Where are the negative rational numbers placed on a vertical number line

In Mathematics, to calculate the number of different license plates with 2 letters followed by 3 numbers, multiply the possibilities for each position: 26 × 26 for letters and 10 × 10 × 10 for numbers to get 676,000 different license plates.

The question pertains to the concept of permutations and combinations in Mathematics, specifically calculating the number of different license plates that can be manufactured when the format is two letters followed by three numbers. The number of possible license plates is found by multiplying the number of options for each component. For the letters, there are 26 possible choices for each of the two letter positions (assuming the English alphabet is used and letters can be repeated). For the numbers, there are 10 possible choices for each of the three number positions (using digits 0-9).

To calculate the total number of different license plates, we multiply the possibilities for each part: 26 × 26 × 10 × 10 × 10 = 676,000 different license plates. This calculation is known as the Rule of Product in combinatorics, which states that if one event can occur in 'm' ways and a subsequent event can occur in 'n' ways, then the total number of ways the two events can occur is m × n.

To determine the number of different license plates, multiply the number of alphabetic combinations (26 for each of the 2 letters) by the numeric combinations (10 for each of the 3 numbers), resulting in 676,000 possible plates.

The question is asking us to calculate the number of different license plates that can be manufactured with a specific format, which is 2 letters followed by 3 numbers. To solve this, we will assume there are 26 possibilities for each letter (A through Z) and 10 possibilities for each number (0 through 9).

For the two letters at the start, since both positions can hold any of the 26 letters in the alphabet, the total number of combinations for the two letters is 26 × 26.

For the three numbers following, each position can hold any digit from 0 to 9, giving us 10 × 10 × 10 combinations for the numbers.

To find the total number of different license plates, we multiply the number of possibilities for the letters by the number of possibilities for the numbers:

Total license plates = 26 × 26 × 10 × 10 × 10 = 676,000.

Therefore, there can be 676,000 different license plates manufactured for this state with the given format.

The expression 3(4x + 6) - 9x simplifies to 3x + 18 by distributing the 3 and then combining like terms.

To simplify the expression 3(4x + 6) - 9x, we need to follow the steps of distribution and then combine like terms.

Therefore, the simplified form of 3(4x + 6) - 9x is 3x + 18.

Answer:

C. the formation of mental hospitals

Step-by-step explanation:

During that time the jail and asylum conditions were worse.

The inmates especially the mentally ill, were bound in chains and locked in cages.

Hence, with the reform movement, came the formation of mental hospitals. Public asylums were made for the mentally ill incarcerated people.

The height of the door in the drawing will be 1/2 centimeters.

Scale factor is used to compare the size of two objects. Mathematically, we can write -

{K} = S{O1}/S{O2}

13 mg

Given is that the height of a door on a scale drawing if the door is 2 meters tall and the scale is 1 centimeter = 4 meters.

Height of the door = 2 meters

Scale :  1 centimeter = 4 meters.

So, in one meters, there will be - 1/4 centimeters.

In 2 meters, there will be -

(1/4) x 2 = 1/2 centimeters

Therefore, the height of the door in the drawing will be 1/2 centimeters.

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The rate at which the distance from the observer to the car is increasing is 25 m/s, both when the car passes in front of the observer and 10 seconds later.

To find the rate at which the distance from the observer to the car is increasing, we need to use the concept of relative velocity. When the car passes in front of the observer, its velocity is perpendicular to the line connecting the observer and the car. Therefore, the rate at which the distance is increasing is equal to the speed of the car. In this case, the rate is 25 m/s.

To find how fast the distance is increasing 10 seconds later, we need to consider the fact that the car is still moving at a constant velocity of 25 m/s. Therefore, the rate at which the distance is increasing remains the same. So, the rate is still 25 m/s.

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Final answer:

The expected value of the gambling game with a cost of $5, and potential winnings of $10 for a sum of 10 or $20 for a sum 3, is −$2.78. The calculation shows the player will lose $2.78 on average per game, indicating it is not a profitable game to play long term. So, option (b) is correct.

Explanation:

The student is interested in determining the expected value of a gambling game where rolling two dice can result in either winning money or losing the cost to play. To find the expected value, we must consider the probability of each outcome and its associated payoff.

First, we calculate the chances of rolling a sum of 10 with two dice. There are three combinations that give a sum of 10: (4,6), (5,5), and (6,4). Since there are 36 possible outcomes when rolling two dice, the probability of obtaining a sum of 10 is 3/36 or 1/12.

Similarly, the only combinations that result in a sum of 3 are (1,2) and (2,1). Thus, the probability of rolling a sum of 3 is 2/36 or 1/18.

