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3 years ago

Identify the monomial function(s) that have a maximum.

Mathematics

2 answers:

Irina-Kira [14]3 years ago

7 0

y=-3x^4

y=-2x^12

3 and 4 are the correct options

natima [27]3 years ago

4 0

Answer:

Step-by-step explanation:

For a function f to have a maximum as per derivative rule we have to have

f'(x) =0, f"(x) <0

If second derivative =0 also then it is not maximum but point of inflections

Whenever f(x) = ax^n

we have

f'(x) = 0 gives x=0 and

f"(x) = n(n-1) ax ^(n-2)

So for n greater than or equal to there cannot be any maximum

And also for a straight line

y =-4x

y'=-4 and y"-0

No maximum

So only maximum can be for a funciton of the form y = ax^2

Here we do not have that all degrees are either 1 or greater than 1.

So no maximum for any funciton.

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Researchers at the National Cancer Institute released the results of a study that investigated the effect of weed-killing herbic

jolli1 [7]

Answer:

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

The randomly sampled 400 dogs from homes where an herbicide was used on a regular basis, diagnosing lymphoma in 230 of them.

This means that:

$p_h = \frac{230}{400} = 0.575, s_h = \sqrt{\frac{0.575*0.425}{400}} = 0.0247$

Of 200 dogs randomly sampled from homes where no herbicides were used, only 25 were found to have lymphoma.

This means that:

$p_n = \frac{25}{200} = 0.125, s_n = \sqrt{\frac{0.125*0.875}{200}} = 0.0234$

Distribution of the difference:

$p = p_h - p_n = 0.575 - 0.125 = 0.45$

$s = \sqrt{s_h^2+s_n^2} = \sqrt{0.0247^2 + 0.0234^2} = 0.034$

Confidence interval:

The confidence interval is:

$p \pm zs$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower bound is $0.45 - 1.96(0.034) = 0.3834$

The upper bound is $0.45 + 1.96(0.034) = 0.5166$

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

3 0

3 years ago

There are 2 blue, 6 yellow, 10 red, 3 green, 5 orange, and 4 purple marbles in a jar. What is the probability that a red marble

seraphim [82]

Answer:

1/3

Step-by-step explanation:

sum of numbers = 30 marbles

probability = 10/30 or simplified 1/3

6 0

2 years ago

89 + 217 = 1,564 – 1,438 = 11 X 5 = 72 : 8 = 6 X 10 = 88 + 8 = 4,632-4,608 =

denpristay [2]

Answer:

use a calculator

7 0

3 years ago

The lifetime of a certain type of battery is normally distributed with mean value 10 hours and standard deviation 1 hour. There

Oksi-84 [34.3K]

Answer:

$z=1.64$

And if we solve for a we got;

$10 +1.64*1=11.64$

So the value of height that separates the bottom 95% of data from the top 5% is 11.64

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent certain lifetime of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,1)$

Where $\mu=10$ and $\sigma=1$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.05$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.64$

And if we solve for a we got;

$10 +1.64*1=11.64$

So the value of height that separates the bottom 95% of data from the top 5% is 11.64

4 0

3 years ago

Sue has 18 sweets.

Norma-Jean [14]

Easy:

((18-x) -5) + ((18+x)➗2)

7 0

3 years ago