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3 years ago

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Mathematics

1 answer:

scoundrel [369]3 years ago

3 0

Step-by-step explanation:

a rectangle has two pairs of equally long sides and each of the 4 angles between the sides is 90 degrees.

given that ABCDEF is a regular hexagon, it means that all its sides are equally long, and therefore also all internal angles are the same size.

that means for ACDF that the sides DC and FA are equally long.

DEF and ABC are congruent triangles, as the sides DE = BC, EF = AB, and the angle E is congruent to angle B.

based on the SAS criteria this confirms that DF is congruent to AC.

the angles ACB, CAB, EDF and EFD have to be all the same, and therefore also the angles FDC, DCA, CAF and DFA.

so, all 4 angles of the parallelogram ACDF are the same, and the sum of all these angles has to be 360 degrees, we have

360 = 4×angle

angle = 90 degree.

so, all angles are 90 degrees and we have two pairs of equally long sides : this process that ACDF us a rectangle

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The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards (according to GolfWeek). Assume th

Usimov [2.4K]

Answer:

a) $f(x) = \frac{1}{25.9}$

b) 0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

$P(X < x) = \frac{x - a}{b - a}$

The probability of finding a value between c and d is:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

The probability of finding a value above x is:

$P(X > x) = \frac{b - x}{b - a}$

The probability density function of the uniform distribution is:

$f(x) = \frac{1}{b-a}$

The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards.

This means that $a = 284.7, b = 310.6$ .

a. Give a mathematical expression for the probability density function of driving distance.

$f(x) = \frac{1}{b-a} = \frac{1}{310.6-284.7} = \frac{1}{25.9}$

b. What is the probability the driving distance for one of these golfers is less than 290 yards?

$P(X < 290) = \frac{290 - 284.7}{310.6-284.7} = 0.2046$

0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards

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3 years ago

The function shown below was created to track the different intervals of speed that an automobile travels over a period of 28 se

Ksenya-84 [330]

Answer:

1. The car is slowing down at a rate of 2.5mph/s

2. The greatest acceleration is 10 mph/s.

3. In the interval 4s to 16s the speed remains constant and has magnitude 25 mph.

Step-by-step explanation:

1. The deceleration of the car is from 16 seconds to 24 seconds is the slope $m$ of the graph from 16 to 24:

$m=\dfrac{\Delta speed }{\Delta time } = \dfrac{5-25}{24-16} =-2.5mph/s$

the negative sign indicates that it is deceleration.

2. The automobile experiences the greatest change in speed when the slope is greatest because that is when acceleration/deceleration is greatest.

From the graph we see that the greatest slope of the graph is between 28 and 24 seconds. The acceleration the interval is the slope $m$ :

$m= \dfrac{45-5}{28-24}= 10mph/s$

3. The automobile experiences no acceleration in the interval 4 s to 16 s—that's the graph is flat.

The speed of the automobile in that interval, as we see from the graph, is 25 mph.

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hammer [34]

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kiruha [24]

Answer:

$\frac{\pi }{10}$ radians

Step-by-step explanation:

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For any two documents x and z, define k(x; z) to equal the number of unique words that occur in both x and z (i.e., the size of

liq [111]

Answer:

Yes, the function is a kernel

Step-by-step explanation:

Given

Document x an z

Function definition! k(x:z)

We want to show that the above is a kernel.

To do this, we'll explicitly construct feature vectors φ(x) and φ(z)

This gives;

K(x,z) =φ(x)·φ(z).

Given than any document; say x and z

A vocabulary V can be constructed.

Vocabulary V must have a finite size of words in the document set..

The feature mapping is constructed as φ(x) for x by the following:

For the kth word wk in V, if wk appears in document x, assign φ(x) k(the kth element ofφ(x)) to be 1; else φ(x)k to 0.

Then the number of unique words common in x and z is φ(x)·φ(z), giving us the kernel

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