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galben [10]
3 years ago
8

Given: cos α = 4/5, sin β= 4/5, and α and β are both in quadrant 1. find sin (α+β)

Mathematics
1 answer:
mezya [45]3 years ago
8 0
We have the formula (sin x)^2 + (cos x)^2 = 1;
Then, sin α = \sqrt{1-  ( \frac{4}{5}) ^{2} } =  \frac{3}{5} ;
cos β = \sqrt{1- ( \frac{4}{5}) ^{2} } = \frac{3}{5} ;
We apply the formula sin ( α + β ) = sin α x cos β + sin β x cos α = (3/5)x(4/5) + (4/5)x(3/5) = 12/25 + 12/25 = 24/25;
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We are throwing darts on a disk-shaped board of radius 5. We assume that the proposition of the dart is a uniformly chosen point
Vlad1618 [11]

Answer:

the probability that we hit the bullseye at least 100 times is 0.0113

Step-by-step explanation:

Given the data in the question;

Binomial distribution

We find the probability of hitting the dart on the disk

⇒ Area of small disk / Area of bigger disk

⇒ πR₁² / πR₂²

given that; disk-shaped board of radius R² = 5, disk-shaped bullseye with radius R₁ = 1

so we substitute

⇒ π(1)² / π(5)² = π/π25 = 1/25 = 0.04

Since we have to hit the disk 2000 times, we represent the number of times the smaller disk ( BULLSEYE ) will be hit by X.

so

X ~ Bin( 2000, 0.04 )

n = 2000

p = 0.04

np = 2000 × 0.04 = 80

Using central limit theorem;

X ~ N( np, np( 1 - p ) )

we substitute

X ~ N( 80, 80( 1 - 0.04 ) )

X ~ N( 80, 80( 0.96 ) )

X ~ N( 80, 76.8 )

So, the probability that we hit the bullseye at least 100 times, P( X ≥ 100 ) will be;

we covert to standard normal variable

⇒ P( X ≥  \frac{100-80}{\sqrt{76.8} } )

⇒ P( X ≥ 2.28217 )

From standard normal distribution table

P( X ≥ 2.28217 ) = 0.0113

Therefore, the probability that we hit the bullseye at least 100 times is 0.0113

3 0
3 years ago
Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of
Umnica [9.8K]

Answer:

a. X is a binomial random variable with n = 50 and p = 0.04

b. Y is a binomial random variable with n = 40 and p = 0.015

Step-by-step explanation:

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.

X: the number of US residents (out of 50) with blood type AB.

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States

This means that p = 0.04, n = 50

Y: the number of Australians (out of 40) with blood type AB.

In Australia, only 1.5% of the population has blood type AB.

This means that p = 0.015, n = 40

Z: the total number of individuals (out of 90) with blood type AB.

Here

n = 90, p = 0.04*\frac{50}{90} + 0.015*\frac{40}{90} = 0.0289

Which of the following is true about the random variables X, Y, and Z?

Options a and b are true, while c is false.

7 0
3 years ago
Evaluate the expression 3.14(a2 + ab) when a = 4 and b = 3
barxatty [35]

when a=4 and b=3,

3.14((4 x 2)+ (4 x 3)) = 3.14(8+12) = 3.14 x 20 = 62.8

7 0
3 years ago
What percentage is equal to the fraction 4 over 25?
Vikki [24]
4/25 = 0.16. 0.16 is equal to 16%
5 0
3 years ago
James invests some money into an account that pays 4% compounded annually. If the account has $851.66 after 5 years, how much di
Charra [1.4K]

Answer:

the third option, "what number, when added to negative four, is equal to negative five?"

Step-by-step explanation:

"what number, when added to negative four, is equal to negative five?" can be expressed as g + (- 4) = - 5, which is the same as in the equation.

i hope this helps! :D comment if you need any clarification.

6 0
3 years ago
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