∆STU is located at S (-3, 0), T (0, -3), and U (3, -3). Which statement correctly classifies ∆STU? A. ∆STU is a scalene triangle. B. ∆STU is an isosceles triangle. C. ∆STU is an equilateral triangle. D. ∆STU is a right triangle.

A. Scalene

Step-by-step explanation:

1)   Plot the three points and it is observe the three sides are different lengths

2)   Calculate lengths of three sides: (using c^2 = a^2 + b^2)

  length (ST) = sqrt( (-3 - 0)^2 + (0 - -3)^2 )

                     = sqrt( 9 + 9)

                     = sqrt( 18 )

                     = 4.24

  length (TU) = sqrt( (0 - 3)^2 + (-3 - -3)^2 )

                     = sqrt( 9 + 0)

                     = sqrt( 9 )

                     = 3

  length (SU) = sqrt( (-3 - 3)^2 + (0 - -3)^2 )

                     = sqrt( 36 + 9)

                     = sqrt( 45 )

                     = 6.71

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;