The main property is as follow
(A^p)^q=A^pxq
so only Sam's work is correct because
(8^4)^5 x(7^3)^9=(8^4x5)x(7^3x9)=8^20x 7^27
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.
We do like the following:
Set the first number is a and the second is b.
We have two equations: a+2xb=24, 2xa+b=21
And we have 2xa+4xb=48 or 2xa=48-4xb
So: 48-4xb+b=21 or -3xb=21-48=-27 and we got b=-27:(-3)=9 and a= 6
a=6 and b=9
Answer:
459/99
Step-by-step explanation:
0.6363... is equal to 63/99.
We want to add 4.
4 = 396/99
396/99 + 63/99 = 459/99
We can double check with a calc.
