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3 years ago

If θ is an angle in standard position that passes through (-3, 4), find sin2θ.

Mathematics

1 answer:

julia-pushkina [17]3 years ago

8 0

Answer:

Correct answer: sin 2Θ = - 24/25

Step-by-step explanation:

If under the standard position you think that the first arm (side) belongs to the positive direction of the x axis and the second one passes through a given point then it is:

if we form a right triangle with sides 3 and 4 then the hypotenuse is 5.

sin Θ = 4/5 and cos Θ = - 3/5

we know that the formula for double the value of the angle is:

sin 2Θ = 2 sinΘ cosΘ = 2 · 4/5 · ( - 3/5) = - 24/25

sin 2Θ = - 24/25

God is with you!!!

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A certain plant runs three shifts per day. Of all the items produced by the plant, 50% of them are produced on the first shift,

Snezhnost [94]

Answer:

0.2941 = 29.41% probability that it was manufactured during the first shift.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: Manufactured during the first shift.

Probability of a defective item:

1% of 50%(first shift)

2% of 30%(second shift)

3% of 20%(third shift).

$P(A) = 0.01*0.5 + 0.02*0.3 + 0.03*0.2 = 0.017$

Probability of a defective item being produced on the first shift:

1% of 50%. So

$P(A \cap B) = 0.01*0.5 = 0.005$

What is the probability that it was manufactured during the first shift?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.005}{0.017} = 0.2941$

0.2941 = 29.41% probability that it was manufactured during the first shift.

6 0

2 years ago

For every gallon of water in a swimming pool, you’ Instructed to add four grams of chlorine. How many grams of chlorine would yo

Kruka [31]

Answer:

Step-by-step explanation:

Multiply grams per gallon times gallons to get grams.

$4\,\dfrac{g}{gal}\times 13\,gal=4\times 13\,\dfrac{g\cdot gal}{gal}=52\,g$

7 0

3 years ago

Read 2 more answers

The cost of a ticket to an amusement park is $42 per person. for each group of up to eight people the cost per ticket decreases

zalisa [80]

This might not be correct but....
I’m going to use rounding,
42 x 2 = 84
84 divides by 3 = 28,
Which is near 30......So the number of people in the group is rounding to about 2 people.

8 0

3 years ago

Need help

aleksandr82 [10.1K]

Using the normal distribution, the probabilities are given as follows:

a. 0.4602 = 46.02%.

b. 0.281 = 28.1%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by: