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GalinKa [24]
3 years ago
8

The exact value of cos 17pi/8 is . . a) square root of 2+the square root of 2/4 . b.) 0.38. c.) 0.99. d.)square root of 2-the sq

aure root of 2/4
Mathematics
1 answer:
alexgriva [62]3 years ago
7 0
Cos(17pi/8)

cos(17π/8)

But π radians = 180°

17π/8 radians = (17/8) * 180 = 382.5

But this is more than 360°,  so we have the basic angle by subtracting 360°

382.5 - 360 = 22.5

cos(17π/8) = Cos22.5

Recall double angle formula for cos.

cos2θ = 2cos²θ - 1

Therefore

cos(2*22.5) = 2cos²(22.5) - 1

cos45 = 2cos²(22.5) - 1

(√2)/2  =  2cos²(22.5) - 1

2cos²(22.5) - 1 =  (√2)/2


2cos²(22.5)  = (√2)/2 + 1

 2cos²(22.5)  = (2 + √2) / 2

cos²(22.5) = (2 + √2) / 4

cos22.5  =   √( (2 + √2)/4) ................(note)

cos22.5 = √(2 + √2) / 2

Option (a) seems like the closest, comparing to (note) above.
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Identify the parameters p and n in the following binomial distribution scenario. Jack, a bowler, has a 0.38 probability of throw
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Answer:

p = 0.38, n = 20

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Step-by-step explanation:

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of times Jack wants to bowl = 20

x = Number of successes required = number of strikes he intends to get

p = probability of success = probability that Jack throws a strike = 0.38

q = probability of failure = probability that Jack doesn't throw a strike = 0.62

P(X > x) = Σ ⁿCₓ pˣ qⁿ⁻ˣ (summing from x+1 to n)

P(X > 10) = Σ ²⁰Cₓ pˣ qⁿ⁻ˣ (summing from 11 to 20)

P(X > 10) = [P(X=11) + P(X=12) + P(X=13) + P(X=14) + P(X=15) + P(X=16) + P(X=17) + P(X=18) + P(X=19) + P(X=20)

P(X > 10) = 0.09233

There are binomial distribution cacalculators that can calculate all of this at once. Get one to minimize errors.

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A town has a population of 20000 and grows at 4% every year. What will be the population after 6 years, to the nearest whole num
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Answer:

25306

Step-by-step explanation:

a=starting value = 20000

r=\text{rate = }4\% = 0.04

r=rate = 4%=0.04

\text{Exponential Growth:}

Exponential Growth:

b=1+r=1+0.04=1.04

b=1+r=1+0.04=1.04

\text{Write Exponential Function:}

Write Exponential Function:

y=20000(1.04)^x

y=20000(1.04)  

x

 

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=20000(1.04)^{6}

y=20000(1.04)  

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y= 25306.38037

y=25306.38037

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Answer:

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