase shift left)

D is the vertical displacement (+D is above and -D is below)

Given the conditions of the function to build and the general form, we can write:

** Note: period needs to be 3, so 2π/B = 3, hence B = 2π/3

Now we can write:

y = 5 cos ((2π/3)x - 2) + 2

first answer choice is right.

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3.30 Survey response rate. Pew Research reported in 2012 that the typical response rate to their surveys is only 9%. If for a pa
Artist 52 [7]

Answer:

0% probability that at least 1,500 will agree to respond

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

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)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 15000, p = 0.09

So

\mu = E(X) = np = 15000*0.09 = 1350

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15000*0.09*0.91} = 35.05

What is the probability that at least 1,500 will agree to respond

This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{1499 - 1350}{35.05}

Z = 4.25

Z = 4.25 has a pvalue of 1.

1 - 1 = 0

0% probability that at least 1,500 will agree to respond

6 0
3 years ago
HURRY!!
Sophie [7]
8 ounce (280 milligrams of calcium)
128 ounces (? milligrams of calcium)
128/8 = 16 (eight is sixteen times in 128)
Then
16 * 280 = 4,480 milligrams of calcium per gallon
8 0
2 years ago
Use the net to find the surface area of the square pyramid.
dangina [55]
C because 40•27/2•4+27•27 is 2,889 40 is height 27 is base area of triangle u divide by 2 then there is 4 sides so u multiply by 4 and u need to add the base which is base times height and base is 27 and height is 27 so when u do all that u get C
8 0
2 years ago
Read 2 more answers
In △MDK, m=16.4, d=22, and k=19. Identify m∠D rounded to the nearest degree. The figure shows triangle M D K. The length of side
Alex_Xolod [135]

The length of the sides,MD, DK, and KM gives the measure of the angle m<D as c) 76°

<h3>Which method can be used to find the measure of angle m<D?</h3>

In triangle ∆MDK, we have;

m = 16.4

d = 22

k = 19

Using cosine rule, we get;

d² = m² + k² - 2•m•k•cos(D)

Therefore;

2•m•k•cos(D) = m² + k² - d²

D = arccos \left( \frac{ {m}^{2} +  {k}^{2}  -  {d}^{2}   }{2 \cdot m \cdot k}  \right)

Which gives;

D = arccos \left( \frac{ {16.4}^{2} +  {19}^{2}  -  {22}^{2}   }{2  \times  16.4  \times  19}  \right)  \approx  {76}^{ \circ}

  • m<D = 76°

The correct option is therefore;

  • c) 76°

Learn more about the rule of cosines here:

brainly.com/question/4316134

#SPJ1

6 0
1 year ago
Round 2.705 to the nearest tenth
ehidna [41]

That would be 2.7 for the nearest tenth

4 0
2 years ago
Read 2 more answers
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