1. in cecilia’s cd collection, 1/5 of her jazz cds represents 1/10 of all her cds. what is the ratio of her jazz cds to her non-jazz cds? 2. how would you change 5^6(50) to a number times 25?

1. The ratio of Jazz and non-Jazz CDs is 1:1.

2. The given expression can be written as 25 times 31250 .

1. Given information:

In Cecilia’s CD collection, 1/5 of her Jazz CDs represents 1/10 of all her CDs.

Let jazz CDs be J in number and T be the total number of CDs.

The given condition can be written as,

So, the ratio of Jazz CDs to non Jazz CDs will be,

Therefore, the ratio of Jazz and non-Jazz CDs is 1:1.

2. The given expression is . It is required to write the given number as a number times 25.

So, it can be written as,

Therefore, the given expression can be written as 25 times 31250 .

For more details, refer to the link:

link

1)

Ratio is 1:1.

2)

The required number is:

Step-by-step explanation:

1)

Let us consider that Cecilia's has a total of 'x' CDs

and let 'y' represent the number of Jazz CDs.

Now we are given information that:

1/5 of her Jazz CDs represents 1/10 of all her CDs.

i.e.

i.e. the Jazz CDs are half of the total CDs.

Hence, the number of Non-Jazz CDs(z)

=

Hence, the ratio of Jazz to Non-Jazz CDs

Hence, the required Ratio is 1:1.

2)

How would you change to a number times 25?

We will find the number by dividing the quantity   by 25 to find the required number.

i.e.

Hence the required number is:

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

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part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

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

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

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

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).