A car manufacturer is trying to develop a new sports car. Engineers are hoping that the average amount of time that the car takes to go from 0 to 60 miles per hour is below 6 seconds. The car company tested 12 of the cars and clocked their performance times. Three of the cars clocked in at 5.8 seconds, 5 cars at 5.9 seconds, 3 cars at 6.0 seconds, and 1 car at 6.1 seconds. At a 5% level of significance, test if the new sports car is meeting its goal to go from 0 to 60 miles per hour in less than 6 seconds. Assume a normal distribution for the analysis. a. Specify the competing hypotheses to test this belief. a. H0: μ = 6; HA: μ ≠ 6b. H0: μ ≥ 6; HA: μ < 6c. H0: μ ≤ 6; HA: μ > 6b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
b-2. Select the p-value.
a. 0.005 < p-value < 0.01
b. p-value < 0.01
c. 0.01 ≤ p-value < 0.025
d. 0.025 ≤ p-value < 0.05
e. 0.05 ≤ p-value < 0.10
d. p-value ≥ 0.10

Using the t-distribution, we have that:

a) H0: μ ≥ 6; HA: μ < 6

b) The test statistic is t = -3.08

c) a. 0.005 < p-value < 0.01

Item a:

At the null hypothesis, it is tested if the mean is of at least 6 seconds, that is:

At the alternative hypothesis, it is tested if the mean is of less than 6 seconds, that is:

Item b:

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:

The parameters are:

For this problem, the values of the parameters are:

Hence, the value of the test statistic is:

Item c:

The p-value of the test is found using a left-tailed test, as we are testing if the mean is less than a value, with t = -3.08 and 12 - 1 = 11 df.

Using a t-distribution calculator, it is of 0.0052, hence:

a. 0.005 < p-value < 0.01

A similar problem is given at link

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

the answer is simply just 6n add the two together as they have an n