Drag each expression to show whether it is equivalent to (5⋅9x)+(5⋅1), 45x+15, or 15(3x−1).

Part A: Option e:

           Option f:

Part B: Option c:

           Option d:

Part C: Option a:

           Option b:

Explanation:

Part A: The equation is

Simplifying, we have,

Taking the term 5 common out, we have,

Thus, the above two expressions are equivalent to the equation .

Hence, Option e and Option f are the correct answers.

Part B: The equation is

Taking the term 15 common out, we have,

Also, the equation can be rewritten as,

Thus, the above two expressions are equivalent to the equation

Hence, Option c and Option d are the correct answers.

Part C: The equation is

Multiplying, we have,

The above expression can be rewritten as,

Thus, the above two expressions are equivalent to the equation

Hence, Option a and Option b are the correct answers.

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;