Given a+b=7 and a–b=3, find:
3^a÷3^b

a=  -2 and b=3

Step-by-step explanation:

Step 1) Solve the first equation for a:

a + 3b = 7

a + 3b - 3b = 7 - 3b

a + 0 = 7 - 3b

a = 7 - 3b

Step 2) Substitute(7 - 3b)  for a in a second equation and solve for b:

2a = b - 7 becomes:

2(7 - 3b) = b-7

(2 multi.7) - (2 multi.3b)= b-7

14  - 6b = b - 7

14  + 7 - 6b + 6b = b + 6b = b + 6b - 7 +7

21  - 0 = 1b + 6b - 0

21=(1 + 6)b

21  = 7b

21 /7 = 7b/7

3  = 7b/7

3  = b

b  = 3

Step 3) Substitute  3  for  b  in the solution to the first equation at the end of Step 1 and calculate  a :

a  = 7 - 3b becomes:

a  =  7  −  ( 3  ⋅  3)

a  =  7  − 9

a  =  − 2

7.3

step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;