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DaniilM [7]
1 year ago
7

A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must

function. Two of the parts have a .96 probability of functioning, and two have a probability of .99. What is the overall probability that the product will function properly
Mathematics
1 answer:
svet-max [94.6K]1 year ago
3 0

Answer:

P(working product) = .99*.99*.96*.96 = .0.903

Step-by-step explanation:

For the product to work, all four probabilities must come to pass, so that

P(Part-1)*P(Part-2)*P(Part-3)*P(Part-4)

where

P(Part-1) = 0.96

P(Part-2) = 0.96

P(Part-3) = 0.99

P(Part-4) = 0.99

As all parts are independent, so the formula is P(A∩B) = P(A)*P(B)

P (Working Product) =  P(Part-1)*P(Part-2)*P(Part-3)*P(Part-4)

P (Working Product) = 0.96*0.96*0.96*0.99*0.99

P(Working Product) = 0.903

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A red candle is 8 inches tall and burns at a rate of 7/10 inch per hour. A blue candle is 6 inches tall and burns at a rate of 1
kogti [31]

Answer:

The heights are the same after 4 hours.

Step-by-step explanation:

The red candle burns at a rate of 7/10 inches per hour. In t hours, (7/10)t inches have burned. The height of the candle after t hours is 8 - (7/10)t.

The blue candle burns at a rate of 1/5 inch per hour. In t hours, (1/5)t inches have burned. The height of the candle after t hours is 6 - (1/5)t.

You need to find the time, t, when their heights are equal.

8 - (7/10)t = 6 - (1/5)t

Multiply both sides by 10 (the LCD).

80 - 7t = 60 - 2t

-5t = -20

t = 4

The heights are the same after 4 hours.

3 0
2 years ago
Consider the initial value problem: 2ty′=8y, y(−1)=1. Find the value of the constant C and the exponent r so that y=Ctr is the s
VikaD [51]

The correct question is:

Consider the initial value problem

2ty' = 8y, y(-1) = 1

(a) Find the value of the constant C and the exponent r such that y = Ct^r is the solution of this initial value problem.

b) Determine the largest interval of the form a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.

c) What is the actual interval of existence for the solution obtained in part (a) ?

Step-by-step explanation:

Given the differential equation

2ty' = 8y

a) We need to find the value of the constant C and r, such that y = Ct^r is a solution to the differential equation together with the initial condition y(-1) = 1.

Since Ct^r is a solution to the initial value problem, it means that y = Ct^r satisfies the said problem. That is

2tdy/dt - 8y = 0

Implies

2td(Ct^r)/dt - 8(Ct^r) = 0

2tCrt^(r - 1) - 8Ct^r = 0

2Crt^r - 8Ct^r = 0

(2r - 8)Ct^r = 0

But Ct^r ≠ 0

=> 2r - 8 = 0 or r = 8/2 = 4

Now, we have r = 4, which implies that

y = Ct^4

Applying the initial condition y(-1) = 1, we put y = 1 when t = -1

1 = C(-1)^4

C = 1

So, y = t^4

b) Let y = F(x,y)................(1)

Suppose F(x, y) is continuous on some region, R = {(x, y) : x_0 − δ < x < x_0 + δ, y_0 −ę < y < y_0 + ę} containing the point (x_0, y_0). Then there exists a number δ1 (possibly smaller than δ) so that a solution y = f(x) to (1) is defined for x_0 − δ1 < x < x_0 + δ1.

Now, suppose that both F(x, y)

and ∂F/∂y are continuous functions defined on a region R. Then there exists a number δ2

(possibly smaller than δ1) so that the solution y = f(x) to (1) is

the unique solution to (1) for x_0 − δ2 < x < x_0 + δ2.

c) Firstly, we write the differential equation 2ty' = 8y in standard form as

y' - (4/t)y = 0

0 is always continuous, but -4/t has discontinuity at t = 0

So, the solution to differential equation exists everywhere, apart from t = 0.

The interval is (-infinity, 0) n (0, infinity)

n - means intersection.

7 0
1 year ago
Work out ( 8x10 -3) x(2x10 -4) standard form
zheka24 [161]

Answer:  1232

Step-by-step explanation:  ( 8x10 -3) x(2x10 -4)  

( 8x10 -3) = 77

(2x10 -4) = 16

77 x 16 = 1232

Answer = 1232

4 0
2 years ago
A doctor is measuring the average height of male students at a large college. The doctor measures the heights, in inches, of a s
denpristay [2]

Answer:

For this case the  95% confidence interval is given (63.5 , 74.4) and we want to conclude about the result. For this case we can say that the true mean of heights for male students would be between 63.5 and 74.4. And the best answer would be:

b. The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches.

Step-by-step explanation:

Notation

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=40-1=39

For this case the  95% confidence interval is given (63.5 , 74.4) and we want to conclude about the result. For this case we can say that the true mean of heights for male students would be between 63.5 and 74.4. And the best answer would be:

b. The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches.

3 0
2 years ago
Last year Lenny had an annual earned income of $58,475. He also had passive income of $1,255, and capital gains of $2,350. What
Lelechka [254]

<u>Answer:</u>  d. $62,080

<u>Step-by-step explanation:</u>

<u></u>

The capital gain is the profit earned from an investment whereas the passive income is the income generated by very minimal daily efforts.

Given: Annual income earned by Lenny = \$58,475

Passive income =  \$1,255

Capital gain =  \$2,350

Now,  \text{Total gross income =Annual income+Passive income+Capital gain}

=\$58,475+\$1,255+\$2,350=\$62,080

Hence, Lenny's total gross income for the year = $62,080

4 0
1 year ago
Read 2 more answers
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