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7nadin3 [17]
2 years ago
7

Q5 Q3.) How​ far, to the nearest​ foot, is the ship from the​ statue's base?

Mathematics
1 answer:
dusya [7]2 years ago
7 0
Distance from base = 305 / tan(29.5deg)
= 539 ft
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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
3 years ago
A bouncy ball is dropped such that the height of its first bounce is 5.5 feet and each successive bounce is 64% of the previous
ahrayia [7]

Answer:

  0.4 ft

Step-by-step explanation:

It can be convenient to let a spreadsheet compute the values for you. Here, we have written an explicit formula for the height of the n-th bounce:

  h = 5.5×0.64^(n-1)

We have written the formula this way because we are given the height of the first bounce, not the starting height. Each bounce multiplies the height by a factor of 0.64. Then the 7th bounce will have a height of ...

  h = 5.5×0.64^6 ≈ 0.378 ≈ 0.4 . . . . feet

6 0
3 years ago
HELP ME!!! 25 POINTS!!
riadik2000 [5.3K]

Answer:

The total distance walked by Paulo is 3750 feet.

Step-by-step explanation:

Here the four points are<em> (-2,1) (-2,-7) (5,-7) (5,1)</em>

Moving from stop A to B, only the y coordinate changes,

the change is ,

=1-(-7) = 1+7 = 8 units

Moving from stop B to C, only the x coordinate changes,

the change is ,

=5-(-2) = 5+2 = 7 units

Moving from stop C to D, only the y coordinate changes,

the change is

=1-(-7) = 1+7 = 8 units

Moving from stop D to A, only the x coordinate changes,

the change is

=5-(-2) = 5+2 = 7 units

Thus, the total distance traveled is 8+7+8+7 = 30 units

It is given that <em>1 unit = 125 feet</em>

Thus, the total distance traveled is = (125)(30) = 3750 feet

The total distance walked by Paulo is 3750 feet.

3 0
3 years ago
If i have 1500 dollars and are left with 65.06 dollars how much money did i spend
Novay_Z [31]
$1500 - $65.06 = $1434.94
Hope I helped!
~ Zoe
6 0
2 years ago
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1. A shirt, x, is discounted 20%; what is the sale price?
julsineya [31]

Answer:the shirt is .8x the tip one is 1.2x and the last one is 1.2x

Step-by-step explanation:

7 0
3 years ago
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