1 Given the functions f(x) and g(x) = find the following. 1 + x2 (a) (gºf)(x) 1 (b) (gºf)(6)

A network provider investigates the load of its network. The number of concurrent users is recorded at fifty locations (thousand

beks73 [17]

Answer:

see explaination

Step-by-step explanation:

Using the formulla that

sum of terms number of terms sample mean -

Gives the sample mean as \mu=17.954

Now varaince is given by

s^2=\frac{1}{50-1}\sum_{i=1}^{49}(x_i-19.954)^2=9.97

and the standard deviation is s=\sqrt{9.97}=3.16

b) The standard error is given by

\frac{s}{\sqrt{n-1}}=\frac{3.16}{\sqrt{49}}=0.45

c) For the given data we have the least number in the sample is 12.0 and the greatest number in the sample is 24.1

Q_1=15.83, \mathrm{Median}=17.55 and Q_3=19.88

d) Since the interquartile range is Q_3-Q_1=19.88-15.83=4.05

Now the outlier is a number which is greater than 19.88+1.5(4.05)=25.96

or a number which is less than 15.83-1.5(4.05)=9.76

As there is no such number so the given sample has no outliers

5 0

3 years ago

How are the 4s related in 44,268

Ahat [919]

Well they are close to eachother and are both have a thousand. Such as the 1st 4 is 10 thousand but the 2nd 4 us in the thousands.

6 0

3 years ago

Find the 76th term of the arithmetic sequence 17, 19, 21, ...

Dominik [7]

Answer: 167

Step-by-step explanation: To find the 76th term of this arithmetic sequence, we will be using our explicit formula which is shown below.

$^{a}n = ^{a}1 (n - 1)d$

Since we want to determine the 76th term, we are going

to substitute 76 in for <em>n</em> in our explicit formula.

Then, $^{a}1$ will be our first term in our sequence which is 17.

Lastly, <em>d</em> is our common difference or the difference between each of the terms in our arithmetic sequence which is 2.

So we have $^{a} 76 = 17 + (76 - 1)(2)$ .

Now we have all the information we need. Just simplify from here.

Make sure to apply order of operations because this is where many

students make mistakes. Inside the parentheses first!

(76 - 1) is going to be 75.

So we have $^{a} 76 = 17 + (75)(2)$ .

Then, we have to make sure we multiply before we add.

So (75)(2) is going to give us 150.

So we have $^{a} 76 = 17 + 150$ .

Now just add to find that $^{a} 76 = 167$ .

So the 76th term is 167.

5 0

3 years ago

A country's population in 1991 was 114 million. In 1997 it was 120 million. Estimate the population in 2014 using exponential gr

Rufina [12.5K]

The answer is 138 million.

Step 1. Calculate the growth rate.
Step 2. Calculate the population number in 2014.

We will use the formula for exponential growth:
A = P * eⁿˣ
where:
A - the final amount (value)
P - the initial amount (value)
e - the mathematical constant (e ≈ 2.72)
n - the growth rate
x - the time

Step 1:
A = 120 million = 120 000 000
P = 114 million = 114 000 000
n = ?
x = 1997 - 1991 = 6
Therefore:
$120 000 000 = 114 000 000 * e ^{n*6} \\ e ^{n*6} =120 000 000 /114000000 \\ e ^{n*6} =1.05 \\$
Logarithm both sides of the equation:
$ln(e ^{n*6})=ln(1.05) \\ n*6*ln(e) = ln(1.05) \\ 6n=ln(1.05) \\ n = \frac{ln(1.05)}{6} \\ n = \frac{0.05}{6} \\ n = 0.0083$

Step 2:
Now when we know the growth rate, it is easy to estimate the population in 2014
A = ?
P = 120 000 000
n = 0.0083
t = 2014 - 1997 = 17
$A = 120 000 000 * e ^{0.0083*17} \\ 
A = 120 000 000 * e^{0.1411} \\ 
A = 120 000 000 * 1.15 \\ 
A = 138 000 000
$
Thus, the population will be 138 million in 2014

8 0

3 years ago

If Addison types at a constant rate of 2 pages per hour, how many hours will it take to type a paper that is 5 pages long?

LUCKY_DIMON [66]

Answer:

2.5 hours

Step-by-step explanation:

Find unit rate so 1 page per 30 mins. 30 x 5 = 150 minutes. Since it asks for hours, 150/60= 2 hours and 30 minutes or 2.5 hours

8 0

2 years ago

Read 2 more answers

1 Given the functions f(x) and g(x) = find the following. 1 + x2 (a) (gºf)(x) 1 (b) (gºf)(6)​

1 Given the functions f(x) and g(x) = find the following. 1 + x2 (a) (gºf)(x) 1 (b) (gºf)(6)