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Eva8 [605]
3 years ago
9

What is the length of RM or RN

Mathematics
1 answer:
lorasvet [3.4K]3 years ago
6 0
RM is 8 and RN is 12
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A triangular prism is shown. a cylinder is cut out of the center of the prism. the triangular base has side lengths of 14 and 10
Whitepunk [10]

The expression that represents the volume, in cubic units, of the shaded region of the composite figure is: A. One-half(14)(10)(8) – π(2.52)(8).

<h3>Expression</h3>

Given:

Base side length=14 and 10 units

Height=8 units

Diameter=5 units


Hence:

Expression= 1-( half 14)(10)(8) - π(2.52)(8)

Expression=1-(7) (10)(8) - π(2.52)(8)

Expression=1- (560)- 63.33

Expression=-559-63.33

Expression=-622.33

Therefore the expression that represents the volume, in cubic units, of the shaded region of the composite figure is: A. One-half(14)(10)(8) – π(2.52)(8).

Learn more about expression here:brainly.com/question/723406

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5 0
1 year ago
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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.

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3 years ago
Linear System Word Problem - Animals
Margaret [11]

Answer:

There were 15 birds at the shelter on Monday

Step-by-step explanation: 15 birds x 5$ =75$ and 8 cats x 6$=48$ 75$ + 48$=123$  


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2 years ago
Please help<br><br>1 through 5​
Arte-miy333 [17]

Answer:

Step-by-step explanation:

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3 years ago
6. Craig and James both live 4 miles up a hill. Craig hikes uphill at a rate of 1 mile every two hours.
Iteru [2.4K]

Answer:

James

Step-by-step explanation:

James rate:

2x + 2 = 4

2x = 2

x = 1 hour

Rate = distance/time = 4/1 = 4 miles per hour

Craig's rate = 1/2 = 0.5 miles per hour

James is faster

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2 years ago
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