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3 years ago

What is the product of 25.785 and 0.27?

Mathematics

1 answer:

Ganezh [65]3 years ago

7 0

Answer:

6.96195

Step-by-step explanation:

Solve by multiplying

25.785

0.270

------------

6.96195

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What is the equation of the line that passes through the point (-3, 0) and has a slope of -1/3?

ANTONII [103]

Answer:

Y=-1/3x-1

Step-by-step explanation:

Y-0=-1/3(x+3)

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

y = –6x 2 –12x – 2y = –4 how many solutions does this linear system have? one solution: (0, 0) one solution: (1, –4) no solution

lara [203]

Y = -6x + 2 . . . . . . . . (1)
-12x - 2y = -4 . . . . . . (2)
Putting (1) into (2), we have
-12x - 2(-6x + 2) = -4
-12x + 12x - 4 = -4
-4 = -4

Therefore, the system has infinite number of solutions.

5 0

3 years ago

Read 2 more answers

Manuel bought x x movie tickets for $6.50 each and y y bags of popcorn for $2.50 each. write an algebraic expression for the tot

Alekssandra [29.7K]

6.50x+2.50y = total
with x = # of movie tickets
with y= # of bags of popcorn

5 0

4 years ago

Suppose the correlation between height and weight for adults is 0.80. What proportion (or percent) of the variability in weight

gulaghasi [49]

Answer: 64% of the variability in weight can be explained by the relationship with height.

Step-by-step explanation:

In statistics, Correlation coefficient is denoted by 'r' is a measure of the strength of the relationship between two variables.
Coefficient of determination, $r^2$ , is a measure of variability in one variable can be explained variation in the other.

Here, r= 0.80

$\Rightarrow\ r^2= (0.80)^2=0.64$

That means 64% of the variability in weight can be explained by the relationship with height.

8 0

3 years ago