Answer:
Step-by-step explanation:
Simplifying
-3a + 8 = 2z + -12
Reorder the terms:
8 + -3a = 2z + -12
Reorder the terms:
8 + -3a = -12 + 2z
Solving
8 + -3a = -12 + 2z
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + -3a = -12 + -8 + 2z
Combine like terms: 8 + -8 = 0
0 + -3a = -12 + -8 + 2z
-3a = -12 + -8 + 2z
Combine like terms: -12 + -8 = -20
-3a = -20 + 2z
Divide each side by '-3'.
a = 6.666666667 + -0.6666666667z
Simplifying
a = 6.666666667 + -0.6666666667z
I would say it would most certainly have to be B
Answer:
$2353 at 12.5% and $7647 at 8.25%
Step-by-step explanation:
I'll say a is the amount he invested in one market, and b is the amount in the other.
a + b = 10000, or b = 10000 - a
multiplying the investments with the percentages and adding them together will give the total earned interest.
(a × 0.125) + (b × 0.0825) = 925
0.125a + 0.0825b = 925
Use substitution to solve for a.
0.125a + 0.0825(10000 - a) = 925
0.125 a + 825 - 0.0825a = 925
0.0425a = 100
a = 2352.94
Use substitution to find b
b = 10000 - 2352.94
b = 7647.06
The questions are to the nearest dollar so round a and b.
$2353 and $7647
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
Yes the researcher can conclude that the supplement has a significant effect on cognitive skill
b

c
The result of this hypothesis test shows that there is sufficient evidence to that the supplement had significant effect.The measure of effect size is large due to the large value of Cohen's d (0.5778 > 0.30 )
Step-by-step explanation:
From the question we are told that
The sample size is n=16
The sample mean is 
The standard deviation is 
The population mean is 
The level of significance is 
The null hypothesis is 
The alternative hypothesis is
Generally the test statistics is mathematically represented as

=> 
=> 
Generally the p-value is mathematically represented as


From the z-table

=> 
=> 
From the obtained values we see that 
Decision Rule
Reject the null hypothesis
Conclusion
There is sufficient evidence to conclude that the supplement has a significant effect on the cognitive skill of elderly adults
Generally the Cohen's d for this study is mathematically represented as

=> 
=> 
Answer:
1648.5
Step-by-step explanation:
20cm radius - 10
50cm radius- 25
area = 3.14×10²
3.14×100
=314
area= 3.14× 25²
3.14×625
= 1962.5
1962.5
- 314
_________
1648.5