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1 year ago

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Question 6 The mineral content of a particular brand of supplement pills is normally distributed with mean 490 mg and variance o

f 400. What is the probability that a randomly selected pill contains at least 500 mg of minerals

1 answer:

AysviL [449]1 year ago

4 0

Answer:

0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 490 mg and variance of 400.

This means that $\mu = 490, \sigma = \sqrt{400} = 20$

What is the probability that a randomly selected pill contains at least 500 mg of minerals?

This is 1 subtracted by the p-value of Z when X = 500. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{500 - 490}{20}$

$Z = 0.5$

$Z = 0.5$ has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals

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Answer:

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Step-by-step explanation:

Data provided in the question:

Commission on Sales upto and including $40,000 = 5%

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Total commission = $3,860

Now,

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= $2,000

Since the commission received is greater than $2,000

Therefore,

The value of s is greater than $40,000

Thus

Amount qualifying for 10% commission = s - $40,000

therefore,

Total commission = $2,000 + 10% of (s - $40,000)

or

$3,860 = $2,000 + 0.10 × (s - $40,000)

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1 year ago

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Lana is the oldest of four sisters. Her youngest sister is half her age. The other two sisters are twins $2$ years younger than

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Let the youngest sister be n years
Lana will be 2n years, as her youngest sister is half her age
The age of the twins separately will be 2n-2 as they are 2 years younger than Lana
So, the equation looks like this:
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Now solve for n:
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Diane is riding her bicycle. She rides 19.2 kilometers in 3 hours. What is her speed?

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Speed = 19.2 / 3 = 6.4 kilometers per hour

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Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =

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Answer:

Here is the question attached with.

$m\angle CEA =90 \ (deg)$

$m\angle BEF=135\ (deg)$

$\angle CEF$ is a straight line.

$\angle AEF$ is a right angled triangle.

Options $1,4,5,6$ are correct answers.

Step-by-step explanation:

⇒As $\ ray\ AE$ is ⊥ $FEC$ so it will forms right angled triangle then $m\angle CEA =90\ (deg)$ .

⇒Measure of $\angle BEF =135\ (deg)$ as $\angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg)$ as $\angle AEB$ is the bisector of $\angle AEC$ ,meaning that $\angle AEB$ is half of $\angle AEC$ so $\angle AEB = 45\ (deg)$ .

⇒ $\angle CEF$ is a straight line as the angles measure over it is $180\ (deg)$ .

⇒Measure of $\angle AEF = 90\ (deg)$ from linear pair concept.

As $\angle CEA + \angle AEF = 180\ (deg)$ ,plugging the values of $m\angle CEA =90\ (deg)$ we have $\angle AEF = 90\ (deg)$ .

The other two options are false as:

$m\angle CEF=m\angle CEA + m\angle BEF = (90+135)=225$

it is exceeding $180\ (deg)$ whereas $\angle CEF$ is a

straight line.

And $m\angle CEB=2(m\angle CEA)$ is not true.

As $\angle CEA = 90\ (deg)$ and $\angle CEB=45\ (deg)$

So we have total $4$ answers.

The correct options are $1,4,5,6$ .

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2 years ago

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Find a matrix P such that PTAP orthogonally diagonalizes A. Verify that PTAP gives the proper diagonal form. (Enter each matrix

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Answer:

the P matrix you are looking for is P=(1/ $\sqrt{2}$ ) · [[1 1 0 0],[1 -1 0 0],[0 0 1 1],[0 0 1 -1]]

Step-by-step explanation:

Answer:

For an orthogonal diagonalization of any matrix you have to:

1º) Find the matrix eigenvalues in a set order.

2º) Find the eigenvectors of each respective eigenvalues.

Tip: You can write the matrix A like A = $P^{t}$ D P

3º) D is the diagonal matrix with each eigenvalue (in order) in the diagonal.

4º) Write P as the normalized eigenvectors in order (in columns).

Tip 2: Remember, $P^{t}$ ·P = I, so if A = $P^{t}$ D P, then:

P A $P^{t}$ = P $P^{t}$ D P $P^{t}$ = I D I = D

So the P we are looking for is the $P^{t}$ of the diagonalization.

Tip 3: In this case, A is a block matrix with null nondiagonal submatrixes, therefore its eigenvalues can be calculated by using the diagonal submatrixes. The problem is reduced to calculate the eigenvalues of A₁₁ = A ₂₂ = [[5 3],[3 5]]

Solving:

1º)the eigenvalues of A₁₁ are {8,2}, therefore the D matrix is $\left[\begin{array}{cccc}8&0&0&0\\0&2&0&0\\0&0&8&0\\0&0&0&2\end{array}\right]$

2º) the eigenvectors of A₁₁ are P₈= {[1 1]T} P₂= {[1 -1]T}, therefore normalizing the eigenvectors you obtain P = (1/ $\sqrt{2}$ ) · [[1 1 0 0],[1 -1 0 0],[0 0 1 1],[0 0 1 -1]] (you can see that P = $P^{t}$ in this case).

As said in "tip 2": P A $P^{t}$ = P $P^{t}$ D P $P^{t}$ = I D I = D

So the P obtained is the one you are looking for.

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2 years ago