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4 years ago

750 is what percentage of 900

Mathematics

1 answer:

Alenkasestr [34]4 years ago

5 0

The answer is about 83. The exact answer is 83.3333333333, however, rounding to the nearest one, the answer is 83%.

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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

3 years ago

Which of the relations below is not a function?

Ilia_Sergeevich [38]

Answer:

Relations B and E do not represent the function.

Step-by-step explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

If we closely observe relation B, and E i.e.

B) {(3,4), (4,5), (3,6). (6,7)}

E) {(3,4), (4,5), (4,6)}

Relation 'B' IS NOT A FUNCTION

Relation B has duplicated or repeated inputs i.e. x = 3 appears twice times. we can not have duplicated inputs as there should be only 1 output for each input.

Thus, relation B is NOT a function.

Relation 'E' IS NOT A FUNCTION

Relation E has duplicated or repeated inputs i.e. x = 4 appears twice times. we can not have duplicated inputs as there should be only 1 output for each input.

Thus, relation B is NOT a function.

Therefore, relations B and E do not represent the function.

7 0

3 years ago

2(x + 3)=x - 4<br>help me

Irina18 [472]

Answer:

x = -10

Step-by-step explanation:

2(x+3) = x-4 --> multiply (x+2) times 2

2x+6 = x - 4 --> subtract x from both sides

x+6 = -4 --> subtract 6 from both sides

x = -10

4 0

3 years ago

Read 2 more answers

maria y saul trabajan en una oficina en la que hay ocho opersonas, mismas que tienen que dividirse en dos equipos para realizar

solong [7]

Siskkakakakananjakwnwkeleld

6 0

3 years ago

Type it down in the right order thanks

brilliants [131]

Answer:

$53.00 for 4 pounds

$13.25 for 1 pound

Step-by-step explanation:

6 0

3 years ago