Two students were asked to use estimation strategies to find a reasonable solution to this question: Darrell has $1,990 saved and wants to buy a motorcycle. He earns $10 per hour and he works for 39 hours. Estimate how much money, Darrell has left after buying a $2,200 motorcycle. From the choices below, select the student with a more reasonable solution.

To determine the theoretical probabilities, we'll analyze the different possible outcomes for each case.

Total number of cards = 40 (5 cards for each number from 2 to 9)

a) Sum is 12:

There are several combinations of cards that can result in a sum of 12:

• 3 and 9
• 4 and 8
• 5 and 7
• 7 and 5
• 8 and 4
• 9 and 3

Total favorable outcomes = 6 (since there are 6 possible combinations)

Total possible outcomes (since you're drawing two cards) = 40 * 40 = 1600

Probability (sum is 12) = (Number of favorable outcomes) / (Total possible outcomes)

Probability (sum is 12) = 6 / 1600 = 0.00375

b) Difference is less than 5:

There are several combinations of cards that can result in a difference less than 5:

• 2 and 3
• 3 and 2
• 3 and 4
• 4 and 3
• 4 and 5
• 5 and 4
• 5 and 6
• 6 and 5
• 6 and 7
• 7 and 6
• 7 and 8
• 8 and 7
• 8 and 9
• 9 and 8

Total favorable outcomes = 14

Total possible outcomes = 1600

Probability (difference is less than 5) = 14 / 1600 = 0.00875

c) Product is odd:

For the product to be odd, one or both of the numbers drawn must be odd. Since there are five odd numbers (3, 5, 7, 7, 9), and each number has five cards, the total number of favorable outcomes is 5 + 5 + 5 + 5 + 5 = 25.

Total possible outcomes = 1600

Probability (product is odd) = 25 / 1600 = 0.015625

To summarize:

• a) Probability (sum is 12) ≈ 0.00375
• b) Probability (difference is less than 5) ≈ 0.00875
• c) Probability (product is odd) ≈ 0.015625

Answer:

no

Step-by-step explanation:

the outcome of the first event affects the second.

you cannot get the queen of hearts the first time and the queen of hearts the second time so these are dependent events.

flipping a coin is an example of an independent event

The range of the data is 4.2

what is range of the data?

The range in statistics for a given data set is the difference between the highest and lowest values.

Given:

2.2, 0.3, -1.5, 2.6, 1.9, 0.4, 0.6, -1.6, 2.5, -0.6

Arranging the data in some order

-1.6 , -1.5, -0.6, 0.3, 0.4,  0.6, 1.9, 2.2, 2.5, 2.6

So, range

=highest data - lowest data

=2.6 - (-1.6)

=2.6+1.6

=4.2

Hence, the range is 4.2.

Learn more about range here:

brainly.com/question/28135761

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Answer:

The range is -4.2

Step-by-step explanation:

Least to Greatest:

-1.6

-1.5

-0.6

0.3

0.4

0.6

1.9

2.2

2.5

2.6

Subtract Least Number from Greatest Number

-1.6 - 2.6

=-4.2

Answer: D

Step-by-step explanation:

Using the equation plot in the coordinates of the points to see if they fit the equation.

5x-3y < 30  

A)  5(-3) -3(5) < 30

   -15 -15 < 30

    -30 < 30   This is true

B)  5(0) -3(0) < 30

     0 - 0 < 30

     0< 30     This is true

C)  5(-5) - 3(3) < 30

    -25 - 9  < 30

      -34 < 30    This is also true

D) 5(3) - 3(-5) < 30  

   15 + 15 < 30

  30 < 30         This is not true because 30 is not greater that 30