If 180°< α< 270°, cos⁡ α=−8/17, 270°< β< 360°, and sin⁡ β=−4/5, what is cos⁡(α+β)?

cos(\alpha+\beta)=-\frac{84}{85}

Step-by-step explanation:

we know that

Remember the identity

step 1

Find the value of  

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

Find the value of sine

substitute

step 2

Find the value of  

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

Find the value of cosine

substitute

step 3

Find cos⁡ (α + β)

we have

substitute

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

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;