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Lesechka [4]
2 years ago
6

The rocks near the shore between two lighthouses at points A and B make the waters unsafe. The measure of arcAXB is 300. Waters

inside this arc are unsafe. Suppose you are a navigator on a ship at sea. How can you use the lighthouses to keep the ship in safe waters?
Mathematics
1 answer:
belka [17]2 years ago
5 0
As a navigator of this ship, you must consider the measure of the arc. Using the distance between the two lighthouses and the arc measurement, you can find the radius and center of the circle to set a reasonable distance in keeping the ship in safe waters.
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Which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse
Aliun [14]

Answer:

Option C is correct.

Ratio of longer leg to hypotenuse is;  \sqrt{3} : 2

Step-by-step explanation:

This is the special right angle triangle 30°-60°-90°  as shown below in the figure.

  • The side opposite the 30° angle is always the shortest because 30 degrees is the smallest angle.
  • The side opposite the 60° angle will be the longer leg, because 60 degrees is the mid-sized degree angle in this triangle.
  • Finally , the side opposite the 90° angle will always be the largest side(Hypotenuse) because 90 degrees is the largest angle.

In 30°−60°−90° right triangle,

  • the length of the hypotenuse is twice the length of the shorter leg,also
  • the length of the longer leg is \sqrt{3} times the length of the shorter leg.

Then:

the sides are in proportion i.e,  1:\sqrt{3} :2

Therefore, the ratio of the length of the longer leg to the length of its hypotenuse is:  \sqrt{3} : 2



7 0
2 years ago
Read 2 more answers
The life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hour
ikadub [295]
Mean = 12000
Standard Deviation = 2000

We have to find how many standard deviations is 14,500 away from the mean.
This can be achieved by calculating the z-score

Z-score tells us how many standard deviations above or below is a sample value from the mean. A positive z value shows, sample value is above the mean.

z score can be calculated as = (Sample Value - Mean )/Standard Deviation)
So,
Z-score = \frac{14500-12000}{2000} =1.25

This means, 14,500 is 1.25 standard deviations above the mean value 12,000.
4 0
2 years ago
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The graph shows the influence of the temperature T on the maximum sustainable swimming speed S of Coho salmon. (b) Estimate the
Alex17521 [72]
From the graph it appears that S′(5) 2 ≈ and S′(25) 2 ≈ − . The important thing is that they do have opposite signs. The first means that at about 5ºC the Coho gains about 2 cm/sec while at 25ºC it loses about 2 cm/sec in maximum sustainable speed.
3 0
2 years ago
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The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard dev
k0ka [10]

Answer: b. 0.8413

Step-by-step explanation:

Given : The average time taken to complete an exam, X, follows a normal probability distribution with \mu=60\text{ minutes} and \sigma=30\text{ minutes} .

Then, the  probability that a randomly chosen student will take more than 30 minutes to complete the exam will be :-

P(x>30)=P(z>\dfrac{30-60}{30})\ \ [\because\ z=\dfrac{x-\mu}{\sigma} ]\\\\=P(z>-1)=P(z-z)=P(Z

 [using z-value table]

Hence, the probability that a randomly chosen student will take more than 30 minutes to complete the exam =  0.8413

3 0
2 years ago
The plot of land illustrated in the accompanying diagram has a perimeter of 34 yards. Find the length, in yards, of each side of
noname [10]

Answer:

Length of x+3= 6.75

Length of 4x=15

Length of 3x-1=10,25

Step-by-step explanation:

  • First make an equation and find x x+3+3x+1+4x=34
  • Then solve for x, answer will be 3,75
  • 3,75 represents x
3 0
1 year ago
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