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cluponka [151]
3 years ago
8

on a function map, the values for the domain of the function appear on the ______ and the values for the range appear on the ___

____​
Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
3 0

Answer:

domain is x

range is y

Step-by-step explanation:

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Let P(n) be the statement that n! < nn where n is an integer greater than 1.
Ira Lisetskai [31]

Answer: See the step by step explanation.

Step-by-step explanation:

a) First, Let P(n) be the statement that n! < n^n

where n ≥ 2 is an integer (This is because we want the statement of P(2).

In this case the statement would be (n = 2): P(2) = 2! < 2^2

b) Now to prove this, let's complet the basis step:

We know that 2! = 2 * 1 = 2

and 2^2 = 2 * 2 = 4

Therefore: 2 < 4

c)  For this part, we'll say that the inductive hypothesis would be assuming that k! < k^k for some k ≥ 1

d) In this part, the only thing we need to know or prove is to show that P(k+1) is also true, given the inductive hypothesis in part c.

e) To prove that P(k+1) is true, let's solve the inductive hypothesis of k! < k^k:

(k + 1)! = (k + 1)k!  

(k + 1)k!  < (k + 1)^k  < (k + 1)(k + 1)^k

Since k < k+1 we have:

= (k + 1)^k+1

f) Finally, as the base and inductive steps are completed, the inequality is true for any integer for any n ≥ 1. If we had shown P(4)

as our basis step, then the inequality would only be proven for n ≥ 4.

6 0
3 years ago
Formula for triangle are
Greeley [361]

The formula for a triangle:

Base times height divided by 2

Equation Form:

b×h÷2

6 0
3 years ago
Enter the exact product of 5.21 •7.3.
frez [133]

Answer:

3.033

Step-by-step explanation:

5.21*7.3=3.003

6 0
3 years ago
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true or false Microwave ovens cause friction between water molecules, which then generates chemical energy to cook your food.
den301095 [7]
That is true that microwave ovens cause friction to water molecules
8 0
3 years ago
Use the graph of the function to find, f(-2).<br><br> A. -2<br> B. -1<br> C. 1<br> D. 2
Misha Larkins [42]

Since f(-2) means that our x-value is -2, we can go to that position on the graph and slide up the y-axis to find the intersection this point has with the function graphed.

If I am correct the answer should be that the y value is 2!

7 0
3 years ago
Read 2 more answers
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