Mathematics: A deck of cards contains red cards numbered 1 through 9, blue cards numbered 1 through 7, and green cards numbered 1 through 13. If a single card is picked at random, what is the probability that the card is green?

A deck of cards contains red cards numbered 1

Ответ:

akluke6059

07.06.2020

Mathematics

Part A) A reasonable domain is the interval [0,10] $0\leq n\leq 10$

Part B) The y-intercept is the height of the plant at the begin of the scientist study (initial height of the plant)

Part C) The average rate of change is $0.43\ cm/day$ (see the explanation)

Step-by-step explanation:

Part A) When the scientist concluded his study, the height of the plant was approximately 16.13 cm. What is a reasonable domain to plot the growth function?

we have

f(n)=12(1.03^n)

where

n is the number of days

f(n) is the height of the plant in cm

For f(n)=16.13 cm

substitute

16.13=12(1.03^n)

solve for n

(16.13/12)=(1.03^n)

Apply log both sides

log(16.13/12)=log(1.03^n)

log(16.13/12)=(n)log(1.03)

n=log(16.13/12)/log(1.03)

$n=10\ days$

therefore

A reasonable domain is the interval [0,10]

$0\leq n\leq 10$

Part B) What does the y-intercept of the graph of the function f(n) represent?

we have

f(n)=12(1.03^n)

The y-intercept is the value of y when the value of x is equal to zero

In this context the y-intercept is the height of the plant at the begin of the scientist study (initial height of the plant)

For n=0

f(n)=12(1.03^0)

$f(n)=12\ cm)$ -----> initial height of the plant

Part C) What is the average rate of change of the function f(n) from n = 3 to n = 10, and what does it represent?

we know that

To find the average rate of change, we divide the change in the output value by the change in the input value

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

a=3

b=10

f(3)=12(1.03^3)=13.11

f(10)=12(1.03^10)=16.13

Substitute

$\frac{16.13-13.11}{10-3}=0.43\ cm/day$

it tells us that the plant on average grows 0.43 cm each day, between day 3 and day 10

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A deck of cards contains red cards numbered 1 through 9, blue cards numbered 1 through 7, and green cards numbered 1 through 13. If a single card is picked at random, what is the probability that the card is green?

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