A die is rolled 260 times. Predict how many times it will show a 3 or 5.

Answers

Answer 1

Answer:

The chances of getting 3 or 5 by 260 times will be 87.

What is probability?

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that a die is rolled 260 times. The number of times it will show a 3 or 5 will be calculated as below:-

Sample = 6

Number of getting 3 = 1

Number of getting 5 = 1

Probability of getting 3 = 1 / 6

Probability of getting 5 = 1 / 6

Probability of 3 or 5 = ( 1 / 6 ) + ( 1 / 6 )

Probability of 3 or 5 = 2 / 6

Number of times of getting 3 or 5 = ( 2 / 6 ) x 260

Number of times getting 3 or 5 = 87

Therefore, the chances of getting 3 or 5 by 260 times will be 87.

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Shureka Washburn has score of 72,67,82, and 79 on her alebra test. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 77 or higher, given that the final exam counts as two test.

Answers

Answer:

$x \geq 81$

Step-by-step explanation:

Shureka Washburn has score of 72,67,82, and 79 on her algebra test.

Let x be the score on the final exam.

$(72+67+82+79+x+x)/(6) \geq 77$

=> $(300+2x)/(6) \geq 77$

=> $300+2x \geq(77)6$

=> $300+2x \geq 462$

=> $2x \geq 462-300$

=> $2x \geq 162$

=> $x \geq 81$

72+67+82+79=300
300/4=75
300+81+81=462
462/6=77

ANSWER X MUST BE GREATER THAN OR EQUAL TO 81

A ship is sailing due north. At a certain point the bearing of a lighthouse is N 42.8∘E and the distance is 10.5. After a while, the captain notices that the bearing of the lighthouse is now S 59.7∘E. How far did the ship travel between the two observations of the lighthouse?

Answers

Answer:

How far did the ship travel between the two observations of the lighthouse = 9.29

Step-by-step explanation:

the first step to answer this question is drawing the illustration as the attachment.

P is the ship, R is the light house and Q is the bearing.

PR is the distance between the ship and the light house, PR = 10.5

∠P = 42.8°, ∠Q = 59.7°

Thus, ∠R = 180° - ∠P - ∠Q

= 180° - 42.8°- 59.7°

= 77.5°

PQ is the the distance of the ship moving. We can use the sinus equation

$(PR)/(sin R)$ = $(PQ)/(sin Q)$

$(10.5)/(sin 77.5°)$ = $(PQ)/(sin 59.7°)$

PQ = ( $(10.5)/(Sin 77.5°)$ )(sin 59.7°)

= 9.29

Final answer:

Using trigonometric principles, the ship is estimated to have traveled approximately 19.8 miles between the two observations.

Explanation:

Your question involves the application of trigonometry in real life, in this case, calculating the distance traveled by a ship. The first sighting puts the lighthouse at N 42.8 degrees E, and the second sighting puts it at S 59.7 degrees E. So, the angle turned by the ship, relative to the lighthouse is 42.8 degrees + 59.7 degrees = 102.5 degrees.

We know the distance to the lighthouse from the first sighting is 10.5 units (let's say miles), and we need to find the distance traveled by the ship in the meantime. So, if we draw this situation it will resemble a triangle with the lighthouse as one point, and the initial and final positions of the ship as other points. The triangle will have one angle (between the initial position of the ship, the lighthouse, and the final position of the ship) of 102.5 degrees and one side (distance from the lighthouse to the initial position of the ship) of 10.5 miles. Now, the side of a triangle opposite an angle in a triangle is given by the side adjacent to the angle times the tangent of the angle.

So, the distance traveled by the ship = 10.5 * tan(102.5) = 19.8 miles approximately.

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10 over 7 x 3 over 8

Answers

When you multiple fractions, you just multiple numerators and denominators.

10 / 7 × 3 / 8 = (10 × 3) / (7×8) = 30 / 56

Now reduce the fraction:

30 / 56 = 15/28

Final answer: 15/28

The perimeter of a rectangular painting is 318 cm.If the length of the painting is 95 cm, what is its width?