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Evgen [1.6K]
3 years ago
7

What's the next ones?

Mathematics
1 answer:
hammer [34]3 years ago
4 0
3.) 2 × 0.5 = 1 4.) -2 × -0.5 = 1
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The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponenti
melomori [17]

Answer:

a) 0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

b) Capacity of 252.6 cubic feet per second

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \mu e^{-\mu x}

In which \mu = \frac{1}{m} is the decay parameter.

The probability that x is lower or equal to a is given by:

P(X \leq x) = \int\limits^a_0 {f(x)} \, dx

Which has the following solution:

P(X \leq x) = 1 - e^{-\mu x}

The probability of finding a value higher than x is:

P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).

This means that m = 100, \mu = \frac{1}{100} = 0.01

(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

We have that:

P(X > x) = e^{-\mu x}

This is P(X > 190). So

P(X > 190) = e^{-0.01*190} = 0.1496

0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

(b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08?

This is x for which:

P(X > x) = 0.08

So

e^{-0.01x} = 0.08

\ln{e^{-0.01x}} = \ln{0.08}

-0.01x = \ln{0.08}

x = -\frac{\ln{0.08}}{0.01}

x = 252.6

Capacity of 252.6 cubic feet per second

5 0
2 years ago
Evaluate this exponential expression (27/8)^ 4/3<br><br> A: 9/2<br> B: 4/3<br> C: 81/16
valkas [14]

\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \cfrac{27}{8} \right)^{\frac{4}{3}}\implies \left( \cfrac{3^3}{2^3} \right)^{\frac{4}{3}}\implies \left( \cfrac{3^{3\cdot \frac{4}{3}}}{2^{3\cdot \frac{4}{3}}} \right)\implies \cfrac{3^4}{2^4}\implies \cfrac{81}{16}

7 0
3 years ago
What is the distance between the two number s on the number line? -7/4 And 3/8
Ivanshal [37]

Answer:

2 1/8

Step-by-step explanation:

-7/4 is equal to -14/8

14/8 plus 3/8 is 17/8

17/8 = 2 1/8

5 0
2 years ago
Read 2 more answers
2×3+4-5 <br>please help ​
Andru [333]

Step-by-step explanation:

PEMDAS

parentheses, exponents, multiplication, division, addition, subtraction.

first multiply:

2×3=6

6+4-5

Now add

6+4=10

Now subtract

10-5=5

5 is the answer

<em><u>I</u></em><em><u> </u></em><em><u>hope</u></em><em><u> </u></em><em><u>this</u></em><em><u> </u></em><em><u>helped</u></em><em><u>!</u></em><em><u> </u></em><em><u>:</u></em><em><u>)</u></em>

8 0
3 years ago
Read 2 more answers
A fair coin is tossed three times.
qaws [65]

B 2/3
A 3/3. Hsheikdkekekekld

6 0
3 years ago
Read 2 more answers
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