The total angle sum of a triangle is 180°
As such, 180= 78 + 2s +4s
102= 6s
s=17
The inverse of the statement is M be the point on PQ since PM is congruent to QM than M is midpoint on the PQ.
<h3>What do you mean by inverse?</h3>
Inverse of the statement means that explain the condition in reverse way or vice versa.
Since, M is the midpoint of PQ, then PM is congruent to QM.
Proving in reverse way, let m be the point between P and Q the distance M from P is equal to the distance from M to Q. Which implies that M lies as the mid of the P and Q.
Thus, the inverse of the statement is M be the point on PQ since PM is congruent to QM than M is midpoint on the PQ.
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Answer:
Since the calculated value of z= 2.82 does not lie in the critical region the null hypothesis is accepted and it is concluded that the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls.
The value of p is 0 .00233. The result is significant at p < 0.10.
Step-by-step explanation:
1) Let the null and alternate hypothesis be
H0: μboys − μgirls > 0
against the claim
Ha: μboys − μgirls ≤ 0
2) The significance level is set at 0.01
3) The critical region is z ≤ ± 1.28
4) The test statistic
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
Here p1= 397/768= 0.5169 and p2= 331/745=0.4429
pc = 397+331/768+745
pc= 0.4811
qc= 1-pc= 1-0.4811=0.5188
5) Calculations
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
z= 0.5169-0.4429/√ 0.4811*0.5188( 1/768+ 1/745)
z= 2.82
6) Conclusion
Since the calculated value of z= 2.82 does not lie in the critical region the null hypothesis is accepted and it is concluded that the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls.
7)
The value of p is 0 .00233. The result is significant at p < 0.10.
Answer:
0.40 + 0.02
Step-by-step explanation:
4 tenths plus 2 hundredths
Step-by-step explanation:
-2(-3+2)2
(-2×-3)+(-2×2)2
(6-4)2
2(6-4)
(2×6)+(2×-4)
12-8=4