Answer:
4989600 ways
Step-by-step explanation:
From the question,
The word MATHEMATICS can be arranged in n!/(r₁!r₂!r₃!)
⇒ n!/(r₁!r₂!r₃!) ways
Where n = total number of letters, r₁ = number of times M appears r₂ = number of times A appears, r₃ = number of times T appears.
Given: n = 11, r₁ = 2, r₂ = 2, r₃ = 2
Substitute these value into the expression above
11!/(2!2!2!) = (39916800/8) ways
4989600 ways
Hence the number of ways MATHEMATICS can be arranged without duplicate is 4989600 ways
I guess the series is

We have

Recall that

In our limit, we have



which is greater than 1, which means the series is divergent by the ratio test.
On the chance that you meant to write

we have


which is less than 1, so this series is absolutely convergent.
$745 × 40% = $298
$745 - $298 = $447
$447 × 1/3 = $149
$447 - $149 = $298
Answer:

Step-by-step explanation:
We want to simplify:

We rewrite the expression under the radical sign to obtain:

We split the expression under the radical sign to get:

Recall that:

This implies that:

Therefore 
29.

As
,
.
This can be easily verified by looking at the graph (graph of a quadratic equation).
30.
The growth of a population is not linear, it's exponential.
31.
Exponential growth > polynomial, so
.
35.

The question is asking V(t) for t = 40.

36.
The point of symmetry of a quadratic equation
is at its vertice:



The line is x= 3.