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2 years ago

How far are Gustavo and Aiden away from each other

Mathematics

1 answer:

allsm [11]2 years ago

7 0

Answer: Gustavo is 261.96 meters away from Aiden. Or Aiden is 261.96 meters away from Gustavo.

Step-by-step explanation: From the question, considering a North, East, South and west pole, Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal.

Therefore, Where a and b are distances travelled respectively by Gustavo and Aiden. While θ is the angle between them.the total angle between them is 23 + 33 = 56°. Therefore, let the distance between them be c and we can calculate that using the cosine law.c² = a² + b² – 2ab cos θ. Therefore, let the distance between them be c and we can calculate that using the cosine law.c² = a² + b² – 2ab cos θ.

Therefore, they are 261.96 meters apart.

c² = 300² + 250²– 2(300) (250)cos 56

c² = 90000 + 62500 - 83878.9355

c² = 68621.0645

c = √68621.0645

c = 261.96 m

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On any given day, mail gets delivered by either Alice or Bob. If Alice delivers it, which happens with probability 1/4 , she doe

Troyanec [42]

Answer:

(a) The value of fₓ (9.5) is 0.125.

(b) The value of fₓ (10.5) is 0.50.

Step-by-step explanation:

Let X denote delivery time of the mail delivered by Alice and Y denote delivery time of the mail delivered by Bob.

It i provided that:

$X\sim U(9, 11)\\Y\sim U(10, 12)$

The probability that Alice delivers the mail is, p = 1/4.

The probability that Bob delivers the mail is, q = 3/4.

The probability density function of a Uniform distribution with parameters [a, b] is:

$f(x)=\left \{ {{\frac{1}{b-a};\ a, b>0} \atop {0;\ otherwise}} \right.$

The probability density function of the delivery time of Alice is:

$f(X_{A})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[9, 11]} \atop {0;\ otherwise}} \right.$

The probability density function of the delivery time of Bob is:

$f(X_{B})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[10, 12]} \atop {0;\ otherwise}} \right.$

(a)

Compute the value of fₓ (9.5) as follows:

For delivery time 9.5, only Alice can do the delivery because Bob delivers the mail in the time interval 10 to 12.

The value of fₓ (9.5) is:

$f_{X}(9.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times0)\\=\frac{1}{8}\\=0.125$

Thus, the value of fₓ (9.5) is 0.125.

(b)

Compute the value of fₓ (10.5) as follows:

For delivery time 10.5, both Alice and Bob can do the delivery because Alice's delivery time is in the interval 9 to 11 and that of Bob's is in the time interval 10 to 12.

The value of fₓ (10.5) is:

$f_{X}(10.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times\frac{1}{2})\\=\frac{1}{8}+\frac{3}{8}\\=0.50$

Thus, the value of fₓ (10.5) is 0.50.

5 0

3 years ago

A triangle has three different integer side lengths and a perimeter of 20 units. What is the max length of any one side?

Troyanec [42]

X + x+1 + x + 2 = 20
3x + 3 = 20
3x = 17 but can't start with x = 6 because 6+7+8 > 20,
so have start with 5 + 6 + 7 = 18 are the 3 sides.

3 0

2 years ago

- What is the range of the following set of points: {(3, 4), (7, - 2), (11, – 8)}?

konstantin123 [22]

Answer:

B) {-8,-2,3,4,7,11}

Step-by-step explanation:

range is y

3 0

3 years ago

The cost C in dollars of manufacturing x bicycles at a production plant is given by the function shown below.

Andreas93 [3]

Answer:

Minimum 100 bicycles
Minimum cost is 13500

Step-by-step explanation:

Given function:

C(x) = 3x^2- 600x + 43500

Minimum cost is obtained at vertex.

Vertex is determined by formula x = -b/2a, in standard form of

f(x) = ax^2 + bx + c

Vertex of the given function is:

x = -(-600)/(2*3) = 100

Cost at vertex is:

C(100) = 3*100^2 - 600*100 + 43500 = 13500

7 0

3 years ago

For every 3 laps that Jackie swims, Ronnie swims 4 laps. During practice, they swam a combined total of 63 laps. How many laps d

Flura [38]

Answer:

36 laps Ronnie swim during practice .

Step-by-step explanation:

Let us assume that the laps that Ronnie swims be x .

Let us assume that the laps that Jackie swims be y .

As given

For every 3 laps that Jackie swims, Ronnie swims 4 laps.

i.e

3 × laps that Ronnie swims = 4 × laps that Jackie swims

3 × x = 4 × y

3x = 4y

Equation becomes

x + y = 63

Thus by using 3x = 4y .

$y = \frac{3x}{4}$

Thus

$x +\frac{3x}{4} = 63$

4x + 3x = 63 × 4

7x = 252

x = 36

Put the value of x in the equation x + y = 63

36 + y = 63

y = 63 - 36

y = 27

Therefore the 36 laps Ronnie swim during practice .

4 0

3 years ago