1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Leona [35]
3 years ago
12

Prove that 2^n>n+4 for n>or =3​

Mathematics
1 answer:
Anna11 [10]3 years ago
4 0
Türkiye cumhuriyeti CcC
You might be interested in
Almost there .......AAAAHHhH
madreJ [45]

Answer:

12/46

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
What number makes the equation true? Enter the answerin<br> 3= 12
shepuryov [24]

Answer: ?

Step-by-step explanation:

5 0
3 years ago
"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the
STALIN [3.7K]

Answer:

\\ P(z>-2) = 0.97725 or P(x>49) is about 97.725% (or being less precise 97.5% using the <em>empirical rule</em>).

Step-by-step explanation:

We solve this question using the following information:

  1. We are dealing here with <em>normally distributed data</em>, that is "<em>the frequency distribution of the life length data is known to be mound-shaped</em>".
  2. The normal distribution is defined by two parameters: the population mean (\\ \mu) and the population standard deviation (\\ \sigma). In this case, we have that \\ \mu = 55 months, and \\ \sigma = 3 months.
  3. To find the probabilities, we have to use the <em>standard normal distribution</em>, which has \\ \mu = 0 and \\ \sigma = 1. The probabilities for this distribution are collected in the <em>standard normal table</em>, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
  4. For most cases, we need to use the <em>cumulative standard normal table, </em>and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: \\ z = \frac{x - \mu}{\sigma} [1]. A z-score tells us the distance from the mean that a raw score is from it in <em>standard deviations units</em>. If this value is <em>negative</em>, the raw score is <em>below</em> the mean. Conversely, a <em>positive</em> value indicates that it is <em>above</em> the mean.
  5. The <em>cumulative standard normal table </em>is made for positive values of z. Since the normal distribution is <em>symmetrical</em> around the mean, we can find the negative values of z using this formula: \\ P(z [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

<em>First Step: Use formula [1] to find the z-score of the raw score x = 49 months</em>.

\\ z = \frac{49 - 55}{3}

\\ z = \frac{-6}{3}

\\ z = -2

This means that the raw score is represented by a z-score of \\ z = -2, which tells us that it is<em> two standard deviations below</em> the population mean.

<em>Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.</em>

For a z = 2, the probability is 0.97725.  

Then

\\ P(z

\\ P(z2)

\\ P(z2)

But we <em>are not asked</em> for P(z<-2) but for P(z>-2) = P(x>49). This probability is the <em>complement</em> of the previous result, that is

\\ P(z>-2) = 1 - P(z

\\ P(z>-2) = 1 - 0.02275

\\ P(z>-2) = 0.97725

That is, the "<em>percentage of the manufacturer's grade A batteries will last more than 49 months</em>" is

\\ P(z>-2) = 0.97725 or about 97.725%

A graph below shows this result.

Notice that if we had used the <em>68-95-99.7 rule</em> (also known as the <em>empirical rule</em>), that is, in a normal distribution, the interval between <em>one standard deviation below and above the mean</em> contains, approximately, 68% of the observations; the interval between <em>two standard deviations below and above the mean</em> contains, approximately, 95% of the observations; and the interval between <em>three standard deviations</em> below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last <em>less</em> than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the <em>symmetry of the normal distribution</em>, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

6 0
3 years ago
A tire dealer sells 2 tires for as much as he paid for 3 tires. he paid $240 for a dozen tires. What is the total profit on 12 t
tester [92]
First, find how much he paid by tire.
To do so, divide what he paid by how many tires he bought like this :
240$ / 12 = 20$ per tire

Then, calculate how much he sells each tire.
To do so, start by calculating how much he paid for 3 tires:
20$ x 3 = 60$

This is the price he sells 2 tires for, therefore :
60$ / 2 = 30$
he sells his tires 30$ each.

Finally, you have to calculate the profit he made by selling 12.
We already know how much it cost, so you need to find how much money he gets selling them :
12 tires x 30$ = 360$

To find the profit, take off the amount he paid from the amount he made :
360$ - 240$ = 120$

There you go!
3 0
3 years ago
A) If the 5th term of an A.P. is double the 7th term, show that the sum of the 17 terms zero.​
gayaneshka [121]

Answer:

see explanation

Step-by-step explanation:

The nth term of an AP is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₅ is double a₇ , then

a₁ + 4d = 2(a₁ + 6d) , that is

a₁ + 4d = 2a₁ + 12d ( subtract a₁ from both sides )

4d = a₁ + 12d ( subtract 12d from both sides )

- 8d = a₁

The sum of n terms of an AP is

S_{n} = \frac{n}{2} [ 2a₁ + (n - 1)d ] , substitute values

S_{17} = \frac{17}{2} ( 2(- 8d) + 16d)

     = 8.5(- 16d + 16d)

     = 8.5 × 0

     = 0

5 0
2 years ago
Other questions:
  • How do you work out the volume of a cylinder? ​
    8·1 answer
  • Y=5x+2 and 3x=-y+10 what is the soluion of equation
    9·2 answers
  • What is the regular price of a taco before the discount​
    12·1 answer
  • The peak of Mount Everest is at 8,848 meters above sea level. The peak of Kanchenjunga is at 8,586 meters above sea level. The e
    8·1 answer
  • PLS HELP!!
    7·1 answer
  • Item 2
    10·1 answer
  • schoology.com/assignment/4674363703/assessment Question 5 (4 points) (08.01) Consider the following pair of equations: x + y = -
    13·1 answer
  • Someone help please ​
    13·1 answer
  • Given d(t) = -2t^2 - 3t + 13, what is the
    9·1 answer
  • NY Giants jackets sell for $80, there's a 8% sales tax. find the total cost.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!