Determine the value of the first term and write a recursive definition for the following

You are scheduled to work 34 hours per week at your new job, where you earn $13.1 per

Lyrx [107]

13.1 an hour, 34 hours a week
13.1 x 34 = 445.4 a week
to find out how many weeks, divide 4300 and 445.4 which is 9.65 weeks, which is technically 10 weeks

it would take 10 weeks to earn 4300

6 0

1 year ago

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

3 years ago

Which expression is equivalent to 11c-4c? A. 5c+2c B. 3c+7c

timurjin [86]

11c-4c = 7c
5c+2c= 7c
3c+7c= 10c

11c-4c= 5c+2c =A

4 0

3 years ago

What is the mass (in grams) of 8.11×1026 CO2 molecules?

Kobotan [32]

Answer:

It is 59,275.74 grams

Step-by-step explanation:

• Molecular mass of carbon dioxide

$= (12 \times 1) + (16 \times 2) \\ = 12 + 32 \\ = 44 \: g$

[ molar masses: C = 12 g, O = 16 g ]

• From avogadro's number, it says 1 mole contains 6.02 × 10^23 molecules or atoms.

But 1 mole is equivalent to its molar mass in terms of weight, therefore;

${ \sf{6.02 \times {10}^{23} \: molecules = 44 \: g }}\\ { \sf{8.11 \times {10}^{26} \: molecules =( \frac{8.11 \times {10}^{26} }{6.02 \times {10}^{23} } \times 44) \: g}} \\ \\ = { \boxed{ \boxed{ \bf{59275.7 \: \: g}}}}$

6 0

3 years ago

Which of the following best describes the algebraic expression x/3 -15

Dennis_Churaev [7]

Answer:

A. A number divided by three minus fifteen.

7 0

3 years ago