First way:
The easiest and simplest way is to count by 1 starting from 82 till you reach 512.
This will go as follows:
82, 83, 84, 85, ........... , 510, 511, 512

Second way:
We can note that the two given numbers are even numbers. This means that the two numbers are divisible by 2.
Therefore, we can count by 2 starting from 82 till we reach 512.
This will go as follows:
82, 84, 86, 88, ................... , 508, 510, 512

Third way:
We can note that the units digit in both numbers is the same (the digit is 2). This means that we can count from 82 till 512 by adding 10 each time.
This will go as follows:
82, 92, 102, 112, ......................, 492, 502, 512

Hope this helps :)

5 0

1 year ago

The sales manager of a company awarded a total of \$3000$3000 in bonuses to the most productive salespeople. The bonuses were aw

alisha [4.7K]

Answer:

one possible number of bonus is 9.

Step-by-step explanation:

Let, the number of $250 bonus = x and number of $750 bonus = y.

We have that bonuses are given in amounts $250 and $750.

Since, the total bonus is $3000.

So, we get,

250x + 750y = 3000.

As, there is atleast one $250 bonus and atleast one $750 bonus.

Let, the minimum number of bonus of $750 be 1 i.e. y = 1.

Substitute in the equation gives,

250x + 750 × 1 = 3000

i.e. 250x = 3000 - 750

i.e. 250x = 2250

i.e. x = 9

Thus, the maximum number of $250 bonus are 9.

Hence, one possible number of bonus is 9.

4 0

2 years ago

Flip two coins 100 times, and record the results of each coin toss in a table like the one below:

monitta

Answer:

1)The theoretical probability that a coin toss results in two heads showing is 25%.

2)The experimental probability that a coin toss results in two heads showing is 44%.

3) The theoretical probability that a coin toss results in two tails showing is 25%.

4) The experimental probability that a coin toss results in two tails showing is 34%.

5) The theoretical probability that a coin toss results in one head and one tail showing is 50%.

6) The experimental probability that a coin toss results in a head and a tail is 22%.

7) The experimental probabilities are slightly different from the theoretical probabilities because the number of experiments is relatively small. As the number of experiments increase, the experimental probabilities will get closer to the theoretical probabilities.

Step-by-step explanation:

Probability:

What you want to happen is the desired outcome.

Everything that can happen iis the total outcomes.

The probability is the division of the number of possible outcomes by the number of total outcomes.

Theoretical Probability:

The results you expect to happen.

Experimental Probability:

The probability determined from the result of an experiment.

1. What is the theoretical probability that a coin toss results in two heads showing?

In each toss, the theoretical probability that a coin toss results in a head showing is 50%.

So for two coins, the probability is:

$P = (0.5)^{2} = 0.25$

The theoretical probability that a coin toss results in two heads showing is 25%.

2. What is the experimental probability that a coin toss results in two heads showing?

There were 100 flips, and it resulted in two heads 44 times, so:

$P = \frac{44}{100} = 0.44$

The experimental probability that a coin toss results in two heads showing is 44%.

3. What is the theoretical probability that a coin toss results in two tails showing?

In each toss, the theoretical probability that a coin toss results in a tail showing is 50%.

So for two tails, the probability is:

$P = (0.5)^{2} = 0.25$

The theoretical probability that a coin toss results in two tails showing is 25%.

4. What is the experimental probability that a coin toss results in two tails showing?

There were 100 flips, and it resulted in two tails 34 times, so:

$P = \frac{34}{100} = 0.34$

The experimental probability that a coin toss results in two tails showing is 34%.

5. What is the theoretical probability that a coin toss results in one head and one tail showing?

In each toss, the theoretical probability that a coin toss results in a tail showing is 50% and in a head showing is 50%.

They can be permutated, as the tail can appear before the head, or the head before the tail. So:

$P = p_{2,1}*(0.5)*(0.5) = \frac{2!}{1!}*0.25 = 0.50$

The theoretical probability that a coin toss results in one head and one tail showing is 50%.

6. What is the experimental probability that a coin toss results in one head and one tail showing?

There were 100 flips, and it resulted in a head and a tail showing 22 times, so:

$P = \frac{22}{100} = 0.22$

The experimental probability that a coin toss results in a head and a tail is 22%.

6 0

1 year ago