Answer:
a) 
b) When t = 10, Q = 7.845.
Step-by-step explanation:
The value of a quantity after t years is given by the following formula:

In which
is the initial quantity and r is the rate that it changes. If it increases, r is positive. If it decreases, r is negative.
a) Write a formula for Q as a function of t.
The initial value of a quantity Q (at year t = 0) is 112.8.
This means that
.
The quantity is decreasing by 23.4% per year.
This means that 
So


b) What is the value of Q when t = 10?
This is Q(10).


When t = 10, Q = 7.845.
Answer:
Son's Age: 11
Mary's Age: 33
Step-by-step explanation:
Let set Mary and her son as variables,
M = Mary's age
S = Mary's son age
<u>Breakdown:</u>
"Mary is three times as old as her son"
M = 3S
"In <em>12 years</em>, Mary's age will be one less than <u>twice her son's</u> age"
M <em>+ 12</em> = <u>2</u>(S <em>+ 12</em>) - 1
we add 12 to both sides as it will be in 12 years for both
We know that M = 3S, so we plug this in
3S + 12 = 2(S + 12) - 1
Now solve for <em>S (son's age),</em>
3S + 12 - 12 = 2(S + 12) - 1 - 12
3S = 2(S + 12) - 13
3S = 2S + 24 - 13
3S - 2S = 2S - 2S + 24 - 13
S = 24 - 13
S = 11
To find <u>Mary age</u>, plug in her son age ,
M = 3S
M = 3(11)
M = 33
Learn more about Substitution here: brainly.com/question/22340165
The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.
Step-by-step explanation:
The given is,
Detailed view or net diagram of the three dimensional diagram.
Step:1
Three dimensional diagram of the given net diagram is attached.
From the three dimensional diagram given net diagram is rectangular prism.
Step:2
From the three dimensional diagram
Formula for surface area of the rectangular prism,
..............................(1)
Where, w - Width
l - Length
h - Height
From the attachment,
l = 6 cm
w = 2 cm
h = 3 cm
Equation (1) becomes,

= 2 ( 12 + 18 + 6 )
= 2 ( 36 )
A = 72 squared centimeters
( or )
From the net diagram,
Surface area, A = ((6×3)+(2×3)+(2×6)+(2×3)+(3×6)+(2×6))
= 18 + 6 + 12 + 6 + 18 + 12
= 72
Surface area, A = 72 squared centimeters
Result:
The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.
Check the picture below, you can pretty much count the units off the grid for the length and width.
recall area = length * width.
Answer:
convert into slope intercept form by using inverse operations.