Identify each of the following quantities as a vector or a scalar quantity. Select the appropriate term from the dropdown beside each sentence.

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized.

y=b0+b1X+E

where
y= traffic flow of vehicles per hour
X= vehicle speed in miles per hour

The following data were collected during rush hour for six highways leading out of the city.

a) the following Regression equation
y=___________+__________x (2 decimals)
b) use a=0.05 significance
s=________________ (4 decimals)
r2= ______________
r2 adj= ________________

A car company says that the mean gas mileage for its luxury sedan is at least 22 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 6 cars has a mean gas mileage of 19 mpg and a standard deviation of 5 mpg. At alpha equals 0.05, test the company's claim. Assume the population is normally distributed.

A. Which sampling distribution should be used and why?

B. What is the value of the standardized test statistic?

The standardized test statistic is=

C. What is the critical value?

Critical value=

D. What is the outcome and the conclusion of this test?

____Ho. At the 10% significance level, there is _____evidence to ______ the car company's claim that the mean gas mileage for the luxury sedan is at least ….

A container ship is heading for port on a fixed course of
30° (=    60°). The captain sets the autopilot and the ship is making 20 Knots (20 Nautical Miles per hour) relative to the water.
• For the first hour, there are no currents affecting the passage of the ship.

• For the second hour there is a current of 4 Knots flowing in direction
30° (= 300°).
• For the third hour there is a current of 6 Knots flowing in direction
15° (= 105°).
Assuming that the full force of any current acts on the ship:

a) How far does the ship travel in the first hour? (1 mark)

b) Sketch the situations for the second and third hour and introduce your vectors
in words.

c) Calculate the speed that the ship makes in the second hour.

d) Calculate the speed that the ship makes in the third hour.

Jackson, a self-employed taxpayer, uses his automobile 82% for business and during 2020 drove a total of 27,600 business miles. Information regarding his car expenses is listed below.

What is Jackson's deduction in 2020 for the use of his car if he uses:

If required, round your answers to nearest dollar.

a. The actual cost method?

answer is not 12875, thank you.

1. A machine precision-cuts tubing such that μ = 38.00 in. and σ = 0.03 in. If the lengths are normally distributed, find the probability that a piece of tubing selected at random measures as follows. (Round your answers to four decimal places.)

   (a) greater than 38.05 in.
   
   
   (b) less than 38.045 in.
   
   
   (c) between 37.95 and 38.05 in.

2. A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 32 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has the following gas mileages. (Round your answers to four decimal places.)

   (a) less than 30 mpg
   
   
   (b) greater than 38 mpg
   
   
   (c) between 26 and 38 mpg

Does octane matter: Octane is a measure of how much fuel can be compressed before it spontaneously ignites. Some people believe that higher-octane fuels result in better gas mileage for their cars. The number of miles driven for various drivers until the car ran out of gas was recorded. Does high-octane fuel result in better gas mileage? Use significance level 0.05. (Paired samples).

Two ships, A and B, leave port at the same time. Ship A travels northwest at 21 knots and ship B travels at 26 knots in a direction 34° west of south. (1 knot = 1 nautical mile per hour; see Appendix D.) What are (a) the magnitude (in knots) and (b) direction (measured relative to east) of the velocity of ship A relative to B? (c) After how many hours will the ships be 200 nautical miles apart? (d) What will be the bearing of B (the direction of the position of B) relative to A at that time? (For your angles, takes east to be the positive x-direction, and north of east to be a positive angle. The angles are measured from -180 degrees to 180 degrees. Round your angles to the nearest degree.)

Jackson, a self-employed taxpayer, uses his automobile 90% for business and during 2019 drove a total of 14,000 business miles. Information regarding his car expenses is listed below.

What is Jackson’s deduction in 2019 for the use of his car if he uses:

1. The actual cost method?

2. The automatic mileage method?

3. What records must Jackson maintain?

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

Predict the property taxes for a 1,500-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)