Write an inequality that represents the number of museum visits for which the total member cost is less than the non-member cost.

Use the inequality to find the smallest number of visits that satisfies the inequality.

3 answers

Let's assume that the total member cost for each visit is represented by a variable m and the non-member cost is represented by a variable n.

The inequality that represents the number of museum visits for which the total member cost is less than the non-member cost would be:
m < n

To find the smallest number of visits that satisfies the inequality, we need to have a specific value for n or m provided. Without any actual values, we cannot determine the exact number of visits that satisfy the inequality. However, we can provide an example for the smallest non-zero number of visits that satisfies the inequality.

For example, let's assume the total member cost (m) is $20 per visit and the non-member cost (n) is $30 per visit. Plugging these values into the inequality, we have:
20 < 30

Therefore, if the total member cost is $20 and the non-member cost is $30, then the smallest number of visits that satisfies the inequality would be one visit.
Which of the following is an equivalent expression to 13−5 ⋅13−11 with only positive exponents, generated by applying the properties of exponents?(1 point)
Responses

12616
Start Fraction 1 over 26 superscript 16 baseline end fraction

11316
Start Fraction 1 over 13 superscript 16 baseline end fraction

1266
Start Fraction 1 over 26 superscript 6 baseline end fraction

1136
Start Fraction 1 over 13 Superscript 6 baseline End Fraction
To simplify the expression 13−5 ⋅13−11, we can apply the rule of exponents that states a^m ⋅ a^n = a^(m+n).

Starting with the given expression:
13^(-5) ⋅ 13^(-11)

We can rewrite this as:
1/13^5 ⋅ 1/13^11

Using the rule of exponents, we can combine the terms:
1/13^(5+11)

Simplifying further:
1/13^16

Therefore, the equivalent expression to 13−5 ⋅13−11 with only positive exponents is Start Fraction 1 over 13 superscript 16 baseline end fraction.