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natulia [17]
2 years ago
13

Question 31 pts Prove the statement is true using mathematical induction: 2n-1 ≤ n! Use the space below to write your answer. To

make the < symbol, you might want to use the < with the underline feature.
Mathematics
1 answer:
Sladkaya [172]2 years ago
4 0

Answer:

P(3) is true since 2(3) - 1 = 5  < 3! = 6.  

Step-by-step explanation:

Let P(n) be the proposition that 2n-1 ≤ n!. for n ≥ 3

Basis: P(3) is true since 2(3) - 1 = 5  < 3! = 6.  

Inductive Step: Assume P(k) holds, i.e., 2k - 1 ≤ k! for an arbitrary integer k ≥ 3. To show that P(k + 1) holds:

2(k+1) - 1 = 2k + 2 - 1

≤ 2 + k! (by the inductive hypothesis)

= (k + 1)! Therefore,2n-1 ≤ n! holds, for every integer n ≥ 3.

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Ughh i suck at dilation
Ivenika [448]
Look at!!:
Pre image  A(3,4), B(1,5) C(6,6);
If you multiply these coordinates by 3/2, you get its images:

A(3,4)              ⇒ A`(3*3/2, 4*3/2)=(4.5, 6)
B(1,5)              ⇒B`(1.*3/2,  5*3/2)=(1.5, 7.5)
C(6,6)              ⇒C`(6*3/2, 6*3/2)=(9,9)

Therefore the scale factor is 3/2. 
When the scale factor of a dilation is >1, then we have an enlargement, an expansion.
In this case 3/2=1.5>1

Answer: 

The dilation is expansion.
The scale factor is 3/2. 
7 0
3 years ago
Evan lives in Stormwind City and works as an engineer in the city of ironforge in the morning he has three Transportation option
denis-greek [22]

Answer:

The probability that he teleports at least once a day =  \mathbf{\frac{5}{9}}

Step-by-step explanation:

Given -

Evan lives in Stormwind City and works as an engineer in the city of ironforge in the morning he has three Transportation options teleport ride a dragon or walk to work and in the evening he has the same three choices for his trip home.

Total no of outcomes = 3

P( He not choose teleport in the morning ) = \frac{2}{3}

P( He not choose teleport in the evening ) = \frac{2}{3}

P ( he choose teleports at least once a day ) = 1 - P ( he not  choose teleports in a day )

                                                         = 1 - P( He not choose teleport in the morning ) \times P( He not choose teleport in the evening )

                                          =  1 - \frac{2}{3}\times\frac{2}{3}

                                           =  \frac{5}{9}

3 0
3 years ago
How do i find the volume of a pyramid​
Fudgin [204]

Answer:

ask it

Step-by-step explanation:

1st take it in front of ur face

2nd loon at it in eyes

3rd ask it

4 0
2 years ago
Simplify: <br><br> 3c-5d+5d<br><br> Pls
Arturiano [62]

Answer:

3 c

Step-by-step explanation:

Simplify the following:

5 d - 5 d + 3 c

Hint: | Combine like terms in 5 d - 5 d + 3 c.

5 d - 5 d = 0:

Answer: 3 c

5 0
3 years ago
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To decide if 12.5 centimeters is greater than 140 millimeters, the first step is to set up a proportion. Which of the following
Nuetrik [128]
The answer is The one option C
4 0
2 years ago
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