1. Nonpoint source loads are chemical masses that travel to the main stem of a river in flows that are distributed over relatively long stream reaches. Suppose source loads are known to have a mean value of 73 and a standard deviation of 10. We will take a random sample of 48 loads and calculate the sample mean, X. (a) What is the mean of X

Answer:

# of roses   # of bushes

     2                     4

     3                     5

Step-by-step explanation:

If you count, 4 times the data showed 2 and 5 times the data showed 3.

Answer:

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Step-by-step explanation:

2 roses = 4 bushes

3 roses = 5 bushes

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Answer:

(a) ⅛ tan⁻¹(¼)

(b) sec x − ln│csc x + cot x│+ C

Step-by-step explanation:

(a) ∫₀¹ x / (16 + x⁴) dx

∫₀¹ (x/16) / (1 + (x⁴/16)) dx

⅛ ∫₀¹ (x/2) / (1 + (x²/4)²) dx

If tan u = x²/4, then sec²u du = x/2 dx

⅛ ∫ sec²u / (1 + tan²u) du

⅛ ∫ du

⅛ u + C

⅛ tan⁻¹(x²/4) + C

Evaluate from x=0 to x=1.

⅛ tan⁻¹(1²/4) − ⅛ tan⁻¹(0²/4)

⅛ tan⁻¹(¼)

(b) ∫ (sec³x / tan x) dx

Multiply by cos x / cos x.

∫ (sec²x / sin x) dx

Pythagorean identity.

∫ ((tan²x + 1) / sin x) dx

Divide.

∫ (tan x sec x + csc x) dx

Split the integral

∫ tan x sec x dx + ∫ csc x dx

Multiply second integral by (csc x + cot x) / (csc x + cot x).

∫ tan x sec x dx + ∫ csc x (csc x + cot x) / (csc x + cot x) dx

Integrate.

sec x − ln│csc x + cot x│+ C

Answer:

(a) Solution : 1/8 cot⁻¹(4) or 1/8 tan⁻¹(¼) (either works)

(b) Solution : tan(x)/sin(x) + In | tan(x/2) | + C

Step-by-step explanation:

(a) We have the integral (x/16 + x⁴)dx on the interval [0 to 1].

For the integrand x/6 + x⁴, simply pose u = x², and du = 2xdx, and substitute:

1/2 ∫ (1/u² + 16)du

'Now pose u as 4v, and substitute though integral substitution. First remember that we have to factor 16 from the denominator, to get 1/2 ∫ 1/(16(u²/16 + 1))' :

∫ 1/4(v² + 1)dv

'Use the common integral ∫ (1/v² + 1)dv = arctan(v), and substitute back v = u/4 to get our solution' :

1/4arctan(u/4) + C

=> Solution : 1/8 cot⁻¹(4) or 1/8 tan⁻¹(¼)

(b) We have the integral ∫ sec³(x)/tan(x)dx, which we are asked to evaluate. Let's start by substitution tan(x) as sin(x)/cos(x), if you remember this property. And sec(x) = 1/cos(x) :

∫ (1/cos(x))³/(sin(x)/cos(x))dx

If we cancel out certain parts we receive the simplified expression:

∫ 1/cos²(x)sin(x)dx

Remember that sec(x) = 1/cos(x):

∫ sec²(x)/sin(x)dx

Now let's start out integration. It would be as follows:

Solution: tan(x)/sin(x) + In | tan(x/2) | + C

Answer:

Explained below.

Step-by-step explanation:

Let the random variable X be defined as the number of Americans who travel by car look for gas stations and food outlets that are close to or visible from the highway.

The probability of the random variable X is: p = 0.40.

A random sample of n =25 Americans who travel by car are selected.

The events are independent of each other, since not everybody look for gas stations and food outlets that are close to or visible from the highway.

The random variable X follows a Binomial distribution with parameters n = 25 and p = 0.40.

(a)

The mean and variance of X are:

Thus, the mean and variance of X are 10 and 6 respectively.

(b)

Compute the values of the interval μ ± 2σ as follows:

Compute the probability of P (5 ≤ X ≤ 15) as follows:

Thus, 97.72% values of the binomial random variable x fall into this interval.

