What is the value of cosθ given that (−2, −3) is a point on the terminal side of θ ?

-0.555

Step-by-step explanation:

The terminal point of the vector in this problem is

(-2,-3)

So, it is in the 3rd quadrant.

We want to find the angle that gives the direction of this vector.

We can write the components of the vector along the x- and y- direction as:

The tangent of the angle will be equal to the ratio between the y-component and the x-component, so:

However, since we are in the 3rd quadrant, the actual angle is:

So now we can find the cosine of the angle, which will be negative:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

step-by-step explanation: