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70 L+60 S < 5,600
0.02 L+0.01 S <= 2.5
Members of the swim team want to wash their hair. Each short-haired member requires the same number of liters of water and soap, and each long-haired member requires the same number of liters of water and soap. The bathroom has less than 5,600 liters of water and at most 2.5 liters of shampoo. The system of inequalities shown, where
S represents the number of short-haired members and
L the number of long-haired members, describes this situation. Does the bathroom have enough water and shampoo for 8 long-haired members and 7 short-haired members?
Choose 1 answer:
(A) The bathroom has enough water and shampoo.
(B) The bathroom has enough water but not enough shampoo.
(C) The bathroom has enough shampoo but not enough water.
(D) The bathroom has neither enough water nor enough shampoo.

70 L+60 S<5,600 $\newline$ $0.02 L+0.01 S \leq 2.5$ $\newline$ Members of the swim team want to wash their hair. Each short-haired member requires the same number of liters of water and soap, and each long-haired member requires the same number of liters of water and soap. The bathroom has less than $5$ , $600$ liters of water and at most $2$ . $5$ liters of shampoo. The system of inequalities shown, where $S$ represents the number of short-haired members and $L$ the number of long-haired members, describes this situation. Does the bathroom have enough water and shampoo for $8$ long-haired members and $7$ short-haired members? $\newline$ Choose $1$ answer: $\newline$ (A) The bathroom has enough water and shampoo. $\newline$ (B) The bathroom has enough water but not enough shampoo. $\newline$ (C) The bathroom has enough shampoo but not enough water. $\newline$ (D) The bathroom has neither enough water nor enough shampoo.

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Interpret confidence intervals for population means

Full solution

Q.

70 L+60 S<5,600

\newline

0.02 L+0.01 S \leq 2.5

\newline

Members of the swim team want to wash their hair. Each short-haired member requires the same number of liters of water and soap, and each long-haired member requires the same number of liters of water and soap. The bathroom has less than

5

,

600

liters of water and at most

2

.

5

liters of shampoo. The system of inequalities shown, where

S

represents the number of short-haired members and

L

the number of long-haired members, describes this situation. Does the bathroom have enough water and shampoo for

8

long-haired members and

7

short-haired members?

\newline

Choose

1

answer:

\newline

(A) The bathroom has enough water and shampoo.

\newline

(B) The bathroom has enough water but not enough shampoo.

\newline

(C) The bathroom has enough shampoo but not enough water.

\newline

(D) The bathroom has neither enough water nor enough shampoo.

Check Water Availability: First, let's check if the bathroom has enough water for $8$ long-haired members and $7$ short-haired members using the first inequality.70L + 60S < 5,600Substitute $L$ with $8$ and $S$ with $7$ :70(8) + 60(7) < 5,600560 + 420 < 5,600980 < 5,600
Check Shampoo Availability: Now, let's check if the bathroom has enough shampoo for $8$ long-haired members and $7$ short-haired members using the second inequality. $\newline$ $0.02L + 0.01S \leq 2.5$ $\newline$ Substitute $L$ with $8$ and $S$ with $7$ : $\newline$ $0.02(8) + 0.01(7) \leq 2.5$ $\newline$ $0.16 + 0.07 \leq 2.5$ $\newline$ $0.23 \leq 2.5$
Confirm Availability: Since $980$ is less than $5,600$ , the bathroom has enough water for the members. $\newline$ Since $0.23$ is less than or equal to $2.5$ , the bathroom has enough shampoo for the members. $\newline$ Therefore, the bathroom has enough water and shampoo for $8$ long-haired members and $7$ short-haired members.

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