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2 years ago

Help meeeeeeeeeeeeeeeeeeee

Mathematics

1 answer:

Norma-Jean [14]2 years ago

8 0

Answer:

-336/527

Step-by-step explanation:

Trig identities are involved.

tan(2x) = 2tan(x)/(1 -tan(x)²)

Using tan = sin/cos, we can write this in terms of sine and cosine as ...

tan(2x) = (2sin(x)/cos(x))/(1 -sin(x)²/cos(x)²) = 2sin(x)cos(x)/(cos(x)² -sin(x)²)

= 2sin(x)cos(x)/(1 -2sin(x)²)

Now, the cosine can be found from ...

cos(x) = √(1 -sin(x)²)

for sin(θ) = 24/25, cos(θ) = √(1 -(24/25)²) = 7/25 . . . . 1st quadrant angle

Filling in the values in the above identity, we have ...

tan(2θ) = 2(24/25)(7/25)/(1 -2(24/25)²) = 336/-527

tan(2θ) = -336/527

_____

You can use a calculator or estimate that the angle for sin(θ) = 24/25 will be greater than 67.5°, so double the angle will be greater than 135°. (θ ≈ 74°) This means ...

2θ > 135°, so the magnitude of tan(2θ) will be less than 1
2θ is in the 2nd quadrant, so the sign of tan(2θ) will be negative

These observations will help you choose the correct answer without any further math.

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Suppose that the population mean for income is $50,000, while the population standard deviation is 25,000. If we select a random

Fudgin [204]

Answer:

Probability that the sample will have a mean that is greater than $52,000 is 0.0057.

Step-by-step explanation:

We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.

We select a random sample of 1,000 people.

Let $\bar X$ = sample mean

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = $50,000

$\sigma$ = population standard deviation = $25,000

n = sample of people = 1,000

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample will have a mean that is greater than $52,000 is given by = P( $\bar X$ > $52,000)

P( $\bar X$ > $52,000) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{52,000-50,000}{\frac{25,000}{\sqrt{1,000} } }$ ) = P(Z > 2.53) = 1 - P(Z $\leq$ 2.53)

= 1 - 0.9943 = 0.0057

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.53 in the z table which has an area of 0.9943.

Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.

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2 years ago

What is the value of x in the equation 1/5 x - 2/3 y = 30 when y=15

zubka84 [21]

To determine the value of X in the given equation substitute the value of y into the equation and solve for x.

1/5x - 2/3y = 30
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3 years ago