A function is a relation in which no two ordered pairs have the same first element. A function associates each element in its domain with one and only one element in its range. Solution: a) A = {(1, 2), (2, 3), (3, 4), (4, 5)} is a function because all the first elements are different.

Step-by-step explanation:

4 0

3 years ago

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

motikmotik

Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305$

The degrees of freedom for this sample size are:

$df=n-1=50-1=49$

The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.01 \cdot 0.305=0.61$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95$

The 95% confidence interval for the mean is (5.73, 6.95).

4 0

4 years ago

Will mark brainliest!

Tems11 [23]

Answer:

$2,833.47

Step-by-step explanation:

n = [lnA - lnP] / ln(1 + i)

n = [ln15000 - ln10000] / ln(1 + 0.03)

n = [9.6158 - 9.2103] / 0.0296

n = 13.70

13 years, 8 months and 12 Days

Part 2:

P = A / [(1 + i)n]

P = 15000 / [(1.03)4]

P = 15000 / 1.1255

P = $13,327.31

Part 3:

A = 10000 (1 + 0.04)5

A = $12,166.53

The amount of money you need to save to buy a car at $15,000 would be;

$15,000 - $12,166.53

=> $2,833.47

4 0

3 years ago