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3 years ago

Function Operations Picture attached

Mathematics

1 answer:

sergeinik [125]3 years ago

6 0

Answer: Second option

Step-by-step explanation:

You need to make the multiplication of the function $c(x)=\frac{5}{x-2}$ and the function $d(x)=x+3$ . Then:

$(cd)(x)=(\frac{5}{x-2})(x+3)$

You need to apply the Distributive property:

$(cd)(x)=\frac{5(x+3)}{x-2}\\\\(cd)(x)=\frac{5x+15}{x-2}$

Therefore, the domain will be all the number that make the denominator equal to zero.

Then, make the denominator equal to zero and solve for x:

$x-2=0\\x=2$

Therefore, the domain is: All real values of x except $x=2$

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When studying radioactive material, a nuclear engineer found that over 365 days,

Gnom [1K]

Answer:

a) The mean number of radioactive atoms that decay per day is 81.485.

b) 0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\lambda$ is the mean in the given interval.

a. Find the mean number of radioactive atoms that decayed in a day.

29,742 atoms decayed during 365 days, which means that:

$\lambda = \frac{29742}{365} = 81.485$

The mean number of radioactive atoms that decay per day is 81.485.

b. Find the probability that on a given day, 50 radioactive atoms decayed.

This is P(X = 50). So

$P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0$

0% probability that on a given day, 50 radioactive atoms decayed.

5 0

2 years ago

the coordinates of one point of a line segment are (-2,-7). The line segment is 12 units long. Give three possible coordinates o

valentinak56 [21]

(-2,-19) , (-2, 5), ( 2,10)

4 0

3 years ago

A $16,000 robot depreciates linearly to zero in 10 years. (a) find a formula for its value as a function of time, t, in years.

SVETLANKA909090 [29]

We are given, cost of the robot for 0 number of year = $16,000.

0 represents initial time of the robot.

After 10 year cost of the robot is = $0

The problem is about the number of the years and cost of the robot over different number of years.

So, we could take x coordinate by number of hours and y coordinate for y number of hours.

So, from the problem, we could make two coordinates for the given situation.

(x1,y1) = (0, 16000) and (x2,y2) = (10, 0).

In order to find the function of time, we need to find the rate at which robot rate depreciates each year.

Slope is the rate of change.

So, we need to find the slope of the two coordinates we wrote above.

We know, slope formula

$Slope (m) = \frac{y2-y1}{x2-x1}$

Plugging values in formula, we get

$m=\frac{0-16000}{10-0} = \frac{-16000}{-10} = -1600.$

Brecasue of depreciation we got a negative number for slope or rate of change.

Therefore, rate of depreciation is $1600 per year.

We already given inital cost, that is $16,000.

So, we can setup an a function

f(x) = -1600x + 16000.

But the problem is asked to take the variable t for time.

Replacing x by t, we get

f(t) = -1600t + 16000.

8 0

3 years ago

1. Which equation can you use to find the value of x?

Alika [10]

Answer:

It's a proportion.

2 is to x as 15 is to 9, or 2/x = 15/9.

Multiply the means and extremes

15x = 18

divide both sides by 15 to get x by itself.

x = 1.2

Step-by-step explanation:

6 0

2 years ago

Please help 10 Points

QveST [7]

Answer:

Step-by-step explanation:

8 0

3 years ago