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ratelena [41]
3 years ago
12

A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is kno

wn to have a normal distribution with a mean of 5 milliliters (ml) and a standard deviation of 0.4 ml. Answer the following questions based on this information. Find the dye amount that represents the 9th percentile of the distribution.
Mathematics
1 answer:
Anton [14]3 years ago
5 0

Answer:

4.464 ml

Step-by-step explanation:

Given that:

mean (μ) = 5 mm, standard deviation (σ) = 0.4 ml

The z score is a score in statistics used to determine by how many standard deviation the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if the z score is negative then the raw score is below the mean It is given by:

z=\frac{x-\mu}{\sigma}

From the normal distribution table, the 9th percentile (0.09) corresponds to a z score of -1.34

z=\frac{x-\mu}{\sigma}\\\\-1.34=\frac{x-5}{0.4}\\\\x-5=-0.536\\\\x=5-0.536\\\\x=4.464

The dye amount that represents the 9th percentile of the distribution is 4.464 ml

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An equation of the circle whose center is the origin and
tankabanditka [31]

Answer:

\fbox{\begin{minipage}{10em}Option C is correct\end{minipage}}

Explanation:

A circle whose center is (a, b) and radius r, has equation:

(x - a)^{2} + (y - b)^{2} = r^{2}

The center of circle is  given as origin (0, 0), therefore:

a = 0\\b = 0

This circle passes (3, 0), then the radius of circle is the distance (d) between origin (0, 0) and (3, 0)

d = \sqrt{(0 - 3)^{2} + (0 - 0)^{2} } = \sqrt{3^{2} } = 3

=> r = d = 3

Substitute a, b, and r back into original equation:

(x - 0)^{2} + (y - 0)^{2}  = 3^{2}

or

x^{2} + y^{2} = 9

Hope this helps!

:)

3 0
3 years ago
It is 6 kilometers from Linda's house to the nearest mailbox. How far is it in meters?
Zanzabum

Answer:

6000 meters

Step-by-step explanation:

Each kilometer is 1000 meters so 1000 x 6 is 6000

3 0
2 years ago
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.
wel

Answer:

n=42, m=42\sqrt{3}

Step-by-step explanation:

The side opposite the 30° angle is half the size of the hypotenuse. So, 84/2=42. Now, the side opposite the 60° angle is shown as 84/2 · \sqrt{3}, which is the same as 42√3.

6 0
3 years ago
Carol bought a coloring book. It is 11 inches long and 8 inches wide. What is the diagonal length of the book?
Leokris [45]

Answer:

13.6 inches

Step-by-step explanation:

We can use Pythagorean theorem: c=\sqrt{a^{2} +b^{2} }

Let c be the diagonal length, a for length, and b for width.

Substitute the values.

c=\sqrt{11^{2}+8^{2}  }

c=13.6 inches

7 0
3 years ago
You make an initial investment of $500. Fill in the table below to show how much money you would have after 3 years if your acco
Aleksandr [31]
After three years, your investment would be $575. The formula is A=P(1+(r/n)^(n*t) where A is the final amount, P is the initial balance, r is the interest rate, n is the amount of time the interest is compounded in a year, and t is the amount of time that has passed.
P=500
r= 5% is which converted into a decimal by dividing 5 by 100 which is then 0.05
n= 1 since it is compounded annually
t= 3
Hope this helped.
3 0
3 years ago
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