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
Answer:
5/9
Step-by-step explanation:
The experimental probability of rolling a 6 is 9/60 which can be determined by dividing the frequency of the observation 6 with the total frequency of the experiment.
<u>Step-by-step explanation:</u>
Experimental probability is different from theoretical probability because the former is obtained by experimentation while the latter is what we expect theoretically.When we take a number of observations, the experimental probability and theoretical probability need not be the same.
In this question we have to determine the experimental probability of 6. It can be determined by dividing the frequency of the observation 6 by the total frequency of the experiment.
frequency of 6=9
total frequency=frequency of 1+frequency of 2+frequency of 3+frequency of 4+frequency of 5+frequency of 6
=13+11+9+8+10+9
=60
P(6)=frequency of 6/total frequency
=9/60
I think that the answers is b
Answer:
<h3>
ln (e^2 + 1) - (e+ 1)</h3>
Step-by-step explanation:
Given f(x) = ln and g(x) = e^x + 1 to get f(g(2))-g(f(e)), we need to first find the composite function f(g(x)) and g(f(x)).
For f(g(x));
f(g(x)) = f(e^x + 1)
substitute x for e^x + 1 in f(x)
f(g(x)) = ln (e^x + 1)
f(g(2)) = ln (e^2 + 1)
For g(f(x));
g(f(x)) = g(ln x)
substitute x for ln x in g(x)
g(f(x)) = e^lnx + 1
g(f(x)) = x+1
g(f(e)) = e+1
f(g(2))-g(f(e)) = ln (e^2 + 1) - (e+ 1)
