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Mice21 [21]
3 years ago
8

Let [n] represent the greatest even integer less than n that divides n, for any positive integer n. For example, [24] = 12. What

is the value of [20] ...?
Mathematics
1 answer:
ipn [44]3 years ago
7 0
First you write down all even integers that divide 20.

Those are: 2,4,10,20

Since the request is that integer is less than n, 20 cannot be the answer.
This means that greatest even integer is 10

Answer is 10.
You might be interested in
Use the table below to answer this question:
andrew11 [14]
(y_final-y_start)/(x_final-x_start) always! :) that easy

(-6-2)/(2-0) = -4

You probably know that if the interval was pretty small, between 0 and 0.0001, it would take you to the concept of slope and derivatives, but average change is just ignoring anything in between x=0, and x=2 (it could go up/down million times, and still the answer would be -4)

hope it helps
3 0
3 years ago
The state of Maine encourages recycling by giving refunds for certain recycled items. When you recycle a glass bottle, you get b
Klio2033 [76]

Given that cost of 1 drinks in a glass bottle = $2.00

Given that cost of 1 drinks in an aluminum can = $0.50

Given that cost of 1 drinks in a plastic bottle = $1.50

Then sum of costs  of 1 drink from each will be = 2.00+0.50+1.50


Given that you buy two of each then total cost will be given by 2(2.00+0.50+1.50)


Hence expression that represents the amount of money you will spend is 2(2.00+0.50+1.50).

Using distributive property, we can rewrite it as:

2(2.00+0.50+1.50)=2*2.00+2*0.50+2*1.50

This is final answer of part A.


----------

Given that refund on 1 drinks in a glass bottle = $0.05

Given that refund on 1 drinks in an aluminum can = $0.10

Given that refund on 1 drinks in a plastic bottle = $0.15

Then sum of refunds on 1 drink from each will be = 0.05+0.10+0.15


Given that you plan to recycle all of the items you purchased then total refund will be given by 2(0.05+0.10+0.15)


Hence expression to represent the amount of refund you will receive is 2(0.05+0.10+0.15).

Using distributive property, we can rewrite it as:

2(0.05+0.10+0.15)=2*0.05+2*0.10+2*0.15

This is final answer of part B.


----------

Net cost is given by difference of total cost and total refund

Net cost = 2(2.00+0.50+1.50) - 2(0.05+0.10+0.15)

= 2*2.00+2*0.50+2*1.50 - (2*0.05+2*0.10+2*0.15)

= 4+1+3 - (0.10+0.20+0.30)

= 8 - 0.60

= 7.40

Hence net cost is $7.40

5 0
3 years ago
If y=80,when x=32 find x when y=100
Bess [88]
Y        X
80     32
100    x'

80x' = 100*32
80x' = 3200
x' = 3200/80
x' = 320/8
x' = 40
5 0
3 years ago
Let f(x)=5x3−60x+5 input the interval(s) on which f is increasing. (-inf,-2)u(2,inf) input the interval(s) on which f is decreas
o-na [289]
Answers:

(a) f is increasing at (-\infty,-2) \cup (2,\infty).

(b) f is decreasing at (-2,2).

(c) f is concave up at (2, \infty)

(d) f is concave down at (-\infty, 2)

Explanations:

(a) f is increasing when the derivative is positive. So, we find values of x such that the derivative is positive. Note that

f'(x) = 15x^2 - 60


So,


f'(x) \ \textgreater \  0
\\
\\ \Leftrightarrow 15x^2 - 60 \ \textgreater \  0
\\
\\ \Leftrightarrow 15(x - 2)(x + 2) \ \textgreater \  0
\\
\\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textgreater \  0} \text{   (1)}

The zeroes of (x - 2)(x + 2) are 2 and -2. So we can obtain sign of (x - 2)(x + 2) by considering the following possible values of x:

-->> x < -2
-->> -2 < x < 2
--->> x > 2

If x < -2, then (x - 2) and (x + 2) are both negative. Thus, (x - 2)(x + 2) > 0.

If -2 < x < 2, then x + 2 is positive but x - 2 is negative. So, (x - 2)(x + 2) < 0.
 If x > 2, then (x - 2) and (x + 2) are both positive. Thus, (x - 2)(x + 2) > 0.

So, (x - 2)(x + 2) is positive when x < -2 or x > 2. Since

f'(x) \ \textgreater \  0 \Leftrightarrow (x - 2)(x + 2)  \ \textgreater \  0

Thus, f'(x) > 0 only when x < -2 or x > 2. Hence f is increasing at (-\infty,-2) \cup (2,\infty).

(b) f is decreasing only when the derivative of f is negative. Since

f'(x) = 15x^2 - 60

Using the similar computation in (a), 

f'(x) \ \textless \  \ 0 \\ \\ \Leftrightarrow 15x^2 - 60 \ \textless \  0 \\ \\ \Leftrightarrow 15(x - 2)(x + 2) \ \ \textless \  0 \\ \\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textless \  0} \text{ (2)}

Based on the computation in (a), (x - 2)(x + 2) < 0 only when -2 < x < 2.

Thus, f'(x) < 0 if and only if -2 < x < 2. Hence f is decreasing at (-2, 2)

(c) f is concave up if and only if the second derivative of f is positive. Note that

f''(x) = 30x - 60

Since,

f''(x) \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow 30x - 60 \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow 30(x - 2) \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow x - 2 \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow \boxed{x \ \textgreater \  2}

Therefore, f is concave up at (2, \infty).

(d) Note that f is concave down if and only if the second derivative of f is negative. Since,

f''(x) = 30x - 60

Using the similar computation in (c), 

f''(x) \ \textless \  0 &#10;\\ \\ \Leftrightarrow 30x - 60 \ \textless \  0 &#10;\\ \\ \Leftrightarrow 30(x - 2) \ \textless \  0 &#10;\\ \\ \Leftrightarrow x - 2 \ \textless \  0 &#10;\\ \\ \Leftrightarrow \boxed{x \ \textless \  2}

Therefore, f is concave down at (-\infty, 2).
3 0
3 years ago
What is 1.07 + 42.5 HELP PLSSSSSSSSSSSS
Ber [7]

Answer:

43.57

Step-by-step explanation:

Line up the decimal points.

Add a 0 for 1.07 so the numbers have the same length.

01 . 0 7

42. 5 0

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

43.57

5 0
3 years ago
Read 2 more answers
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