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Sloan [31]
3 years ago
6

One brand of coffee is packaged in cylinders where the height is equal to the radius, r. The volume of the package, in cubic cen

timeters, can be found using the function V(r) = πr3. The number of ounces of coffee in the cylinder depends on the volume of the cylinder, V, in cubic centimeters. This can be modeled by the function C(V) = 3.2V.
Mathematics
1 answer:
igor_vitrenko [27]3 years ago
7 0

Answer:

<h2>C(V(r)) = 3.2πr3</h2>

Step-by-step explanation:

This problem is a composition of function defined by C(V(r)), now we have the functions V(r)= \pi r^{3} and C(V)=3.2V, where the first depends on the radius, and the second dependes on the volume, that means, to find the number of ounce of coffe, we need to determine the volume of the cylinder, that's why we have to replace the volume function inside the ounces function,

C(V(r))=3.2(\pi r^{3} )

Therefore, the right answer is the last choice.

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A Microgates Industries bond has a 10 percent coupon rate and a $1,000 face value. Interest is paid semiannually, and the bond h
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Answer:

a. $849.45

Step-by-step explanation:

In the above question, we are given the following information

Coupon rate = 10%

Face value = 1000

Maturity = n = 20 years

t = number of periods = compounded semi annually = 2

Percent yield = 12% = 0.12

Bond Value formula =

C/t × ([1 -( 1/ 1 + r/t)-^nt ÷] r/t) +( F/ (1 + r/t)^nt)

C = coupon rate × face value = 10% × 1000 = 100

Bond value:

= 100/2 × ( [1 - (1 /1 + 0.12/2)^-20×2]÷ 0.12/2)+ (1000/( 1 + 0.12/2)^20×2

= 50 × ( [1 - (1 /1 + 0.06) ^40] ÷ 0.06) + ( 1000/ (1 + 0.06) ^40

= 50 × ( [1 - (1/ (1.06) ^40] ÷ 0.06 ) + (1000/(1.06)^40)

= 50 × 15.046296872 + 97.222187709

= $849.45

Bond value = $849.45

8 0
3 years ago
Francesca is a single mother making $645 per week after taxes. She spends one-third of her money on rent and utilities and puts
AleksandrR [38]

Answer:

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Step-by-step explanation:

4 0
3 years ago
Which statement describes the definition of a function?
Tom [10]

Answer:

an activity or purpose natural to or intended for a person or thing.

Step-by-step explanation:

: >

3 0
3 years ago
Read 2 more answers
Find a quadratic function that includes the set of values below.<br> (0,9). (2,15) (3,12)
nlexa [21]

Answer:

f(x) = -2x^2 + 7x + 9

Step-by-step explanation:

f(x) = ax^2 + bx + c\\f(0) = 9 => c = 9;\\f(2) = 15 = 4a + 2b + 9  2a + b  = 3\\f(3) = 9a + 3b + 9 = 12  3a + b = 1\\Subtract the second equation from the first:\\-a = 2 => a = -2; b = 7; c = 9\\f(x) = -2x^2 + 7x + 9

3 0
3 years ago
What is the equation of the line that passes through the point (3,-3) and has a slope of 0?
Blizzard [7]

Answer:

given us,

slope= 0

(x1y1)= (3,-3)

here

(y-y1) =m(x-x1)

or, (y+3)=0(x-3)

or (y+3)= x-3

or, x+y= -3-3

x+y= -6

Step-by-step explanation:

x+y= -6

7 0
3 years ago
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