Which graph represents the solution set of the compound inequality? −5 < a − 4 < 2

Answer:

Expected counts: 55 ducks, 25 geese, 13 cranes, 11 swans, 6 herons

Observed counts:

61 ducks, 17 geese, 11 cranes, 15 swans, and 6 herons.

Step-by-step explanation:

Counting reveals there are 110 birds in total on the lake: 61+17+11+15+6.

The calculated expected counts are:

0.50*110 = 55 ducks

0.23*110 = 25 geese

0.12*110 = 13 cranes

0.10*110 = 11 swans

0.05*110 = 6 herons

What the biologist recorded were the observed counts.

Answer:

For the first year, the total amount comes to $266, and with an hourly wage of $5.50, you can express this as the equation 5.50x=266

Step-by-step explanation:

The expected value is calculated by subtracting the expected cost from the anticipated income.

The expected cost is fixed at $5.

The anticipated income arises from the probability associated with each outcome multiplied by its respective reward.

=> For the first prize: probability * prize = (1 / 100) * $ 100 = $1

=> For the second prize: probability * prize = (5 / 100) * $20 = $1

Thus, the expected value comes out to $1 + $1 - $5

This gives us an expected value of - $3

Final answer: - $ 3

Answer:

The answer is the scatter plot that displays a pronounced positive slope along the curve of best fit.

Step-by-step explanation:

A scatter plot illustrates the relationships between two variables for an individual. It is essentially a graph in which a best-fit curve is drawn to encapsulate the complete dataset. A scatter plot is considered to have a robust correlation if the correlation coefficient is near r = 1, indicating a very strong connection between the two variables.

A scatter plot exhibits a solid correlation when its data points are closely aligned to the line or curve of best fit.

For r = 1, the correlation is regarded as strong and positive.

The fox’s speed needs to exceed that of the rabbit to successfully catch up. Thus, the required speed for the fox is expressed as 35/t + 40.

The distance separating the rabbit from the fox is 35 feet.

The speed of the rabbit is 40 feet per second.

Fox's speed = F

To calculate a precise speed for the fox, a specific time for the pursuit must be provided.

Let’s denote the time as t.

Recall that:

Speed = distance / time

Distance = speed × time

The distance the rabbit moves away from the fox after time t will be:

35 + (40 × t) = 35 + 40t

The distance traveled by the fox after time t is: fox speed × t = F × t.

To catch the rabbit, both the fox and rabbit must cover the same distance:

Rabbit's distance at time t equals Fox's distance at that time.

35 + 40t = Ft

To determine F, the fox's speed:

Dividing both sides by t yields:

(35 + 40t) / t = Ft/t

35/t + 40 = F

<pThus, the speed of the fox should be: 35/t + 40

To find out the exact speed of the fox, a specific time value must be provided.

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