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djverab [1.8K]
3 years ago
10

LM = JK then JK = LM What property is this?

Mathematics
1 answer:
konstantin123 [22]3 years ago
5 0
This example is the Symmetric Property.

I hope this helps you!
xo, Leafling
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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
Which expressions represents twelve diminished by six times a number:. 12-6n; 6n-12; 12n-6
Ede4ka [16]
12-6n
.......................
4 0
3 years ago
Read 2 more answers
A girl ran to the store at a speed of 6mph, and walked back at 4mp. If her round trip took 15 minutes, how far away is the store
MariettaO [177]

Answer:

0.6 miles

Step-by-step explanation:

Let's say the store is x miles away, she walks to the store in a hours, and she walks back in b hours.

First, her total time = time walked there + time walked back = a + b = 15 minutes = 1/4 of an hour = 0.25 hours

a + b = 0.25 (because a and b are in hours)

distance = speed * time

x = 6 miles/hour * a hours = 6a miles

x = 4 miles/hour * b hours = 4b miles

If we can find a or b, we can find x.

4b = x = 6a

4b = 6a

a + b = 0.25

We now have two equations with two variables. Using substitution, we can solve for one of them

a + b = 0.25

subtract a from both sides to find b

0.25 - a = b

plug that into the other equation, 4b = 6a

4(0.25-a) = 6a

1 - 4a = 6a

add 4a to both sides to isolate a and its coefficient

1 = 10a

divide both sides by 10 to solve for s

a = 1/10 of an hour = 0.1 of an hour = 60 minutes / 10 = 6 minutes

6a = x

6(0.1) = x

0.6 = x

the store is 0.6 miles away

6 0
2 years ago
Which of the following best describes the pattern in the diagram as you move<br> from left to right?
olga_2 [115]
The answer is a, it adds one block
5 0
3 years ago
a recent survey determained that 7 out of 9 students eat school lunch at least once a week. if 54 students were surveyed how man
Setler [38]

Answer:

12 students

Step-by-step explanation:

Given

Students = 54

Required

Determine the number of students that eat lunch once a week

In Sets;

If out of 9, at least 7 eats one a week then

9 - 7 eats lunch once a week

9 - 7 = 2

<em>In other words;</em>

2 out of 9 students eat lunch once a week

Number of students in this category is then calculated as thus;

Number = \frac{2}{9} * 54

Number = \frac{2 * 54}{9}

Number = \frac{108}{9}

Number = 12

3 0
3 years ago
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