Which statement is TRUE concerning the slope of the line formed by the hypotenuse of each triangle? A) The slope formed by ΔABC
has a value that is 1 2 the slope formed by ΔCDE. B) The slope formed by ΔCDE has a value that is 2 times greater than the slope formed by ΔABC. C) The slope formed by ΔABC has a value that is 2 times greater than the slope formed by ΔCDE. D) The slope formed by ΔABC has a slope that is equal to the slope formed by ΔCDE.
1 answer:
Answer:
<em>A. The slope formed by ΔABC has a value that is 1/2 the slope formed by ΔCDE</em>
Step-by-step explanation:
Find the diagram attached.
Slope is the change in y coordinates tom that of x coordinate of a line.
Slope = Δy/Δx
Slope = y2-y1/x2-x1
For ΔABC,
A(-3, 6) and C = (-1, 3)
Slope = 3-6/-1-(-3)
Slope = -3/-1+3
Slope = -3/2
Slope of line AC is -3/2
For ΔCDE,
C = (-1, 3) and E = (3, -3)
Slope = -3-3/3-1
Slope = -6/2
Slope = -3
Slope of line CE is -3
From the calculation above, it can be seen that Slope of ΔABC = 1/2(slope of ΔCDE)
-3/2 = 1/2 (-3)
-3/2 = -3/2
<em>Hence the correct option is A. The slope formed by ΔABC has a value that is 1/2 the slope formed by ΔCDE</em>
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Answer:
Claim is rejected
Step-by-step explanation:
Solution:-
- The claim was made on the effectiveness of medication on the market of Parkinson's disease to be p = 75%.
- A random sample was taken of N = 150 individuals and n = 100 number of people reported that it was effectively.
- We are to test the claim made by the manufacturer of the medication based on the statistics available for the sample N.
- State the hypothesis for the effectiveness of medication:
Null Hypothesis: p = 0.75 ... Claim
Alternate hypothesis: p < 0.75 .... Test
- The conditions of standard normality:
- n*p > 5 , 150*0.75 = 112.5 .. ( Check )
- n*(1-p) > 5 , 150*0.25 = 37.5 .. ( Check )
Hence, the standard normal test is applicable. Assuming the population proportion to be normally distributed.
- We will estimate the population proportion with the sample proportion ( p* ):
p* = n / N
p* = 100 / 150
p* = 2/3 = 0.667
- Testing against the claimed population proportion ( p ) = 0.75. The standard normal statistic value is given by:
- We will see whether the Z-test statistic falls in the rejection region defined by the critical value of Z at significance level ( α ) of 0.05.
- The rejection region is defined by the Alternate hypothesis which is less than the claimed value. So, the rejection region defined by the lower tail of the standard normal.
- So for lower tailed test the critical value of statistics is:
P ( Z < Z-critical ) = α = 0.05
Z-critical = - 1.645
- The rejected values all lie to the left of the Z-critical value -1.645
- The claim test value is compared the rejection region:
-2.35607 < -1.645
Z-test < Z-critical
Hence, Null hypothesis rejected because test lies in the rejection region.
Conclusion:
The Null hypothesis or claim made by the manufacturer of Parkinson's disease medication of 75% effectiveness is without sufficient evidence. Hence, the claim made is false or has no statistical evidence.