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Anastaziya [24]
3 years ago
12

As baby boomers enter their golden years, the number of people afflicted with Alzheimer's disease is expected to rise dramatical

ly. In a study published in the Journal of Neurology, the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be
N(t) = 0.00525t² + 0.075t + 4.7 (0 ≤ t ≤ 4)

millon in decate t, where t = 0 corresponds to 2010.

(a) What is the projected number of people with Alzheimer's disease in the United States age 65 and over in 2020? (Round your answer to four decimal places.)
_________ million
(b) How fast is the number of people with Alzheimer's disease in the United States age 65 years and over projected to grow in 2020?
_________ million
(c) How fast is the rate of growth of people with Alzheimer's disease in the United States age 65 years and over projected to change in the period covered by the study?
_________ million per decade per decade.
Mathematics
1 answer:
dybincka [34]3 years ago
4 0

Answer:

Step-by-step explanation:

Given that the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be

N(t) = 0.00525t^2 +0.075t+4.7,(0 ≤ t ≤ 4)

where N is in millions where year 2010 corresponds to t=0

For 2020, 10 years lapsed hence t= 1

a) N(1) = 0.00525(1)^2 + 0.075(1) + 4.7\\=4.78025

So 4.78025 million people

b) Growth = N(1)-n(0) =0.08025 million

c) N(4) = 5.084

Average rate of change = (5.084-4.7)/4 =0.096 million per decade

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Five digit serial numbers for a product are to be made using letters and/or numbers, e.G. JGR29. The serial number could have al
S_A_V [24]

Answer:

1,404,000 serial numbers can be made

Step-by-step explanation:

For the five digit serial numbers, since all letters and all numbers could be used, then we can use 26 letters (A,B,C,...Z) and 10 numbers (0,1,2,...9).

Now, say the letters and numbers are to occupy the labeled spaces below

_  _  _  _  _

1   2  3  4  5

(NOTE: Spaces 1,2,3 are to be occupied by any of the 26 letter while spaces 4 and 5 are to be occupied by any of the 10 numbers)

For space 1, there are 26 possibilities

For space 2, there will be (26 -1 ) 25 possibilities (since repetition of characters is NOT allowed)

For space 3, there will be (26-2) 24 possibilities (since repetition of characters is NOT allowed)

For space 4, we have 10 possibilities

and for space 5, we (10-1) 9 possibilities (since repetition of characters is NOT allowed)

Therefore, the number of serial numbers that can be made is

26 × 25 × 24 × 10 × 9 = 1404000

Hence, 1,404,000 serial numbers can be made

OR

Using permutation, nPr = n!/(n-r)!

For the letters,

n is the total number; n = 26

and r is the number of available spaces, r = 3

For the numbers,

n = 10

r = 2

Then, we get

26P3 × 10P2

26!/(26-3)! × 10!/(10-2)!

26!/23! × 10!/8!

15600 × 90 = 1404000

5 0
3 years ago
In factored form please help
Brilliant_brown [7]

Answer:

3rd option

Step-by-step explanation:

\frac{3x^2-3}{x^2-5x+4} ( factorise numerator and denominator )

3x² - 3 ← factor out 3 from each term

= 3(x² - 1²) ← x² - 1 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

x² - 1

= x² - 1²

= (x - 1)(x + 1) , then

3x² - 3 = 3²(x - 1)(x + 1) ← in factored form

--------------------------------

x² - 5x + 4

consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)

the factors are - 1 and - 4 , since

- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then

x² - 5x + 4 = (x - 1)(x - 4)

then

\frac{3x^2-3}{x^2-5x+4} = \frac{3(x-1)(x+1)}{(x-1)(x-4)} ← in factored form

3 0
1 year ago
What is the measure of the major arc?
Sav [38]

The answer is D) 210 because arc eog is 150 and is the minor arc. A whole circle is 360 therefore 360-150=210

8 0
3 years ago
What does the off center rectangle mean in the picture?
Alla [95]
2/5+4/7=2
14/35+20/35=2
34/35=2
FALSE
so the rectangle must be a placeholder that is added
so 34/35+x=2
x=1 1/35 or 36/35
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3 years ago
Put one half two fifths and six tenths in order from least to greatest.
Citrus2011 [14]
Six tenths, one half, two fifths
6 0
3 years ago
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