The expected value (EV) can be calculated using the formula:

EV = (−cost to play) + [P(sum of 10) × winnings for 10] + [P(sum of 3) × winnings for 3]

Substituting the given values yields:

EV = (−5) + [(1/12) × 10] + [(1/18) × 20]

After calculating, we find tha-

EV = −$2.78.

Since the expected value is negative, this implies that, on average, the player will lose $2.78 per game. Therefore, playing this game would result in an average loss over time.

In this situation, the expression 400 + 0.1s represents Tasha's total earnings for the week, including her base salary and commission.

In this situation, the expression 400 + 0.1s represents Tasha's total earnings for the week. The $400 represents her base salary, and the 0.1s represents the commission she earns on her sales. The value of s represents Tasha's total sales for the week.

For example, if Tasha's total sales for the week are $2000, then her commission would be 0.1($2000) = $200. Adding this to her base salary of $400, her total earnings for the week would be $400 + $200 = $600.

Therefore, the expression 400 + 0.1s represents Tasha's total earnings for the week, including her base salary and commission.

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Answer:

24 has 8 factors with 1,2,3,4,6,8,12,and 24

Step-by-step explanation:

To multiply 4 x 362 using place value and expanded form, first expand 362 to (300 + 60 + 2). Then multiply 4 with each value, resulting in 1200, 240, and 8. The sum of these results gives the final answer, 1448.

The multiplication expression of 4 x 362 using expanded form and place value can be represented as follows:

So, 4 multiplied by 362 using place value and expanded form equals to 1448.

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The probability of drawing a blue marble and then another blue marble from a bag, with replacement of the first marble, is calculated by multiplying the probability of the first event by the probability of the second event since the first event's outcome does not change the conditions for the second draw. In this case, the probability is 1/16.

The question involves calculating the probability of drawing two blue marbles consecutively from a bag, with replacement of the first marble before drawing the second one. To find this probability, we calculate the chance of drawing a blue marble twice, taking into account that the composition of the bag remains the same after the first draw due to replacement.

The total number of marbles is 5 red + 3 blue + 2 green + 2 yellow = 12 marbles. The probability of drawing a blue marble is the number of blue marbles divided by the total number of marbles, which is 3/12 or 1/4. Since the first marble is replaced, the probabilities remain the same for the second draw. Therefore, the probability of drawing a blue marble on the second draw is also 1/4.

To find the combined probability of both events happening in succession, we multiply the probabilities of each individual event: (1/4) * (1/4) = 1/16. Thus, the probability of drawing a blue marble and then another blue marble, with replacement, is 1/16.

Tommy would be able to get $16.50.

The first step would be to find out the number of dollars you need to exchange for a single Euro.

If 8 Euros go for $11, one Euro would be:

= Amount of dollars / Amount of Euros

= 11 / 8

= $1.375 per Euro

For 12 Euros therefore, the number of dollars Tommy would get is:

= Amount of Euros x conversion factor

= 1.375 x 12

= $16.50

In conclusion, Tommy would get $16.50.

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The error in using a scale that is too small on a bar graph falls under the data organization phase. This phase involves selecting a scale that accurately represents data without distorting trends or variations.

When creating a bar graph to represent data, if the researcher uses a scale that is too small, resulting in a graph that shows very little variation, it is likely an error in the data organization phase. This is because choosing an appropriate scale is a key part of the process of organizing data for visualization. A scale that's too small can compress the data too much and fail to show important differences between data points, while a scale that's too large can exaggerate these differences. In a well-organized graph, the scale should be such that it both accurately represents all the data and makes it easy to identify trends and variations.

It is important to be skeptical of graphs and understand that data organization can have a significant impact on how the information is perceived. A graph is a single visual perspective, and therefore, it is crucial that the scale used does not distort the underlying relationship it is intended to represent. When organizing data in a graph, it's essential to select a scale that neither overshadows nor exaggerates the significant figures and trends of the data points.

Using a scale that is too small in a bar graph is an error in the data organization phase of inferential statistics.

The error of using a scale that is too small and resulting in a bar graph that shows very little variation is a classic example of an error in data representation, which falls under the phase of  in inferential statistics.

Answer:

20/52+13/52-5/52=.538

Step-by-step explanation:

The probability that the card is between four and eight (inclusive) or is a club is 4/13.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The number of cards can be written as,

Now, the probability that the card is between four and eight (inclusive) or is a club is,

Probability

= (Number of club cards+ Number of cards between 4 and 8)/(Total number of cards)

= (13+15)/(52)

= 28/52

= 4/13

Hence, the probability that the card is between four and eight (inclusive) or is a club is 4/13.

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