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3 years ago

Simplify: (sin Θ − cos Θ)2 + (sin Θ + cos Θ)2 options are 1 2 sin2 Θ cos2 Θ

Mathematics

1 answer:

I am Lyosha [343]3 years ago

6 0

Answer:

2 is the right answer.

Step-by-step explanation:

(sin∅-cos∅)²+(sin∅+cos∅)² in this expression we will open the brackets first by squaring the expressions given inside.

(sin²∅+cos²∅-2sin∅cos∅)+(sin²∅+cos²∅+2sin∅cos∅)

Since (a+b)² = a²+b²+2ab and (a-b)² = a²+b²-2ab

⇒(1-2sin∅cos∅) + (1+2sin∅cos∅)

Since (sin²∅+cos²∅) =1

⇒ 1-2sin∅cos∅+1+2sin∅cos∅

⇒ 1+1

⇒ 2

Therefore the option 2 is right answer.

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Construct a linear equation for the linear data presented in the table

yaroslaw [1]

Answer:

y = -7x

Explanation:

Take two points from table: (-4, 28), (-3, 21)

Find slope:

$\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points$

$\rightarrow \sf slope\ (m): \dfrac{21-28}{-3-(-4)} = -7$

Now find equation:

$\sf y - y_1 = m (x - x_1)$

$\rightarrow \sf y - 21 = -7(x - (-3))$

$\rightarrow \sf y = -7(x +3) + 21$

$\rightarrow \sf y = -7x -21 + 21$

$\rightarrow \sf y = -7x$

5 0

2 years ago

Read 2 more answers

In a certain clinical study, 15% of participants were classified as heavy smokers, 25% as light-smokers, and the rest as non-smo

Natasha_Volkova [10]

Answer:

There is a 28.57% probability that a randomly selected participant who died by the end of the study was a non-smoker.

Step-by-step explanation:

We have the following probabilities:

A 15% probability that a participant is classified as a heavy smoker.

A 25% probability that a participant is classified as a light smoker.

A 100% - 25% - 15% = 60% probability that a participant is classified as a non smoker.

A x% probability that a non smoker dies.

A 3x% probability that a light smoker dies.

A 5x% probability that a heavy smoker dies.

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

This problem is:

What is the probability of the participant being a non-smoker, given that he died?

P(B) is the probability that the participant is a non smoker. So

$P(B) = 0.6$

P(A/B) is the probability that the participant dies, given that he is a non smoker. So:

$P(A/B) = x$

P(A) is the probability that the participant dies:

$P(A) = P_{1} + P_{2} + P_{3}$

$P_{1}$ is the probability that a heavy smoker is selected and that he dies. So:

$P_{1} = 0.15*5x = 0.75x$

$P_{2}$ is the probability that a light smoker is selected and that he dies. So:

$P_{2} = 0.25*3x = 0.75x$

$P_{3}$ is the probability that a non-smoker is selected and that he dies. So:

$P_{3} = 0.60*x = 0.60x$

The probability that a participant dies is:

$P(A) = P_{1} + P_{2} + P_{3} = 0.75x + 0.75x + 0.60x = 2.10x$

The probability of the participant being a non-smoker, given that he died, is:

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.6x}{2.10x} = \frac{0.6}{2.10} = 0.2857$

There is a 28.57% probability that a randomly selected participant who died by the end of the study was a non-smoker.

7 0

3 years ago

A tv has a listed price of $896.99 before tax. If the sales tax rate is 7.75%, find the total cost of the tv with sales tax incl

nadezda [96]

Answer:69.52

Step-by-step explanation:First set up a proportion which is basically a fraction.To set it up first you must put two fractions together with an equals sign in between both fractions.Then add the whole on the denominator to the left then an x for the one above the whole cause were looking for a part.Then add the percent to the top right which in this case is 7.75 then 100 as the denominator cause it represents a whole.Then when looking for a part multiply Denominator on left which in this case is 896.99 then multiply it by the percent 7.75 which should give you 6951.6725 then divide by 100 which is 69.516725 then round which is 69.52.

7 0

3 years ago

Divide 33 into two groups so the ratio is 4 to 7 how do you divide it

Vladimir79 [104]

Split 33 into two numbers that when added up are 33.
So 12 to 21, which when divided by 3, are 4 to 7.

7 0

3 years ago

Read 2 more answers

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Answer:

Step-by-step explanation: