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fiasKO [112]
3 years ago
7

Pythagoras and True Love

Mathematics
1 answer:
Katena32 [7]3 years ago
6 0

Let us find the length of rope Jules will need using the pythagoras theorem .

Width of the moat ( let the moat be the base of this triangle ) = 14 foot

Distance from Roma's window to the boat ( let this be the side of the triangle where the right angle is present ) =20 feet

Then the length of rope needed ( hypotenuse ) =

= Let us name the triangle that is formed as △ ABC . Then ;

In △ ABC :

AB = the width of moat ( leg of triangle ) = 14 foot

BC = The distance from the window to the moat ( base ) = 20 feet

AC = Length of rope needed ( hypotenuse ) =

= AB ² + BC² = AC² ( according to the pythagoras theorem the square on the hypotenuse will be equal to the sum of the squares on the other two legs )

= 14² + 20² = AC²

= 196 + 400 = AC²

= 596 = AC²

= 24 × 24 = AC × AC

= 24 foot = AC = length of rope needed by jules .

Therefore , Jules will need a 24 foot rope so that his girlfriend can slide down and escape from her apartment .

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Answer:

Follows are the solution to the given choices:

Step-by-step explanation:

In choice a:

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In choice b:

\to \mu \neq 100

In choice c:

\to \ pop  \ average=100 \\\\ \to \ variance \ of \ pop = 100  \\\\\to pop  \ \  \sigma = \sqrt {(!00)} \\

               = 10

z= \frac{\bar x - \mu}{ \frac{\sigma}{\sqrt(n)}}\\\\

   =\frac{(105-100)}{\frac{10}{ \sqrt(16)}}\\\\=\frac{(5)}{ \frac{10}{4}}\\\\=\frac{5}{ \frac{5}{2}}\\\\= \frac{10}{5}\\\\=2

\to p==2\times (1- \ righttail)\\\\\to \ righttail\ \ p = \text{NORM.S.DIST(2,TRUE)}

                        =0.977249868

\therefore \\P=2 \times (1-0.9772)\\\\P=0.0455\\\\P

Null hypothesis to dismiss  

Alternate solution assumptions embrace  

There is really no valid proof at the 5% stage that  

Knowledge is legacy

In choice d:

Possibly information such as this reflect a sample population with such a true p = 0.0455 meaning in the hypothesis  

u is around 100.  

11 +001

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3 years ago
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5
iris [78.8K]

Answer:

By the Empirical Rule, 99.7% of the students have grade point averages that are between 1.28 and 3.8.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 2.54

Standard deviation = 0.42.

Between 1.28 and 3.8?

1.28 = 2.54 - 3*0.42

So 1.28 is 3 standard deviations below the mean

3.8 = 2.54 + 3*0.42

So 3.8 is 3 standard deviations above the mean

By the Empirical Rule, 99.7% of the students have grade point averages that are between 1.28 and 3.8.

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2 years ago
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On a scale drawing, a building is 5.5 tall. If the scale if the drawing is 1 inch: 8 ft, how tall is the building
arsen [322]
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Given that p=9i+12j and q=-6i-8j. Evaluate |p-q|-{|p|-|q|}
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Answer:

|p-q|-(|p|-|q|) = 20

Step-by-step explanation:

First let's find the value of 'p-q':

p - q = 9i + 12j - (-6i - 8j)\\p - q = 9i + 12j + 6i + 8j\\p - q = 15i + 20j\\

To find |p-q| (module of 'p-q'), we can use the formula:

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Where 'a' is the coefficient of 'i' and 'b' is the coefficient of 'j'

So we have:

|p - q| = |15i + 20j| = \sqrt{15^{2}+20^{2}} = 25

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|q| = |-6i - 8j| = \sqrt{(-6)^{2}+(-8)^{2}} = 10

Then, evaluating |p-q|-{|p|-|q|}, we have:

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Answer:

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Factor out 4x^3.

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