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2 years ago

10

Most television showsUse 13 minutes of every hour for commercials leaving the remaining 47 minutes for the actual show. One popu

lar told me that she wants to change the ratio of commercial time to Showtime to be 3:7. Which way would have left commercials if the if you were still watching for two hours?

1 answer:

babunello [35]2 years ago

6 0

Answer:

Step-by-step explanation:née

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Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

4 0

2 years ago

viva [34]

Answer:

A.

5

8

−

3

8

=

2

0

B.

5

8

−

3

8

=

2

8

C.

5

8

+

3

8

=

8

8

D.

5

8

+

3

8

=

8

16

Step-by-step explanation:

4 0

2 years ago

At a pie eating contest Jonny, Jonny are 8 pies in 5 minutes. How much time did he spend on each pie?

Klio2033 [76]

Johnny ate 8 pies in 5 minutes

He must have ate 1 pie in (5/8) minutes

(5/8) minutes = 5/8 * 60 = 75/2 = 37.5 seconds

On each pie he spent 37.5 seconds.

7 0

3 years ago

Read 2 more answers

Rational numbers can be ______ or _______

chubhunter [2.5K]

Answer:

whole number or an integer.

Step-by-step explanation: hope this helps.

7 0

3 years ago

A total investment of $10,700 is made into two savings accounts. One account yields 5% simple interest and the other 6% simple i

AlladinOne [14]

Answer:

He earn $535.00 in the 5% account

Step-by-step explanation:

$I = \frac{prt}{100}$

I = interest amount

p = $10 700

r = 5%

t = 1 year

I = (10700×5×1)/100

= $535.00

(Correct me if i am wrong)

5 0

2 years ago

Read 2 more answers