First ABC is reflected across the y axis to become A'B'C'
Then A'B'C' is rotated 90 counterclockwise about the origin to make it A"B"C"
Because the transformations are both rigid, the pre-image and image are congruent
Hope this helped
A functions is discontinuous if it has stuff like holes, jumps, or vertical asymptotic. In addition, it's continuous if it stays in a line the whole time (it doesn't have to be straight or anything!)
Answer:
(a) Test statistic is -2.85 and p-value is 0.0022
(b) Reject the null hypothesis. The population mean of dissolved oxygen content is not equal to 10 mg/L
Step-by-step explanation:
H0: mu equals 10
Ha: mu not equals 10
The test is a two-tailed test because the alternate hypothesis is expressed using not equal to
(a) Test statistic (z) = (sample mean - population mean) ÷ (sd/√n) = (9.14 - 10) ÷ (2/√44) = -0.86 ÷ 0.302 = -2.85
Cumulative area of the test statistic = 0.9978
p-value = 2(1 - 0.9978) = 2(0.0022) = 0.0044
(b) The critical value using 0.02 significance level is 2.422. For a two-tailed test, the region of no rejection of the test statistic lies between -2.422 and 2.422.
Conclusion:
Reject the null hypothesis because the test statistic -2.85 falls outside the region bounded by the critical values -2.422 and 2.422.
The population mean of dissolved oxygen content is not equal to 10 mg/L
Answer:
k = -12/77
Step-by-step explanation:
OG problem: k(3k−6)−7k(6k+10)=12
Step-by-step:
3k - 6k - 42k - 70k = 12
-3k - 42k - 70k = 12
-7k - 70k = 12
-77k = 12
k = -12/77
Answer:
There are 15 halves in 7 1/2.
