On Monday, Courtney spent 14 minutes solving 1 math problem and 2 biology problems. On Tuesday, Courtney spent 16 minutes solving 2 math problems and 1 biology problem. Write and solve a system of equations to find how long it takes Courtney to solve each math problem and each biology problem

the timing taken to solve each math problem and each biology problem is 4 minutes each respectively

Step-by-step explanation:

Let us assume the timing taken for math problem be x

And, the time taken for biology problem be y

Now as per the question

The following equations should be considered

x + 2y = 14 (1)

2x + y = 16. (2)

Multiply by 2 in equation 1

So,

2x + 4y = 28

2x + y = 16

3y = 12

y = 4 minutes

So, x = 14 - 2(4)

= 12 - 8

= 4 minutes

hence, the timing taken to solve each math problem and each biology problem is 4 minutes each respectively

two data sets with the same median will not have the same varaibility

step-by-step explanation:

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!