the table gives the distance between a lighthouse and a cruise ship at different times. the cruise ship is traveling at a uniform speed.

complete the following sentences based on the data in the table.

distance from lighthouse
(nautical miles)
2 53
4 95.5
6 138
10 223
12 265.5

after 11 hours, the cruise ship will be nautical miles from the lighthouse.

at the start of the journey, the cruise ship was nautical miles from the lighthouse.

the cruise ship is traveling at a speed of nautical miles per hour.

Ques 1)

After 11 hours, the cruise ship will be 244.25 nautical miles from the lighthouse.

Ques 2)

At the start of the journey, the cruise ship was 10.5 nautical miles from the lighthouse.

Ques 3)

The cruise ship is traveling at a speed of 21.25 nautical miles per hour.

We are given a table that represents the number of hours and distance from the Lighthouse as:

Time (in hours)              Distance from Lighthouse

                                       (nautical miles)

       2                                   53

       4                                  95.5

       6                                   138

       10                                   223

       12                                 265.5

As the speed is uniform hence, we can find the equation that represents the distance in term of the number of hours.

( As the speed is uniform hence, we get a constant slope i.e. we get a equation of a line)

As we know that the equation of a line passing through two points (a,b) and (c,d) is given by:

Let (a,b)=(2,53) and (c,d)=(4,95.5)

where y denote the distance from lighthouse and x denotes the number of hours.

Hence, the equation of line is:

Hence,

After 11 hours, the cruise ship will be 244.25 nautical miles from the lighthouse.

Hence,

At the start of the journey, the cruise ship was 10.5 nautical miles from the lighthouse.

We have slope=21.25

Hence,

The cruise ship is traveling at a speed of 21.25 nautical miles per hour.

the answer is b.)

< 1=< 2

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.