Mathematics, 30.08.2019 18:30 smortandsons

1) the table below represents the displacement of a turtle from its nest as a function of time:
time(hours)x: 0, 1, 2, 3, 4
displacement from best(miles)y:
5, 27, 49, 71, 93
part a) what is the y-intercept of the function, and what does this tell you about the turtle?
part b) calculate the average rate of change of the function represented by the table between x=1 to x=4 hours, and tell what the average rate represents.
part c) what would be the domain of the function if the turtle continued to walk at this rate until it traveled 225 miles from the nest?
2) part a) sam rented a boat at $225 for 2 days. if he rents the same boat for 5 days, he has to pay a total rent of $480.
write an equation in the standard form to represent the total rent (y) that sam has to pay for renting the boat for x days.
part b) write the equation obtained by part a using function notation.
part c) describe the steps to graph the equation obtained above on the coordinate axes. mention the labels on the axes and the intervals.

Answers: 1

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Answers

Question #1

Part A:
The y-intercept can be found when x = 0. If you look at your table, when x = 0, y = 5. So the y-intercept is 5.

Part B:
$\sf Slope = \frac{27-5}{1-0} = \frac{22}{1} = \boxed{22}$
The slope is 22.

Part C:
y = mx + b
y = 22x + 5

We are given 225 as the range, or in place of y.
225 = 22x + 5
220 = 22x
x = 10

The domain is 10.

Question #2

Part A:

(2,255)
(5,480)

Standard form is Ax + By = C

$\sf Slope = \frac{y_2-y_1}{x_2-x_1} = \frac{480-225}{5-2} = \frac{255}{3} = \boxed{85}$

Let's plug this into this form first:
$y - y_1 = m(x-x_1)\\\\y -225 = 85(x-2)\\\\y - 225 = 85x - 170\\\\y = 85x + 55$

Now, let's make it into Standard Form.
$y = 85x + 55\\\\y - 85x + 55\\\\ -85x + y = 55\\\\ -1(-85x +y) = -1(55)\\\\\boxed{85x - y = -55}$
What, which is in the box, is your final answer. :)

Part B:
Function notation simply means replacing y with f(x).
We had y = 85x + 55
So your answer is:
$\boxed{f(x) = 85x + 55}$

Part C:
Using the final answer which we got in Part A, we would know that the y-intercept is (0,55) and the x-intercept is (-55/85, 0). We would plot these 2 points, and then draw a line between them. :)

Answer from: Quest

the answer is 99.

Answer from: Quest

step-by-step explanation:

i found the life tables for the year 2012.

life table of males at age 30. probability of dying between ages x and x+1

total population:

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old.

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

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