MATHEMATICS HIGH SCHOOL

What Is probability ?
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Answers

Answer 1
Answer:

Final answer:

Probability is a mathematical practice used to measure the likelihood of an event occurring. It is used extensively in various fields to predict the outcome of an experiment or event. The empirical probability is calculated from observed data, while the theoretical probability assumes equal likelihood for all outcomes.

Explanation:

Probability is a mathematical discipline that deals with the chance of an event occurring. It is a measure of certainty or uncertainty related to outcomes and activities, especially in experiments whose results are not predetermined, termed as chance experiments.

Whenever an experiment is carried out, it is referred to as a sample event. The set of all possible results of this experiment is termed as the sample space. The various results or outcomes of the event are subsets of this sample space, and each is associated with a probability.

The empirical probability of an event is calculated by dividing the number of times the event occurs by the total number of opportunities for it to occur. On the other hand, the theoretical probability is computed by dividing the number of expected occurrences of the event by the total number of potential occurrences. In most situations, the probabilities of individual outcomes are assumed to be equal, but this might not always be the case.

Probability is used extensively in various fields from forecasting weather conditions to predicting the outcome of an experiment or an event. For example, genetics, where it helps predict the outcomes of genetic crosses; finance, where it helps a stockbroker determine the rate of return on investments and many more.

Learn more about Probability here:

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Classify triangle ABC by its sides if side AB = 6x, side AC = 4x + 6 and side BC = 8x + 3. The perimeter of triangle ABC is 63. Show all your work.

Answers

Answer:

So the triangle ABC is an isosceles triangle

Step-by-step explanation:

By definition the perimeter of a triangle is equal to the sum of the lengths of its sides.

In this case we know that the perimeter is 63

The lengths of its sides depend on x.

AB = 6x\nAC = 4x + 6\nBC = 8x + 3

So:

6x + 4x + 6 + 8x + 3 = 63

Now we solve for the variable x.

6x + 4x + 6 + 8x + 3 = 63

18x + 9 = 63

18x = 54

x=(54)/(18)\n\nx=3

Therefore:

AB = 6(3)=18\nAC = 4(3)+6=18\nBC = 8(3) + 3=27

The triangle has two sides of equal length. The triangles that have two equal sides are the isosceles triangles.

So the triangle ABC is an isosceles triangle

when the 69th even natural number is subtracted from the 119th odd natural number, what is the result

Answers

69th even number is: 69*2 = 138
119th odd number is: (2*119) - 1 = 237
69th even natural number subtracted from the 119th odd natural number is:
237 - 138 = 99.

Answer:

99

Step-by-step explanation:

The answer is 99 since you need to double 69 and also 119 and then subtract 1 from the double of 119. Then you would subtract them to get 99.

Three candidates: A, B, C. Candidate A received 20% of the votes, while candidate B received exactly 3 times as many votes as candidate C. What percentage of votes did candidate C receive? a) 10% b) 15% c) 20% d) 5%

Answers

Answer: C received 20% of the votes so C would be your answer

Answer:

Step-by-step explanation:

Let C received x% votes. Then B received 3x% votes. B and C together received 80% of votes because A received the remaining 20%.

x + 3x = 80

4x = 80

x = 20

Answer: c) 20%

( 4,?)Is on the line y=2×+3. find the other half of the coordinate

Answers

(4, ?).      Let ? = b

(4, b) on line y = 2x + 3

x =4, y = b.        

y = 2x + 3

b = 2*4 + 3

b = 8 + 3

b = 11.

The other half of coordinate is 11.
You do y=2x(4)+3
that equals 11 
so the coordinate is (4,11)

There were 6954 cases filed with the Supreme Court. Of these only 82 were decided by the Supreme Court. What percentage was decided by the Supreme Court

Answers

Answer:

Total no. of cases = 6954

No. of cases decided = 82

Percentage decided = (82/6954)x100 = 1.17%

Answer:

1.18%

Step-by-step explanation:

A percentage can be found by dividing the part by the whole. then multiplying by 100.

(part/whole) * 100

In this problem, the part is the cases decided by the Supreme Court. The whole is the total number of cases filed.

(cases decided / cases filed) *100

There were 82 cases decided by the Supreme Court, out of a total of 6,954 cases filed.

(82/6954) *100

First, solve the parentheses and divide.

0.0117917745* 100

Multiply

1.17917745 %

Round to the nearest hundredth. The 9 in the thousandth place tells us to round the 7 up to an 8 in the hundredth place.

1.18 %

About 1.18% of the cases filed were decided by the Supreme Court.

a 5ft ladder is leaning against a 4 ft wall. how far must the bottom of the ladder be from the wall so that the top of the ladder rests on the top of the wall?

Answers

The ladder leaning against the wall forms a right angled triangle with the gound and the wall. So we can use the formula:

a² + b² = c²

The ladder is the hypotenuse c²

The vertical leg is b²

The base or horizontal leg is a²

We need to find the length of the base a²,  so:

a² = c² - b²

a² = 5² - 4²

a² = 25 - 16

a² = 9

a = √9

a = 3

Therefore the bottom of the ladder must be 3 feet  from the wall.

 
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