Solve : |3x-1/2|

Which of the following is not part of the converse of the triangle proportionality theorem?

professor190 [17]

Converse-if a line drawn frm one side of a triangle to the other side divides the 2 sides in equal ratio then the line is parallel to the third side.

3 0

3 years ago

Read 2 more answers

What is the difference between a rate that is compounded annually and a rate that is compounded semiannually

8090 [49]

Answer:

the rate compounded semi-annually is compounded twice in a year. thus, this rate is higher than the rate compounded annually which is compounded once in a year

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r/m)^mn

FV = Future value

P = Present value

R = interest rate

N = number of years

m = number of compounding

For example, there are two banks

Bank A offers 10% rate with semi-annual compounding

Bank B offers 10% rate with annual compounding.

If you deposit $100, the amount you would have after 2 years in each bank is

A = 100x (1 + 0.1/2)^4 = 121.55

B = 100 x (1 + 0.1)^2 = 121

The interest in bank a is 0.55 higher than that in bank B

3 0

3 years ago

The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a m

castortr0y [4]

Answer:

a) 50.34% probability that the arrival time between customers will be 7 minutes or less.

b) 24.42% probability that the arrival time between customers will be between 3 and 7 minutes

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:

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

Mean of 10 minutes:

This means that $m = 10, \mu = \frac{1}{10} = 0.1$

A. What is the probability that the arrival time between customers will be 7 minutes or less?

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

$P(X \leq 7) = 1 - e^{-0.1*7} = 0.5034$

50.34% probability that the arrival time between customers will be 7 minutes or less.

B. What is the probability that the arrival time between customers will be between 3 and 7 minutes?

$P(3 \leq X \leq 7) = P(X \leq 7) - P(X \leq 3)$

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

$P(X \leq 7) = 1 - e^{-0.1*7} = 0.5034$

$P(X \leq 3) = 1 - e^{-0.1*3} = 0.2592$

$P(3 \leq X \leq 7) = P(X \leq 7) - P(X \leq 3) = 0.5034 - 0.2592 = 0.2442$

24.42% probability that the arrival time between customers will be between 3 and 7 minutes

3 0

3 years ago

a gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sel

adell [148]

Answer:

The price per wind chime that will maximize revenue = $ 315

Step-by-step explanation:

Given - A gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sell 5 fewer wind chimes per month.

To find - Find the price per wind chime that will maximize revenue.

Proof -

Given that,

Total Wind chimes selling = 160

Price of each Wind chime = $150

Now,

Given that, for each $15 increase in price, they will sell 5 fewer wind chimes per month.

So,

Let the price = 150 + 15x

So,

Number of wind Chimes sold per month = 160 - 5x

So,

Total Revenue, R = (150 + 15x)(160 - 5x)

= 24000 - 750x + 2400x - 75x²

= 24000 + 1650x - 75x²

⇒R(x) = 24000 + 1650x - 75x²

Differentiate R with respect to x , we get

R'(x) = 1650 - 150x

Now,

For Maximize Revenue, Put R'(x) = 0

⇒1650 - 150x = 0

⇒150x = 1650

⇒x = 1650/150

⇒x = 11

∴ we get

Price per Wind chime = $ 150 + 15(11)

= $ 150 + 165

= $ 315

So,

The price per wind chime that will maximize revenue = $ 315

3 0

3 years ago

(0,1), (1,5),(2,9), (3,13),(4,17)<br> Figure out the rule for x

Julli [10]

Answer:

where in the heck is the x tho

where is x in the equation I am hella confused and I don't understand how to help

8 0

2 years ago

Solve : |3x-1/2| < 1 1/2