$\bf ~~~~~~ \textit{Simple Interest Earned}
\\\\
I = Prt\qquad 
\begin{cases}
I=\textit{interest earned}\to &\$1575\\
P=\textit{original amount deposited}\to& \$6000\\
r=rate\to r\%\to \frac{r}{100}\\
t=years\to &7
\end{cases}
\\\\\\
1575=(6000)(r)(7)\implies \cfrac{1575}{(6000)(7)}=r\implies 0.0375=r
\\\\\\
r\%=0.0375\cdot 100\implies r=\stackrel{\%}{3.75}$

4 0

3 years ago

A water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock P(R)equals=0.

GaryK [48]

The tree diagram for the probability is shown below

P(Clay|Positive) is read 'Probability of Clay given the result is Positive'.

This is a case of conditional probability.

The formula for conditional probability is given as
P(Clay|Positive) = P(Clay∩Positive) ÷ P(Positive)

P(Clay∩Positive) = 0.21×0.48 = 0.1008

P(Positive) = P(Rock∩Positive) + P(Clay∩Positive) + P(Sand∩Positive)
P(Positive) = (0.53×0.53) + (0.21×0.48) + (0.26×0.75)
P(Positive) = 0.2809 + 0.1008 + 0.195
P(Positive) = 0.5767

Hence,
P(Clay|Positive) = 0.1008÷0.5767 = 0.175 (rounded to 3 decimal place)

5 0

2 years ago