Complete question :
Members of the swim team want to wash their hair. The bathroom has less than 5600 liters of water and at most 2.5 liters of shampoo. 70L+ 60S < 5600 represents the number of long-haired members L and short-haired members S who can wash their hair with less than 5600 liters of water. 0.02L + 0.01S < or equal to 2.5 represents the number of long-haired members and short-haired members who can wash their hair with at most 2.5 liters of shampoo. Does the bathroom have enough water and shampoo for 8 long-haired members and 7 short -haired members?
Answer:
Yes , there is enough water and shampoo
Step-by-step explanation:
Given that:
Number of long and short hair member who can wash their hair with less than 5600 litres of water.
70L+ 60S < 5600
Number of long and short hair member who can wash their hair with at most 2.5 litres of shampoo
0.02L + 0.01S ≤ 2.5
To check if bathroom has enough water and shampoo for 8 long haired and 7 short haired members.
Water check:
70L+ 60S < 5600
L = 8 ; S = 7
70(8) + 60(7) < 5600
560 + 420 < 5600
980 < 5600
Inequality constraint is satisfied ; There is enough water.
Shampoo check:
0.02L + 0.01S ≤ 2.5
L = 8 ; S = 7
0.02(8) + 0.01(7) ≤ 2.5
0.16 + 0.07 ≤ 2.5
0.23 ≤ 2.5
Inequality constraint is satisfied ; There is enough shampoo
Step-by-step explanation:
4(8x + 3y)
= 4 × 8x + 4 × 3y. [Gets multiplied with 4]
= <u>32x + 12y (Ans)</u>
Answer:
s = sqrt [ Σ ( x i - x ) 2 / ( n - 1 ) ]
Step-by-step explanation:
where s is the sample standard deviation, x is the sample mean, x i is the ith element from the sample, and n is the number of elements in the sample. And finally, the standard deviation is equal to the square root of the variance.
Answer:
8cm²
Step by step explanation:
A= ½×4cm×4cm
A= ½×16cm²
A= 8cm²
Answer:
13/6
Step-by-step explanation:
1 Simplify \sqrt{8}
8
to 2\sqrt{2}2
2
.
\frac{2}{6\times 2\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})
6×2
2
2
2
−(−
81
18
)
2 Simplify 6\times 2\sqrt{2}6×2
2
to 12\sqrt{2}12
2
.
\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})
12
2
2
2
−(−
81
18
)
3 Since 9\times 9=819×9=81, the square root of 8181 is 99.
\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{9})
12
2
2
2
−(−
9
18
)
4 Simplify \frac{18}{9}
9
18
to 22.
\frac{2}{12\sqrt{2}}\sqrt{2}-(-2)
12
2
2
2
−(−2)
5 Rationalize the denominator: \frac{2}{12\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{2\sqrt{2}}{12\times 2}
12
2
2
⋅
2
2
=
12×2
2
2
.
\frac{2\sqrt{2}}{12\times 2}\sqrt{2}-(-2)
12×2
2
2
2
−(−2)
6 Simplify 12\times 212×2 to 2424.
\frac{2\sqrt{2}}{24}\sqrt{2}-(-2)
24
2
2
2
−(−2)
7 Simplify \frac{2\sqrt{2}}{24}
24
2
2
to \frac{\sqrt{2}}{12}
12
2
.
\frac{\sqrt{2}}{12}\sqrt{2}-(-2)
12
2
2
−(−2)
8 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}
b
a
×c=
b
ac
.
\frac{\sqrt{2}\sqrt{2}}{12}-(-2)
12
2
2
−(−2)
9 Simplify \sqrt{2}\sqrt{2}
2
2
to \sqrt{4}
4
.
\frac{\sqrt{4}}{12}-(-2)
12
4
−(−2)
10 Since 2\times 2=42×2=4, the square root of 44 is 22.
\frac{2}{12}-(-2)
12
2
−(−2)
11 Simplify \frac{2}{12}
12
2
to \frac{1}{6}
6
1
.
\frac{1}{6}-(-2)
6
1
−(−2)
12 Remove parentheses.
\frac{1}{6}+2
6
1
+2
13 Simplify.
\frac{13}{6}
6
13
Done
