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4 years ago

In a small town, electricity prices have been rising 2% each year since 2008. Which

Mathematics

1 answer:

mihalych1998 [28]4 years ago

4 0

<h3>Answer: p = 0.12*(1.02)^t</h3>

Explanation:

The general exponential growth equation is

p = A*B^t

where t is the number of years that have gone by after 2008, A is the starting amount, B is the growth multiplier, and p is the price t years after 2008

We know that A = 0.12 is the starting price

The value of B is B = 1.02 which is in the form 1+r since 1.02 = 1 + 0.02 = 1+r

The r value is r = 0.02 and it is positive to represent growth. Keep in mind that 2% = 2/100 = 0.02

So we go from

p = A*B^t

p = 0.12*(1.02)^t

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Seventy-two percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of th

Anton [14]

Answer:

a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) 0.064 = 6.4% probability that 7 of them are discovered.

Step-by-step explanation:

For itens a and b, we use conditional probability.

For item c, we use the binomial distribution along with the conditional probability.

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

a) If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator

Event B: Not located.

Probability of having an emergency locator:

66% of 72%(Are discovered).

20% of 100 - 72 = 28%(not discovered). So

$P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312$

Probability of having an emergency locator and not being discovered:

20% of 28%. So

$P(A cap B) = 0.2*0.28 = 0.056$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105$

0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) If it does not have an emergency locator, what is the probability that it will be discovered?

Probability of not having an emergency locator:

0.5312 of having. So

$P(A) = 1 - 0.5312 = 0.4688$

Probability of not having an emergency locator and being discovered:

34% of 72%. So

$P(A \cap B) = 0.34*0.72 = 0.2448$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522$

0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

p is the probability of being discovered with the emergency recorder:

0.5312 probability of having the emergency recorder.

Probability of having the emergency recorder and being located:

66% of 72%. So

$P(A \cap B) = 0.66*0.72 = 0.4752$

Probability of being discovered, given that it has the emergency recorder:

$p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946$

This question asks for P(X = 7) when $n = 10$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064$

0.064 = 6.4% probability that 7 of them are discovered.

8 0

3 years ago

PLESE HELP NOW BIG TEST! Margarite leaves her home to run several errands. Her house, the supermarket, the municipal building, a

Brums [2.3K]

She would have traveled 24 miles since from the house to the supermarket is 7 miles then from the supermarket to the municipal building is 5 miles then back 7 miles and then 5 miles. If you add all of that together then you will get 24 miles.

6 0

3 years ago

Evaluate each function following the specification.

telo118 [61]

Answer:

#3 a. g(-1) = 2, g(0) = 3, and g(1) = 2

b. No restrictions for all real numbers

$\#4 \ a. \ h(-1) = \dfrac{1}{3}, \ h(0) =0, \ h(2) = \infty$

b. Yes, x ≠ 2

Step-by-step explanation:

#3 The function is given as g(x) = -x² + 3

a. From the given function, by plugging in the value of 'x' in the bracket, we have;

g(-1) = -(-1)² + 3 = -1 + 3 = 2

g(-1) = 2

g(0) = -0² + 3 = 3

g(0) = 3

g(1) = -1² + 3 = -1 + 3 = 2

g(1) = 2

g(-1) = 2, g(0) = 3, and g(1) = 2

b. The given function g(x) = -x² + 3 for finding the value of g can take any value of x which is a real number

Therefore, therefore, there are no restrictions

#4 a. The given function is given as follows;

$h(x) = \dfrac{x}{x - 2}$

By substitution, we get;

$h(-1) = \dfrac{-1}{(-1) - 2} = \dfrac{-1}{-3} = \dfrac{1}{3}$

$\therefore h(-1) = \dfrac{1}{3}$

$h(0) = \dfrac{0}{0 - 2} = \dfrac{0}{-2} =0$

$\therefore h(0) =0$

$h(2) = \dfrac{2}{2 - 2} = \dfrac{2}{0} = \infty$

$\therefore h(2) = \infty$

$h(-1) = \dfrac{1}{3}, \ h(0) =0, \ h(2) = \infty$

b. From the values of the function, we have that h(x) is not defined at x = 2

Therefore, there is a restriction for x in the function, which is x ≠ 2

3 0

3 years ago

Consider the formula for the average velocity, v, of a moving particle. In the formula, d, and dy represent the distance travele

il63 [147K]

Answer:

Option C.

Step-by-step explanation:

Note: The question and options are not in correct form.

Let the correct question is "Consider the formula for the average velocity, v, of a moving particle. In the formula, d1 and d2 represent the distance traveled by the particle at times t1 and t2 respectively.

v = (d2 - d1)/(t2 - t1)

Which of the following equations is equivalent to the formula for velocity?

A. t1=v(d2-d1)-t2

B. d1=v (t2-t1)-d2

C. d2=v(t2-t1)+d1

D. t2=v(d2-d1)+t1 "

The given formula is

$v=\dfrac{d_2-d_1}{t_2-t_1}$