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ale4655 [162]
2 years ago
10

A pet store has 8 ​puppies, including 3 ​poodles, 2 ​terriers, and 3 retrievers. If Rebecka selects one puppy at​ random, the pe

t store replaces the puppy with a puppy of the same​ breed, then Aaron chooses a puppy at random. Find the probability that they both select a poodle.
Mathematics
1 answer:
Debora [2.8K]2 years ago
6 0

Answer:

9 / 64

Step-by-step explanation:

- In this task you have 2 events and you are looking for a joint probability. The first event is "Rebecca chooses a poodle". The probability of this event is:

                    P ( Rebecca chooses a poodle ) = 3 / 8

- because among 8 dogs there are 3 poodles.

- The second event is "Aaron selects a poodle".

This event has a probability of  that is equivalent to previous selection:

                   P ( Aaron chooses a poodle ) = 3 / 8

- Because after Rebecca's choice the chosen poodle is replaced with the poodle; hence, there are 8 pets in total and among them there are 3 poodles.

- To calculate probability of both events ("Rebeca selects a poodle and Aaron selects a poodle") with replacement you have to multiply both calculated probabilities - condition of independent events :

     P ( Aaron and Rebecca both select poodle ) = 3 / 8 * 3 / 8

                                                                                = 9 / 64

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List below are the speeds (mi/h) measured from southbound traffic on I-280 near Cupertino, CA. Use the sample data to construct
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Answer:

The 99% confidence interval of the population standard deviation is 1.7047 < σ < 7.485

Step-by-step explanation:

Confidence interval of standard deviation is given as follows;

\sqrt{\dfrac{\left (n-1  \right )s^{2}}{\chi _{1-\alpha /2}^{}}}< \sigma < \sqrt{\dfrac{\left (n-1  \right )s^{2}}{\chi _{\alpha /2}^{}}}

s = \sqrt{\dfrac{\Sigma (x - \bar x)^2}{n - 1} }

Where:

\bar x = Sample mean

s = Sample standard deviation

n = Sample size = 7

χ = Chi squared value at the given confidence level

\bar x = ∑x/n = (62 + 58 + 58 + 56 + 60 +53 + 58)/7 = 57.857

The sample standard deviation s = \sqrt{\dfrac{\Sigma (x - \bar x)^2}{n - 1} } = 2.854

The test statistic, derived through computation, = ±3.707

Which gives;

C. I. = 57.857 \pm 3.707 \times \dfrac{2.854}{\sqrt{7} }

\sqrt{\dfrac{\left (7-1  \right )2.854^{2}}{16.812}^{}}}< \sigma < \sqrt{\dfrac{\left (7-1  \right )2.854^{2}}{0.872}}

1.7047 < σ < 7.485

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3 years ago
What are the measures of 1 and 2? 37.1 1 2 17.30 121.8°​
Lady_Fox [76]

Answer:

Option 2 : m∠1 = 67.4°, m∠2 = 104.5°

Step-by-step explanation:

Lets find the measure of angle 2 first:

180° - 17.3° - (180° - 121.8°) = Angle 2

                             ↑

             Angle of the straight line = 180°

             The angle should be 180 - 121.8

Angle 2 = 104.5

At this point the only answer that works is the second option, but let's still work out Angle 1

Angle 1 :

Theory of opposite angles state that the opposite angles inside a triangle = the exterior angle

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Angle 1 + 37.1 = Angle 2

Since we know angle 2 = 104.5, lets solve

Lets say angle 1 = x

x + 37.1 = 104.5

x = 104.5 - 37.1

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8 x 6 = 48

Next, it says that four desks were removed. All you need to do is subtract 4 from 48.

48 - 4 = 44.
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