The probabilities are 0.4, 0.2, 0.3 and 0.1, respectively, that a delegate to a certain convention arrived by air, bus, automobi

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Detailed solution:

Question 1)

We are provided with two linear equations representing lines, and we need to find the intersection point that solves the system.

The lines given are:

Line 1 equation:

This line passes through points (0, 2.5) and (2.2, -1.4).

Line 2 equation:

The second line goes through (0, -3) and (2.2, -1.4).

According to the graph and data, the solution to the system is the coordinate where both lines intersect.

The solution to a system of linear equations is the coordinate pair common to both lines, i.e., the intersection point.

Here, both lines share the point (2.2, -1.4), indicating it is their intersection and the solution.

Therefore, the solution for question 1 is (2.2, -1.4).

Question 2)

The equations given are:

y = 1.5x - 1               Equation 1

y = 1                           Equation 2

The method of substitution can be used to find the solution.

Replacing y from Equation 2 into Equation 1 gives:

1 = 1.5x - 1

Add 1 to both sides:

2 = 1.5x

Dividing both sides by 1.5 yields:

x = 2/1.5

x = 1.33

y = 1

Thus, the solution of the system is (1.33, 1).

Answer:

Area of land = 0.056 hectares

Detailed explanation: Knowing that

A typical person in the country requires 2,450 kilocalories each day. This means

An individual consumes 2450 kilocalories daily

The average kcal produced per hectare (ha) from the available food in the nation is 15,737,000 kcal/ha.

Thus, in one day, for one individual, we have

15737000 = 2450/hec

Hectare = 2450/15737000

Hectare = 1.5568 × 10 -4

The total land area required to provide sufficient kilocalories for a single person for one year in this developing country will be

Calculated hectare × 365.25

Hectare = 1.5568 × 10 -4 × 365.25

Area of land = 0.056 hectares

a) The sequence is geometric.

b) The subsequent term is 486

c) The rule is:

The 20th term will be: a_{20}=6973568802

Step-by-step explanation:

The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.

Part a) Is this sequence arithmetic or geometric?

An arithmetic sequence has a constant difference between consecutive terms.

In the given series 6, 18, 54, 162,

18-6 = 12

54-18= 36

The differences are not constant, thus it isn’t arithmetic.

A geometric sequence maintains a constant ratio between consecutive terms.

In this series 6, 18, 54, 162,

18/6 = 3

54/18 = 3

162/54 = 3

The ratios remain constant; therefore, the sequence is geometric.

The sequence in question is geometric.

Part b) How can you determine the next number in the series?

The next number can be calculated using the following formula:

where a_n= nth term

a= first term

r= common ratio

The next number represents the 5th term of the sequence.

To find the 5th term:

Thus, the next term in the sequence is 486

Part c) What is the rule for determining the 20th week? Calculate the 20th week.

The rule for determining the 20th week is:

Here n=20

Calculating the 20th week

Answer:

The mean and center will be nearly identical, while the variability in simulation B will exceed that of simulation A.

Step-by-step explanation:

Solution

In general, the size of the sample significantly influences the distribution.

As a guideline, by quadrupling the sample size, the sampling error typically reduces by half.

Here, simulation B has a sample size that is twice that of simulation A.

Thus, the sampling error related to the mean is affected, and it stands that A does not have a greater value.

However, its sample size is considerable for this context, making them nearly equal.

Additionally, increased trials lead to decreased variability in simulation. A displays lesser variability.

As trial numbers increase, variability in simulation declines, hence A has lesser variability.