Question

Choose the inequality that matches this situation.
Use "t" for time (in hours)
Trevon practices his clarinet at least 1 hour each day.

Answer 1

Choose the inequality that matches this situation.
At some colleges, students must work `20` hours or less per week.

Answer 2

Give me the symbol for "leq"

Answer 3

So "h" is less then or equal to 20?

Answer 4

Choose the inequality that matches this situation.
Sarah will spend at most $26 on candy. Each item costs $3, and she has a coupon for a $5 disco

Answer 5

Choose the inequality that matches this situation.
Company A charges $312 to power-wash the siding of a house plus $12 for each window. Company B charges $36 per window, and the price includs the siding. How many windows must a house have to make the total cost from Company A be less expensive than Company B?

Answer 6

The inequality that matches the situation is:

\( t \geq 1 \)

This represents that Trevon practices his clarinet for a minimum of 1 hour each day.

Answer 7

The inequality that matches this situation is:

\( h \leq 20 \)

This represents that students must work 20 hours or less per week.

Answer 8

The symbol for "leq" is \( \leq \). It stands for "less than or equal to."

Answer 9

Yes, that's correct! The notation \( h \leq 20 \) means that \( h \) (representing the number of hours students work per week) is less than or equal to 20.

Answer 10

To find the inequality that matches the situation, we first need to account for the coupon. If each item costs $3 and Sarah has a coupon for $5, her effective budget for candy after applying the coupon is:

\[
26 - 5 = 21
\]

Now, if \( x \) represents the number of candy items Sarah buys, the total cost for the candy would be \( 3x \).

We want to ensure that her spending does not exceed her effective budget of $21. The inequality can be expressed as:

\[
3x \leq 21
\]

This means that Sarah can spend at most $21 on candy after using her coupon.

Answer 11

To set up the inequality, we need to express the total costs of Company A and Company B in terms of the number of windows, \( w \).

**Company A's total cost:**
- Fixed cost for power-washing the siding: $312
- Cost per window: $12

Thus, the total cost for Company A can be expressed as:
\[
\text{Total cost for Company A} = 312 + 12w
\]

**Company B's total cost:**
- Cost per window (including siding): $36

Thus, the total cost for Company B can be expressed as:
\[
\text{Total cost for Company B} = 36w
\]

We want to find when the total cost of Company A is less expensive than the total cost of Company B. This gives us the inequality:
\[
312 + 12w < 36w
\]

Now, we can solve this inequality.

Subtract \( 12w \) from both sides:
\[
312 < 36w - 12w
\]
\[
312 < 24w
\]

Dividing both sides by 24 gives:
\[
\frac{312}{24} < w
\]
\[
13 < w
\]

Thus, the inequality that matches the situation is:
\[
w > 13
\]

This means a house must have more than 13 windows for Company A to be less expensive than Company B.