(c)

Compute the value of P (6 ≤ X ≤ 14) as follows:

The value of P (6 ≤ X ≤ 14) is 0.9361.

According to the Tchebysheff's theorem, for any distribution 75% of the data falls within μ ± 2σ values.

The proportion 0.9361 is very large compared to the other distributions.

Whereas for a mound-shaped distributions, 95% of the data falls within μ ± 2σ values. The proportion 0.9361 is slightly less when compared to the mound-shaped distribution.

Final answer:

The mean of x is 10 and the variance is 6. The interval μ ± 2σ is 10 ± 2√6. P(6 ≤ x ≤ 14) can be calculated using the binomial probability formula.

Explanation:

To find the mean of x, we multiply the sample size (n) by the probability of success (p), which is 40% or 0.4. So, the mean (μ) is 0.4 * 25 = 10. To find the variance of x, we multiply the sample size (n) by the probability of success (p) and the probability of failure (1-p), which is 0.6. So, the variance is 25 * 0.4 * 0.6 = 6.

To calculate the interval μ ± 2σ, we need to find the standard deviation (σ) first. The standard deviation is the square root of the variance, so σ = √6. Then, the interval is μ ± 2σ. Plugging in the values, the interval is 10 ± 2√6. To find the values of x that fall into this interval, we can subtract and add 2√6 from the mean, resulting in the range 10 - 2√6 to 10 + 2√6.

To find P(6 ≤ x ≤ 14), we need to find the probability of x being between 6 and 14. We can use the binomial probability formula to calculate this. P(6 ≤ x ≤ 14) = P(x = 6) + P(x = 7) + ... + P(x = 14). Using a binomial probability table or a calculator, we can find the probabilities of each x value and sum them up.

Learn more about Mean, Variance, Binomial Probability here:

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Answer: 1.7 x 10^6

Step-by-step explanation:

6^8 = 1,679,616

1,679,616 = 1.7 x 10^6

Answer: its b, 6/18

Step-by-step explanation:

Answer:

The correct answer is x = 32.

Step-by-step explanation:

To solve this problem, we must remember the concept of supplementary angles.  Two angles that are supplementary together make an angle of 180 degrees (a straight line).

In this case, we can see that inside the triangle, we will have an angle of 80 degrees.  We know this because the angle at the top of the triangle is supplementary with the angle measuring 100 degrees, so its measure should be 180-100 = 80 degrees.

On the lower right hand of the triangle, a similar rationale can be applied.  The angle inside of the triangle must measure 68 degrees, since it is supplementary to an angle measuring 112 degrees, and 180-112=68.

Finally, to solve this problem, we must remember that the sum of the three interior angles of a triangle should be 180 degrees.  This lets us set up the following equation:

80+68+x = 180

Now, we can solve this equation. Our first step is to simplify the left side of the equation by adding together the constant terms.

148 + x = 180

Next, we should subtract 148 from both sides of the equation.

x = 180-148

x = 32

Therefore, the correct answer is x = 32 degrees.

Hope this helps!  

The tax DeShawn has to pay is $8100

What is Tax?

Taxes are mandatory contributions levied on individuals or corporations by a government entity.

Given that, DeShawn earned $66,000 last year and the first $30,000 is taxed at 9% and income above that is taxed at 15%,

DeShawn will owe 9% tax on the first $30,000, which is $30,000×9% = $2,700.

The remaining $66,000 - $30,000 = $36,000 will be taxed at 15%.

So DeShawn will owe an additional $36,000 * 15% = $5,400 in tax.

In total, DeShawn will owe $2,700 + $5,400 = $8,100 in tax.

Hence, The tax DeShawn has to pay is $8100

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Hello,

I hope you and your family are doing well!

DeShawn will owe 9% tax on the first $30,000, which is $30,000 * 9% = $2,700.

The remaining $66,000 - $30,000 = $36,000 will be taxed at 15%.

So DeShawn will owe an additional $36,000 * 15% = $5,400 in tax.

In total, DeShawn will owe $2,700 + $5,400 = 8,100 in tax.

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Happy Holidays!