Someone plz help me

HELP ME Timed Complete the recursive formula of the arithmetic sequence 9,−1,−11,−21,

NARA [144]

Answer:

Step-by-step explanation:

5 0

3 years ago

The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) for Determine

salantis [7]

The question is incomplete. Here is the complete question.

The probability density function of the time to failure of an electronic component in a copier (in hours) is

$f(x)=\frac{e^{\frac{-x}{1000} }}{1000}$

for x > 0. Determine the probability that

a. A component lasts more than 3000 hours before failure.

b. A componenet fails in the interval from 1000 to 2000 hours.

c. A component fails before 1000 hours.

d. Determine the number of hours at which 10% of all components have failed.

Answer: a. P(x>3000) = 0.5

b. P(1000<x<2000) = 0.2325

c. P(x<1000) = 0.6321

d. 105.4 hours

Step-by-step explanation: <em>Probability Density Function</em> is a function defining the probability of an outcome for a discrete random variable and is mathematically defined as the derivative of the distribution function.

So, probability function is given by:

P(a<x<b) = $\int\limits^b_a {P(x)} \, dx$

Then, for the electronic component, probability will be:

P(a<x<b) = $\int\limits^b_a {\frac{e^{\frac{-x}{1000} }}{1000} } \, dx$

P(a<x<b) = $\frac{1000}{1000}.e^{\frac{-x}{1000} }$

P(a<x<b) = $e^{\frac{-b}{1000} }-e^\frac{-a}{1000}$

a. For a component to last more than 3000 hours:

P(3000<x<∞) = $e^{\frac{-3000}{1000} }-e^\frac{-a}{1000}$

Exponential equation to the infinity tends to zero, so:

P(3000<x<∞) = $e^{-3}$

P(3000<x<∞) = 0.05

There is a probability of 5% of a component to last more than 3000 hours.

b. Probability between 1000 and 2000 hours:

P(1000<x<2000) = $e^{\frac{-2000}{1000} }-e^\frac{-1000}{1000}$

P(1000<x<2000) = $e^{-2}-e^{-1}$

P(1000<x<2000) = 0.2325

There is a probability of 23.25% of failure in that interval.

c. Probability of failing between 0 and 1000 hours:

P(0<x<1000) = $e^{\frac{-1000}{1000} }-e^\frac{-0}{1000}$

P(0<x<1000) = $e^{-1}-1$

P(0<x<1000) = 0.6321

There is a probability of 63.21% of failing before 1000 hours.

d. P(x) = $e^{\frac{-b}{1000} }-e^\frac{-a}{1000}$

0.1 = $1-e^\frac{-x}{1000}$

$-e^{\frac{-x}{1000} }=-0.9$

${\frac{-x}{1000} }=ln0.9$

-x = -1000.ln(0.9)

x = 105.4

10% of the components will have failed at 105.4 hours.

5 0

4 years ago

Suppose 56% of students chose to study Spanish their senior year, and that meant that there were 98 such students. How many stud

Varvara68 [4.7K]

The number of students who chose not to study Spanish in their senior year is 124.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given that

56% Students studied Spanish, which means 44% did not study Spanish.

In mathematics, a ratio shows how many times one number contains another.

Hence if the ratio is:

56 : 44 = 14:11

Then, the number of students who did not study Spanish is:

(14/11)×98 = 124.

Therefore the correct answer is 124.

To know more about probability.

visit-: brainly.com/question/11234923

#SPJ1

5 0

2 years ago

This graph shows the amount of rain that falls in a given amount of time.

8_murik_8 [283]

Using the formula for finding slope...

y2 - y1 10 - 5 5
---------- = -------- = -----
x2 - x1 4 - 2 2

The slope of the line is 5/2.
This means that 5 mm of rain falls every 2 hours.

6 0

4 years ago

PLEASE HELP

Annette [7]

Answer:

im pretty sure 20.47

Step-by-step explanation:

even though it doesnt tell you to round up, i think you should still be safe and round up to the nearest hundred

3 0

3 years ago