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Sagot :
Answer:
a.) a = -34 and b = 2
b.) a = -91.11 b = 2.22
c.) David scored 124, nancy scored 84.27
David scored higher
Step-by-step explanation:
for those in the 3rd grade
mean u = 67
s = 10
we used the z formula
[tex]z=\frac{x-u}{s}[/tex]
[tex]z=\frac{x-67}{10}[/tex]
we have the new score
u = 100
s = 20
we use this formula [tex]z*s+u[/tex]
[tex][\frac{x-67}{10} ]20\\[/tex] + 100
multiply through by 20
[tex][\frac{20x-1340}{10} ] +100[/tex]
dividing the bracket by 10
= [tex]2x-134+100[/tex]
= [tex]2x-34[/tex]
from this solution above,
a = -34 and b = 2
b.)
we solve for those in the 6th grade
u = 86
s = 9
[tex]\frac{x-86}{9}[/tex]
for new score,
y = 100
s = 20
[tex][\frac{x-86}{9} ]20+100[/tex]
[tex]2.22x-191.11+100\\= 2.22x - 91.11[/tex]
from this solution
a = -91.11
b = 2.22
c.) if David scored 79
[tex]= 2(x)-34[/tex]
= 2(79) - 34
= 158 - 34
= 124
if nancy scored 79
= 2.22(79) - 91.11
= 175.38 - 91.11
= 84.27
from these scores we can see that David scored higher in his grade
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