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3 years ago

Sheldon wants to access the money in this checking account. Which of the following will work?

Mathematics

1 answer:

bulgar [2K]3 years ago

7 0

D. he can access it by taking it out of his account

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Use mathematical induction to prove that for each integer n > 4,5" > 2^2n+1 + 100.

Flura [38]

Answer:

The inequality that you have is $5^{n}>2^{2n+1}+100,\,n>4$ . You can use mathematical induction as follows:

Step-by-step explanation:

For $n=5$ we have:

$5^{5}=3125$

$2^{(2(5)+1)}+100=2148$

Hence, we have that $5^{5}>2^{(2(5)+1)}+100.$

Now suppose that the inequality holds for $n=k$ and let's proof that the same holds for $n=k+1$ . In fact,

$5^{k+1}=5^{k}\cdot 5>(2^{2k+1}+100)\cdot 5.$

Where the last inequality holds by the induction hypothesis.Then,

$5^{k+1}>(2^{2k+1}+100)\cdot (4+1)$

$5^{k+1}>2^{2k+1}\cdot 4+100\cdot 4+2^{2k+1}+100$

$5^{k+1}>2^{2k+3}+100\cdot 4$

$5^{k+1}>2^{2(k+1)+1}+100$

Then, the inequality is True whenever $n>4$ .

3 0

3 years ago

Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation i

Mnenie [13.5K]

Answer:

The population mean = sample mean = x`= 67.5

Population standard deviation = 13.369

Sample standard deviation= 4.225

Step-by-step explanation:

AS the population mean is not given we will calculate it from the sample.

The mean of the sampling distribution is equal to the population mean .

The sample mean is calculated by

x`= ∑x/n= 75,+ 62, +69,+65,+66,+64, +67,+70,+74 + 63/10

x`=675/10= 67.5

The standard deviation of the sample is equal to

u = σ/ √n where σ is the population standard deviation and n is the number of observations.

Calculating the sample mean

s= √∑xi²/n- (∑x/n)²

s= √(45741/10)- (675/10)²

s= 4.2249

σ= u*√n= 4.229 *√10

σ=13.360

3 0

3 years ago

A freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later, a passenger train leaves the same stat

Degger [83]

I'm going to assume that they are on parallel tracks, and not the same track.

60x=40(x+2)

60x=40x+80

20x=80

x=4

You can check the work I've provided by filling in the answer for x into the initial question.

ʕ·ᴥ·ʔ

3 0

3 years ago

Formula for the flow of current in an electrical<br> circuit, V= IH, for I

HACTEHA [7]

Answer:V/H=I

Step-by-step explanation:

v=IH

V/H=I

3 0

3 years ago

This one a little weird

Ludmilka [50]

Answer:

It might be 10 but tell me if I'm right or wrong

Step-by-step explanation:

6 0

3 years ago