Afruit company ships boxes of apples and pears in a crate that measures
15. in. by 18. in. by 24 in.
• the apple box measures 15 in. by 15 in. by 10-in.
• the pear box measures 12 in. by 12 in. by 12in.
if one box of each fruit is placed in the crate, what part of the crate is not filled with
fruit?
a 6,882 in.
b. 4,162 in.
c. 2,719
in.
d. 1,800 in.

  none of the above

Step-by-step explanation:

The crate has a volume of ...

  V = LWH = (15 in)(18 in)(24 in) = 6480 in³

The apple box has a volume of ...

  V = LWH = (15 in)(15 in)(10 in) = 2250 in³

The pear box has a volume of ...

  V = LWH = (12 in)(12 in)(12 in) = 1728 in³

__

Together, one box of each fruit takes up a volume of ...

  (apple box) + (pear box) = (2250 in³) + (1728 in³) = 3978 in³

Then the part of the crate not filled has a volume of ...

  6480 in³ -3978 in³ = 2502 in³ . . . . not among the answer choices

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!