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2 years ago

Enter the expression 2cos2(θ)−1 , where θ is the lowercase Greek letter theta. 2cos2(θ)−1 2 c o s 2 ( θ ) − 1 = nothing

Mathematics

1 answer:

yulyashka [42]2 years ago

8 0

We have to evaluate

=2 cos 2Ф - 1

⇒cos 2Ф

A =2cos²Ф-1

B =1 -2 sin²Ф

C = cos²Ф - sin²Ф

Possible Answers are

=2 ×(2cos²Ф-1)-1

=4cos²Ф-2-1

=4cos²Ф - 3

=2×(1 -2 sin²Ф)-1

=2- 4sin²Ф-1

=1 - 4sin²Ф

=2× ( cos²Ф - sin²Ф) -1

=2 cos²Ф - 2sin²Ф-1

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Trisomy 18 (T18) is a rare genetic disorder that severely disrupts a baby's development prior to birth. Many die before birth an

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Answer:

3.74% probability that her baby has T18

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Positive test.

Event B: The baby having T18.

T18 occurs in only 1 in 2500 pregnancies in the U.S.

This means that $P(B) = \frac{1}{2500} = 0.0004$

The probability of a positive test result for a baby with T18 is 0.97.

This means that $P(A|B) = 0.97$

The overall probability of a positive test result is 0.010384.

This means that $P(A) = 0.010384$

What is the probability that her baby has T18

$P(B|A) = \frac{0.0004*0.97}{0.010384} = 0.0374$

3.74% probability that her baby has T18

5 0

2 years ago

An icicle drips at a rate that can be represented by the function f(x) = −x2 + 11x − 18, where 0 ≤ x ≤ 10 and x is the number of

FrozenT [24]

Calculate f(x) for all numbers between 0 and 10:

f(0) = −0^2 + 11(0) − 18 = -18

f(1) = −1^2 + 11(1) − 18 = -8

f(2) = −2^2 + 11(2) − 18 = 0

f(3) = −3^2 + 11(3) − 18 = 6

f(4) = −4^2 + 11(4) − 18 = 10

f(5) = −5^2 + 11(5) − 18 = 12

f(6) = −6^2 + 11(6) − 18 = 12

f(7) = −7^2 + 11(7) − 18 = 10

f(8) = −8^2 + 11(8) − 18 = 6

f(9) = −9^2 + 11(9) − 18 = 0

f(10) = −10^2 + 11(10) − 18 = -8

When the value is negative it doesn't drip, so it starts and stops dripping when the values = 0

Which is f(2) and f(9), the values are 2 and 9.

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2 years ago

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Step-by-step explanation:

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2 years ago

Carmen is going to roll an 8-sided die 200 times. She predicts that she will roll a multiple of 4 twenty-five times. Based on th

iren2701 [21]

Answer:

Carmen's prediction is low because 200 times $\frac{1}{4}$ is 50.

Step-by-step explanation:

First of all we are going to define the sample space for this exercise.

The sample space is Ω = {1,2,3,4,5,6,7,8}

Given the event A : ''Roll an 8-sided die an get a multiple of 4''

The probability for the event A is $P(A)=\frac{2}{8}=\frac{1}{4}$

Because they are two numbers (4 and 8) over a total of eight numbers (1,2,3,4,5,6,7,8) that are multiple of 4.

Now, given the random variable X : ''Total of numbers multiples of 4 If she rolls

an 8-sided die 200 times''

X can be modeled as a Binomial random variable.

X ~ Bi (n,p)

X ~ Bi (200, $\frac{1}{4}$ )

In which n is the total times she rolls the 8-sided die and p is the success probability.We define a success as obtain a number multiple of 4.

The mean for this variable is

$E(X)=np=200.\frac{1}{4}=50$

We answer that Carmen's prediction is low because 200 times $\frac{1}{4}$ is 50.

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2 years ago

Read 2 more answers

A survey was done of 160 households to find out if they watch cable television, internet television, or

murzikaleks [220]

Answer: 2) 0.275

Step-by-step explanation:

Total households = 160

Watch Cable TV: 109

Watch internet TV: 88

Watch neither: 7

We want to find the number that watch both of them.

Now, the total number of housholds that watch at least one thing is:

160 - 7 = 153.

Now, if we add the number that watch by cable and the number that watch by internet we have:

109 + 88 = 197

The difference is:

197 - 153 = 44

This means that we have 44 households that watch both things.

This is because we are counting those 44 in the 109 for cable and also in the 88 for internet (because they watch both) and this is why we have a surpass.

Then the number that watch both things is 44, then the probability that a random household watched both things is equal to:

P = 44/160 = 0.275

The correct option is 2

5 0

2 years ago