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WARRIOR [948]
3 years ago
6

The temperature dropped 5 °F every hour for 5 hours. What was the total number of degrees the temperature changed in the 5 hours

?
Mathematics
2 answers:
olasank [31]3 years ago
8 0

Answer:

it changed by 25 degrees

Step-by-step explanation:

for every hour it goes down by 5 and you have five hours so its

5+5+5+5+5

so basically its 5×5 and that equals 25

solong [7]3 years ago
4 0

Answer:

25

Step-by-step explanation:

you just multiple 5 times 5

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(a) A lamp has two bulbs of a type with an average lifetime of 1600 hours. Assuming that we can model the probability of failure
lara [203]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The probability is P_T= 0.4560

b

The probability is P_F= 0.0013

Step-by-step explanation:

From the question we are told that

The mean for the exponential density function of bulbs failure is \mu = 1600 \ hours

Generally the cumulative distribution for exponential distribution is mathematically represented as

       1 - e^{- \lambda x}

The objective is to obtain the p=probability of the bulbs failure within 1800 hours

So for the first bulb the probability will be

        P_1(x < 1800)

 And for the second bulb the probability will be

       P_2 (x< 1800)

So from our probability that we are to determine the area to the left of 1800 on the distribution curve

    Now the  rate parameter  \lambda is mathematically represented as

                           \lambda = \frac{1}{\mu}

                          \lambda = \frac{1}{1600}

The probability of the first bulb failing with 1800 hours is mathematically evaluated as

                   P_1(x < 1800) = 1 - e^{\frac{1}{1600} * 1800 }

                                        = 0.6753

Now the probability of both bulbs failing would be

              P_T=P_1(x < 1800) * P_2(x < 1800)

           = 0.6375 * 06375

           P_T= 0.4560

Let assume that one bulb failed at time T_a and the second bulb failed at time T_b  then

                 T_a + T_b = 1800\ hours

The mathematical expression to obtain the probability that the first bulb failed within between zero and T_a and the second bulb failed between T_a \ and \  1800 is represented as

             P_F=\int_{0}^{1800}\int_{0}^{1800-x} \f{\lambda }^{2}e^{-\lambda x}* e^{-\lambda y}dx dy

            =\int_{0}^{1800} {\lambda }e^{-\lambda x}\int_{0}^{1800-x} {\lambda } e^{-\lambda y}dx dy

            =\int_{0}^{1800} {\frac{1}{1600} }e^{-\lambda x}\int_{0}^{1800-x} \frac{1}{1600 } e^{-\lambda y}dx dy

          =\int_{0}^{1800} {\frac{1}{1600} }e^{-\lambda x}[e^{- \lambda y}]\left {1800-x} \atop {0}} \right. dx        

          =\int_{0}^{1800} {\frac{1}{1600} }e^{-\frac{x}{1600} }[e^{- \frac{1800 -x}{1600} }-1] dx

            =[ {\frac{1}{1600} }e^{-\frac{1800}{1600} }-\frac{1}{1600}[e^{- \frac{x}{1600} }] \left {1800} \atop {0}} \right.

           =[ {\frac{1}{1600} }e^{-\frac{1800}{1600} }-\frac{1}{1600}[e^{- \frac{1800}{1600} }] -[[ {\frac{1}{1600} }e^{-\frac{1800}{1600} }-\frac{1}{1600}[e^{-0}]

           =[\frac{1}{1600} e^{-\frac{1800}{1600} } - \frac{1}{1600} e^{-0}  ]

         =0.001925 -0.000625

         P_F= 0.0013

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