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3 years ago

Ken is going to throw a biased dice once.

Mathematics

1 answer:

satela [25.4K]3 years ago

7 0

Answer:

0.7

Step-by-step explanation:

Given a biased dice :

Probability of landing on 6 = P(6) ;

P(6) = 0.3

Recall :

P(A') = 1 - P(A)

Therefore,

P(6) = 0.3

P(not landing on 6) ; P(not 6) ;

P(not 6) = 1 - P(6)

P(not 6) = 1 - 0.3 = 0.7

Hence, Probability of not landing on 6 = 0.7

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Evaluate the integral:

Bogdan [553]

Substitute x = √7 sin(t) and dx = √7 cos(t) dt. Then

∫ √(7 - x²) dx = ∫ √(7 - (√7 sin(t))²) • √7 cos(t) dt

… = √7 ∫ √(7 - 7 sin²(t)) cos(t) dt

… = 7 ∫ √(1 - sin²(t)) cos(t) dt

… = 7 ∫ √(cos²(t)) cos(t) dt

We require that -π/2 ≤ t ≤ π/2 in order for the substitution we made to be reversible. Over this domain, cos(t) ≥ 0, so

√(cos²(t)) = |cos(t)| = cos(t)

and the integral reduces to

… = 7 ∫ cos²(t) dt

Recall the half-angle identity for cosine:

cos²(t) = (1 + cos(2t))/2

Then the integral is

… = 7/2 ∫ (1 + cos(2t)) dt

… = 7/2 (t + 1/2 sin(2t)) + C

… = 7t/2 + 7/4 sin(2t) + C

Get the antiderivative back in terms of x. Recall the double angle identity for sine:

sin(2t) = 2 sin(t) cos(t)

We have t = arcsin(x/√7), which gives

sin(t) = sin(arcsin(x/√7)) = x/√7

cos(t) = cos(arcsin(x/√7)) = √(7 - x²)/√7

Then

∫ √(7 - x²) dx = 7/2 arcsin(x/√7) + 7/4 • 2 sin(arcsin(x/√7)) cos(arcsin(x/√7)) + C

… = 7/2 arcsin(x/√7) + x/2 √(7 - x²) + C

5 0

2 years ago

The equation C = 20n + 35 represents the relationship between the cost of school volleyball uniforms, C, in dollars, and the num

Margaret [11]

The equation represent a linear relation with the y-intercept

representing the amount of initial fee.

Correct response:

1. 28 volleyball uniforms

2. Price per uniform

3. Initial flat order fee

4. 10 fewer volleyball uniform

<h3>Methods used for finding the above values</h3>

The given equation that represents the relationship between the cost of school volleyball uniform is; C = 20·n + 35

Where;

C = The uniform costs

n = The number of volleyball uniform ordered

The maximum amount the school has to spend = $600

1. The number of uniforms the school can buy is given by setting C = 600 as follows;

C = 20·n + 35

Therefore;

600 = 20·n + 35

20·n = 600 - 35 = 565

$n = \dfrac{565}{20} = \mathbf{28.25}$

Rounding down to the nearest whole number, we have;

The number of uniforms the school can buy, n = 28 volleyball uniforms.

2. The number 20 represent the additional cost for each extra uniform, which is the unit cost therefore;

20 represents a $20 price per uniform.

3. The 35 in the equation represents an initial flat fee, such as an

ordering or initial fee, which is fixed.

Therefore;

The number 35 represent the fixed cost for producing the uniforms

4. The price per uniform of $30 changes the coefficient of n from 20 to 30 as follows;

C = 30·n + 35

The number of uniforms the school can by with $600 is therefore;

$n = \dfrac{600 - 35}{30} = \mathbf{18.8 \overline 3}$

Which gives;

The number of uniforms the school can purchase at $30 per uniform is n = 18 volleyball uniforms

The difference in the number of uniforms purchased = 28 - 18 = 10

Therefore;

The school can purchase 10 fewer uniforms at $30 per uniform

Learn more about linear equations here:

brainly.com/question/10452752

4 0

2 years ago

I am a prime factors are 2 3 and 5

tia_tia [17]

Yes they are prime if that's the question u just asked

4 0

3 years ago

What interest will be charged on a $300 loan for 6 months if the rate is 18% simple interest?

Yakvenalex [24]

Answer: 540.00

Step-by-step explanation:

4 0

3 years ago

Brian's comic book collection increased from 120 to 150 comic books. By what percentage did his collection increase?

FrozenT [24]

To do these use the new number minus the old number, all divided by the old number

(150-120)/120=
30/120=
¼.

the collection increased by 25%

5 0

4 years ago