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murzikaleks [220]
3 years ago
14

Many physical processes are exponential in nature. A typical way of cleaning a tank of contaminated water is to run in clean wat

er at a constant rate, stir, and let the mixture run out at the same rate. Suppose there are initially 100 pounds of a contaminant in a large tank of water. Assume that the cleaning method described above removes 20% of the remaining contaminant each hour. How much contaminant is removed during the first three hours
Mathematics
1 answer:
Alisiya [41]3 years ago
8 0

Answer:

The amount of the contaminant removed during the first three hours will be 48.8 pounds.

Step-by-step explanation:

There, in a large tank of water, are initially 100 pounds of a contaminant.

Also given that the cleaning method removes 20% of the remaining contaminant each hour.

So, after the first hour, the amount of the contaminant will remain by 100(1 - \frac{20}{100}) = 80 pounds.

Now, after the second hour, the amount of the contaminant will remain by

80(1 - \frac{20}{100}) = 64 pounds.

Finally, after the third hour, the amount of the contaminant will remain by 64(1 - \frac{20}{100}) = 51.2 pounds.

Therefore, the amount of the contaminant removed during the first three hours will be (100 - 51.2) = 48.8 pounds. (Answer)

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For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test
Basile [38]

Answer:

a) p_v =P(Z>2.05)=1-P(z

b) p_v =P(Z>-1.84)=1-P(z

c) p_v =P(Z>0.4)=1-P(z

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: \mu=10

Alternative hypothesis: \mu >10

If the random variable is distributed like this: X \sim N(\mu,\sigma)

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

z_o=\frac{\bar X -\mu}{\sigma}

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

p_v =P(Z>2.05)=1-P(z

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

p_v =P(Z>-1.84)=1-P(z

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

p_v =P(Z>0.4)=1-P(z

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say \alpha=0.05. For part a the p_v so then we can reject the null hypothesis at this significance level.

For part b the p_v>\alpha so then we FAIL to reject the null hypothesis at this significance level.

For part c the p_v>\alpha so again we FAIL to reject the null hypothesis at this significance level.

3 0
3 years ago
The roots of the quadratic equation $z^2 + az + b = 0$ are $2 - 3i$ and $2 + 3i$. What is $a+b$?
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We know for our problem that the zeroes of our quadratic equation are (2-3i) and (2+3i), which means that the solutions for our equation are x=2-3i and x=2+3i. We are going to use those solutions to express our quadratic equation in the form a x^{2} +bx+c; to do that we will use the <span>zero factor property in reverse:
</span>x=2-3i
x-2=-3i
x-2+3i=0
<span>
</span>x=2+3i
x-2=3i
x-2-3i=0
<span>
Now, we can multiply the left sides of our equations:
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6 0
3 years ago
A building is 2 ft from a 7 - ft fence that surrounds the property . A worker wants to wash a window in the building 11 ft from
White raven [17]

<u>Answer:</u>

The height of the ladder is 14.491 feet

<u>Explanation</u>:

Given the height is 11 feet

Base = 7 + 2 = 9 feet

Consider the ladder to be the hypotenuse

Applying Pythagoras Theorem,  

H^2   = P^2 + B^2

Substituting the values in the above formula,

H^2  = 112 + 92

H^2  = 121 + 81

H^2 = 210

H = sqrt(210)

H = 14.491

Therefore, the height of the ladder is 14.491 feet

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20 people show up to the party, and Robert decides to give them each the same
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Answer:

depends on how much pizza he has.

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