1.

Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance o

g100num [7]

Answer:

The value is $k =109.6 \ miles$

Step-by-step explanation:

The diagram illustrating the question is shown on the first uploaded image

From the question we are told that

The distance from city A to B is AB = 467.3 miles

The bearing from B to C is $\theta_{BC} = N 28.7E$

The bearing from B to A is $\theta_{BA} = N 60.7E$

The bearing from A to B is $\theta_{AB} = S60.7W$

The bearing from A to C is $\theta_{AC} = S79.1W$

Generally from the diagram

$\theta_A = 180 - 60.7 -79.1$

=> $\theta_A = 40.2 ^o$

Also

$\theta_B = 32^o$

and

$\theta_C = 180 - (\theta_A +\theta_B )$

=> $\theta_C = 180 - (40.2 + 32 )$

=> $\theta_C = 107.8 ^o$

Generally according to Sine Rule

$\frac{BC}{sin (\theta_A)} = \frac{CA}{sin (\theta_B)} =\frac{AB}{sin (\theta_C)}$

=> $\frac{BC}{sin (40.2)} = \frac{CA}{sin (32)} =\frac{467.3 }{sin (107.8)}$

So

$\frac{BC}{sin (40.2)} = \frac{467.3 }{sin (107.8)}$

=> $BC = 316.8 \ miles$

Also

$\frac{CA}{sin (32)} = \frac{467.3 }{sin (107.8)}$

$CA = 260 .1 \ miles$

Generally the additional flyer miles that Adam will receive if he takes the connecting flight rather than the direct flight is mathematically represented as

$k = [CA +BC] - AB$

=> $k = [260 .1 +316.8]- 467.3$

=> $k =109.6 \ miles$

4 0

3 years ago

Can you please answer my question number9

inn [45]

X=25... hope this helps

6 0

3 years ago

Read 2 more answers

Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded a

aksik [14]

Answer:

the expected value of this raffle if you buy 1 ticket = -0.65

Step-by-step explanation:

Given that :

Five thousand tickets are sold at $1 each for a charity raffle

Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $500, 3 prizes of $300, 5 prizes of $50, and 20 prizes of $5.

Thus; the amount and the corresponding probability can be computed as:

Amount Probability

$500 -$1 = $499 1/5000

$300 -$1 = $299 3/5000

$50 - $1 = $49 5/5000

$5 - $1 = $4 20/5000

-$1 1- 29/5000 = 4971/5000

The expected value of the raffle if 1 ticket is being bought is as follows:

$E(x) = \sum x * P(x)$

$E(x) = (499 * \dfrac{1}{5000} + 299 *\dfrac{3}{5000} + 49 *\dfrac{5}{5000} + 4 * \dfrac{20}{5000} + (-1 * \dfrac{4971}{5000} ))$

$E(x) = (0.0998 + 0.1794+0.049 + 0.016 + (-0.9942 ))$

$E(x) = (0.3442 -0.9942 )$

$\mathbf{E(x) = -0.65}$

Thus; the expected value of this raffle if you buy 1 ticket = -0.65

7 0

3 years ago

Complementary events are described as the events of one outcome happening and that outcome not happening. Given that definition,

masya89 [10]

Complementary events are the events which are opposite of the given event.

For example, for a "rainy day", its complimentary event is "not a rainy day".

We can also say, If A is a given event, then " not A" is its complimentary event.

In the given question we have been given the event of choosing a girl's name when drawing names from a cup in class.

Now in class as there can be boys or girls, the complimentary even of choosing a girl's name is choosing a boy's name.

Option C) is the right answer.

3 0

3 years ago

Read 2 more answers

What property would you use first to solve 1/2x-6=10

NISA [10]

I don't know what you mean by property. Do you mean like, commutative, distributive, etc?

but, if this is what you mean:

to solve this:

The operation here is subtraction. Do the inverse. So, add 6 to both sides of the equation

10 + 6 = 16

1/2x - 6 + 6 = 1/2x. (the 6 cancels out)

1/2x = 16

Now, I'm going to assume 1/2 is supposed to be a fraction (not division). So, 1/2 is right next to x which represents multiplication, so do the opposite which is division.

16 divided by 1/2 = 32

1/2x divided by 1/2 = x

x = 32.

(:

6 0

2 years ago