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3 years ago

Express your answer in the smallest unit: 338km+ 62km 71m

Mathematics

1 answer:

Alexeev081 [22]3 years ago

8 0

Adding all of the together would be 471... but I need clarification on the problem

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The sum of three consecutive odd numbers is 123 what is the smallest of the three numbers

Inga [223]

Answer:

Step-by-step explanation:

Let the three consecutive odd numbers be:

x+2, x+4, x+6.

The sum of the consecutive numbers is 123 i.e

x+2 + (x+4) + (x+6) = 123

x + 2 + x + 4 + x + 6 = 123

3x + 12 = 123

Collect like terms

3x = 123 — 12

3x = 111

Divide both side by the coefficient of x i.e 3

x = 111/3

x = 37

Now let us find the value of the three odd numbers. This is illustrated:

1st : x + 2 = 37 + 2 = 39

2nd : x + 4 = 37 + 4 = 41

3rd : x + 6 = 37 + 6 = 43

The smallest of the three consecutive odd numbers is 39

5 0

3 years ago

When grading an exam, 90% of a professor's 50 students passed. If the professor randomly selected 10 exams, what is the probabil

Damm [24]

Using the binomial distribution, it is found that there is a:

a) 0.9298 = 92.98% probability that at least 8 of them passed.

b) 0.0001 = 0.01% probability that fewer than 5 passed.

For each student, there are only two possible outcomes, either they passed, or they did not pass. The probability of a student passing is independent of any other student, hence, the binomial distribution is used to solve this question.

<h3>What is the binomial probability distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

90% of the students passed, hence $p = 0.9$ .

The professor randomly selected 10 exams, hence $n = 10$ .

Item a:

The probability is:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

In which:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{10,8}.(0.9)^{8}.(0.1)^{2} = 0.1937$

$P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874$

$P(X = 10) = C_{10,10}.(0.9)^{10}.(0.1)^{0} = 0.3487$

Then:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1937 + 0.3874 + 0.3487 = 0.9298$

0.9298 = 92.98% probability that at least 8 of them passed.

Item b:

The probability is:

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

Using the binomial formula, as in item a, to find each probability, then adding them, it is found that:

$P(X < 5) = 0.0001$

Hence:

0.0001 = 0.01% probability that fewer than 5 passed.

You can learn more about the the binomial distribution at brainly.com/question/24863377

3 0

2 years ago

If it snows tomorrow the probability is 0.8 that John will practice his trombone if it does not snow tomorrow there is only a 0.

Bas_tet [7]

Answer:

0.68

Step-by-step explanation:

Given that :

P(trombone | snow) = 0.8 ;

P(trombone | no snow) = 0.5

P(snow) = 0.6

P(trombone) = P(trombone | snow) * p(snow) + P(trombone | no snow) * p(no snow)

P(no snow) = 1 - 0.6 = 0.4

Hence,

P(trombone) = P(trombone | snow) * p(snow) + P(trombone | no snow) * p(no snow)

P(trombone) = (0.8 * 0.6) + (0.5 * 0.4)

P(trombone) = 0.48 + 0.20

P(trombone) = 0.68

7 0

3 years ago

Stan borrows $5,500 at a rate of 12% interest per year. What is the amount due at the end of 5 years if the interest is compound

kolbaska11 [484]

<span>Without compound interest, Stan would earn only $8,800.00. This means that thanks to the power of compound interest Stan will earn an additional $1,191.83 in interest at the end of the 5-year-term.</span>

7 0

4 years ago

I need help please if you can help I will give you 10 points

valentina_108 [34]

Answer:

option A

Step-by-step explanation:

7 0

3 years ago