Answer:
D
Step-by-step explanation:
complementary means it equals 90
Answer:
b. It will decrease by a factor of 2
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence interval
, we have the following confidence interval of proportions.

In which
z is the zscore that has a pvalue of
.
The lower end of the interval is given by:

The upper end of the interval is given by:

The length of the interval is the subtraction of the upper end by the lower end, so it is:

This means that the length is inverse proportional to the square root of the size of the sample.
So, if the sample size is multiplied by 4, the length of the interval is going to decrease by a factor of 2.
Answer:
Salamander Trail is longer than Great Oak Trail
Step-by-step explanation:
The given parameters are;
The scale of the map is 36 mi = 6 cm
The length of Great Oak Trail = 4.5 cm
The scale of a different map is 24 mi = 3 cm
The length of Salamander Trail = 3.5 cm
Therefore, we have;
The actual length of Great Oak Trail based on the first map is given as follows;
36 mi = 6 cm
6 cm = 36 mi
1 cm = 36 mi/6 = 6 mi
4.5 cm = 4.5 × 6 mi = 27 mi
The actual length of Salamander Trail based on the second map is given as follows;
24 mi = 3 cm
3 cm = 24 mi
1 cm = 24 mi/3 = 8 mi
3.5 cm = 3.5 × 8 mi = 28 mi
Therefore, Salamander Trail with an actual length of 28 mi is longer than Great Oak Trail which has an actual length of 27 mi.
Answer: The required probability is 
Step-by-step explanation:
Since we have given that
Number of kids = 10
Number of kids in Team A = 5
Number of kids in Team B = 5
There are three kids in the group, Alex and his two best friends Jose and Carl.
So, number of favourable outcome is given by

Total number of outcomes is given by

So, the probability that Alex ends up on the same team with at least one of his two best friends is given by

Hence, the required probability is 