Find the product and quotient of each pair of numbers

a. 24.6 and 1.2
b. 1.95 and .25

The passenger's velocity relative to the road is calculated by subtracting the passenger's speed from the bus's speed since they are moving in opposite directions. Thus, the passenger's velocity relative to the road is 12 km/h south.

The passenger's velocity relative to the bus is 3.0 km/h towards the back of the bus. However, given that the bus is moving south at 15 km/h, the passenger's velocity relative to the road is actually the bus's speed subtracted by the passenger's speed (as they're moving in opposite directions). Therefore, the passenger's velocity relative to the road is 15 km/h - 3.0 km/h = 12 km/h towards the south or simply 12 km/h south.

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Answer:

B

Step-by-step explanation:

Final answer:

To find the length of the ladder, we can use trigonometry. The length of the ladder is approximately 3.25 feet.

Explanation:

To find the length of the ladder, we can use trigonometry. In this case, we have a right triangle formed by the ladder, the wall, and the ground. The angle between the ladder and the ground is given as 70°, and the base of the ladder is given as 3 feet.

Using the sine function, we can set up the equation: sin(70°) = opposite/hypotenuse. The opposite side is the height of the ladder on the wall, and the hypotenuse is the length of the ladder. Rearranging the equation, we get: hypotenuse = 3 feet / sin(70°).

Calculating the value, we find that the length of the ladder is approximately 3.25 feet.

The question deals with a simple random sampling method for a statistics class, discussing various techniques such as proportionate random sampling, systematic sampling, and the importance of each individual having an equal chance of being selected to ensure a representative sample.

The student's question involves selecting a simple random sample of 30 students from a population of 250 students in a large statistics class, using the sampling frame of students present next Monday. The concept described relates to sampling methods within the field of statistics, used to infer characteristics of a larger population. One method mentioned is proportionate random sampling, where a sample is obtained from each class based on the proportion of students in the college (e.g., if 30% of students are freshmen, then 30% of the sample would come from the freshman class). Another method is systematic sampling, where a starting point is chosen using a random number generator and then every nth student is selected (e.g., every 50th student). An important characteristic of a good sample is that every individual in the population should have an equal chance of being included, which is a hallmark of both random and systematic sampling methods. Finally, stratification, such as by class standing or other demographic factors, ensures that the sample is representative of the population under study, which might involve working with local schools to select a random sample of students from various backgrounds.

Final answer:

Julio started with the number 20. Cubing a number and then taking the cube root of the result returns the original number.

Explanation:

If Julio ends with 20 after cubing a number and then taking the cube root of the result, it means that the original number he started with must be 20. This is because the operations of cubing a number and then taking the cube root are inverse operations. Performing these operations one after the other will return the original value. So, the cube root of a number cubed is the number itself.

For example, if Julio starts with the number x, cubes it to get x3, and then takes the cube root of x3, he will end up with the original number x. In this case, since he ends up with 20, this means x equals 20.

The solution to the equality statement "twice a number increased by 4 is at least 10 more than a number" is x ≥ 6.

Given the parameter:

Twice a number increased by 4 is at least 10 more than a number.

First, we convert the statement to an inequality;

Let x represent the unknown number:

Twice a number increased by 4 ⇒ 2x + 4

Is at least ⇒ ≥

10 more than a number ⇒ x + 10

Let's combine the inequality:

2x + 4 ≥ x + 10

Now, we solve for x:

2x - x + 4 ≥ x - x + 10

2x - x + 4 - 4 ≥ 10 - 4

x ≥ 6

Therefore, the solution to the inequality is x ≥ 6.

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To solve the problem, two equations were set up: 6A + 4S = 548 and S = A + 12. By substituting A + 12 for S in the first equation and solving, it was determined that 50 adult tickets and 62 student tickets were sold.

To solve the problem of finding the number of adult and student tickets sold, we can set up two equations based on the given information. Let A be the number of adult tickets and S be the number of student tickets sold.

Firstly, we know that the total amount collected for tickets was $548. Thus, the first equation is: 6A + 4S = 548.

Secondly, we are told that 12 more student tickets were sold than adult tickets, which gives us the second equation: S = A + 12.

Using the substitution method, we can replace S in the first equation with A + 12, leading us to: 6A + 4(A + 12) = 548. Simplifying the equation, we have 6A + 4A + 48 = 548, so 10A = 500 and A = 50.

Now that we have the number of adult tickets, we can solve for the number of student tickets by plugging the value of A into the second equation: S = 50 + 12 = 62.

Therefore, the number of adult tickets sold is 50 and the number of student tickets sold is 62.

Answer:

Left

Step-by-step explanation:

We are given that 0.555

We have to fill the correct value in the blank space

5 which is placed left side of middle 5 is at tenth place.

Therefore, the place value of this 5  =[tex]\frac{5}{10}[/tex]

Middle 5 is placed at hundredth place.

Therefore, the place value of middle 5 =[tex]\frac{5}{100}[/tex]

The place of 5 at right side of middle 5 is thousandth .

Therefore, the place value of this 5 =[tex]\frac{5}{1000}[/tex]

Therefore, middle 5 in 0.555 is [tex]\frac{1}{10}[/tex] the value of the 5 to its left.