Answer: 4
Step-by-step explanation:
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.
All of them except for letter Z
Answer:
540°
Step-by-step explanation:
Just divide the shape into triangles and count the number of triangles. This is what your formula is doing for you. It's telling you how many triangles make up the shape and then multiplying that number by 180 degrees to find the sum of your interior angles.
The perimeter of the rectangle based on the factors given is 46.
<h3>How to calculate the perimeter?</h3>
The area of the rectangle is given as (x² + 13x - 90). This will be:
= (x² + 13x - 90)
= x² + 18x - 5x - 90
= x(x + 18) - 5(x + 18)
= (x - 5)(x + 18)
The sides of the rectangle are 5 and 18. The perimeter will be:
= 2(l + w)
= 2(5 + 18)
= 46
The area of the rectangle is given as (x² + 24x - 81.
= (x² + 24x - 81)
= x² + 27x - 3x - 81
= x(x + 27) - 3(x + 27)
= (x - 3)(x + 27)
The sides are 3 and 27. The perimeter will be:
= 2(l + w)
= 2(27 + 3)
= 60
= (x + 1)² + 3(x + 1) + 2
= (x + 1)(x + 1) + 3x + 3 + 2
= x² + x + x + 1 + 3x + 5
= x² + 5x + 6
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