Answer:
Option A
f(x) = 12.5(1.6)^x
Step-by-step explanation:
The number of gnats the scientists have gathered
At 0 hours, they gathered 12 gnats.
Checking all the options, applying x = 0 makes the index part become 1 (Anything raised to the power zero is 1).
So, we have the following functions
f(x) = 12.5
f(x) = 12.6
f(x) = 6.2
f(x) = 1.6
This has reduced our work, as we can screen out options C and D, they are too far from 12. This leaves us with option A and B.
At 1 hour, they gathered 20 gnats.
Checking options A and B
A. f(x) = 12.5(1.6)
= 20
B. f(x) = 12.6(6.2)
By inspection, 12 × 6 is already 72,
12.6 × 6.2 will be more.
By these, we can conclude that f(x) = 12.5(1.6)^x has the best models the number of gnats the scientists have gathered after the number of hours listed in the given table.
Answer:
Are the events A and B disjoint? Yes
Step-by-step explanation:
Disjoint events are those events that cannot occur at the same time, i.e. for events <em>X</em> and <em>Y</em> to be disjoint, 
.
The event <em>A</em> is defined as the number of students whose age is at most 32.
And event <em>B</em> is defined as the number of students whose age is at least 37.
The events <em>A</em> and <em>B</em> are disjoint events.
- The sample space for event <em>A</em> consists of all the students of age group (under 21), (21 - 24), (25 - 28) and (29 - 32).
- Whereas the sample space for event <em>B</em> consists of all the students of age group (33 - 36), (37 - 40) and (Over 40).
The sample space for the intersection of these two events is:
Sample space of (<em>A</em> ∩ <em>B</em>) = 0
As there are no common terms in both the sample.
Hence proved, events <em>A </em> and <em>B</em> are disjoint.
Answer:
<h3>The best interpretation of this equation 4x=3x is that the equation has no solution</h3>
Step-by-step explanation:
Given that Kate begins solving the equation
<h3>To find the best interpretation of the given equation :</h3><h3>Katie's steps are</h3>
When she adds 2 to both sides, the equation becomes
Therefore 
<h3>Therefore the given equation has no solution </h3><h3>The best interpretation of this equation 4x=3x is that the equation has no solution.</h3><h3>Therefore the option no solution is correct</h3>
Answer:337.5 miles
Step-by-step explanation:
Find the unit rate 135/6 = 22.5/1
He can drive 22.5 miles on 1 gallon of gas
Then multiply by 15
22.5x15= 337.5
I don't think this is middle school...
(2^8 x 3^-5 x 6^0)^-2 x ((3^-2)/(2^3))^4 x (2^28)
(256 x (1/243))^-2 x ((1/9)/(8))^4 x 268435456
1.05349794239^-2 x (<span>0.01388888888)^4 x 268435456
</span><span>
0.90101623534 x </span><span>3.72108862e-8 x 268435456
</span>8.99999997623
9
9 is your answer.
