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3 years ago

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The number of pieces of popcorn in a large movie theater popcorn bucket is normally distributed, with a mean of 1610 and a stand

ard deviation of 10. Approximately what percentage of buckets contain between 1600 and 1620 pieces of popcorn?
A. approximately 68%
B. approximately 75%
C. approximately 95%
D. approximately 99.7%

2 answers:

Elena L [17]3 years ago

7 0

Answer:

A. Approximately 68%

Step-by-step explanation:

Number of pieces of popcorn in a bucket is normally distributed.

Mean = μ = 1610

Standard deviation = б = 10

We know that in normal distribution, approximately 34% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34 + 34 = 68 % of bags will fall.

A table of normal distribution about mean is attached for better understanding.

Our range is:

1600 to 1620

1610 - 10 to 1610 + 10

μ ± б

mean ± 1 standard deviation

Our range is within 1 standard deviation. Hence, Approximately 68% of buckets contain between 1600 and 1620 pieces of popcorn.

bearhunter [10]3 years ago

6 0

Answer:

a

Step-by-step explanation:

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liq [111]

Answer:

Reflection over y axis

Step-by-step explanation:

When you reflect over y axis it makes the points go from (x,y) to (-x,y) so this is the right answer

Hope this helped!

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1 year ago

3. R: {(1, 2), (2, 2), (−1, −2), (−3, 4)}?

Natali [406]

Yes it is a function Bc the x values don’t repeat

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2 years ago

Lines k and n intersect on the y-axis

avanturin [10]

a) The equation of line k is:

$y = -\frac{202}{167}x + \frac{598}{167}$

b) The equation of line j is:

$y = \frac{167}{202}x + \frac{1546}{202}$

The equation of a line, in <u>slope-intercept formula</u>, is given by:

$y = mx + b$

In which:

m is the slope, which is the rate of change.
b is the y-intercept, which is the value of y when x = 0.

Item a:

Line k intersects line m with an angle of 109º, thus:

$\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}$

In which $m_1$ and $m_2$ are the slopes of <u>k and m.</u>

Line k goes through points (-3,-1) and (5,2), thus, it's slope is:

$m_1 = \frac{2 - (-1)}{5 - (-3)} = \frac{3}{8}$

The tangent of 109 degrees is $\tan{109^{\circ}} = -\frac{29}{10}$
Thus, the slope of line m is found solving the following equation:

$\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}$

$-\frac{29}{10} = \frac{m_2 - \frac{3}{8}}{1 + \frac{3}{8}m_2}$

$m_2 - \frac{3}{8} = -\frac{29}{10} - \frac{87}{80}m_2$

$m_2 + \frac{87}{80}m_2 = -\frac{29}{10} + \frac{3}{8}$

$\frac{167m_2}{80} = \frac{-202}{80}$

$m_2 = -\frac{202}{167}$

Thus:

$y = -\frac{202}{167}x + b$

It goes through point (-2,6), that is, when $x = -2, y = 6$ , and this is used to find b.

$y = -\frac{202}{167}x + b$

$6 = -\frac{202}{167}(-2) + b$

$b = 6 - \frac{404}{167}$

$b = \frac{6(167)-404}{167}$

$b = \frac{598}{167}$

Thus. the equation of line k, in slope-intercept formula, is:

$y = -\frac{202}{167}x + \frac{598}{167}$

Item b:

Lines j and k intersect at an angle of 90º, thus they are perpendicular, which means that the multiplication of their slopes is -1.

Thus, the slope of line j is:

$-\frac{202}{167}m = -1$

$m = \frac{167}{202}$

Then

$y = \frac{167}{202}x + b$

Also goes through point (-2,6), thus:

$6 = \frac{167}{202}(-2) + b$

$b = \frac{(2)167 + 202(6)}{202}$

$b = \frac{1546}{202}$

The equation of line j is:

$y = \frac{167}{202}x + \frac{1546}{202}$

A similar problem is given at brainly.com/question/16302622

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2 years ago

bacteria colonies can triple in size every 4 days. If you start with 150 bacteria microorganisms, how large with the colony be a

-Dominant- [34]

It triples in size every 4 days. In 16 days it will be 3 * 3 * 3 * 3 times bigger.

3 * 3 * 3 * 3 = 81
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2 years ago

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brilliants [131]

1) Well you divide the copies by 14 for the amount of friends that Ivan has helping him then multiply that to the 0.25 cents that he is playing them.

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3 years ago

Read 2 more answers